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Psychonomic Bulletin & Review2001, 8 (2), 221-243 Psychonomic Bulletin & Review2001, 8 (2), 221-243

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Psychonomic Bulletin & Review2001, 8 (2), 221-243 - PPT Presentation

1 INTRODUCTIONLittle is known of how the brain represents informationat the higher levels of cognitive processing We suggestthat the problem of how letter position within a word isencoded provides a ID: 343709

INTRODUCTIONLittle known

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Psychonomic Bulletin & Review2001, 8 (2), 221-243 1. INTRODUCTIONLittle is known of how the brain represents informationat the higher levels of cognitive processing. We suggestthat the problem of how letter position within a word isencoded provides a tractable area of investigation into thisrealm. This problem is circumscribed, yet it involves im-portant higher level processes, such as the composition ofa representation from constituent entities, and the forma-tion of a representation that is independent of absolutelocation in visual space. Furthermore, there is a wealth ofrelevant experimental evidence. So how does the brain rep-resent that the string “ART” is composed of the letters “A,”then “R,” then “T,” and not “R,” then “A,” then “T,” or “T,”then “A,” then “R”?Recent computational models of word recognition haveused one of two approaches to the coding of letter posi-tion. In a scheme, it is hypothesized thatdifferent sets of letter units exist for each string position.That is, there are separate units representing “A” in thefirst position, “A” in the second position, and so on (Colt-heart, Curtis, Atkins, & Haller, 1993; McClelland & Rum-elhart, 1981; Whitney, Berndt, & Reggia, 1996). Encod-ing the string “ART” corresponds to activating the unitfor “A” in the first set, “R” in the second set, and “T” in thethird set. A disadvantage of such a scheme is that it de-mands a high degree of item redundacy, requiring a repre-sentation of each letter in each possible position. More-over, it is not consistent with recent studies indicatingthat relative order among sets of letters, not their absoluteposition, is important in letter-position coding (Humphreys,Evett, & Quinlan, 1990; Peressotti & Grainger, 1999) andthat priming across letter positions can occur (Peressotti& Grainger, 1995).In encoding, the basic unit is not a singleletter, but rather a group of ordered letters, usually trigrams(Mozer & Behrmann, 1992; Seidenberg & McClelland,1989). For example, the string “ART” would be representedby activating units representing “_AR,” “ART,” and “RT_,”where “_” represents a word boundary. Such a scheme ismore consistent with evidence of the importance of let-ter order than a channel-specific one. It has been proposedthat context units can also be activated by nonadjacent let-ters (Mozer, 1987). For example, under a nonadjacentscheme, the trigrams “_RT,” “_AT,” “AT_,” and “AR_”would also be activated by the string “ART.” Humphreysetal. (1990) have indicated that such a noncontiguousrepresentation is necessary to fully account for experimen-tal results on relative order and have suggested that acti-vations of context units are graded by the proximity of theirconstituent letters within the string. However, no mech-anism has been proposed for generating such activations.Thus, the difficult question of how such contextual unitscould be recognized and activated remains unaddressed.Another possible encoding is a scheme,in which an individual letter unit can represent any posi-tion, since it is marked for the ordinal position in whichit occurred when a word is read. For example, “ART”would be represented by “A–1,” “R–2,” “T–3.” Such aproposal reduces item redundancy and allows for prim-ing across letter positions, since a letter unit can representany position. However, it is unknown how such taggingcould be realized in physiological terms.In considering the nature of letter-position coding, we be-lieve that results from studies on the perceptibility of letters 221Copyright 2001 Psychonomic Society, Inc. The author is grateful to Udaya Shankar, Rita S. Berndt, and JamesA.Reggia for helpful suggestions. The author also thanks John Wixted,Joseph Hellige, and two anonymous reviewers for their detailed, sup-portive, and constructive comments. Correspondence should be ad-dressed to C.Whitney, Department of Philosophy, University of Mary-land, College Park, MD 20742 (e-mail: cwhitney@cs.umd.edu). How the brain encodes the order of lettersin a printed word: The SERIOL modeland selective literature reviewCAROL WHITNEYUniversity of Maryland School of Medicine, Baltimore, MarylandThis paper describes a novel theoretical framework of how the position of a letter within a string isencoded, the SERIOL model (sequential encoding regulated by inputs to oscillations within letterunits). Letter order is represented by a temporal activation pattern across letter units, as is consistentwith current theories of information coding based on the precise timing of neural spikes. The frame-work specifies how this pattern is invoked via an activation gradient that interacts with subthresholdoscillations and how it is decoded via contextual units that activate word units. Using mathematicalmodeling, this theoretical framework is shown to account for the experimental data from a wide vari-ety of string-processing studies, including hemispheric asymmetries, the optimal viewing position, andpositional priming effects. 222WHITNEY within strings are directly relevant. Such experiments haveshown that, for briefly presented letter strings,the first letterhas the highest probability of being correctly recognized,the second letter has the second highest probability, withthe probability of recognition generally decreasing from leftto right (with the possible exceptions of the final letter andthe letter at fixation; seeEstes, Allmeyer, & Reder 1976;Lefton, Fisher, & Kuhn, 1978; Montant, Nazir, & Poncet,1998; Wolford & Hollingsworth, 1974). Initial interpreta-tions of these results postulated a serial scanning processacross an input trace (Lefton etal., 1978; Mewhort,Merikle, & Bryden, 1969). More recently, interpretationshave focused instead on weights derived from perceptualfactors and/or position of maximal information within astring (Brysbaert, Vitu, & Schroyens, 1996; Montant etal.,1998; O’Regan, Levy-Schoen, Pynte, & Brugaillere, 1984).We suggest another possibility: that this pattern of per-ceptibility emerges directly from the way in which letterposition is encoded. Consistent with earlier interpreta-tions, we suggest that serial processing is involved andthat letter position is encoded by a temporal firing pat-tern across letter units. Specifically, we propose a letter-tagging scheme in which the tag corresponds to the timeof firing relative to an underlying oscillatory cycle. Inkeeping with the evidence for the importance of letter or-der, we suggest that this temporal representation then ac-tivates contextual units. Thus, we combine two letter po-sition encoding schemes and address their respectiveshortcomings, by attempting to specify how letter posi-tion is tagged and how context units are activated.We have dubbed this model the SERIOL frameworkof letter position encoding (sequential encoding regu-lated by inputs to oscillations within letter units). Our goalwas to construct a theoretical framework for written wordrecognition that is consistent with psychological studiesand to perform computer simulations that reproduce thedata from those studies. At the same time, we wanted aframework that is neurobiologically plausible and is con-sistent with current theories of neural computation andphysiology. In pursuit of this goal, we have constructeda model of word recognition that extends from the retinallevel to the lexicon and accounts for a wide range of phe-nomena, from patterns of letter perceptibility across vi-sual fields to hemispheric modes of processing.The organization of this paper is as follows. First, wepresent the details of SERIOL framework. Then, we dis-cuss how this framework is consistent with and accountsfor data gathered from many studies relevant to variousaspects of letter position encoding and word recognition.The results of some of those studies are reproduced viamathematical models based on the proposed framework.Finally, in the Discussion section, we further address theissues introduced here.2. THE SERIOL FRAMEWORKThis section provides a specification of SERIOL modelby describing its structure and the functionality of eachlayer. The SERIOL model provides a theoretical frame-work. The entire framework has not been implementedin a computational model. However, portions have beenimplemented; those simulations will be described in latersections. We first give an overview of the SERIOL frame-work, followed by a more detailed description.The framework is composed of five layers, each havingdistinct activation dynamics. We will use the term nodeto refer to the basic computational unit. A node may bethought of as corresponding to a neuronal assembly. Ex-cept at the lowest layer, a node’s function is to recognizethe occurrence of a symbol.At the lowest processing layer, the retinal level, a noderepresents a pixel. The nodes in this level are preciselytopographically organized with respect to visual inputfrom external space, and perceptual acuity decreases asdistance from the visual fixation point increases. At thefeature level, nodes tuned to retinal location recognizesuborthographic letter features. At this level, the retinalpattern of activation resulting from perceptual factors istransformed to reflect locational information, wherein acti-vation decreases from left to right across location. At theletter level, nodes recognize individual letters. The vary-ing levels of input from the feature level are convertedinto a temporal firing pattern across the nodes, in whichthe firing order tags position. This is accomplished byinteraction with an underlying subthreshhold oscillation,such that the letter node receiving the most input firesfirst, the letter node receiving the second highest levelof input fires next, and so on. Lateral inhibition ensuresthat only one letter node fires at a time. At the bigramlevel, nodes recognize ordered pairs of letters, convertingthe temporal representation of the letter level to a contex-tual representation. At the word level, nodes recognizesets of bigrams comprising entire words.Figures 1 and 2 summarize how the string “CART”would be represented within this framework. Figure1 di-agrams the activation patterns at the retinal and featurelevels; Figure2 displays the letter level to the word level.In summary, at the feature level, an activation gradient isestablished across the features of the letters; at the letterlevel, “C” fires, then “A,” then “R,” then “T”; at the bigramlevel, “CA,” “AR,” “RT,” “CR,” “AT,” and “CT” becomeactive; at the word level, “CART” becomes the most ac-tive of the word nodes.We next focus on each processing level in more detail.The higher processing layers of the framework, from theletter to word levels, have been previously described(Whitney & Berndt, 1999). Therefore, they will not be pre-sented in as much detail as the lower processing levels,which have not previously been specified.2.1. Retinal LevelOn the physical retina, visual acuity falls off with in-creasing angle from the fixation point, due to the decreas-ing concentration of cones. Thus, in terms of visual acu-ity, objects at fixation are significantly better perceivedthan objects outside of fixation; an early study showed thatperformance in a line detection task decreasedmore than50% within 1º of the center of the fovea (Alpern, 1962). MODEL OF LETTER-POSITION CODING223 For clarity of presentation, we will use the term loca-tion to refer to physical location in space (with respect tovisual fixation) and the term position to refer to a letter’sordinal position within a string. Abstracting away fromphysical retinas, the retinal level in our framework is fullyspecified by acuity, C, which is a function of retinal lo-cation, R. For simplicity, we consider location to be one-dimensional, specifying horizontal distance from thepoint of visual fixation (for which R50). We take loca-tions to the left of fixation (i.e., in the left visual field, LVF)to have negative values and locations to the right of fix-ation (in the right visual field, RVF) to have positive val-ues. Acuity is symmetric around fixation; that is, C(R)5C(2R). Acuity is maximal at R50 and decreases with|R|. We will denote this pattern of activation(i.e., the function C) as the acuity gradient. The activationpattern for the retinal layer in Figure1 corresponds to theacuity gradient.2.2. Feature LevelAt the next processing level, nodes recognize sub-orthographic features. We do not model the process offeature extraction itself, but rather assume that each fea-ture node reaches a level of activation that is consistentwith our specifications of bottom-up and lateral patternsof activation. We make the following assumptions. Fea-ture nodes are broadly tuned to retinal location and senddirectional lateral inhibitory input to each other. Featuresare independently extracted in each hemisphere. Theamount of excitatory and inhibitory input varies with thehemisphere. This hemisphere-specific activation convertsthe acuity gradient into a locational gradient. We next dis-cuss each of these assumptions in more detail.It is commonly assumed that letters are identified byanalyzing suborthographic features (e.g., lines, angles,and curves). Several studies have indicated that letter fea-tures play a role in letter recognition and that similar fea-tures occurring in different locations interact with eachother, where the degree of interaction depends on the spa-tial distance between the features (Bjork & Murray, 1977;Chastain, 1977; Krumhansl & Thomas, 1976; Strangert& Brännström, 1975).As is consistent with the results of these experiments,the next level of our model is composed of feature detec-tors that are tuned to retinal location. There is neurobio-logical evidence that the response patterns of neuronscan be broadly tuned—that is, a neuron responds moststrongly to a specific stimulus, and its response falls offas the similarity to this preferred stimulus decreases. Forinstance, some neurons in the motor cortex are tuned tomovement direction. Such a neuron fires most stronglywhen movement in space occurs in its preferred direction.As the direction of movement increasingly differs fromthis preferred direction, the neuron’s firing level decreases(Georgopoulos, Kalaska, Caminiti, & Massey, 1982). Wepropose a similar pattern of activation for feature nodeswith respect to retinal location. That is, a feature node ismost highly activated when the feature that it recognizesoccurs in a certain optimal area of the retina (the featurenode’s preferred location), less strongly activated whenthat feature occurs near the preferred location, and not atall activated when that feature occurs far from the preferred Figure1. Architecture of the retinal and feature levels of the SERIOL frame-work. The retinal level is precisely topographically organized with respect to ex-ternal stimulus—in this case, “CART.” The activation of retinal nodes decreasesas distance from fixation increases. Feature nodes are tuned to retinal location.The activation of feature nodes decreases from left to right across locations. 