Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 23 for “"finite sets"”.
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Combinatorics of finite sets
… represent the subset lattice of (n) with sets ordered by inclusion. A collection I of subsets of (n) is called an ideal if every subset of a member of I is also in I. An intersecting family S in 2$\sp{\lbrack n\rbrack }$ is called a star if there exists an element of (n) belonging to every …
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Sampling Laws for Stochastically Constrained Simulation Optimization on Finite Sets
… of selecting an optimal system from among a finite set of competing systems, based on a "stochastic" objective function and subject to multiple "stochastic" constraints. In this context, we characterize the asymptotically optimal sample allocation that maximizes the rate at which the …
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Computing the Goodwillie-Taylor tower for discrete modules
A functor from finite sets to chain complexes is called atomic if it is completely determined by its value on a particular set. We present a new resolution for these atomic functors, which allows us to easily compute their Goodwillie polynomial approximations. By a rank filtration, any functor from …
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Hyperfinite transversal theory
… is a subset of the cartesian product of two finite sets X and Y. A matching f of $\Gamma$ is a 1-1 function f which is a subset of $\Gamma$ and which has the same domain as $\Gamma$.) The graph $\Gamma$ can be thought of as a finite family of finite sets $\{\Gamma(x) : {x}{\in}{X})\}$. Thus, …
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On groups and initial segments in nonstandard models of Peano Arithmetic
This thesis concerns M-finite groups and a notion of discrete measure in models of Peano Arithmetic. First we look at a measure construction for arbitrary non-M-finite sets via suprema and infima of appropriate M-finite sets. The basic properties of the measures are covered, along with …
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The Total Interval Number of a Graph
… R of a graph G is a collection of finite sets $\{R(\nu):\nu \in V(G)\}$ of closed bounded intervals so that $u \leftrightarrow \nu$ if and only if there exist $\theta\sb{u} \in R(u), \theta\sb{\nu} \in R(\nu)$ with $\theta\sb{u} \cap \theta\sb{\nu} \not= \emptyset$. The size of a …
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Ramsey theory and its application
… Solecki. Second, we prove a Ramsey theorem for finite sets equipped with a partial order and a fixed number of linear orders extending the partial order. Third, we study the relations between Ramsey theorems which have points in common with the classical Ramsey theorem and the dual Ramsey …
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Additive stucture, rich lines, and exponential set-expansion
… which induce exponential expansion on all finite sets of real numbers.
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Goodwillie calculus and I
… implications of using the indexing category of finite sets and injective maps in Goodwillie's calculus of homotopy functors. By careful analysis of the cross-effects of a reduced endofunctor of based spaces, this point of view leads to a monoidal model for the derivatives. Such structure induces …
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Scissors congruence and K-theory
… congruent if they can be decomposed into finite sets of pairwise-congruent polytopes. We generalize this notion to an abstract problem: given a set of objects and decomposition and congruence relations between them, when are two objects in the set scissors congruent? By packaging the …
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An Application of Combinatorial Methods
… combinatorial analysis when applied to finite sets. For a given finite sample space, probability questions are usually "just" a lot of counting. The purpose of this thesis is to provide some in depth analysis of several combinatorial methods, including basic principles of counting, …
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Extremal Problems On Families of Subsets With Forbidden Subposets
<p>We study the families of subsets of finite sets that have some special properties. For all families with the properties, we look for the largest sizes of the families. In the thesis, we use a method to bound the size of families of subsets, which is what we call the Lubell function now. The …
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Approximation Algorithms using Allegories and Coq
… the model of set-theoretic relations between finite sets. This model is executable and used in our examples. Finally, we provide an example for each of the approximation algorithm.
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Some problems in polynomial interpolation and topological complexity
… and combinatorics of geometrically characterized sets. These are finite sets of n+d choose n points in R^d which impose independent conditions on polynomials of degree n, and which have Lagrange polynomials of a special form. These sets were introduced by Chung and Yao in a 1977 paper in the SIAM …
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Nelson Oppen combination as a rewrite theory
… solvers exist for many such theories or their subsets, it is common for interesting SMT problems to span multiple theories. SMT solvers typically use refinements of the Nelson-Oppen combination method, an algorithm for producing a solver for the quantifier free fragment of the combination of a …
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Constructing K-theory spectra from algebraic structures with a class of acyclic objects
… Our main example is chain complexes of sets with quasi-isomorphisms; these satisfy a Gillet--Waldhausen Theorem, yielding an equivalent presentation of the K-theory of finite sets.
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Valued Constraint Satisfaction Problems over Infinite Domains
… precisely, the input of a VCSP consists of a finite set of variables, a finite set of cost functions that depend on these variables, and a cost $u$; the task is to find values for the variables such that the sum of the cost functions is at most $u$. By restricting the set of possible cost …
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Geometric methods in computational optimal transport and high-dimensional inference
… is developed. For measures supported on finite sets, a dual formulation is derived that enables stochastic updates with O(1) complexity per iteration, independent of support size. Under suitable regularity conditions, non-asymptotic convergence bounds of order O(log(T)/T) for …
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Automata-based decision procedures for weak arithmetics
… which is tightly connected to <br>automata over finite words. Nowadays, automata have also emerged as a <br>tool for effectively mechanizing decision procedures for such logical <br>theories. A notable example is Presburger arithmetic for which <br>effective decision procedures can be built using …
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Machine Learning for Causal Estimation
… via DML. Our framework accommodates both finite sets and continua of functionals, and leverages strong Gaussian approximation results to account for dependence across estimates. This enables rigorous simultaneous inference with control over familywise error rates. Together, these …
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