'Pairwise disjoint' presentation slideshows

Computational Movement Analysis Lecture 2: Clustering Joachim Gudmundsson

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OWL 2

OWL 2. Web Ontology Language. Some material adapted from presentations by Ian Horrocks and by Feroz Farazi. Introduction. OWL 2 extends OWL 1.1 and is backward compatible with it The new features of OWL 2 based on real applications, use cases and user experience

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Krakow, Summer 2011

Krakow, Summer 2011. Partially Ordered Sets Basic Concepts William T. Trotter trotter@math.gatech.edu. Formal Definition and Examples.

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CSE 460: Switching Theory

CSE 460: Switching Theory. David M. Zar Computer Science and Engineering Washington University Spring 2010 dzar@wustl.edu http://classes.engineering.wustl.edu/cse460. Boolean Algebras. Sets, Relations and Functions Orders Boolean Functions Properties of Boolean Algebras

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Set Theory

Set Theory. Section 2.1 Tuesday 20 May. Definition: A set is an unordered collection of objects, called the elements or members of the set. A set is said to contain its elements. The definition does not require any relationship among the members of a set.

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Closures of relations

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On The Achromatic Number Problem

On The Achromatic Number Problem. Guy Kortsarz Rutgers University, Camden. On Independent Sets And Cliques. Independent set: a set W so that no two vertices in W share an edge. In a CLIQUE every two vertices are adjacent. Problem Definition. INPUT: An undirected graph G(V,W)

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Discrete Structures

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Spanning Cubic Graph Designs for Decomposing Complete Graphs

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The Relations between information theory and Set theory

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7.5 Inclusion/Exclusion

7.5 Inclusion/Exclusion. Definition and Example- 2 sets. | A ? B| =|A| + |B| - |A ? B| Ex1: |A|=9, |B|=11, |A?B|=5, | A ? B | = ?. 3 sets. |A ? B ?C |= ?. Proof for 3 sets. |A1 ? A2 ? A3| =?|Ai| - ?|Ai ? Aj | + |A1? A2 ? A3| =?|Ai| =?|Ai| - ?|Ai ? Aj | .

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Basic Definitions of Set Theory

Basic Definitions of Set Theory. Lecture 25 Section 5.1 Mon, Mar 5, 2007. Disjoint Sets. Sets A and B are disjoint if A ? B = ? .

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Minimal NFA Problems are hard Tao Jiang & B. Ravikumar

Minimal NFA Problems are hard Tao Jiang & B. Ravikumar. N Andres Parra. Quick Outline. Presentation of the problem Introduction UFA: Unambiguous Finite Automata NP-completeness results. A B. Problem:. Given a FA of type A, find a minimum equivalent FA of type B. DFA DFA.

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Equivalence Relations

Equivalence Relations. MSU CSE 260. Outline. Introduction Equivalence Relations Definition, Examples Equivalence Classes Definition Equivalence Classes and Partitions Theorems Example. Introduction. Consider the relation R on the set of MSU students:

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Section 7.5: Equivalence Relations

Section 7.5: Equivalence Relations. Def : A relation R on a set A is called an equivalence relation if it is reflexive, symmetric, and transitive. Ex : Let A be any set and define R = {(a, b) | a = b}. That is, every element of A is related to itself only.

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Counting Warmup

Counting Warmup. Strings of 7 bits. How many have a run of at least 3 1s? Let S={0,1} 7 Let R?S be the strings with a run of 3 1s R={0,1} * 111{0,1} * ?S To count R, split it into disjoint subsets and count the subsets

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Complexity of iff. An (curved) edge: Vertices: Only

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