224WHITNEY location. Each possible feature stimulus is detected bymultiple nodes having different preferred locations. Thisproposal can account for the experimental evidence thatsimilar features interact with each other, where the degreeof interaction decreases as the spatial distance betweenfeatures increases.The connections from the retinal level to the featurelevel in our framework correspond to information flowfrom the retinas to the cerebral hemispheres. The visualsystem is connected in such a way that information fromthe LVF is initially processed by the right hemisphere(RH), and information from the RVF is initially pro-cessed by the left hemisphere (LH). However, it is notclear whether there is overlap along the vertical meridianbetween the two visual fields. This issue has importantimplications for letter string processing. If there is suffi-cient overlap, all letters within a string are sent directlyto both hemispheres. If not, normal processing of letterstrings must involve interhemispheric (callosal) transferin order to integrate the two halves of the string. Brys-baert (1994) reports that many authors assume visual fieldoverlap on the order of 1º to 3º. However, Brysbaert ar-gues that assumptions for overlap are based on weak, in-direct evidence from anatomical findings. On the basisof comparisons of the optimal viewing position for wordsin subjects presumed to process language in the RH ver-sus those who process language in the LH, Brysbaert con-cludes that, with respect to reading, functionally there isno overlap and that interhemispheric transfer normallyoccurs for centrally presented stimuli. This result will bediscussed in more detail in Section3.2. Moreover, exper-iments with commissurotomy patients and hemianopicpatients have provided evidence against such an overlap;if any overlap does exist, it is less than one half of a de-gree and provides only partial visual information (Fen-drich & Gazzaniga, 1989; Sugishita, Hamilton, Sakuma,& Hemmi, 1994; Sugishita, Hemmi, Sakuma, Beppu, &Shiokawa, 1993; Trauzettel-Klosinski & Reinhard, 1998).Following this evidence of no visual field overlap, weassume that visual information about letters falling to theleft of fixation (the initial letters in English words) is pro-jected to the RH and that information about letters fall-ing to the right of fixation (the final letters in Englishwords) is projected to the LH. Letter features are extractedseparately in each hemisphere.We propose that the pattern of activation attained byfeature nodes is very different from the pattern of activa-tion at the retinal level. Experimentally, it has been notedthat the pattern of perception of letters within a string vi-olates the pattern of the acuity gradient. Numerous stud-ies of briefly presented letter strings have shown that theinitial letter of a string is the most accurately perceivedof all the letters, even when the initial letter is far from fix-ation (Hammond & Green, 1982; Lefton etal., 1978; Figure2. Architecture of the word, bigram, and letter levels of the SERIOL frame-work, with example of encoding the word “CART.” At the letter level, simultaneousgraded inputs and lateral inhibition create a temporal firing pattern, as indicated bythe timing of firing displayed under the letter nodes. Excitatory connections link theletter nodes and the bigram nodes, which recognize ordered pairs of letters. The acti-vations of the bigrams (shown above the nodes) are proportional to the activations ofthe constituent letters. Excitatory connections link the bigram nodes and the wordnodes. For each word node, connection weights are proportional to the bigram acti-vations evoked by that word. Activation of word nodes is based on conventional neuralnetwork models. MODEL OF LETTER-POSITION CODING225 Mason, 1982; Wolford & Hollingsworth, 1974). Thispattern cannot be attributed to decreased lateral inhibi-tion for boundary letters; when strings of nonletter sym-bols are centrally presented, the initial and final symbolsare the least well perceived, as would be expected if per-ception were simply a function of visual acuity (Hammond& Green, 1982; Mason, 1982). The enhanced perceptionof the initial symbol also holds for strings of numbers.Thus, it appears that a specialized system exists for ana-lyzing symbols that commonly occur in strings. This sys-tem overrides the effects of visual acuity.In brief, we propose that this string-processing systemoperates as follows. The acuity gradient of the retinallevel is transformed into a locational gradient at the fea-ture level. For languages read from left to right, the lo-cational gradient is characterized by decreasing activa-tion from left to right across preferred location. That is,feature nodes with the leftmost preferred locations attainthe highest level of activation, and activation levels de-crease for more rightward preferred locations (see theactivation pattern for the feature layer in Figure1). Atthe letter level, this locational gradient is converted intoa temporal firing pattern that encodes position. As a con-sequence of this encoding process, a positional gradientacross letter node activations emerges. This positionalgradient underlies experimentally observed patterns ofletter recognition within strings.In the remainder of this section, we specify how theacuity gradient is converted to the locational gradient. Forsimplicity, we consider only those feature nodes mosthighly activated by the retinal inputs (i.e., those featurenodes activated by features occurring at their preferredlocations). We assume that this conversion mechanism islearned during reading acquisition. We do not address howit is learned, but rather propose a model of informationprocessing for a skilled reader.Locational gradient formation depends on two impor-tant characteristics of the reader: scanning direction anddominant hemisphere for language processing. In thefollowing specification, we assume that words are readfrom left to right (as in English) by a reader having theusual brain organization—that is, LHdominant. In Sec-tion3, we show how this specification can account forexperimentally observed patterns of letter perceptibility,and we consider other combinations of scanning direc-tion and dominant hemisphere.The proposed locational gradient is monotonically de-creasingfrom left to right. Note that, for English words,the slope of the acuity gradient in the RVF/LH (from fix-ation to the final letter) is in the same direction as ourproposed locational gradient. In contrast, the slope of theacuity gradient in the LVF/RH (from the initial letter tofixation) is increasing—that is, the slope is in the oppo-site direction of our proposed locational gradient (for ex-ample, compare the activation patterns for the retinallayer and the feature layer in Figure1). We propose that,in the LVF/RH, the slope of the acuity gradient is re-versed or inverted as it activates letter features, whereas,in the RVF/LH, it is maintained. This occurs via strongerweights in the LVF/RH on bottom-up excitatory connec-tions and on inhibitory connections within the featurelevel that act from left to right (the differing weight mag-nitudes across hemispheres and the directional nature ofthe inhibition were learned during reading acquisition).Following callosal transfer, the resulting two partial gra-dients are combined, forming a locational gradient thatis monotonically decreasing from left to right.This process of locational gradient formation is illus-trated in Figure3. We assume that letter features in theLVF/RH become more highly activated by retinal inputsthan those in the RVF/LH (see the upper right panel ofFigure3). This allows the first letter’s features to reach ahigh level of activation, even if they are far from fixation.This assumption is consistent with experimental resultsshowing that, in the LVF/RH, perceptibility of the initialletter does not decrease as distance from fixation in-creases, whereas, in the RVF/LH, it does decrease (Estesetal., 1976). (This result will be discussed in greater de-tail in Section3.1.) Within the feature level of the RH, wepropose that strong directional lateral inhibitory connec-tions exist, such that a feature node inhibits all featurenodes with preferred locations to its right. Thus, theamount of inhibitory input increases as distance fromfixation decreases, because more and more features sendinhibition from the left. We assume that this directionalinhibition is strong enough to override the slope of theacuity gradient, inverting it. Thus, the features compris-ing the first letter attain a high level of activation (due tostrong excitation and lack of lateral inhibition), and ac-tivation decreases toward fixation (due to sharply in-creasing directional lateral inhibition; see the lower leftpanel of Figure3.)In the RVF/LH, we assume that the weights on boththe excitatory and the inhibitory connections are weaker,because the acuity gradient is already in the correct di-rection, so strong weights are not necessary. Thus, theacuity gradient is essentially maintained at the featurelevel in the LH (although some directional inhibition maysteepen its slope).Feature information from the RH is then transferredto the LH. We assume that the features from the RH in-hibit the activations of the LH features, such that the fea-ture activations of the LH’s leftmost letter are lower thanthose of the RH’s rightmost letter. As a result, an activa-tion gradient across all features is created in the LH thatis strictly decreasing by left-to-right location (see thelower right panel of Figure3). Thus, the locational gra-dient is formed. A mathematical model of this conversionis given in AppendixA.2.3. Letter LevelWe propose that the locational gradient of the featurelevel induces a temporal firing pattern across letter nodes,wherein position is represented by the precise timing offiring relative to other letter nodes. This idea is consis-tent with current neurobiological models of informationencoding. Hopfield (1995) has proposed that quantitiesare represented by the explicit timing of action potentials, 226WHITNEY rather than by their firing rate. In this phase-advancemodel, encoding neurons undergo internal, subthresh-hold oscillations of excitability. The magnitude of an in-put to such a neuron determines when threshhold is ex-ceeded. For a small input, threshhold is not exceeded untillate in the cycle when the cell’s oscillation brings its po-tential near threshhold. For a larger input, threshhold isexceeded earlier in the cycle. Thus, the size of an inputis represented by spike timing relative to the oscillatorycycle. This scheme implies that individual spikes aremuch more important than has traditionally been as-sumed. Indeed, recent studies have shown that singlespikes encode signficant amounts of information (Reike,Warland, deRuyter vanSteveninck, & Bialek 1997) andthat spike timing is precise and reproducible at a milli-second time scale (Berry, Warland, & Meister, 1997;deRuyter vanSteveninck, Lewen, Strong, Koberle, &Bialek, 1997; Victor & Purpura, 1996).It has been proposed that oscillatory activity in thebrain near 40Hz (gamma frequencies) is related to cog-nitive processing (Tiitinen etal., 1993). There is evi-dence that individual 40–Hz waves are related to indi-vidual auditory stimuli (Joliot, Ribary, & Llinas, 1994).It has been suggested that short-term memories are en-coded on 40-Hz subcycles of a low-frequency (5- to 12-Hz) oscillation (Lisman & Idiart, 1995). This proposal isconsistent with the observation of nested oscillations re-corded in the human cortex in response to auditory stim-uli (Llinas & Ribary, 1993). We suggest that such oscil-lations also underlie visual language processing. Wepropose that each letter position corresponds to a suc-cessive 25-msec subcycle within an oscillatory period of»200msec.This coding scheme does not employ position-specificletter detectors; all feature nodes are connected to all let-ter nodes. Any letter node can represent any position, de-pending on the level of input that it receives and the re-sulting timing of firing. We do not model the process ofletter recognition; we take as given that a mechanism ex-ists to bind the features of a letter together, culminating Figure3. Example formation of the locational gradient across the activations of features. In the upper left graph, the acuity gradi-ent of the retinal level is displayed in abstract units of activation. In the upper right graph, the effects of hemisphere-specific excita-tion, E, at the feature level are shown. Note that in the RVF/LH (retinal location ³0), Eis equivalent to the acuity gradient, whereasin the LVF/RH (retinal location 0), Eis elevated with respect to the acuity gradient. In the lower left graph, the effects of hemisphere-specific leftward lateral inhibition, E2I, are displayed. Note that inhibition is much stronger in the LVF/RH than in the RVF/LH andresults in inversion of the direction of the slope of the gradient in the LVF/RH. In the lower right graph, the hemisphere-specific gra-dients are joined via interhemispheric inhibition of the RVF/LH’s features to form a monotonically decreasing activation gradientacross feature locations, the locational gradient. MODEL OF LETTER-POSITION CODING227 in activation of the correct letter. All letter nodes are as-sumed to undergo synchronous, periodic oscillations ofexcitability. Due to the locational gradient, the letternode representing the letter in the first position receivesthe highest level of excitatory input, the second receivesthe next highest amount, and so on. The letter node re-ceiving the highest level of input fires first because itreaches threshhold before the others; the letter node re-ceiving the second highest level of input fires next, andso on. Suitable input levels and lateral inhibition ensurethat only one letter node fires at a time. We assume thata letter node continues to fire until it receives lateral in-hibition and that, once a letter node receives inhibitionafter it has already fired, it does not fire again in the oscil-latory cycle. A precise description of this temporal encod-ing process is given in Whitney and Berndt (1999).The level of input affects the activation of the receiv-ing letter node, where higher levels of input cause fasterrefiring and, therefore, higher levels of activation. Thus,the locational gradient of the feature level creates a po-sitional gradient across the letter nodes. However, thepositional gradient does not necessarily have the sameshape as the locational gradient, because the positionalgradient results from the interaction of the locationalgradient with other factors (namely, the internal states ofthe letter nodes and lateral inhibition between letternodes). These interactions can result in a pattern of acti-vation at the letter level across positions that is not mo-notonically decreasing. Specifically, we propose that thefinal letter continues to fire until the end of the oscilla-tory cycle, since it is not inhibited by another letter. Asa result, the activation of the final letter depends on whenin the cycle it starts firing. If it starts firing relativelyearlyin the cycle, it can achieve a higher level of activa-tion thanthe internal letters. Also, the relative levels of theinputs toadjacent letters can affect activation levels. Thiscan account for the increased perceptibility of a fixatedletter. We discuss these phenomena in more detail in Sec-tion4.2.2.4. Bigram and Word LevelsAt the next level of our framework, bigram units areactivated by the sequential dynamics of the letter nodesand provide a mechanism for decoding this temporal rep-resentation into a nontemporal encoding. Bigram nodesrecognize ordered pairs of letters, corresponding to neu-ronal assemblies that fire only if input “A” is followed byinput “B.” Such an assembly would not fire if only “A”were received, or if “B” were received prior to “A.” A bi-gram node becomes active if it receives suitable inputswithin the