Mathematics for Computer Science

The thesis mainly aims to solve the following tasks: Firstly, the thesis extensively analyzes a wide range of existing approaches for the ME detection in scientific document images. Then, the thesis investigates and proposes novel methods to improve the detection accuracy of MEs. After enhancing the detection accuracy of MEs, the thesis investigates and pro poses a framework to improve the accuracy of the recognition of MEs in scientific document images.

27p closefriend09 16-11-2021 22 4   Download

The thesis mainly aims to solve the following tasks: Firstly, the thesis extensively analyzes a wide range of existing approaches for the ME detection in scientific document images. Then, the thesis investigates and proposes novel methods to improve the detection accuracy of MEs. After enhancing the detection accuracy of MEs, the thesis investigates and pro poses a framework to improve the accuracy of the recognition of MEs in scientific document images.

154p mintmintt 05-10-2021 14 4   Download

Research and improve scheduling admission control mechanism to enhance QoS based on incoming burst rate prediction at core node to improve scheduling efficiency for low QoS bursts but still ensure a level of service quality for high QoS bursts. The effectiveness of the scheduling admission control mechanism was valued through simulation and mathematical analysis.

26p gaocaolon12 18-06-2021 27 3   Download

The propose a new method aiming to adjust the TXOP parameter according to a dynamic mechanism that suits the priority of each data type from the existing limitations with TXOP parameter in IEEE 802.11 EDCA; the propose a novel fuzzy logic approach for enhancing the fairness of low priority data flows in IEEE 802.11 EDCA.

27p capheviahe27 23-02-2021 33 3   Download

We study unitary random matrix ensembles of the form −1 Zn,N | det M |2α e−N Tr V (M ) dM, where α −1/2 and V is such that the limiting mean eigenvalue density for n, N → ∞ and n/N → 1 vanishes quadratically at the origin. In order to compute the double scaling limits of the eigenvalue correlation kernel near the origin, we use the Deift/Zhou steepest descent method applied to the Riemann-Hilbert problem for orthogonal polynomials on the real line with respect to the weight |x|2α e−N V (x) . ...

42p dontetvui 17-01-2013 73 7   Download

We study the large scale geometry of the mapping class group, MCG(S). Our main result is that for any asymptotic cone of MCG(S), the maximal dimension of locally compact subsets coincides with the maximal rank of free abelian subgroups of MCG(S). An application is a proof of Brock-Farb’s Rank Conjecture which asserts that MCG(S) has quasi-flats of dimension N if and only if it has a rank N free abelian subgroup. (Hamenstadt has also given a proof of this conjecture, using different methods.

24p dontetvui 17-01-2013 69 7   Download

We prove that Cayley graphs of SL2 (Fp ) are expanders with respect to the projection of any fixed elements in SL(2, Z) generating a non-elementary subgroup, and with respect to generators chosen at random in SL2 (Fp ). 1. Introduction Expanders are highly-connected sparse graphs widely used in computer science, in areas ranging from parallel computation to complexity theory and cryptography; recently they also have found some remarkable applications in pure mathematics; see [5],[10], [15], [20], [21] and references therein. ...

19p dontetvui 17-01-2013 49 6   Download

We prove a blow-up formula for cyclic homology which we use to show that infinitesimal K-theory satisfies cdh-descent. Combining that result with some computations of the cdh-cohomology of the sheaf of regular functions, we verify a conjecture of Weibel predicting the vanishing of algebraic K-theory of a scheme in degrees less than minus the dimension of the scheme, for schemes essentially of finite type over a field of characteristic zero. Introduction The negative algebraic K-theory of a singular variety is related to its geometry. ...

26p dontetvui 17-01-2013 54 7   Download

In this article we study several homology theories of the algebra E ∞ (X) of Whitney functions over a subanalytic set X ⊂ Rn with a view towards noncommutative geometry. Using a localization method going back to Teleman we prove a Hochschild-Kostant-Rosenberg type theorem for E ∞ (X), when X is a regular subset of Rn having regularly situated diagonals. This includes the case of subanalytic X. We also compute the Hochschild cohomology of E ∞ (X) for a regular set with regularly situated diagonals and derive the cyclic and periodic cyclic theories. ...

53p dontetvui 17-01-2013 47 7   Download

We describe a Schubert induction theorem, a tool for analyzing intersections on a Grassmannian over an arbitrary base ring. The key ingredient in the proof is the Geometric Littlewood-Richardson rule of [V2]. As applications, we show that all Schubert problems for all Grassmannians are enumerative over the real numbers, and sufficiently large finite fields. We prove a generic smoothness theorem as a substitute for the Kleiman-Bertini theorem in positive characteristic.

