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Solving network design problems via iterative aggregation
In this work, we present an exact approach for solving network design problems that is based on an iterative graph aggregation procedure. The scheme...
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FMMTL: FMM Template Library A Generalized Framework for Kernel Matrices
In response to two decades of development in structured dense matrix algorithms and a vast number of research codes, we present designs and progress...
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Generating Formal Series and Applications
We deepen here the insight on formal power series. We temporarily abandon formality and consider the notion of the convergence of a power series;...
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Approximated perspective relaxations: a project and lift approach
The perspective reformulation (PR) of a Mixed-Integer NonLinear Program with semi-continuous variables is obtained by replacing each term in the...
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Balloons and Hoops and their Universal Finite-Type Invariant, BF Theory, and an Ultimate Alexander Invariant
Balloons are 2D spheres. Hoops are 1D loops. Knotted balloons and hoops (KBH) in 4-space behave much like the first and second homotopy groups of a...
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Random Walk on the Torus and Random Interlacements
In this chapter we consider simple random walk on the discrete torus...
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Evolution Problems
In this chapter, problems involving time are considered. Those expressed by means of ordinary differential equations are the simplest ones. In...
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On universal and periodic β-expansions, and the Hausdorff dimension of the set of all expansions
We study the topology of a set naturally arising from the study of β -expansions. After proving several elementary results for this set we study the...
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Persistence Probabilities and Exponents
This article deals with the asymptotic behavior as $$t \rightarrow +\infty...
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Poincaré and the Three-Body Problem
The Three-Body Problem has been a recurrent theme of Poincaré’s thought. Having understood very early the need for a qualitative study of...
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Rediscovery of Malmsten’s integrals, their evaluation by contour integration methods and some related results
This article is devoted to a family of logarithmic integrals recently treated in mathematical literature, as well as to some closely related results....
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Multiscale modeling of beam and plates using customized second-generation wavelets
We have designed bicubic Hermite-type finite-element wavelets that decouple the multiresolution stiffness matrix obtained from the discretization of...
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Constructing universal graphs for induced-hereditary graph properties
Rado constructed a (simple) denumerable graph R with the positive integers as vertex set with the following edges: For given m and n with m < n , m is...
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Quadrature
Prerequisites: Interpolation and extrapolation (§4.2, 4.2.8) are required. For Gauss quadrature (§9.3), we also need the Newton—Maehly method...
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Graph Searching and Related Problems
Suppose that there is a robber hiding on vertices or along edges of a graph or digraph. Graph searching is concerned with finding the minimum number...
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Branch-cut-and-price for the vehicle routing problem with simultaneous pickup and delivery
This work proposes a Branch-cut-and-price (BCP) approach for the Vehicle Routing Problem with Simultaneous Pickup and Delivery (VRPSPD). We also deal...
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Compactly Supported Wavelets
The objective of this chapter is three-fold: firstly to discuss the theory and methods for the construction of compactly supported wavelets,...
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Lattices and Cryptography
The security of all of the public key cryptosystems that we have previously studied has been based, lattice either...
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On the Group-Theoretic Structure of Lifted Filter Banks
The polyphase-with-advance matrix representations of whole-sample symmetric (WS) unimodular filter banks form a multiplicative matrix Laurent...