time span of an oscillatory cycle; thus, bigramnodes can be activated by noncontiguous letters in theinput string. Bigrams were chosen as the contextual unitsbecause they are the most basic such units. For simplicity,bigrams connect directly to words, but we do not meanto rule out the possibility that there may be higher levelsof organization between bigrams and words.The activation of a bigram node depends on the activa-tions of the letter nodes representing its constituent let-ters (increasing activation with increasing input levels)and the time separation between the firing of those letternodes (decreasing activation with increasing separation).On the basis of their experimental results, Humphreysetal. (1990) have suggested that words are representedby patterns of activations across context units, where ac-tivations are scaled by visual factors, such as the prox-imity of constituent letters and the presence or absenceof lateral masking (which depends on letter position).Our specification of bigram unit activation allows a nat-ural formulation of such graded activations.At the bigram/word interface, the SERIOL frameworkfollows the classical firing-rate model. These connectionsare modeled using the conventional neural network modelmethodology, wherein the input to a word node is thesum of the weighted activations from the bigram level.The weight on a connection from a given bigram node toa given word node is proportional to the activation of thatbigram when that word is being represented across thebigram nodes. A more detailed specification and simu-lations are given in Whitney and Berndt (1999).Our proposed framework of letter position encodingis consistent with a wide range of experimental data. In thefollowing sections, we discuss how our framework canaccount for the results of many studies, and we use math-ematical models to support our proposals. First, we pre-sent studies that are relevant to locational gradient forma-tion. Then, we discuss aspects of the letter level, includingtemporal encoding, the positional gradient, and a groupof studies designed to investigate the nature of letter po-sition coding.3. STUDIES RELEVANT TO FORMATIONOF THE LOCATIONAL GRADIENTOur specification of how the locational gradient isformed can account for a variety of experimental results.First, we discuss studies pertaining to perceptibility ofindividual letters within nonword strings, which revealvisual field differences that we argue arise from the pro-cess of locational gradient formation. Then, we presentstudies concerning optimal viewing position (OVP) andthe RVF advantage, and we discuss the interaction of read-ing direction and dominant hemisphere in those phenom-ena. Finally, we show how this discussion relates to theproposal of different hemispheric “modes of processing”in reading.3.1. Visual Field Effects onPatterns of PerceptibilityStudies have shown a robust pattern of decreasing let-ter perceptibility with increasing string position (withthe possible exceptions of the fixated letter and the finalletter; see Hammond & Green, 1982; Lefton etal., 1978;Mason, 1982; Wolford & Hollingsworth, 1974). This over-all pattern is generally independent of fixation point. How-ever, string position did interact with visual field in sev-eral studies. For example, in Estes etal. (1976), subjectswere to identify briefly presented four-letter strings that 228WHITNEY occurred over one of four possible retinal areas: from28to 25, from 25 to 22, from 2 to 5, or from 5 to 8 (whereunits are in letter widths, and fixation is at 0). In the LVF/RH, perceptibility of the initial letter was unaffected byretinal location, with perceptibility at 80% for locations28 and 25. In the RVF/LH, retinal position did affectperceptibility of the initial letter, with perceptibility forlocation 2 at 80% and for location 5 at 50%. Thus, in theLVF/RH, perceptibility of the initial letter did not fall offas acuity decreased (i.e., as distance from fixation in-creased), as it did in the RVF/LH. Assuming that this dif-ference arises from the feature level, this finding is con-sistent with the SERIOL framework, wherein features inthe LVF/RH receive higher levels of excitatory input thanthose in the RVF/LH, yielding acuity effects on the initialletter in the RVF/LH, but no such effects in the LVF/RH.In another study, subjects were to report the letters com-prising a nine-letter string (Wolford & Hollingsworth,1974). In order to deconfound the effects of retinal loca-tion and string position, the location of the string wasvaried with respect to fixation. The location of the string’sinitial letter varied from 12 letter widths to the left of fix-ation (R5212) to 5letter widths to the right of fixation(R55). This yielded separate retinal location curves forall string positions and yielded separate string positioncurves for retinal locations 24 to 4.An analysis of the data showed an interaction of stringposition with visual field. That is, for a given string posi-tion and distance from fixation (|R|), the result varied withthe direction from fixation. These experimental dataaredisplayed in the upper panels of Figure4 (we display the re-sults only for the first seven string positions because,forsimplicity, we do not consider possible increased activa-tion levels at the end of the string). To summarize, for agiven retinal location in the LVF, perceptibility initiallydrops off quickly with increasing string position and thenlevels off. However, in the RVF, perceptibility is moresmoothly decreasing. For example, at retinal location 3 inthe LVF/RH (R523), perceptibility drops sharply from100% for position1 to 35% for position3. Perceptibilitycontinues to decrease to 20% for position4 but staysroughly constant as position increases from4 to 7. In con-trast, at the analogous location in the RVF/LH(R53), per-ceptibility drops from 95% for position1 to 55% for posi-tion3, a smaller drop than in the LVF/RH. Perceptibilitydrops to 30% for position4 and continues to decrease to5% for position7, rather than stabilizing as in the LVF/RH.We suggest that this visual field effect arises from thedifferences in the formation of the locational gradient inthe two hemispheres. Recall that, in the RVF/LH, the lo-cational gradient is roughly equivalent to the acuity gra-dient, whereas in the LVF/RH, formation of the locationalgradient requires inversion of the slope of the acuity gra-dient via strong excitation and inhibition. It follows thatthe resulting hemisphere-specific locational gradientswould not have the same shape as each other. We devel-oped a mathematical model based on this premise thatgives a good approximation to this data.More specifically, we assume that the amount of inhi-bition received by a letter’s features depends on how manyletters are to its left, the activation of those letters’ features,and the strengths of the inhibitory connections. Theseassumptions on leftward lateral inhibition underlie themodel’s ability to recreate the pattern in the experimentaldata. In the LVF/RH, perceptibility at a given locationinitially decreases quickly as string position increases,because inhibitory input increases quickly as more let-ters occur to the left. However, after a certain point, thelevel of inhibitory input flattens out as more letters occurto the left. This occurs because those additional letterscontribute lower and lower levels of inhibitory input be-cause they are farther from fixation, and, thus, their ac-tivation levels are lower. As a result, the amount of inhib-itory input received increases nonlinearly as string positionincreases. However, in the RVF/LH, overall levels of lat-eral inhibition are weaker, so this nonlinear effect is notas strong, resulting in a smoother decrease in percepti-bility. The results of the mathematical model are shownin the lower panels of Figure4. Note that the model ac-curately recreates the differing patterns of perceptibilityby visual field. The details of the model are given inAppendixA.We suggest that the assumptions underlying the mech-anism of locational gradient formation could be testedmore directly using the sequential blanking paradigm.When stimuli are presented briefly (for 20msec) acrossspatial locations, a stimulus that is followed 100mseclater by another stimulus in a neighboring location is notperceived (Mayzner & Tresselt, 1970). This masking orblanking is sensitive to the form of the stimuli and isthought to arise from lateral inhibition at the level of“geo-metric analyzers” (i.e., feature detectors). If the intensityof the masked stimuli is sufficiently increased relative tothe masking stimuli, then blanking no longer occurs. Bytesting the minimal increase in intensity required toovercome the blanking for different retinal positions, thelocational gradient formation hypothesis could be inves-tigated. It predicts that there should be a directional ef-fect, where masking stimuli on the left exhibit more in-hibition than those on the right. It also predicts a visualfield effect, where inhibition is greater in the LVF than inthe RVF. However, even if such effects were not observed,it would not necessarily imply that the hypothesis is in-correct, because the directional inhibition could occur athigher processing level than that which underlies the se-quential blanking effect.We have seen how proposed processes underlying theformation of a locational gradient can account for ex-perimental results regarding visual field effects in letteridentification. Next, we address experiments examiningthe role of fixation point in the identification of entirewords, leading us to generalize the discussion of locationalgradient formation to address the effects of reading direc-tion and dominant hemisphere and to consider the pro-cessing time required to perform interhemispheric trans-fer and acuity gradient inversion. MODEL OF LETTER-POSITION CODING229 3.2. Costs of Transfer and InversionIn our specification of locational gradient formation,scanning direction determines the hemisphere for whichacuity gradient inversion occurs. That is, inversion shouldoccur for the visual field in which the slope of the acuitygradient is with increasing string position. Forlanguages scanned from left to right, this is the LVF/RH,as previously discussed. For languages read from right toleft, inversion should occur in the opposite visual field,theRVF/LH. The other directional factor involved in loca-tional gradient formation is callosal transfer, which is de-termined by which hemisphere is dominant for language.For the typical brain organization, transfer occurs from theRH to the LH. For the atypical organization, transfer oc-curs in the opposite direction, from the LH to the RH.We will refer to the process of inverting the slope of theacuity gradient as inversion, and we will refer to the pro-cess of callosal transfer as transfer. These two processesare independent of each other. We assume that each in-curs some processing delay. We propose that transferimposes a constant delay (independent of the number ofletters transferred), whereas inversion incurs a delay thatincreases with the number of letters involved. We nextdiscuss how this view is consistent with a variety of stud-ies in which visual field of presentation, reading direc-tion, and hemispheric dominance are varied. Figure4. Experimental and modeled results for interaction of string position and retinal location from Wolford and Hollingsworth(1974). Graphs display percent correct at each string position for various retinal locations,R. The upper graphs display experimen-tal data, and the lower graphs display the model’s results. Graphs on the left display LVF/RH data, and graphs on the right displayRVF/LH data. 230WHITNEY It has been found that an OVP exists for words that dif-fers from the effects of acuity alone. In French and En-glish, words are most easily perceived when fixationfalls approximately one character to the left of the word’scenter (i.e., so that more of the word appears in the RVFthan in the LVF; see Brysbaert, 1994; O’Regan etal.,1984). Presumably, the main determinant of the OVP isacuity; fixation at the word’s center minimizes the loss ofacuity at the retinal level (i.e., maximizes the minimalacuity). This implies that the leftward bias arises at somehigher level of processing (Brysbaert etal., 1996; O’Re-gan etal., 1984).O’Regan etal. (1984) proposed that the rightward shiftoccurs because the initial part of a word is usually the mostuseful in distinguishing the word from other words. Theyinvestigated the influence of locus of maximal informa-tion on OVP by varying the lexical structure of the wordstimuli. Under fixation near the end of the word, wordshaving unique combinations of letters at the end were morequickly processed than were words with unique letters atthe beginning. Thus, they demonstrated that informationalcontent does influence OVP. However, lexical structurecannot account for the entire OVP effect, because the rel-ative advantage for information at the beginning is muchgreater than for information at the end. That is, the ad-vantage for fixating on the information-rich part of theword (versus fixating on the opposite part of the word) ismuch greater if that part is at the beginning of the wordthan if it is at the end. Thus, it appears that an additionalprocess is at work in determining the OVP.For words presented entirely within a single visualfield, a robust RVF/LH advantage (relative to the LVF/RH) in both reaction time and accuracy has been found(for reviews, see Bryden, 1982, and Hellige, 1993). Brys-baert etal. (1996) have shown that there is a continuumof advantage for the RVF/LH as foveal presentation (in-volving both visual fields) changes to parafoveal presen-tation (involving a single visual field). This result impliesthat the leftward bias in the OVP and the hemifield RVF/LH advantage both arise from the same underlying mech-anism, as argued by Brysbaert etal. (1996).What are these mechanisms that are responsible forthis RVF/LH superiority? Various proposals have focusedon different factors. Since information in the RVF is sentdirectly to the usually dominant LH, the advantage mayarise from hemispheric factors. Alternatively, it may beassociated with the scanning direction employed for a spe-cific language, or it may depend on the position of dis-tinguishing information within a word (Brysbaert etal.,1996; O’Regan etal., 1984). In addition to any informa-tional influences, we propose that the effect depends onan interplay of both scanning and hemispheric influences.Namely, for presentation in the RVF/LH, neither inver-sion nor transfer is required for locational gradient for-mation, whereas, for presentation in the LVF/RH, bothprocesses are necessary. Thus, the RVF has a large advan-tage over the LVF because less processing is required.3.2.1. Right-to-left readers. Our proposal predictsthat this RVF advantage should be reduced for a lan-guage read from right to left, because inversion becomesnecessary for RVF/LH presentation and is no longer nec-essary for LVF/RH presentation. This prediction is con-sistent with current studies on reading direction and hemi-field superiority (in the following discussion, subjectsare assumed to be LHdominant). Previously, such exper-iments were designed to detect only the presence or ab-sence of RVF/LH superiority. It was noted that an RVF/LHadvantage does exist in Hebrew, and researchers con-cluded that reading direction did not affect visual fieldsuperiority (Carmon, Nachson, Isseroff, & Starinsky,1976; Faust, Kravetz, & Babkoff, 1993). Because we pro-pose that the RVF/LH superiority arises from the inter-play of hemispheric dominance and reading direction,we suggest that it is important to consider the relativesizes of RVF/LH