Violator Spaces: Structure and Algorithms

Sharir and Welzl introduced an abstract framework for optimization problems, called LP-type problems or also generalized linear programming problems, which proved useful in algorithm design. We define a new, and as we believe, simpler and more natural framework: violator spaces, which constitute a proper generalization of LP-type problems. We show that Clarkson's randomized algorithms for low-dimensional linear programming work in the context of violator spaces. For example, in this way we obtain the fastest known algorithm for the P-matrix generalized linear complementarity problem with a constant number of blocks. We also give two new characterizations of LP-type problems: they are equivalent to acyclic violator spaces, as well as to concrete LP-type problems (informally, the constraints in a concrete LP-type problem are subsets of a linearly ordered ground set, and the value of a set of constraints is the minimum of its intersection).Comment: 28 pages, 5 figures, extended abstract was presented at ESA 2006; author spelling fixe

Space-efficient Feature Maps for String Alignment Kernels

String kernels are attractive data analysis tools for analyzing string data. Among them, alignment kernels are known for their high prediction accuracies in string classifications when tested in combination with SVM in various applications. However, alignment kernels have a crucial drawback in that they scale poorly due to their quadratic computation complexity in the number of input strings, which limits large-scale applications in practice. We address this need by presenting the first approximation for string alignment kernels, which we call space-efficient feature maps for edit distance with moves (SFMEDM), by leveraging a metric embedding named edit sensitive parsing (ESP) and feature maps (FMs) of random Fourier features (RFFs) for large-scale string analyses. The original FMs for RFFs consume a huge amount of memory proportional to the dimension d of input vectors and the dimension D of output vectors, which prohibits its large-scale applications. We present novel space-efficient feature maps (SFMs) of RFFs for a space reduction from O(dD) of the original FMs to O(d) of SFMs with a theoretical guarantee with respect to concentration bounds. We experimentally test SFMEDM on its ability to learn SVM for large-scale string classifications with various massive string data, and we demonstrate the superior performance of SFMEDM with respect to prediction accuracy, scalability and computation efficiency.Comment: Full version for ICDM'19 pape

Reconstruction and actual trends of landslide activities in Bruust–Haltiwald, Horw, canton of Lucerne, Switzerland

A spatiotemporal reconstruction of slope movements on the edge of Lake Lucerne near the municipality of Horw, canton of Lucerne, is presented. The reconstruction was realized by analyzing growth reactions of beech (Fagus sylvatica L.) and fir (Abies alba Mill.) trees growing on this slope. Before dendrochronological sampling, a detailed geomorphological mapping of the landslide was conducted with the aim to determine the spatial extent of the sliding area. For tree-ring analyses, 124 increment cores from 62 trees were analyzed following standard techniques of dendrogeomorphology. In addition, long micro-sections were prepared from the entire cores to extend the common eccentricity analyses by microscopic determination of the onset of reaction wood in fir and beech. Results clearly show that the area is moving at least since 1948. A significant concentration of events was observed between the years 1990 and 2000 as well as after 2006. The definition of a threshold to define events using an eccentricity index alone is problematic and needs to be adapted to specific site conditions. For this reason, we recommend always combining the application of an eccentricity index with a detailed visual (anatomical) inspection to check for the occurrence of reaction wood.</p

Crossover to the KPZ equation

We characterize the crossover regime to the KPZ equation for a class of one-dimensional weakly asymmetric exclusion processes. The crossover depends on the strength asymmetry $an^{2-\gamma}$ ($a,\gamma>0$) and it occurs at $\gamma=1/2$. We show that the density field is a solution of an Ornstein-Uhlenbeck equation if $\gamma\in(1/2,1]$, while for $\gamma=1/2$ it is an energy solution of the KPZ equation. The corresponding crossover for the current of particles is readily obtained.Comment: Published by Annales Henri Poincare Volume 13, Number 4 (2012), 813-82

Исследование зон усталостного разрушения шнеков

Шнек - основной рабочий орган машин для переработки отходов - экструдеров. От качества его изготовления зависит производительность цеха и целостность корпуса машины. При переработке многокомпонентного сырья, которым является Refuse Derived Fuel - это общее название альтернативных видов топлива, получаемых при переработке отходов. В качестве сырья используется практически любой органический материал: целлюлоза, резина, пластик, кожа, дерево, пищевые заменители. В исследовании использован пример на базе работы с RDF-сырьем Мусороперерабатывающего комбината "Янино", Ленинградская область. Именно при работе с такими высокоабразивными отходами возникает необходимость многократно повышать ресурс шнеков за счет использования новых технологий обработки металлов, так как в составе данного сырья могут встречаться металлические компоненты и трудно размалываемые силикаты.Screw - the main working organ of machines for processing waste - extruders. From the quality of its production depends the productivity of the shop and the integrity of the machine body. When refining a multicomponent raw material, which is Refuse Derived Fuel - this is the general name for alternative fuels obtained from recycling. As raw material, almost any organic material is used: cellulose, rubber, plastic, leather, its substitutes. The study used an example based on work with RDF-raw materials of the Janino Refuse Processing Plant. Leningrad region. It is when working with such highly abrasive waste that it becomes necessary to increase the service life of screw augmentedly by using new processing technologies, since metal components and hard-to-break silicates can occur in the composition of this raw material

