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• Cell decomposition of images
  ...ixel]]s. Normally, it is assumed that objects are black and the background is white. ...ent the object simply as a list of pairs of numbers and this is the way it is commonly done. We will follow this convention.
  11 KB (1,829 words) - 19:26, 10 February 2015
• Algebraic topology: course
  ...uctory, two semester course on algebraic topology and its applications. It is intended for advanced undergraduate and beginning graduate students. ...dated. The source of material is currently in a draft of a book called ''[[Topology Illustrated]]''.
  3 KB (448 words) - 13:32, 17 March 2014
• Euclidean space made discrete
  ...<!--\index{finite differences}-->. Usually only the time (i.e., ${\bf R}$) is discretized: ...wave propagation<!--\index{ wave propagation}--> etc. This time the space is discretized as well:
  11 KB (1,801 words) - 15:50, 25 July 2014
• Pattern recognition in computer vision
  ...and then match them with those of the other image or images. This approach is complex and limited to face identification. In order to develop a content i ...and pattern recognition methods can be used. Nice! The most common method is probably [[clustering]] – looking for groups of points unusually close to
  9 KB (1,526 words) - 17:54, 1 July 2011
• Diffusion with various geometry
  Recall that, naively, [[diffusion]] is modeled with [[Excel]] as follows: On a deeper level, the geometry is supplied by [[Hodge duality]] and affects the forms that we deal with.
  13 KB (2,121 words) - 16:33, 7 June 2013
• Filtering output data
  ...ick only one. This is to be done by the user based on his criteria of what is [[noise]]: too small, low [[contrast]], low [[roundness]] etc. ...[[Pixcavator]]. In fact, [[Pixcavator's output table]] gives you a sample topology. After that you are on your own. And you have several ruler/sliders to use.
  3 KB (598 words) - 15:02, 9 October 2010
• Classification of points with respect to a subset
  For the background see [[Introduction to point-set topology]]. *a point $x$ is called an ''interior point'' of $A$ if there is a [[Neighborhoods and topologies|neighborhood]] $W$ of $x$ that lies entire
  4 KB (703 words) - 01:55, 1 October 2013
• Computational science training: 2010 projects
  <li>''[[The topology of data]]'' by Joseph Snyder, and</li> ...se issues were mostly resolved. Unfortunately, in either case there wasn't enough time to test the programs with real-life data.
  6 KB (926 words) - 17:02, 7 February 2011
• Geometry in calculus
  <center>$\lim_{x\to a}f(x)=L$ if for any $\epsilon >0$ there is a $\delta >0$ such that $0<|x-a|<\delta$ implies that $|f(x)-L|<\epsilon$. ...m_{x\to a}f(x)=L$ if for any open [[neighborhood]] $\epsilon$ of $L$ there is an open neighborhood $\delta$ of $a$ such that $x\in\delta$ implies $f(x)\i
  9 KB (1,604 words) - 18:08, 27 August 2015
• How to compute homology
  The $k$-[[chain group]] $C_k(K)$ is given as a vector space with [[basis of vector space|basis]] consisting of Its dimension is then obvious.
  6 KB (1,049 words) - 09:21, 3 September 2011
• Bad math
  ...ut a more typical problem with how [[mathematics]] is used in applications is '''made-up and hidden parameters'''. Compare: ...sentation of the topology of gray scale images|graph representation of the topology of images]] (and [[Pixcavator]] in particular),
  3 KB (453 words) - 10:35, 26 February 2013
• How to compute Betti numbers
  The $k$-[[chain group]] $C_k(K)$ is given as a vector space with [[basis of vector space|basis]] consisting of Its dimension is then obvious.
  5 KB (890 words) - 14:47, 24 August 2014
• Simply connected spaces
  *Can you can get from $A$ to $B$ in two ([[topology|topologically]]) different ways? So, $X$ is called ''simply connected'' if every closed curve can be "contracted" -- vi
  5 KB (785 words) - 22:07, 3 January 2014
• Connectivity
  ...ent the object simply as a list of pairs of numbers and this is the way it is commonly done. ...ent" they are connected by an edge, as shown in these pictures. The result is a ''graph representation of the binary image''.
  4 KB (636 words) - 14:53, 9 October 2010
• Examples of homology of cubical complexes
  The simplest way to capture the [[topology]] of $X$ is by considering a square and an edge as on the right. Its cubical representa (This is called the $0$-[[skeleton]] of $K$.)
  3 KB (519 words) - 18:06, 27 August 2015
• Stages of analysis
  Suppose we have found the [[topology graph]] of the [[gray scale image]]. '''Image -> its topology graph -> one of the possible topologies'''
  1 KB (174 words) - 18:34, 30 January 2011
• Intro to Higher Mathematics -- Spring 2018 -- final exam
  *Show enough work to justify your answers. $\bullet$ '''2.''' Below is the addition (multiplication) table of a group. Complete it.
  2 KB (284 words) - 18:23, 4 May 2018
• Advanced Topology -- Spring 2013 -- final exam
  *Show enough work to justify your answers. Refer to theorems whenever necessary. #A set $Y \subset {\bf R}^n$ is called star-shaped if there is $a\in Y$ such that for any $x \in Y$ the segment from $x$ to $a$ lies entir
  3 KB (532 words) - 15:09, 8 May 2013
• Peter Saveliev
  Hello! My name is Peter Saveliev (rhymes with “leave”). Pronouns are available upon reque *''Topology Illustrated'' (Note: Due to my day job, the second edition is postponed indefinitely.)
  4 KB (652 words) - 14:02, 15 April 2024
• Topology I -- Fall 2013 -- final exam
  *Show enough work to justify your answers. Refer to theorems whenever necessary. ...Y U I O P [ ] \. Think of them as if they are made of wires so that there is no width in these lines. Classify them "up to homeomorphism". (Just the ans
  2 KB (317 words) - 16:34, 10 December 2013

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