superiorities by reading direction.Indeed, in a recent study of Farsi (a right-to-left lan-guage) versus English designed to study this issue (Mela-med & Zaidel, 1993), the RVF/LH advantage in Farsiwas significantly smaller than in English for a word nam-ing task. In a lexical decision task (i.e., where processingis dominated by letter encoding and lexical access, ratherthan phonological encoding), there was no RVF/LHad-vantage for Farsi. This combination of results led the au-thors to conclude that the increased RH contribution inFarsi (relative to English) selectively involves the visualinput processing aspect of word recognition. Since in-version is a component of visual input processing, this isconsistent with our suggestion that the RVF/LH advan-tage is reduced for languages scanned from right to leftas a result of the cost of inversion in the RVF/LH. The re-sults of an OVP study in Arabic (another right-to-left lan-guage) are also consistent with this proposal. In Arabic,the OVP is located at the center of the word, with no left-ward bias (Farid & Grainger, 1996). We suggest that therightward shift of the OVP in Arabic (relative to left-to-right languages) arises from the same underlying mech-anisms as the reduced (or obliterated) RVF/LH advantagein Farsi—namely, that the cost of acuity gradient inver-sion is no longer incurred in the LVF/RH.3.2.2. RH-dominant readers. Our proposal also pre-dicts that the RVF/LH advantage should be reduced forRH-dominant, left-to-right readers, because transfer be-comes necessary, whereas for LVF/RH presentation,transfer is no longer necessary. The results of the follow-ing experiment are consistent with this prediction andallow us to quantify the relative costs of inversion andtransfer using a mathematical model.Brysbaert (1994) studied the effect of cerebral domi-nance and viewing position on French readers, whosehemispheric dominance was determined by a battery oflaterality tests. Subjects were to name words, where fix-ation point and word length were varied. The word waspresented with either its initial letter or its final letter oc-curring at the central fixation point. The reaction timedata are displayed in the upper panels of graphs in Fig-ure5. LH-dominant subjects showed the usual strongRVF/LH advantage: For words of three, four, five, seven,and nine letters, reaction times were significantly shorter MODEL OF LETTER-POSITION CODING231 for initial-letter fixation (i.e., word in RVF/LH) than forfinal-letter fixation (i.e., word in LVF/RH). The size ofthis difference increased with increasing word length,denoted as an increasing RVF/LH advantage. In RH-dominant subjects, the RVF advantage was greatly re-duced. For three-letter words, RH-dominant subjects hadshorter reaction times for fixation on the final letter thanon the initial letter (i.e., a trend toward a LVF/RH advan-tage). For four- and five-letter words, there was no dif-ference between initial- and final-letter fixation. For thelonger words, RH-dominant subjects, like LH-dominantsubjects, displayed shorter reaction times for initial fix-ation than for final fixation. However, the size of the dif-ference was much smaller in the RH-dominant subjectsthan in the LH-dominant subjects.Brysbaert (1994) has argued that these data are con-sistent with the proposal that interhemispheric transfer isnecessary for information falling in the visual field thatprojects to the nondominant hemisphere. That is, for LH-dominant readers, information in the LVF/RH must un-dergo callosal transfer, and, for RH-dominant readers,information in the RVF/LH must undergo transfer. ForLH-dominant readers, the shift from initial-letter fixation(word in RVF/LH) to final-letter fixation (word in LVF/ Figure5. Experimental and modeled results for naming latency from Brysbaert (1994). Graphs display reaction times (in millisec-onds) for initial- and final-letter fixations, where connected points represent words of the same length. Initial-letter fixation results inpresentation to the RVF/LH, and final-letter fixation results in presentation to the LVF/RH. The upper graphs display experimentaldata, and the lower graphs display the modeled results. Graphs on the left display data for LH dominance, and graphs on the rightdisplay data for RH dominance. 232WHITNEY RH) exacts a large cost in naming latency, because inter-hemispheric transfer becomes necessary. However, forRH-dominant readers, the shift from initial-letter tofinal-letter fixation removes the necessity of interhemi-spheric transfer, resulting in a greatly reduced cost forsuch a shift, relative to that for LH-dominant subjects.Presumably, the fact that the two patterns were not mir-ror images of each other (i.e., for most word lengths, therewas no LVF/RH advantage for RH-dominant readers) isrelated to factors other than hemispheric dominance,such as reading direction (Brysbaert, 1994), as is con-sistent with our proposal.On the basis of the increasing RVF/LH advantage withword length, Brysbaert (1994) proposed that the time re-quired for interhemispheric transfer depends on the num-ber of letters to be transferred. That is, because differencesin latencies between final-letter fixation and initial-letterfixation increased as word length increased, Brysbaertconcluded that callosal transfer time increases as thenumber of letters to be transferred increases. However, thisinterpretation is not fully consistent with the data. If trans-fer time depends on the number of letters being trans-ferred, the difference in initial-letter fixation latenciesfor RH-dominant and LH-dominant readers should alsoincrease with increasing word length. However, this dif-ference does not increase; it is constant at about 15msecfor all word lengths.Our interpretation of this data is that interhemispherictransfer time is constant, whereas the time required to in-vert the acuity gradient increases with the number of let-ters involved. Such an assumption accounts for all aspectsof the data. Because the time cost of inversion increaseswith the number of letters to invert, both hemispheres showan increasing RVF/LH advantage with word length. Be-cause inversion is necessitated by LVF/RH presentationregardless of dominant hemisphere, both hemispheresshow an RVF/LH advantage for long words. However,since LVF/RH presentation to LH-dominant readers in-volves both acuity gradient inversion and hemispherictransfer (whereas only inversion is involved for LH-dominant readers), the size of the RVF/LH advantage islarger for LH-dominant readers. For RVF/LH presenta-tion to RH-dominant readers, a constant interhemispherictransfer time is involved with no inversion time cost, ac-counting for the constant difference in initial-letter fix-ation times across dominant hemispheres. Possible pro-cesses underlying this proposed increasing inversion timewill be discussed below.On the basis of these ideas, we have developed a math-ematical model of these naming data. The results of a fitof this mathematical model are displayed in the lowerpanels of Figure5. The details of the model are given inAppendixB. Note that the model captures the salient as-pects of the data. For final-letter fixation in LH-dominantreaders, reaction times increase steeply with increasinglength. For RH-dominant readers, the cost of final-letterfixation is not as steep. In fact, for three-letter words,atrend toward an LVF/RH advantage for RH-dominantreaders appears. However, as word length increases, anRVF/LH advantage emerges.3.2.3. Time cost of inversion. It seems reasonable toassume that the time required for inversion increaseswith word length. Consider fixation on the final letter ofa word. The amount by which the activations of this finalletter’s features must be reduced (in forming the loca-tional gradient) depends on the number of features (let-ters) to its left. That is, a longer word results in a greaterreduction in activation than does a shorter word. If it doestake longer to accomplish a larger reduction, it would in-deed be the case that the time cost of inversion increaseswith the number of letters involved (word length). How-ever, increasing processing time with increasing lengthis usually taken as a sign of serial processing. How canthis length-dependent process be reconciled with the as-sumption of parallel processing at the feature level? Morespecifically, parallel processing would imply that the fea-tures of the letter at fixation receive more inhibition (overthe same time period) as the number of features to theleft increases, implying that activation reduction timeshould be constant with increasing length. However, thisreasoning depends on the assumption that increasingamounts of inhibitory input can be processed in the sameamount of time. If it takes longer for incoming inhibitionto take effect as the amount of that inhibition increases,a length effect would indeed emerge. Thus, a length effectfor inversion is not necessarily contrary to the assump-tion of parallel inputs to feature nodes. This scenario isconsistent with a theoretical analysis showing that a par-allel process with exponential processing rates canmimic a serial system (Townsend, 1971).If the increasing RVF/LH advantage does result fromthe necessity of acuity gradient inversion in the LVF/RH,this effect should disappear for a right-to-left language,since inversion is necessary for RVF/LH presentation,and not for LVF/RH presentation. The results of a studyof Hebrew readers are consistent with this prediction. Ina visual hemifield study of right-handed (presumably LH-dominant) subjects who named Hebrew words of two tofive characters, latency increased with word length (aswould be expected due to the cost of phonological encod-ing), but this effect was independent of visual field (Ko-riat, 1985). That is, there was no increasing advantage ofRVF/LH presentation versus LVF/RH presentation.However, since we propose that inversion underlies theincreasingly large RVF/LH advantage in a left-to-right lan-guage, why then was there no increasingly large LVF/RHadvantage observed in the Koriat (1985) study? We sug-gest that the answer depends on the length of the Hebrewwords used, coupled with the fact that RVF/LH presen-tation of Hebrew incurs inversion only, rather than bothtransfer and inversion. We propose that the time cost ofinversion without transfer for five or fewer letters is smalland is roughly equal to the time cost of transfer. This isconsistent with the analogous results from Brysbaert(1994) for RH-dominant individuals (i.e., the mirror-image case of LH-dominant, right-to-left readers), where MODEL OF LETTER-POSITION CODING233 LVF/RH and RVF/LH presentation latencies were roughlyequivalent to each other for words of five or fewer letters;an RVF/LH advantage for RH-dominant, left-to-rightreaders emerged only for words longer than five letters,where, according to our model, the time cost of inver-sion became larger than the time cost of transfer. Analo-gously, we would expect a LVF/RH advantage for LH-dominant, right-to-left readers to emerge only for wordslonger than five letters; such words were not included inthe Koriat (1985) experiment.Thus, our proposal implies that, in order to obtain aconsistent LVF/RH advantage, subjects would have to beRH-dominant, right-to-left readers. Indeed, in a study ofHebrew readers, left-handed subjects showed an LVF/RHadvantage, whereas right-handed subjects did not (Orbach,1967). Thus, a theory based on the time cost of interhemi-spheric transfer and acuity gradient inversion is consistentwith the results of a range of studies contrasting dominanthemispheres, reading direction, and word lengths.3.2.4. Position-specific reading deficit. Such a the-ory can also account for an unusual pattern of errors ob-served in several patients with LH damage (Costello &Warrington, 1987; Cubelli, Nichelli, Bonito, DeTanti, &Inzaghi, 1991; Katz & Sevush, 1989). These patients suf-fered from parietal/occipital lesions that caused visualneglect or extinction on the right side of space, with nor-mal perception on the left side. However, this pattern wasreversed when reading words. Under central fixation, thesepatients tended to make errors that involved the initialletter (from the left side of space), while correctly retain-ing the other letters. They did not have any other languageproblems. This pattern of dysfunction was taken to sup-port the notion of position-specific letter detectors. It washypothesized that patients suffered from damage to let-ter detectors representing the first position (Katz & Se-vush, 1989).We offer an alternative explanation for this error pat-tern, based on callosal transfer. We propose that visualfeature information that is sent from the RH (i.e., repre-senting the first half of the word) is not correctly re-ceived in the LH during locational gradient formation,as a result of the lesion. Because the initial letter has thelowest acuity, it is the most prone to degradation. (Al-though we propose that the activation of the first letter’sfeatures are elevated during locational gradient forma-tion, this process cannot insert information that is not al-ready there; it is like magnifying a noisy picture.) Thus,we propose that the lesion interferes with the callosaltransfer of information pertaining to the first part of theword, where the first letter is the most vulnerable.This analysis is consistent with several aspects of thepatients’ profiles. In their reading errors, patients tendedto substitute, rather than omit, the initial letters, reflect-ing a misinterpretation of available information. Whenwords were presented entirely in the RVF/LH to the pa-tient described by Katz and Sevush (1989), errors wereno more likely on the initial letter than on the other let-ters. Thus, when the initial letter had the highest acuityand did not have to undergo callosal transfer, it was nolonger the most vulnerable. The location of the patients’lesions in posterior LH regions close to the visual areasis consistent with our proposal of impaired callosal trans-fer of visual information. In contrast, in Section4.2, wediscuss how the SERIOL framework can account for thebehavior of patients having more anterior/central LH le-sions, who show no frank spatial neglect, have general-ized language problems, and make errors on the final let-ters of words.3.3. Hemispheric Modes of ProcessingWe believe that our discussion of the roles of the hemi-spheres in locational gradient formation is relevant tocurrent debates concerning supposed differing hemi-spheric “modes of processing” in reading. On the basisof visual hemifield data, researchers have proposed thatstring processing operates in parallel in the LH and seri-ally in the RH (the studies described here were per-formed with left-to-right readers, unless specified oth-erwise). For example, normal subjects show no lengtheffect in lexical decision for three- to six-letter wordspresented to the RVF/LH. However, for words presentedto the LVF/RH, each additional letter increases reactiontime by approximately 20msec (Ellis, Young, & Ander-son, 1988; Young & Ellis, 1985). We suggest that it is notthe case that the two hemispheres utilize different modesof processing, but rather that length effects arise withLVF/RH presentation due to the cost of acuity gradientinversion, as discussed above.A similar pattern of results emerged in a study of acallosotomized patient (Reuter-Lorenz & Baynes, 1992).Lexical decision reaction times for words of three to fiveletters were constant for RVF/LH presentation. However,for LVF/RH presentation, reaction times were 100mseclonger for five-letter words than for three- or four-letterwords (which were equivalent). These results were takento be consistent with those of normal subjects and to befurther