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Algorithms and Models for the Web Graph
No full textThis book constitutes the proceedings of the 18th International Workshop on Algorithms and Models for the Web Graph, WAW 2023, held in Toronto, Canada, in May 23–26, 2023.The 12 Papers presented in this volume were carefully reviewed and selected from 21 submissions. The aim of the workshop was understanding of graphs that arise from the Web and various user activities on the Web, and stimulate the development of high-performance algorithms and applications that exploit these graphs
Encyclopedia of Optimization
No full textThe goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. In 2000, the first edition was widely acclaimed and received high praise. J.B. Rosen crowned it “an indispensable resource” and Dingzhu Du lauded it as “the standard most important reference in this very dynamic research field”. Top authors such as Herbert Hauptman (winner of the Nobel Prize) and Leonid Khachiyan (the Ellipsoid theorist) contributed and the second edition kept these seminal entries. The second edition built upon the success of the first edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as “Algorithms for Genomics”, “Optimization and Radiotherapy Treatment Design”, and “Crew Scheduling”. The third edition will include 200 or more new entries in several of the areas that have burgeoned since publication of the second edition, such as AI, Machine Learning, Robust Optimization, optimization of pharmaceutical manufacturing, and more
Wiener-Filter Enhanced Estimation of the Intrinsic Laser Linewidth from Delayed Self-Heterodyne Beat Note Measurements
No full textNarrow-linewidth lasers exhibiting low phase noise are core elements of coherent optical communication systems, gravitational wave interferometers and emerging quantum technologies (e.g., optical atomic clocks, matter-wave interferometers, ion-trap quantum-computers etc.). For many of these applications, the performance depends critically on the laser's intrinsic (Lorentzian) linewidth [1], which is typically obscured by additional 1/f-like technical noise. Because of this so-called flicker noise, the laser linewidth alone is not a well-defined quantity and needs to be specified for a given measurement time. For a detailed characterization of the frequency noise exhibited by the laser, the measurement of the frequency noise power spectral density (FN-PSD) is required
12th Japanese-Hungarian Symposium on Discrete Mathematics and Its Applications
No full textAs a part of the long history of cooperation among Japanese and Hungarian scientists in the field of discrete mathematics, the 1st Japanese-Hungarian Symposium on Discrete Mathematics and Its Applications took place in Kyoto in 1999. The participants decided to continue their existing cooperation on a more regular basis and have established a biennial series of conferences
High-probability convergence for composite and distributed stochastic minimization and variational inequalities with heavy-tailed noise
Get PDFHigh-probability analysis of stochastic first-order optimization methods under mild assumptions on the noise has been gaining a lot of attention in recent years. Typically, gradient clipping is one of the key algorithmic ingredients to derive good high-probability guarantees when the noise is heavy-tailed. However, if implemented naïvely, clipping can spoil the convergence of the popular methods for composite and distributed optimization (Prox-SGD/Parallel SGD) even in the absence of any noise. Due to this reason, many works on high-probability analysis consider only unconstrained non-distributed problems, and the existing results for composite/distributed problems do not include some important special cases (like strongly convex problems) and are not optimal. To address this issue, we propose new stochastic methods for composite and distributed optimization based on the clipping of stochastic gradient differences and prove tight high-probability convergence results (including nearly optimal ones) for the new methods. Using similar ideas, we also develop new methods for composite and distributed variational inequalities and analyze the high-probability convergence of these methods
Finite Volumes for Simulation of Large Molecules
No full textWe study a finite volume scheme for simulating the evolution of large molecules within their reduced state space. The finite volume scheme under consideration is the SQRA scheme developed by Lie, Weber and Fackeldey. We study convergence of a more general family of FV schemes in up to 3 dimensions and provide a convergence result for the SQRA-scheme in arbitrary space dimensions
Transition to anomalous dynamics in a simple random map
Get PDFThe famous Bernoulli shift (or dyadic transformation) is perhaps the simplest deterministic dynamical system exhibiting chaotic dynamics. It is a piecewise linear time-discrete map on the unit interval with a uniform slope larger than one, hence expanding, with a positive Lyapunov exponent and a uniform invariant density. If the slope is less than one the map becomes contracting, the Lyapunov exponent is negative, and the density trivially collapses onto a fixed point. Sampling from these two different types of maps at each time step by randomly selecting the expanding one with probability , and the contracting one with probability , gives a prototype of a random dynamical system. Here we calculate the invariant density of this simple random map, as well as its position autocorrelation function, analytically and numerically under variation of . We find that the map exhibits a non-trivial transition from fully chaotic to completely regular dynamics by generating a long-time anomalous dynamics at a critical sampling probability , defined by a zero Lyapunov exponent. This anomalous dynamics is characterised by an infinite invariant density, weak ergodicity breaking and power law correlation decay
Nonsmooth Regular Perturbations of Singularly Perturbed Problems
No full textWe consider families u =uε,0 of boundary layer solutions to singularly perturbed quasilinear problems of the type ε2(a (x , u (x) , ε)u' (x)) ' = b (x , u (x) , ε) for x ∈ (- 1 , 1), u (- 1) =u' (1) = 0, and we describe the behaviour of these solution families under small regular, but nonsmooth perturbations, i.e. we show existence and local uniqueness of solutions u =uε,δ ≈uε,0 to If g is a Dirac function, then for all small ε > 0 and δ ≥ 0, such that δ / ε is small, those solutions exist, and ‖uε,δ -uε,0 ‖ ∞ = O (δ / ε) for δ → 0 uniformly with respect to ε. If g ∈L2 (- 1 , 1), then for all small ε > 0 and δ ≥ 0, such that δ /√{ ε } is small, those solutions exist, and ‖uε,δ -uε,0 ‖ ∞ = O (δ /√{ ε }) for δ → 0 uniformly with respect to ε. And if g ∈L∞ (- 1 , 1), then for all small ε > 0 and δ ≥ 0 those solutions exist, and ‖uε,δ -uε,0 ‖ ∞ = O (δ) for δ → 0 uniformly with respect to ε. Finally we show that these asymptotic estimates are optimal