Dynamical aspects of mean field plane rotators and the Kuramoto model

The Kuramoto model has been introduced in order to describe synchronization phenomena observed in groups of cells, individuals, circuits, etc... We look at the Kuramoto model with white noise forces: in mathematical terms it is a set of N oscillators, each driven by an independent Brownian motion with a constant drift, that is each oscillator has its own frequency, which, in general, changes from one oscillator to another (these frequencies are usually taken to be random and they may be viewed as a quenched disorder). The interactions between oscillators are of long range type (mean field). We review some results on the Kuramoto model from a statistical mechanics standpoint: we give in particular necessary and sufficient conditions for reversibility and we point out a formal analogy, in the N to infinity limit, with local mean field models with conservative dynamics (an analogy that is exploited to identify in particular a Lyapunov functional in the reversible set-up). We then focus on the reversible Kuramoto model with sinusoidal interactions in the N to infinity limit and analyze the stability of the non-trivial stationary profiles arising when the interaction parameter K is larger than its critical value K_c. We provide an analysis of the linear operator describing the time evolution in a neighborhood of the synchronized profile: we exhibit a Hilbert space in which this operator has a self-adjoint extension and we establish, as our main result, a spectral gap inequality for every K>K_c.Comment: 18 pages, 1 figur

Evidence for structural and electronic instabilities at intermediate temperatures in κ\kappa-(BEDT-TTF)2_{2}X for X=Cu[N(CN)2_{2}]Cl, Cu[N(CN)2_{2}]Br and Cu(NCS)2_{2}: Implications for the phase diagram of these quasi-2D organic superconductors

We present high-resolution measurements of the coefficient of thermal expansion $\alpha (T)=\partial \ln l(T)/\partial T$ of the quasi-twodimensional (quasi-2D) salts $\kappa$-(BEDT-TTF)$_2$X with X = Cu(NCS)$_2$, Cu[N(CN)$_2$]Br and Cu[N(CN)$_2$]Cl. At intermediate temperatures (B), distinct anomalies reminiscent of second-order phase transitions have been found at $T^\ast = 38$ K and 45 K for the superconducting X = Cu(NCS)$_2$ and Cu[N(CN)$_2$]Br salts, respectively. Most interestingly, we find that the signs of the uniaxial pressure coefficients of $T^\ast$ are strictly anticorrelated with those of $T_c$. We propose that $T^\ast$ marks the transition to a spin-density-wave (SDW) state forming on minor, quasi-1D parts of the Fermi surface. Our results are compatible with two competing order parameters that form on disjunct portions of the Fermi surface. At elevated temperatures (C), all compounds show $\alpha (T)$ anomalies that can be identified with a kinetic, glass-like transition where, below a characteristic temperature $T_g$, disorder in the orientational degrees of freedom of the terminal ethylene groups becomes frozen in. We argue that the degree of disorder increases on going from the X = Cu(NCS)$_2$ to Cu[N(CN)$_2$]Br and the Cu[N(CN)$_2$]Cl salt. Our results provide a natural explanation for the unusual time- and cooling-rate dependencies of the ground-state properties in the hydrogenated and deuterated Cu[N(CN)$_2$]Br salts reported in the literature.Comment: 22 pages, 7 figure

Green coloring of GaN single crystals introduced by Cr impurity

In this study unintentionally doped GaN grown by hydride vapor phase epitaxy that exhibits a sharply delimited region of green color was investigated. Optical analysis was performed by absorption and photoluminescence spectroscopy. An absorption band between 1.5 and 2.0 eV was found to be responsible for the green color and was related to a sharp emission at 1.193 eV by luminescence and excitation spectroscopy. The appearance of both optical signatures in the region of green color was related to an increase of Cr contamination detected by secondary ion mass spectrometry. We propose that the origin of green color as well as the emission line at 1.193 eV is attributed to internal transitions of Cr⁴⁺

Positive Semidefiniteness and Positive Definiteness of a Linear Parametric Interval Matrix

We consider a symmetric matrix, the entries of which depend linearly on some parameters. The domains of the parameters are compact real intervals. We investigate the problem of checking whether for each (or some) setting of the parameters, the matrix is positive definite (or positive semidefinite). We state a characterization in the form of equivalent conditions, and also propose some computationally cheap sufficient\,/\,necessary conditions. Our results extend the classical results on positive (semi-)definiteness of interval matrices. They may be useful for checking convexity or non-convexity in global optimization methods based on branch and bound framework and using interval techniques