evidence of different modes of processing acrossthe hemispheres. However, we propose that the two lengtheffects arose from different underlying processes. Notethe difference in time scale between normals and the pa-tient. For normals, each letter invoked a cost on the scaleof 10msec, as is consistent with our above mathematicalmodel of the cost of interhemispheric transfer and acuitygradient inversion. However, the increase of 100msecfor the patient is not on this scale; rather, it is on the scaleof the proposed oscillatory cycle. Due to the destructionof the callosum, the patient would have to process wordspresented to the LVF/RH entirely within the RH. We pro-pose that letter nodes in the RH are more slowly activatedthan those in the LH, so strings of letters that are normallyrepresented in one oscillatory cycle in the LH require anadditional oscillatory cycle in the RH. This proposal isconsistent with the observation that there was a sharpdiscontinuity in the patient’s reaction times (i.e., 0-msecdifference between three- and four-letter words, and 100-msec difference bewteen four- and five-letter words), asis consistent with going from one oscillatory cycle to twocycles. Also, letter priming experiments with the patient 234WHITNEY showed greatly reduced facilitation in the RH relative tothe LH, as is consistent with the proposal of inadequateactivation of letter nodes in the RH.In summary, we propose that different factors under-lie the length effects for LVF/RH presentation observedin normals and in the patient. For normals, it arises at thefeature level from processes underlying the formation ofthe locational gradient. For the patient, it arises at the let-ter level, as a direct result of the proposed temporal basisof letter position coding. (In Section4.1, we discuss whyno length effect emerges directly from the temporal en-coding at the letter level for normal subjects.)Patterns of positional errors have also been taken asevidence for different hemispheric modes of processing(Hellige, Cowin, & Eng, 1995; Hellige & Scott, 1997;Marks & Hellige, 1999). Subjects were to identify quicklydisplayed CVC trigrams presented in a vertical column,with each letter in the upright position. For LVF/RH pre-sentation, subjects made many more errors involving thelast letter than the first letter of the string. For RVF/LHpresentation, this finding was greatly attenuated: Therewere more errors on the first letter and fewer errors onthe last letter (relative to LVF/RH presentation), resultingin a more even distribution of errors across the string.There was also a strong effect of visual field on accuracy,with more total errors in the LVF/RH than in the RVF/LH.These patterns were taken to be evidence of parallel pro-cessing of strings by specialized linguistic modules in theLH and less efficient, serial processing in the RH.However, a counterintuitive result arises when input isdirected to both hemispheres simultaneously. When stim-uli are presented bilaterally, the error pattern that emergesis more similar to the LVF/RH pattern than to the RVF/LHpattern (Marks & Hellige, 1999). Thus, even though theLH is more effective than the RH at performing the task,the RH’s mode of processing (i.e., error pattern) seems todominate when the stimuli are presented to both hemi-spheres simultaneously.On the basis of locational gradient formation, we offeran explanation of these results that accounts for both theasymmetry of the error patterns and the bilateral pattern.Despite the unorthodox vertical format, we assume thatencoding processes similar to those used for horizontalpresentation were invoked. Hellige and colleagues (Hel-lige etal., 1995; Hellige &Scott, 1997; Marks &Hellige,1999), in theiranalyses, also assume that the data fromthese experimentsare relevant to normal string process-ing. More specifically, we assume that the elements ofthe string are mentally rotated to the canonical horizontalposition, and, then,the rotated image is processed asusual. This mental rotation assumption is consistent withthe finding that reaction time for lexical decision in-creases smoothly with rotation angle for two-letter strings(Koriat & Norman, 1985). (For longer strings, reactiontime does not increasesmoothly with angle of rotation.We have shown that this effect could result from mentalrotation progressively degrading inputs to the letter level,requiring increasing numbers of oscillatory cycles to rep-resent the string. See Whitney, in press.)The proposed inhibitory processing underlying loca-tional gradient formation can acount for the differinghemispheric error patterns. As discussed above, in thehemisphere in which inversion occurs, the acuity gradi-ent is transformed in the locational gradient by strongexcitation to the initial letter, coupled with strong direc-tional inhibition. This transformation could result in asteeper partial locational gradient in that hemisphere.Thus, for English readers, the partial locational gradientcould be steeper for the LVF/RH than for the RVF/LH.That is, the inputs to the first letter in each hemisphere aresimilar, whereas the input to the final letter in the LVF/RHis lower than in the RVF/LH (see Figure3, lower leftpanel). This accounts for the greater percentage of errorson the final letter in the LVF/RH.Following callosal transfer, the RH features inhibit theLH features to form a monotonically decreasing locationalgradient. We propose that, under bilateral stimulation, theerror pattern of the RH predominates because the LVF/RHfeatures inhibit the RVF/LH features. This is not incon-sistent with the finding that recognition is better in theLH/RVF than in the RH/LVF with respect to presentationto a single visual field; recognition is better in the RVF/LHbecause there is no degradation due to callosal transfer.However, when both visual fields receive input, we pro-pose that input from the LVF/RH dominates due to the wayin which hemispheric representations of letter strings arenormally integrated.This analysis implies that the asymmetry of hemi-spheric error patterns should vary with reading direction.For languages read from right to left, the patterns shouldbe reversed, since acuity gradient inversion should thenoccur in the RVF/LH. This is precisely the finding reportedin a study of Hebrew readers performing the trigram iden-tification task; for those readers, percentage of final-lettererrors was greater in the RVF/LH than in the LVF/RH, andthe bilateral pattern was the same as that of the RVF/LH(Eviatar, 1999). For languages that are read from top tobottom, there should be no hemispheric asymmetry, sinceacuity gradient inversion should occur along the verticalaxis, not the horizontal axis. Indeed, a study of Japanesekana, for which the vertical orientation is normal, showedno differences between LVF/RH, RVF/LH, and bilateralpatterns (Hellige & Yamauchi, 1999). Thus, these findingsare inconsistent with a hemispheric specialization accountbut are predicted by the locational gradient account.This type of experiment has also been performed withthe trigrams presented horizontally rather than vertically(Eviatar, 1999; Hellige & Cowin, 1996), yielding conflict-ing results. Eviatar reports abolition of the the hemi-spheric asymmetries for both English and Hebrew,whereas Hellige and Cowin report that the asymmetryfor English is maintained. These findings can also be ac-counted for within the SERIOL framework. For verticalpresentation, the resulting mentally rotated image has noacuity gradient, because all letters were originally pre-sented at essentially the same distance from fixation. Inthe hemisphere in which inversion occurs, the steepnessof the locational gradient is much greater than usual, be- MODEL OF LETTER-POSITION CODING235 cause there is no opposing acuity gradient. In the hemi-sphere in which inversion does not occur, the resultinglocational gradient is shallower than usual, because thereis no supporting acuity gradient. Thus, vertical presenta-tion should accentuate differences in directional inhibitionacross the two hemispheres. For horizontal presentation,this asymmetry may or may not be evident, dependingon the actual acuity gradients associated with the stim-uli. The locations of the stimuli differed across the twoexperiments cited above. An analysis based on locationalgradient formation, presented in AppendixA, showedthat there should be more asymmetry for the locationused by Hellige and Cowin than that used by Eviatar. Sothe difference in stimulus location can account for thedifference in asymmetry across the experiments.Thus, we conclude that the seemingly different modesof processing across the two hemispheres are not attrib-utable to serial versus parallel processing. We propose thatletter activations are always serial and that hemisphericdifferences stem from the direction of slope of the acuitygradient relative to that of the locational gradient.4. STUDIES RELEVANT TOLETTER LEVEL REPRESENTATIONNow, we turn our attention to experimental data bestaddressed at the letter level of the SERIOL framework.Recall that the locational gradient, in conjunction withthe dynamics of the letter level nodes, induces a temporalfiring pattern across the letter nodes. As a consequence ofthis process, a positional activation gradient arises acrossthe letter nodes. First, we discuss studies relevant to thetemporal aspect of letter position coding. Then, we exam-ine the activation pattern of the positional gradient.4.1. Temporal EncodingWe propose that the encoding of letter position isbased on sequential firing of letter nodes. As is consis-tent with the observation of nested oscillations recordedin the human cortex in cognitive processing (Llinas &Ribary, 1993), we suggest that each letter position cor-responds to a successive 25-msec subcycle within an os-cillatory period of »200msec. This proposal is consis-tent with some curious results from a study involvingsequential letter presentation. In that study, the letters ofeight-letter words were presented one at a time across ahorizontal row (Mewhort & Beal, 1977). The interval be-tween successive letters (interstimulus interval, ISI) wasvaried, and performance was measured as probability ofcorrectly identifying the word. For ISIs of 0msec, 50msec,and 125msec, performance declined from 98% to 70%to 50%, respectively. However, for an ISI of 250msec,performance rebounded to 65%, rather than continuingto fall off. Our interpretation of this result is that sequen-tial letter presentation interfered with the normal phasiccoding of letter position. Letter presentations were max-imally out of phase with respect to normal at an ISI of125msec (worst performance). Performance levels for50msec and 250msec were similar, consistent with anoscillatory cycle length of 200msec. This interpretationpredicts that, when performance is impaired, the orderof the letters should be perceived incorrectly due to pre-sentation rate and internal encoding being out of phase.The subjects’ reports for incorrectly identified words wereconsistent with this prediction: Detection of individualletters was not impaired at 125msec (the ISI of worst per-formance) relative to the other ISIs, whereas report ofthe preceived order of letters at 125msec was impairedrelative to the other ISIs.This temporal encoding hypothesis is countered by theresults of lexical decision experiments, which have beeninterpreted as supporting strictly parallel processing ofletter strings. Lexical decision tasks have shown that re-action times for words of three to six letters are equiva-lent under central fixation (Forster & Chambers, 1973;Frederiksen & Kroll, 1976; Green & Shallice, 1976) andunder RVF/LH presentation, as discussed above. Can atemporal, serial representation of letter position be rec-onciled with the lack of a word length effect? We suggestthat this finding should not be thought of as indicatingthat six-letter words are recognized as quickly as three-letter words, but rather that three-letter words are as slowto be recognized as six-letter words. In other words, aminimum reaction time exists. This minimum reactiontime is based on completion of an oscillatory cycle. Wordsthat can be represented within one oscillatory cycle havesimilar reaction times.As mentioned above, we propose that the final letternode of a string continues to fire until the end of the os-cillatory cycle. We suggest that this mechanism is in-volved in distinguishing short words from longer words.It should be the case that the string “cat” activates theword node “CAT” more strongly than it activates the wordnode “CART.” In our scheme, the letter node “T” be-comes more active as a result of the presentation of “cat”than as a result of the presentation of “cart” because itstarts firing earlier in the cycle. Assuming that the con-nection weights reflect this difference, the string “cat”will indeed activate the node “CAT” more than the node“CART” since the weights (via the bigrams) from “T” to“CAT” are larger than from “T” to “CART.” The longerthe “T” letter node fires (i.e., the higher its activation),the larger the difference in activation levels between“CAT” and “CART” becomes. Sufficient information todistinguish a winner and inhibit other word contendersmay not be available until the end of the oscillatory cycle.As a result, it takes as long to recognize three-letter wordsas it does to recognize six-letter words. So, we argue thatthe absence of a length effect does not necessarily indi-cate parallel processing. Thus, words that can be repre-sented in a single cycle (i.e., of approximately seven let-ters or less) should have equivalent reaction times.Thus, under normal reading conditions, the temporalnature of letter position coding is not evident. However,if artificial presentation conditions (such as sequentialletter presentation) are introduced, then temporal effectscan emerge. Strong length effects on reaction times forrotated letter strings have also been observed. For rotation 236WHITNEY angles of 120º or more, each additional letter increasesreaction time by 200msec (Koriat & Norman, 1985). Notethat this increase is exactly the length of the proposedoscillatory cycle. We have constructed a model based onencoding within oscillatory cycles that accurately ac-counts for the complex interaction of angle and lengthon lexical decision reaction time observed for rotatedstrings (Whitney, in press).Thus, we suggest that sharp jumps in reaction timesresult when information that can normally be representedin a single cycle must be represented across multiple cy-cles due to degradation of the input. What about wordsthat are too long to be represented in a single cycle? Thereis no evidence for a sharp jump in reaction times as wordlength increases above seven letters. Presumably, undernormal conditions, a mechanism exists for composinginformation smoothly across cycles. That mechanism isbeyond the scope of this paper.4.2. Positional GradientWe have proposed that the varying levels of input to let-ter nodes that serve to induce the temporal firing patternalso create a positional activation gradient across the let-ter nodes. We believe that this mechanism can account forconflicting findings regarding the perceptibility ofstrings’ final letters. In general, the final letter has beenfound to be preferentially perceived with respect to the in-ternal letters, denoted a final-letter advantage (Hammond& Green, 1982; Lefton etal., 1978; Mason, 1982; Perea,1998). However, in other studies the final letter was theleast well perceived of all the letters (Hellige etal., 1995;error data analysis in Humphreys etal., 1990;five- andsix-letter words in Montant etal., 1998). In the SERIOLframework, the activation level of the node representingthe final letter is sensitive