PPT-“Ergodic” (Invariant) Measures Applied to n-Dimensional, Lag Embeddings of Expanding

Biological Dynamical Systems Arnold J Mandell MD Multi Modal Imaging Laboratory MMIL Department of Psychiatry UCSD and FetzerFranklin Fund Ornstein theorem MostAll suitably normalized measures made on chaotic dynamical systems are equivalent to their informational entropy . 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 15. 14. A Chessboard Problem. ?. A . Bishop . can only move along a diagonal. Can a . bishop . move from its current position to the question mark?. Violating Measurement Independence without fine-tuning, conspiracy, or constraints on free will. Tim Palmer. Clarendon Laboratory. University of Oxford. T. o explain the experimental violation of Bell Inequalities, a putative theory of quantum physics must violate one (or more) of:. Alex Andoni. (. Microsoft Research . SVC). The NNS prism. High dimensional. geometry. dimension reduction. space partitions. embedding. …. NNS. small dimension. sketching. Small Dimension. What if . V.E.Kravtsov. ICTP, Trieste. and Landau Institute. Collaboration: . Ivan . Khaymovich. , . Aaalto. Emilio Cuevas, Murcia. Many-body localization. Anderson localization model on random regular graph (RRG). The Brown Bag. Hassan Bukhari. BS . Physics . 2012. 墫鱡뱿轺. . Stat . Mech. Project. . “. It is not less important to understand the foundation of such a complex issue than to calculate useful quantities”. Rahul Sharma and Alex Aiken (Stanford University). 1. Randomized Search. x. = . i. ;. y = j;. while . y!=0 . do. . x = x-1;. . y = y-1;. if( . i. ==j ). assert x==0. No!. Yes!.  . 2. Invariants. NIPandVCdimensionILetFbeafamilyofsubsetsofasetX.IForasetBX,letF\B=fA\B:A2Fg.IWesaythatBXisshatteredbyFifF\B=2B.ITheVCdimensionofFisthelargestintegernsuchthatsomesubsetofSofsizenisshatteredbyF(otherw Ergodic phases in strongly disordered random regular graphs. V.E.Kravtsov. ICTP, Trieste. . Collaboration: . Boris . Altshuler. , Columbia U.. Lev . Ioffe. , Paris and Rutgers. Ivan . Khaymovich. , Aalto. Reid . Calamita. Motivation: Why Dynamics?. Modeling motion through time. Analytical Solutions. Numerical Approximations. Qualitative Results. Fixed Points. Robustness. General Behavior. Bounds. Limit Cycles. Map nodes to low-dimensional . embeddings. .. 2) Graph neural networks. Deep learning architectures for graph-structured data. 3) Applications. Representation Learning on Networks, snap.stanford.edu/proj/embeddings-www, WWW 2018. What Is the Feature Vector . x. ?. Typically a vector representation of a single character or word. Often reflects the . context. in which that word is found. Could just do counts, but that leads to sparse vectors. Textual word embeddings map words to meaning and are thus based on semantics. Different words can map to a similar location in the features space even though the letters composing the word are not the same.. Gabriel P. Hughes, Ph.D.. Risk Manager – Entomology . USDA-APHIS-PPQ. February 26, 2022. United States Department of Agriculture. Animal and Plant Health Inspection Service. Photo credit: Jack Kelly, University of California. Patrick Wilson. Compliance Officer. The Co-operative Bank. Key takeaways. - The concept of ergodicity. - How lawyers can help avoid ruin. - Volatility is stability. - We want to be antifragile. - Small is beautiful.