PPT-Persistent homology I

Peter K álnai Autumn school   Department of Algebra Ústupky 24th 27th November 2016 Algebraic topology Dont be afraid of these ideas you see them for the first time When you see them for the tenth time you wont be afraid any more They will have been safely stored on the list of things that you simply dont understand . (APT). Sasha Browning. Breakdown . Advanced. Combination of attack methods and tools. Persistent. . Continuous. monitoring and interaction. “Low-and-slow” approach. Threat. . Attacker. is skilled, motivated, organized and well funded. EVALUATING & DEVELOPING, . STICKING WITH DIFFICULTY, . NOT SCARED OF MAKING MISTAKES. PERSISTENT. EVALUATING & DEVELOPING. STICKING WITH DIFFICULTY. NOT SCARED OF MAKING MISTAKES. A QUICK WARM UP EXERCISE. Multi-dimensional . Persistent Homology. Matthew L. Wright. Institute for Mathematics . and . its Applications. University of Minnesota. in collaboration with Michael . Lesnick. What is persistent homology?. a case study on transmembrane protein. Jia-Ming Chang. 2013-July-09. Chang, J-M, P Di Tommaso, J-. Fß. Taly, C Notredame. 2012. Accurate multiple sequence alignment of transmembrane proteins with PSI-Coffee. BMC Bioinformatics 13.. Yusu. . Wang. Ohio State University. AMS Short Course 2014. Introduction. Much recent developments in computational topology. Both in theory and in their applications. E.g. , the theory of persistence homology. Presenter: Ronen . Talmon. Topological Methods in Electrical Engineering and Networks. January 19, 2011. January 19, 2011. Manifold Learning via Homology. 2. Sources. P. . Niyogi. , S. . Smale. , and S. Weinberger, . Matthew L. Wright. Institute for Mathematics and its Applications. University of Minnesota. Preliminaries. Let . be a . simplicial. complex, and let . be the two-element field.. denotes the vector space generated by the . Sept 4, 2013. Clustering Via Persistent Homology. Creating a simplicial complex. Step 0.) Start by adding 0-dimensional vertices . (0-simplices). Creating a simplicial complex. 1. .) . A. dding . 1. Persistent Homology. Matthew L. Wright. Institute for Mathematics . and . its Applications. University of Minnesota. in collaboration with Michael . Lesnick. What is persistent homology?. e.g. components, holes, . Comparative study of . morphological and anatomical structures. of animals and plants also indicate that they are constructed on the same basic plan and they shows certain similarities.. Such similarities are observed in:. Prove It!. Biogeography. Homologous and Analogous Structures. Fossil record. biogeography. The geographic distribution of plants and animals over the surface of the Earth. Pangaea. 270 million years ago all of the planet’s land mass was combined into one super continent. Ragesh. Kumar Ramachandran and Spring Berman. Autonomous collective systems Laboratory. Robotic Embedded Systems Laboratory. Motivation. Basic idea. Scalar field associated with occupancy grid maps.. 2. -based conductors. M.D. . Sumption. , . C. Kovacs. , . F. Wan, . M. . Majoros. , E.W. . . Collings. Center for Superconducting and Magnetic Materials, MSE, The Ohio State University. Funded by . an NIH bridge grant, and also an . Chronic pain is a pain which has failed to improve with standardised medical treatments and recurs or lasts for more than 3 to 6 months, beyond the healing time of an injured tissue. All tissues in the human body heal within approximately 3 to 6 months after the initial injury but sometimes pain continues despite complete tissue healing. Therefore, chronic pain doesn’t indicate the actual tissue damage anymore. Here, pain which was supposed to be a protective starts to behave like a nuisance, restricting you from all the things, and activities you enjoy in life. .