to when in the cycle it starts tofire. Recall that a letter node continues to fire until it is in-hibited by another letter node. However, the final letternode does not undergo such inhibition and continues tofire until it cannot pass threshhold due to the down phaseof the oscillatory cycle. If overall input levels to the letternodes are low, the final letter node cannot start firing untillate in the cycle, and, therefore, it attains only low level ofactivation. If overall input levels are high, the final letternode can start firing earlier in the cycle and can reach alevel of activation that exceeds that of the interior letters.We propose that a very short presentation duration re-sults in such a low overall level of input, whereas normalpresentation conditions correspond to higher input levelsthat give a final-letter advantage. This proposal explainsthe above experimental findings: All those experimentsin which a final-letter advantage did occur involved pre-sentation durations of 75msec or more, whereas all thoseexperiments in which a final-letter advantage did not oc-cur involved presentation durations of 50msec or less. Italso explains the finding in Eviatar (1999) that, for targetletter detection within a trigram, decreasing exposure du-ration from 80msec to 40msec increases misses for tar-gets in the final position but does not increase misses inthe initial position.Studies with brain-damaged patients have also demon-strated difficulties with the final letter of strings. In astudy of a group of patients with LH damage who havelanguage problems and are prone to reading errors, thefinal letter of a word was the letter least likely to be cor-rectly retained in an error response. In fact, the probabil-ity of retention in the error response monotonically de-creased as letter position within the word increased(Berndt & Haendiges, 1997; Whitney & Berndt, 1999).This pattern of errors is easily accounted for within theSERIOL framework by making two assumptions: (1)Theexcitability of letter nodes is reduced, pushing the firingof the letter nodes late into oscillatory cycle (as does ashort presentation duration for normal subjects), negatingany final-letter advantage, and (2)high levels of noiseare incorporated into the word node activations. Becauseinitial letters have the highest activations, word nodesthat share initial letters with the target word are also sig-nificantly activated and are likely to be selected in the pres-ence of noise. In simulations, these assumptions allowedreplication of various aspects of the patients’ error pat-terns (Whitney & Berndt, 1999).Montant etal. (1998) studied a patient, C.P., with purealexia. C.P. suffered LH damage and showed an unusualOVP, where word recognition was optimal when fixationoccurred near the last letter of the word (so that the wordappeared mostly in the LVF). On the basis of a series ofexperiments, the authors observed that C.P. suffered frompoor perceptual processing of letter stimuli in the RVF/LH. However, this finding did not fully account for C.P.’sperformance, since processing of words’ final letters wasalways significantly impaired, independently of visualfield of presentation. In experiments with normal sub-jects using very short presentation durations, the authorsalso found a pattern of reduced accuracy in processingthe final letters of words.On the basis of these data, the authors concluded thatC.P.’s performance reflected an exaggeration of normalaspects of word processing. They suggested that C.P.’sdysfunction had uncovered a “prelexical level of wordprocessing, where letter information is weighted differ-ently as a function of letter position in a word-centeredspace” (Montant etal., 1998, p.123). This conclusion isquite similar to our proposed positional gradient. How-ever, the authors attribute this weighting to a differentsource—namely, perceptual learning. That is, they pro-posed that “the reading system weights letter units as afunction of the quality of available visual information”(Montant etal., 1998, p.125). However, we think thatthis account is not consistent with the data. If the weight-ing is perceptually based, it should have roughly the sameshape as the acuity gradient: highest at fixation, and lowerat the word boundaries. However, this is not the observedpattern; perceptibility is highest at the initial letter andgenerally falls off from left to right.Rather, as is consistent with the observed pattern, wepropose a more significant role for the apparent weight-ing of letter units, as arising from mechanisms directlyinvolved in the encoding of letter position. These mech- MODEL OF LETTER-POSITION CODING237 anisms override the effects of perception, inverting theacuity gradient to form a locational gradient that inducesa temporal encoding of letter position, as well as a posi-tional activation gradient. This positional gradient hasroughly the same shape as the locational gradient.Although, for normal subjects, letter perceptibility fallsoff from left to right (with the exception of the final po-sition) for strings presented entirely within a single visualfield (Lefton etal., 1978), this monotonicity is not main-tained if the string is presented centrally. In that case, aW-shaped pattern of perceptibility emerges, with in-creased perceptibility for the letter under fixation (in ad-dition to the initial and final letters; see Hammond &Green, 1982; Lefton etal., 1978; Mason, 1982). This re-sult is not inconsistent with our model. Such a pattern ofactivation can arise at the letter level in our model if theslope of the locational gradient is not smooth near thefixated letter. More precisely, this can occur if the amountof input reaching the fixated letter is only slightly lessthan that of the previous letter but much greater than thatof the next letter. The firing of the previous letter is trun-cated by the firing of the fixated letter, whereas the fixatedletter fires for an extended period until it is inhibited bythe next letter. This scenario results in a higher level ofactivation for the fixated letter than for its neighbors. Be-cause we propose that the two partial hemispheric loca-tional gradients are joined at the letter under fixation, sucha lack of smoothness is plausible (see Figure3, bottomright panel).5. STUDIES OF LETTERPOSITION ENCODINGWe now turn to recent experiments specifically designedto investigate the nature of letter position encoding innormal readers (Grainger & Jacobs, 1991; Humphreysetal., 1990; Peressotti & Grainger, 1995, 1999). First, wegive an overview of these experiments; then, we discusshow the SERIOL framework accounts for these results.5.1. Results of Position Encoding ExperimentsSome of the studies involved nonword letter strings inorder to eliminate top-down influences, whereas othersinvolved words. First, we will discuss those utilizing non-word strings. Grainger and Jacobs (1991) asked subjectsto perform an alphabetic decision task, in which they wereto identify whether or not a character embedded in a stringof hash marks was a letter. The target character appearedin either the initial or the terminal position of a five-character test string (e.g., “####T” or “T####”). The teststring was preceded by a prime string, which was a neu-tral string (“xxxxx”), a five-letter word containing thetarget letter, or a target letter embedded in “x”s. For bothtypes of primes, the target letter could appear in the sameposition as in the test string (e.g., prime string “xxxxT”for test string “####T”) or in the opposite position (cross-position case; e.g., prime string “TABLE” for test string“####T”). In addition, the presentation duration of theprime string was varied (16 vs. 64msec). Priming wasmeasured as decrease in reaction time (with respect to aneutral prime) in identifying the target letter. In ordertoensure that facilitatory effects of prime presentation didnot result from physical overlap, the target letter in theprime and test strings occupied different absolute loca-tions on the screen.The results showed priming for most of the same-position cases. There was also evidence for priming inone of the cross-position cases (64msec, nonword, tar-get letter in the initial position of the prime string). Theseexperiments indicate that same-position priming is morerobust than cross-position priming but that cross-positionpriming can occur. The following experiments providefuther evidence for cross-position priming.Peressotti and Grainger (1995) also asked subjects toperform an alphabetic decision task, in which they wereto determine whether or not strings of three charactersconsisted solely of letters (e.g., “TBR” vs. “TB$”). Primeswere also trigrams, consisting of characters from the teststring, either in the same order (same-position cases) orin a different order (cross-position cases). The presenta-tion duration of the prime string was varied (33, 50, and66msec). Performance was measured as response timeto the test string. In order to ensure that facilitation did notresult from physical overlap, prime strings and test stringswere presented in different-sized fonts.Overall, the results of Peressotti and Grainger (1995)are similar to those of Grainger and Jacobs (1991). Cross-position priming occurred, but only when prime exposuredurations were at least 50msec. Same-position primingwas more robust, occurring even at shorter prime durationsand giving higher levels of facilitation.The next pair of studies involved word recognition. InHumphreys etal. (1990), subjects were to identify wordsthat were presented briefly (40msec), such that recogni-tion levels were not at ceiling. Performance was measuredas percentage of words correctly identified. Primes werenonwords in which the positions of letters in common withthe test word were manipulated. Primes were presented inlowercase, and test words were presented in uppercase.For primes composed of the same letters as the testword but rearranged into a different order, no facilitationwas observed. Thus, no cross-position priming was ob-served for test words. For primes having letters in the sameorder as the test word but in different absolute positions,facilitation was observed. For example, the prime “okte”enhanced recognition of the test word “WHITE,” eventhough the common letters “TE” were at positions 3 and4 in the prime string but at positions 4 and 5 in the testword. We will designate this result as priming, because letter order and word boundaries of a por-tion of the prime string were the same as the test word.These same results (lack of cross-position priming andoccurrence of relative-position priming) were also ob-served by Peresotti and Grainger (1999). In those exper-iments, subjects performed lexical decision on six-letterstrings, and performance was measured as response time.Primes and test strings were in fonts of different sizes. Atexposure durations of 50msec, four-letter primes con- 238WHITNEY sisting of the first, third, fourth, and sixth letters of thetest string in that order were facilitatory (e.g., “BLCN”for the French word “BALCON”), whereas primes con-sisting of those letters in a different order were not. Primesincorporating space fillers among the letters to preserveabsolute position (e.g., “B_LC_N”) were no more facil-itatory than primes without space fillers.The results of Humphreys etal. (1990) and Peressottiand Grainger (1999) are similar, indicating that, for wordtest strings, relative-position, but not cross-position, prim-ing occurs. Although the prime durations employed inHumphreys etal. (durations of »40msec) were some-what shorter than those that invoked cross-position prim-ing for nonwords in Peressotti and Grainger (1995) (du-rations of 50 and 66msec), the results of Peressotti andGrainger (1999) indicate that cross-position priming doesnot occur for word test strings even at 50-msec durations.Thus, it appears that the absence of cross-position prim-ing in these word-based experiments arises from the na-ture of the test string (i.e., word vs. nonword), rather thanfrom the prime exposure duration.In summary, the results of the above four studies indi-cate that cross-position priming can occur under the properconditions: when prime exposure duration ³50msec, andboth prime and test strings are not words. For word teststrings, relative-position priming is as effective as same-position priming.5.2. The SERIOL Framework andPosition Encoding ExperimentsWhat do these results imply about the nature of letterorder encoding? The fact that relative-position primingoccurs when absolute position is violated indicates thatsome representation other than a channel-specific cod-ing scheme is involved. These results are consistent witha context-unit coding scheme. However, the fact that prim-ing of individual letters occurs suggests that activation ofcontext units requires activation of constituent letters.These results are consistent with a scheme in which let-ter units activate context units, as we propose. The exis-tence of separate letter and bigram levels in the frame-work provides a mechanism for the activation of contextunits by constituent letters and thus accounts for indi-vidual letter priming and relative-position priming in wordtest strings. In the above experiments, cross-positionpriming was found to occur for nonword test strings, butnot for word test strings. This result is consistent with theassumption that the activation of bigram nodes, ratherthan of letter nodes, dominates the efficacy of primingfor word test strings. Cross-position primes do not activatethe proper bigram nodes, so facilitation does not occurfor word test strings. However, nonword test strings iso-late activations at the letter level, revealing cross-positionpriming.Could the initial encoding of letters be channel spe-cific? The above experiments have demonstrated thatsame-position priming is quite robust, as is consistentwith a channel-specific model. However, since cross-position priming can occur, a channel-specific model isnot sufficient. In order to accommodate this finding, Per-essotti and Grainger (1995) proposed a two-level modelconsisting of channel-specific letter units and position-independent letter units.Our framework incorporates a single set of letter nodes(as opposed to separate sets for each position, as in channel-specific coding), where position is tagged by timing offiring. Since different positions can be represented by thesame letter node, cross-position priming at the letterlevel is possible. How then can we account for the robustsame-position priming in the absence of channel-specificletter units within the SERIOL framework? We proposethat the same-position results arose from the preortho-graphic level. Although the target letters appeared at dif-ferent physical locations in the prime and test string pre-sentations, we propose that interactions at the feature levelcould produce the appearance of position-specific prim-ing, due to the proposed locational tuning of the featurenodes. On the basis of this hypothesis, we have devel-oped mathematical models that replicate the experimen-tal data (they are described in Whitney, 2001).Thus, the SERIOL framework can account for the dif-ferent types of priming observed in these experiments.We propose that same-position priming arises at the fea-ture level, cross-position priming arises at the letter level,and relative-position priming arises at the bigram level.This analysis is consistent with the differing time coursesand types of stimuli that evoked these types of priming.6. DISCUSSIONAs discussed in the introduction, the interpretation ofexperimental results showing decreasing letter percepti-bility with increasing string position has changed overthe years. Initially, it was assumed that these resultsemerged from a