25p noel_noel 17-01-2013 49 5   Download

Dedicated to C´sar Camacho for his 60th birthday e Abstract After gluing foliated complex manifolds, we derive a preparation-like theorem for singularities of codimension-one foliations and planar vector fields (in the real or complex setting). Without computation, we retrieve and improve results of Levinson-Moser for functions, Dufour-Zhitomirskii for nondegenerate ˙ codimension-one foliations (proving in turn the analyticity), Str´zyna-Zoladek o˙ ´ for non degenerate planar vector fields and Bruno-Ecalle for saddle-node foliations in the plane. ...

15p noel_noel 17-01-2013 49 5   Download

Using Guerra’s interpolation scheme, we compute the free energy of the Sherrington-Kirkpatrick model for spin glasses at any temperature, confirming a celebrated prediction of G. Parisi. 1. Introduction The Hamiltonian of the Sherrington-Kirkpatrick (SK) model for spin glasses [10] is given at inverse temperature β by (1.1) β HN (σ) = − √ N gij σi σj .

44p noel_noel 17-01-2013 38 6   Download

The infinite-dimensional unitary group U(∞) is the inductive limit of growing compact unitary groups U(N ). In this paper we solve a problem of harmonic analysis on U(∞) stated in [Ol3]. The problem consists in computing spectral decomposition for a remarkable 4-parameter family of characters of U(∞). These characters generate representations which should be viewed as analogs of nonexisting regular representation of U(∞). The spectral decomposition of a character of U(∞) is described by the spectral measure which lives on an infinite-dimensional space Ω of indecomposable characters. ...

105p noel_noel 17-01-2013 43 5   Download

We consider a specialization of an untwisted quantum affine algebra of type ADE at a nonzero complex number, which may or may not be a root of unity. The Grothendieck ring of its finite dimensional representations has two bases, simple modules and standard modules. We identify entries of the transition matrix with special values of “computable” polynomials, similar to Kazhdan-Lusztig polynomials. At the same time we “compute” q-characters for all simple modules. The result is based on “computations” of Betti numbers of graded/cyclic quiver varieties.

42p tuanloccuoi 04-01-2013 52 8   Download

Two centuries ago, in his celebrated work Disquisitiones Arithmeticae of 1801, Gauss laid down the beautiful law of composition of integral binary quadratic forms which would play such a critical role in number theory in the decades to follow. Even today, two centuries later, this law of composition still remains one of the primary tools for understanding and computing with the class groups of quadratic orders. It is hence only natural to ask whether higher analogues of this composition law exist that could shed light on the structure of other algebraic number rings and fields. ...

35p tuanloccuoi 04-01-2013 53 9   Download

Characteristic cohomology classes, defined in modulo 2 coefficients by Stiefel [26] and Whitney [28] and with integral coefficients by Pontrjagin [24], make up the primary source of first-order invariants of smooth manifolds. When their utility was first recognized, it became an obvious goal to study the ways in which they admitted extensions to other categories, such as the categories of topological or PL manifolds; perhaps a clean description of characteristic classes for simplicial complexes could even give useful computational techniques.

25p tuanloccuoi 04-01-2013 60 6   Download

In this paper we present the solution to a longstanding problem of differential geometry: Lie’s third theorem for Lie algebroids. We show that the integrability problem is controlled by two computable obstructions. As applications we derive, explain and improve the known integrability results, we establish integrability by local Lie groupoids, we clarify the smoothness of the Poisson sigma-model for Poisson manifolds, and we describe other geometrical applications. Contents 0. Introduction

47p tuanloccuoi 04-01-2013 45 7   Download

This paper introduces a rigorous computer-assisted procedure for analyzing hyperbolic 3-manifolds. This procedure is used to complete the proof of several long-standing rigidity conjectures in 3-manifold theory as well as to provide a new lower bound for the volume of a closed orientable hyperbolic 3-manifold. Theorem 0.1. Let N be a closed hyperbolic 3-manifold.

98p tuanloccuoi 04-01-2013 49 6   Download

We prove a closed formula for integrals of the cotangent line classes against the top Chern class of the Hodge bundle on the moduli space of stable pointed curves. These integrals are computed via relations obtained from virtual localization in Gromov-Witten theory. An analysis of several natural matrices indexed by partitions is required. 0. Introduction 0.1. Overview. Let Mg,n denote the moduli space of nonsingular genus g curves with n distinct marked points (over C).

29p tuanloccuoi 04-01-2013 49 7   Download