serial scan on an input trace (Lefton etal.,1978; Mewhort etal., 1969). Current accounts focus onperceptual factors and/or attention to the area of maxi-mal information within the string, where maximal infor-mation is conditioned by top-down processes (Brysbaertetal., 1996; Montant etal., 1998; O’Regan etal., 1984).We return to the earlier notion of a serial process. Ourproposal that a locational gradient across letter featuresinduces a temporal firing sequence is similar to a serialscan. However, we do not characterize this process as a“scan,” because that term implies that some entity is shift-ing attention across a representation of the input string.Rather, we propose that the serial firing emerges frominteractions between graded inputs, lateral inhibition, andsubthreshhold oscillations. This account implies that theserial firing arises at a very low level of processing thatdoes not correspond to attentional mechanisms.Attention may play a role in acquiring the mechanismsthat allow this process to take place automatically, just asconscious effort is required in learning any new skill be-fore it becomes automatic. Once learned, however, thisprocess is not subject to conscious, attentional control.This conclusion is consistent with various studies. Instring matching experiments (Proctor & Healy, 1987), the MODEL OF LETTER-POSITION CODING239 position of difference between two strings strongly in-fluenced how long it took subjects to respond, despite thefact that position was irrelevant in determining the re-sponse. This was a very robust result, indicating that po-sitional information is impossible to ignore and, thus, notunder conscious control. In another study, subjects whohad suffered right parietal damage (resulting in atten-tional deficits) were to read letter strings that were eitherwords or pronounceable nonwords (Sieroff, Pollatsek, &Posner, 1988). Subjects did not exhibit deficits when read-ing words, but they did when reading nonwords. Thispattern of results was replicated in normal subjects usingmisdirected attentional cues to interfere with deploy-ment of attention while reading (Sieroff & Posner, 1988).These results were interpreted as indicating that top-down,conscious attention is not required to access the lexicon;however, when a letter string does not receive lexical sup-port (i.e., is a nonword), attention is invoked in process-ing, revealing deficits or interference. Thus, these resultsare consistent with our proposal that top-down processesare not necessary for formation of the locational gradi-ent (a prelexical process), and, therefore, attentional pro-cesses are not involved in the perceptual advantage forinitial letters of strings.We propose that the letter perceptibility pattern arisesfrom a temporal encoding of letter position. Thus, we at-tribute a much more important role to the underlyingsource of positional effects than do current accounts.There is a level in the SERIOL framework that is roughlyconsistent with perceptual and attentional accounts—namely, the bigram-to-word connections. In that inter-face, connection weights correspond to the activations ofbigrams constituting each word. Bigram activations de-pend on letter activations, which depend on letter posi-tion. Thus, weights are learned that correspond to letteractivations, as proposed by a perceptual account. How-ever, our proposed letter activations arise as a conse-quence of the letter position encoding process, not as aresult of perceptual factors. As discussed above, the lackof congruity between the acuity gradient and the ob-served pattern of perceptibility is more consistent withour account than with a perceptual account.The bigram node that is activated by the first and sec-ond letters of a word will have the highest connectionweight to that word node. Thus, this bigram confers themost information about the word, as is similar to theoriesof attentional deployment to the locus of maximal infor-mation. However, the accounts of causality are reversed.Attentional accounts suggest that the initial letters of aword carry the most information due to the patterns ofspelling in a language; therefore, weights on initial lettersare high (Brysbaert etal., 1996; O’Regan etal., 1984).In contrast, we propose that weights on initial letters arehigh because their activations are elevated as a conse-quence of the levels of input necessary to induce them tofire early in the oscillatory cycle; therefore, initial letterscarry the most information. Of course, both factors couldbe at work.Although our framework shares some features of cur-rent accounts, the underlying assumption of serial en-coding is contrary to many current formulations. Whatfactors resulted in the abandonment of the serial-scan as-sumption? We conclude that it was due to an absence ofa length effect in lexical decision experiments (Forster& Chambers, 1973; Frederiksen & Kroll, 1976; Green &Shallice, 1976), coupled with the advent of the empha-sis on parallel computation in connectionist modeling. Inresponse to the former factor, we have argued above thatif word recognition is unitized by an oscillatory cycle,then no length effect would emerge even if a string isrepresented by the serial firing of letter nodes. Thus, lackof a length effect does not necessarily imply purely par-allel processing. The latter factor (emphasis on parallelcomputation) pertains to a current paradigm, not specif-ically to experimental evidence. In fact, in contrast to therate-coding assumption underlying most parallel con-nectionist models, neurobiologists have recently con-cluded that timing of firing is important in informationalencoding (Berry etal., 1997; deRuyter vanStevenincketal., 1997; Reike etal., 1997; Victor & Purpura, 1996).The SERIOL framework traces the encoding and de-coding of a temporal representation of letter positionfrom the formation of a locational gradient at the featurelevel, to the induction of a serial firing pattern at the let-ter level, to the conversion to context coding at the bi-gram level, to the representation of entire words at thetopmost level. Is such an elaborate scheme really neces-sary? Couldn’t letter position be directly coded by an ac-tivation gradient across letter positions, without induc-ing a temporal firing pattern, and without bigrams?We conclude that the answer to this question is “no.”In an early computational version of our model, we rep-resented letter position as an activation gradient (with notemporal aspect) across letter nodes, with letter nodesconnecting directly to word nodes. Such a model was notvery robust, and the types of errors that arose when themodel was lesioned were not consistent with those pro-duced by brain-damaged patients. The addition of the bi-gram level alleviated these problems (Whitney & Berndt,1999) and is consistent with evidence from normal read-ers on the importance of letter order (Humphreys etal.,1990; Peressotti & Grainger, 1999). A letter level is nec-essary, in addition to the bigram level, to be consistentwith experimental evidence on individual letter priming(Grainger & Jacobs, 1991; Humphreys etal., 1990; Per-essotti & Grainger; 1995) and to provide a mechanism toactivate the bigram nodes.Why then is a temporal encoding necessary? Couldn’ta positional gradient across letter nodes directly activatebigram nodes? One could postulate a bigram unit that isactivated when its constituent letters have the correct relative activation levels (i.e., the first letter is more ac-tive than the second), rather than requring a specificorder of firing. Recent neurobiological studies and the-ories have indicated that timing of firing of individualspikes is an important method of encoding information 240WHITNEY (Hopfield, 1995; Reike etal., 1997). If indeed the neuralsystem operates in such a manner, comparing timing offiring, ratherthan rates of firing, is simpler and more pre-cise. That is, the combination of firing rate (input level toa letter node)with the letter nodes’ internal dynamics tocreate a temporal firing pattern results in a more preciserepresentation of information than firing rate alone, and,therefore, neural systems can compare firing timingsmore accurately than firing rates. Additionally, all othermodalities of language perception and production in-volve serial processing (i.e., speaking, listening, andwriting), so it is plausible that a canonical temporal rep-resentation for language exists, into which visual input isconverted.Why then couldn’t the temporal letter position encod-ing, with its strong representation of letter order, activateword nodes directly without bigram nodes? Such a schemewould require precise comparison of the relative timingof many inputs and could lead to errors. It is computa-tionally more robust to compare the timing of pairs of in-puts and to consolidate those results, as specified in thebigram and word levels of our framework.Thus, we conclude that the functionality of each levelof representation is necessary. As a whole, the SERIOLframework unifies and provides an account of many here-tofore puzzling experimental results on reading: positionalperceptibility of letters in strings, the paradox of the final-letter advantage/disadvantage, visual field differences inletter perceptibility, the location of the OVP and its rela-tionship to reading direction, hemispheric modes of pro-cessing, and patterns of same-position, cross-position, andrelative-position letter priming.REFERENCESAlpern, M. (1962). Introduction. In H.Dawson (Ed.), The eye (Vol.3,pp.3-5). New York: Academic Press.Berndt, R. S., & Haendiges, A. N. (1997). Positional effects in dys-lexic “visual errors”: Constraints on the interpretation of word sub-Brain & Language, 60, 112-115.Berry, M. J., Warland, D. K., & Meister, M.(1997). The structureand precision of retinal spike trains. Proceedings of the NationalAcademy of Sciences, 94, 5411-5416.Bjork, E. L., & Murray, J. T.(1977). On the nature of input channelsin visual processing. Psychological Review, 84, 472-484.Bryden, M. P.(1982). Laterality: Functional asymmetry in the intactbrain. New York: Academic Press.Brysbaert, M. (1994). Interhemispheric transfer and the processing offoveally presented stimuli. Behavioural Brain Research, 64, 151-161.Brysbaert, M., Vitu, F., & Schroyens, W. (1996). The right visualfield advantage and the optimal viewing position effect: On the rela-tion between foveal and parafoveal word recognition. ogy, 10, 385-395.Carmon, A., Nachson, I., Isseroff, A., & Starinsky, R. (1976). De-velopment aspects of visual hemifield differences in perception ofverbal material. Brain & Language, 3, 463-469.Chastain, G.(1977). Feature analysis and the growth of a percept. Jour-nal of Experimental Psychology:Human Perception &Performance,3, 291-298.Coltheart, M., Curtis, B., Atkins, P., & Haller, M.(1993). Mod-els of reading aloud: Dual-route and parallel-distributed-processingPsychological Review, 100, 589-608.Costello, A. D. L., & Warrington, E. K. (1987). The dissociation ofvisuospatial neglect and neglect dyslexia. Journal of Neurology,Neurosurgery, & Psychiatry, 50, 1110-1116.Cubelli, R., Nichelli, P., Bonito, V., De Tanti, A., & Inzaghi, M.G.(1991). Different patterns of dissociation in unilateral spatial neglect.Brain & Cognition, 15, 139-159.De Ruyter van Steveninck, R. R., Lewen, G.D., Strong, S.P.,Koberle, R., & Bialek,W. (1997). Reproducibility and variabilityin neural spike trains. Science, 275, 1805-1808.Ellis, A. W., Young, A. W., & Anderson, C.(1988). Modes of wordrecognition in the left and right cerebral hemispheres. Brain & Lan-guage, 35, 254-273.Estes, W. K., Allemeyer, D. H., & Reder, S. M. (1976). Serial posi-tion functions for letter identification at brief and extended exposurePerception & Psychophysics, 19, 1-15.Eviatar, Z.(1999). Cross-language tests of hemispheric strategies inreading nonwords. , 13, 498-515.Farid, M., & Grainger, J. (1996). How initial fixation position influ-ences visual word recognition: A comparison of French and Arabic.Brain & Language, 53, 351-368.Faust, M., Kravetz, S., & Babkoff, H. (1993). Hemispheric special-ization or reading habits: Evidence from lexical decision researchwith Hebrew words and sentences. Brain & Language, 44, 254-263.Fendrich, R., & Gazzaniga, M. S. (1989). Evidence of foveal split-ting in a commissurotomy patient. , 27, 273-281.Forster, K. I., & Chambers, S. M. (1973). Lexical access and namingtime. Journal of Verbal Learning & Verbal Behaviour, 12, 627-635.Frederiksen, J. R., & Kroll, J. F. (1976). Spelling and sound: Ap-proaches to the internal lexicon. Journal of Experimental Psychol-ogy: Human Perception & Performance, 2, 361-379.Georgopoulos, A. P., Kalaska, J. F., Caminiti, R., & Massey, J. T.(1982). On the relation between the direction of two-dimensional armmovements and cell discharge in the motor cortex.Journal of Neuro-science, 2, 1527-1537.Grainger, J., & Jacobs, A. M. (1991). Masked constituent letter prim-ing in an alphabetic decision task. European Journal of CognitivePsychology, 3, 413-434.Green, D. W., & Shallice, T.(1976). Direct visual access in readingfor meaning. Memory & Cognition, 4, 753-758.Hammond, E. J., & Green, D. W. (1982). Detecting targets in letter andnon-letter arrays. Canadian Journal of Psychology, 36, 67-82.Hellige, J. B. (1993). Hemispheric asymmetry: What’s right and what’sleft? Cambridge, MA: Harvard University Press.Hellige, J. B., & Cowin, E. L.(1996). Effects of stimulus arrangementon hemispheric differences and interhemispheric interaction for pro-cessing letter trigrams. , 10, 247-253.Hellige, J. B., Cowin, E. L., & Eng, T. L.(1995). Recognition of CVCsyllables from LVF, RVF, and central locations: Hemispheric differ-ences and interhemispheric interactions. Journal of Cognitive Neuro-science, 7, 258-266.Hellige, J. B., & Scott, G. B.(1997). Effects of output order on hemi-spheric asymmetry for processing letter trigrams. Brain & Language,59, 523-30.Hellige, J. B., & Yamauchi, M. (1999). Quantitative and qualitativehemispheric asymmetry for processing Japanese kana. Brain & Cog-nition, 40, 453-463.Hopfield, J. J.(1995). Pattern recognition computation using actionpotential timing for stimulus representation. Nature, 376, 33-36.Humphreys, G. W., Evett, L. J., & Quinlan, P.T. (1990). Ortho-graphic processing in visual word identification. Cognitive Psychol-ogy, 22, 517-560.Joliot, M., Ribary, U., & Llinas, R.(1994). Human oscillatory brainactivity near 40Hz coexists with cognitive temporal binding. Pro-ceedings of the National Academy of Sciences, 91, 11748-11751.Katz, R. B., & Sevush, S. (1989). Positional dyslexia. Brain & Lan-guage, 37, 266-289.Koriat, A. (1985). Lateralization effects in pointed and unpointed He-brew. British Journal of Psychology, 76, 161-173.Koriat, A., & Norman, J.(1985). Reading rotated words. Journal ofExperimental Psychology: Human Perception & Performance, 11,490-508.Krumhansl, C. L., & Thomas, E. A. C.(1976). Extracting identity andlocation information from briefly presented letter arrays. Perception& Psychophysics, 20, 243-258.Lefton, L. A., Fisher, D. F., & Kuhn, D. M.(1978). Left-to-right pro- MODEL OF LETTER-POSITION CODING241 cessing of alphabetic material is independent of retinal location. Bul-letin of the Psychonomic Society, 12, 171-174.Lisman, J. E., & Idiart, M. A. P. (1995). Storage of 7 ±2 short-termmemories in oscillatory subcycles. Science, 267, 1512-1515.Llinas, R., & Ribary, U. (1993). Coherent 40-Hz oscillation charac-terizes dream state in humans. Proceedings of the National Academyof Sciences, 90, 2078-2081.Marks, N. L., & Hellige, J. B. (1999). Effects of bilateral stimulationand stimulus redundancy interhemispheric interaction.ogy, 13, 475-487.Mason, M. (1982). Recognition time for letters and nonletters: Effectsof serial position, array size, and processing order. Journal of Exper-imental Psychology, 8, 724-738.Mayzner, M. S., & Tresselt, M. E. (1970). Visual information pro-cessing with sequential inputs: A general model for sequential blank-ing, displacement, and overprinting phenomena. In E.Harms & M.E.Tresselt (Eds.), Third Conference on the Fundamentals of Psychol-ogy: Various approaches to the study of perception (Annals of theNew York Academy of Sciences, Vol.169, pp.599-618). New York:New York Academy of Sciences.McClelland, J. L., & Rumelhart, D. E. (1981). An interactive acti-vation model of context effects in letter perception: Part 1. An ac-count of basic findings. Psychological Review, 88, 375-407.Melamed, F., & Zaidel, E.(1993). Language and task effects on lat-eralized word recognition. Brain & Language, 45, 70-85.Mewhort, D. J. K., & Beal, A. L. (1977). Mechanisms of word iden-tification. Journal of Experimental Psychology, 3, 629-640.Mewhort, D. J. K., Merikle, P. M., & Bryden, M. P. (1969). On thetransfer from iconic to short-term memory. Journal of ExperimentalPsychology, 81, 89-94.Montant, M., Nazir, T. A., & Poncet, M. (1998). Pure alexia and theviewing position effect in printed words. Cognitive Neuropsychology,15, 93-140.Mozer, M. C. (1987). Early parallel processing in reading: A connec-tionist approach. In M.Coltheart (Ed.), Attention and performanceXII:The psychology of reading (pp.83-104). London: Erlbaum.Mozer, M. C., & Behrmann, M. (1992). On the interaction of selec-tive attention and lexical knowledge: A connectionist account of ne-glect dyslexia. Journal of Cognitive Neuroscience, 2, 96-123.Orbach, J. (1967). Differential recognition of Hebrew and Englishwords in right and left visual fields as a function of cerebral dominanceand reading habits. , 5, 127-134.O’Regan, J. K., Levy-Schoen, A., Pynte, J., & Brugaillere,B.(1984). Convenient fixation location within isolated words of differentlength and structure. Journal of Experimental Psychology: HumanPerception & Performance, 10, 289-298.Perea, M.(1998). Orthographic neighbors are not all equal: Evidenceusing an identification technique. Language & Cognitive Processes,13, 77-90.Peressotti, F., & Grainger, J.(1995). Letter-position coding in randomconsonant arrays. Perception & Psychophysics, 57, 875-890.Peressotti, F., & Grainger, J.(1999). The role of letter identity andletter position in orthographic priming. Perception & Psychophysics,61, 691-706.Plaut, D. C., & Shallice, T.(1993). Deep dyslexia: A case study ofconnectionist neuropsychology. Cognitive Neuropsychology, 10,377-500.Proctor, R. W., & Healy, A. F. (1987). Task-specific serial position ef-fects in comparisons of multiletter strings. Perception & Psycho-physics, 42, 180-194.Reuter-Lorenz, P. A., & Baynes,K.(1992). Modes of lexical accessin the callosotomized brain. Journal of Cognitive Neuroscience, 4,155-164.Rieke, F., Warland, D. [K.], De RuytervanSteveninck, R., &Bialek,W. (1997). Spikes: Exploring the neural code. Cambridge,MA: MIT Press.Seidenberg, M. S., & McClelland, J. L.(1989). A distributed devel-opmental model of word recognition and naming. Psychological Re-view, 96, 523-568.Sieroff, E., Pollatsek, A., & Posner, M. I. (1988). Recognition of vi-sual letter strings following injury to the posterior visual spatial at-tentional system. Cognitive Neuropsychology, 5, 427-449.Sieroff, E., & Posner, M. I.(1988). Cueing spatial attention duringprocessing of words and letter strings in normals. Cognitive Neuro-psychology, 5, 451-472.Strangert, B., & Brännström, L. (1975). Spatial interaction effectsin letter processing. Perception & Psychophysics, 17, 268-272.Sugishita, M., Hamilton, C. R., Sakuma, I., & Hemmi, I.(1994).Hemispheric representation of the central retina of commissuroto-mized subjects. , 32, 399-415.Sugishita, M., Hemmi, I., Sakuma, I., Beppu,H., & Shiokawa,Y.(1993). The problem of macular sparing after unilateral occipital le-sions. Journal of Neurology, 241, 1-9.Tiitinen, H., Sinkkonen, J., Rainikainen, K., Alho, K., Lavi-Kainen, J., & Näätänen,R. (1993). Selective attention enhancesthe 40-Hz response in humans. Nature, 364, 59-60.Townsend, J. T. (1971). A note on the identifiability of parallel and se-rial processes. Perception & Psychophysics, 10, 161-163.Trauzettel-Klosinski, S., & Reinhard, J.(1998). The vertical fieldborder in hemianopia and its significance for fixation and read-ing. Investigations inOphthalmology & Visual Science, 39, 2177-2186.Victor, J. D., & Purpura, K. P. (1996). Nature and precision of tempo-ral coding in visual cortex: A metric-space analysis. Journal of Neuro-physiology, 76, 1310-1326.Whitney, C. S.(2001). Position-specific effects within the SERIOL frame-work of letter-position coding. Manuscript submitted for publication.Whitney, C. S.(in press). An explanation of the length effect for ro-tated words. Proceedings of the Fourth International Conference onCognitive Modeling.Whitney, C. S., & Berndt, R. S. (1999). A new model of letter stringencoding: Simulating right neglect dyslexia. Progress in Brain Re-search, 121, 143-163.Whitney, C. S., Berndt, R. S., & Reggia, J. A.(1996). Simulation ofneurogenic reading disorders with a dual-route connectionist model.In J.A. Reggia, E.Ruppin, & R.S. Berndt (Eds.), Neural modelingof brain and cognitive disorders (pp.201-228). Singapore: WorldWolford, G., & Hollingsworth, S. (1974). Retinal location andstring position as important variables in visual information process-ing. Perception & Psychophysics, 16, 437-442.Young, A. W., & Ellis, A. W.(1985). Different modes of lexical ac-cess for words presented in the left and right visual hemispheres. Brain& Language, 24, 326-358. (Continued on next page) 242WHITNEY APPENDIXA Locational Gradient We denote the activation of a feature node as F. For simplicity,we consider all feature nodes comprising a single letter to reacha similar level of activation, which is determined by the letter’sstring position, P, and retinal location of its center, R(P). For no-tational convenience, we will write Rrather than R(P) in thefollowing. We first consider feature activations in the absence ofhemisphericinteraction, denoted Fh. For simplicity, we assignfixation, R50, to a single hemisphere—namely, the RVF/LH.Fhis determined by the combination of bottom-up excitatoryinput, E, and lateral inhibitory input, I, and is restrictedto a max-imal value, denoted by constant cM. That is,Fh(P,R)5M(E(R)2I(P,R)),where M(x)5min(cM,x).Bottom-up excitatory input is a function of acuity, denoted C,and visual field:where cEis a constant �� 1, reflecting our assumption of strongerexcitatory input to the LVF/RH.Lateral inhibitory input is the sum of inhibitory inputs fromfeatures having preferred locations to the left of R. This quantityincreases with the number of such features, their activation lev-els, and the strengths of the inhibitory connections. Rather thandirectly modeling the feedback processes underlying such lat-eral inhibition, we approximate the amount of inhibitory inputas the activation of the leftmost letter’s features weighted by anincreasing function of the number of letters to the left of R.The leftmost letterdesignates the letter that lies farthest tothe left within the same visual field as R. Its position, denoted Pl,is 1 if the first letter of the string lies in the same visual field asR; otherwise, it is the position of the letter occurring at fixation,because then Ris in the RVF, and R(1) is not. Thus, we haveI(P,R)5M(E(R(Pl)))*W (P2Pl, R),where M(E(R(Pl))) gives the feature activation of the leftmost let-ter (which does not receive any inhibition), and Wdenotes theweighting function. Wincreases as the number of letters to theleft(given by P2Pl) increases. Walso depends on hemisphere;inhibitory connections are stronger in the LFV/RH than in theRVF/LH (as is necessary to invert the acuity gradient). That is,for a given P2Pl, Wis larger for R 0 than for R&#x -29;&#x 000; 0.The individual hemispheric gradients are joined via inhibitionof the RVF/LH’s feature nodes by an amount proportional to thenumber of letters coming from the LVF/RH. That is,where cFis a positive constant. This yields a decreasing gradient,such that F(P,R)&#x -29;&#x 000; F(P+ 1, R(P+ 1)).The modeled results discussed in Section3.1 were carriedout as follows. To instantiate this model, values for the constantscM, cE, and cFand definitions of the functions Cand Wmust besupplied. The displayed results used the following definitions,where Ris in units of letter width:The definition of Wis best displayed in tabular form (see Ta-bleA1).These definitions specify the feature level activations for agiven retinal location and string position. We assume that theletter level activations (positional gradient) have a similar shapeto the locational gradient (except at the final letter, which is notbeing considered here). We converted the feature activations toletter activations, L, and then to perceptibility, PL, in the follow-ing way:For simplicity, we set letter level activations to be equivalent tofeature level activations, except at the first position (in order togive a better fit to the data, which does not affect the overallshape of the curves). Multiplying letter activation by 100 andbounding it between 0 and 100 gives the modeled value, PL, forpercentage of correct recognitions, as displayed in Figure4.Next, we consider error patterns for horizontal presentationof trigrams, as discussed in Section3.3. The trigrams were pre-sented such that their middle letters were the same distance fromfixation in each visual field. We denote the retinal location of thefirst letter in the RVF as RN(near fixation) and the retinal lo-cation of the third letter in the RVF as RF(far from fixation). Inthe LVF, the first letter then has location 2RF, and the third let-ter has location 2RN.We assume the probability of correct recognition of a letteris proportional to its feature level activation. We assume this istrue even for the final letter, because presentation durationswereshort enough (»50msec) to push the firing of the final let-ter near the end of the oscillatory cycle, removing a final-letteradvantage. We are interested in the proportion of initial-letterrecognitions versus final-letter recognitions, across visualfields. We calculate an asymmetry measure, A, byA(RN,RF)5(Fh(1,2RF)2Fh(3,2RN))2(Fh(1,RN)2Fh(3,RF)).That is, for each visual field we subtract the number of final-letter recognitions from the number of initial-letter recognitions,to get a recognition slope. The recognition slope of the RVF iscompared with that of the LVF by subtracting it from that of theLVF. If Ais 0, there is no asymmetry. Aincreases as the propor- LPRFPRPFPRPPLPRLPR(,)(,).(,)(,)min(,max(,(,))).=+�ìíî=*02111000100if =if cccCCRCRCRCRRRRRMEFdiffdiff=====--=£££ìíïïîïï1018020111010300736005690049...().(||)(||)(||)(||).||.||.||.||.if if if if FPRFPRRRFPRcPhhFl(,)(,)()(,)(),=³-*-ìíîif or otherwise 0101 ERCRRcCRRE()()(),=³*ìíîif if 00 Table A1 Definition of W P2PlR ³0R£000.000.0010.150.8020.251.1030.301.2540.501.3550.501.45 60.501.65 MODEL OF LETTER-POSITION CODING243 tion of final-letter recognitions in the LVF decreases relative tothose in the RVF—that is, as the visual field asymmetry increases.Next, we derive expressions for the Fhs from the definitionsabove. We assume that the stimuli are far enough from fixationthat the bounding by function Mis not necessary. We getFh(1,2RF)5cE*C(RF)Fh(3,2RN)5cE*C(RN)2W(2,2RN)*cE*C(RF)Fh(1,RN)5C(RN)Fh(3,RF)5C(RF)2W(2,RF)*C(RN).Substituting into the definition of Aand combining terms yieldsA(RN,RF)5(cE1W(2,2RN)11)*C(RF)2(cE1W(2,RF)11) *C(RN).We are interested in the value of Afor the stimulus locationused by Hellige and Cowin (1996) versus that used by Eviatar(1999). In the former experiment, the far edge of the stimulusfell 3.0º of visual angle from fixation, and the near edge fell 1.5ºfrom fixation. In the latter experiment, the locations were 3.0ºand 1.0º, respectively. The difference in the locations of the far letters’ centers (resulting from letter size) is negligible; weconsider the RFs to be the same across experiments. This yieldsthesame value for the first term of Afor both experiments. Onlythesign of the second argument to Wmatters, so the fact that theRNsdiffered does not affect the value of W(2,2RN). Super-scripting to denote experiment, RHN� REN, so C(RHN) C(REN).Thus, the second term is smaller for AHthan for AE, so AH&#x -29;&#x 000; AE.This analysisis consistent with the results; the Hellige andCowin experiment showed asymmetry, whereas the Eviatar ex-periment did not. APPENDIXA (Continued) APPENDIXB Model of Brysbaert (1994) We model the naming latency, denoted RT, as the sum of thetimes required for transfer, inversion, phonological assembly,and all other processing. That is,RT(h,len,fix)5Ttr(TR(h,fix))1Tin(TR(h,fix),INV (fix))1cP*len1cB,where RTis a function of the dominant hemisphere (h), wordlength (len), and fixation point (fix). Ttris the time cost of in-terhemispheric transfer, which is a function of the number ofletters to transfer, TR. Tinis the time cost of acuity gradient in-version, which is a function of TRand the number of letters toinvert, INV. The quantity cP*lencorresponds to phonologicalassembly time, where cPis a positive constant. The constant cBdenotes the base time required for all other processing.The number of letters to transfer, TR, depends on both fixa-tion point and dominant hemisphere; when the word appears inthe visual field projecting to the dominant hemisphere, TR50;TR5len. As explained in Section3.2, it is assumedthat transfer time does not vary with the number letters to betransferred; that is, Ttr(x)5cTfor x� 0, where cTis a positiveconstant, while Ttr(0)50. Thus,andThe number of letters to invert, INV, depends only on the fix-ation point; for initial-letter fixation, INV50 (because theword falls into the RVF/LH); for final-letter fixation, INV5len(because the word falls into the LVF/RH). That is,It is assumed that Tinincreases with increasing INV(i.e., thetime required for acuity gradient inversion increases with thenumber of letters to invert, as proposed in Section3.2). We alsoassume that Tin(0,INV) Tin(len,INV) (i.e., the time cost of in-version increases if transfer is also necessary). This assumptionindicates that the cost of both inversion and transfer is greaterthan the sum of inversion only and transfer only. Such an assump-tion is necessary to fit the data; moreover, it seems reasonableto assume that nonlinear effects arise when feature informationis degraded by both inversion and transfer.The displayed results for RTin Figure5 instantiated the modelusing the following definitions of the constants cTtransfer time), cP(phonological assembly time per letter),and cB(base processing time), and the function Tin(inversion time):whereTin(INV)5(INV23)2+ 4.The modeled results are consistent with the experimental data.For final-letter fixation in LH-dominant readers, reaction timesincrease steeply with increasing length due to the derivative of thefunction Tin(len,len). For RH-dominant readers, the cost of final-letter fixation is not as steep because Tin(0,len) Tin(len,len).In fact, for three-letter words, a trend toward an LVF/RH ad-vantage for RH-dominant readers appears because Tin(0, 3)Ttr(3). However, as len increases, an RVF/LH advantage emerges,as Tin(0,len) increases while Ttr(0,len) stays constant. cccTTRINVINVTINVINVTRTINVINVTRTPBininin====£�=*��ìíïîï9342903301730(,)().(),if if and if and INVfixfixlenfixlen().===ìíî01if if TTRTRcTRlentrT().===ìíî00if if TRhfixhfixhfixlenlenhfixlenlenhfix(,).=====ìíïïîïï0101if =LH and if =RH and if =LH and if =RH and (Manuscript received January 7, 2000;revision accepted for publication October 10, 2000.)