A min-max theorem on tournaments

We present a structural characterization of all tournaments T = (V, A) such that, for any nonnegative integral weight function defined on V, the maximum size of a feedback vertex set packing is equal to the minimum weight of a triangle in T. We also answer a question of Frank by showing that it is N P-complete to decide whether the vertex set of a given tournament can be partitioned into two feedback vertex sets. In addition, we give exact and approximation algorithms for the feedback vertex set packing problem on tournaments. ©2007 Society for Industrial and Applied Mathematics.published_or_final_versio

A New HDG Method for Dirichlet Boundary Control of Convection Diffusion PDEs II: Low Regularity

In the first part of this work, we analyzed a Dirichlet boundary control problem for an elliptic convection diffusion PDE and proposed a new hybridizable discontinuous Galerkin (HDG) method to approximate the solution. For the case of a 2D polygonal domain, we also proved an optimal superlinear convergence rate for the control under certain assumptions on the domain and on the target state. In this work, we revisit the convergence analysis without these assumptions; in this case, the solution can have low regularity and we use a different analysis approach. We again prove an optimal convergence rate for the control, and present numerical results to illustrate the convergence theory

Structure-Induced Reversible Anionic Redox Activity in Na Layered Oxide Cathode

Anionic redox reaction (ARR) in lithium- and sodium-ion batteries is under hot discussion, mainly regarding how oxygen anion participates and to what extent oxygen can be reversibly oxidized and reduced. Here, a P3-type Na0.6[Li0.2Mn0.8]O2 with reversible capacity from pure ARR was studied. The interlayer O-O distance (peroxo-like O-O dimer, 2.506(3) Å), associated with oxidization of oxygen anions, was directly detected by using a neutron total scattering technique. Different from Li2RuO3 or Li2IrO3 with strong metal-oxygen (M-O) bonding, for P3-type Na0.6[Li0.2Mn0.8]O2 with relatively weak Mn-O covalent bonding, crystal structure factors might play an even more important role in stabilizing the oxidized species, as both Li and Mn ions are immobile in the structure and thus may inhibit the irreversible transformation of the oxidized species to O2 gas. Utilization of anionic redox reaction (ARR) on oxygen has been considered as an effective way to promote the charge-discharge capacity of the layered oxide cathodes for lithium- or sodium-ion batteries. The detailed mechanism of ARR, in particular how crystal structure affects and coordinates with the ARR, is not yet well understood. In the present work, a combination of X-ray and neutron total scattering measurements has been performed to study the structure of the prototype P3-type layered Na0.6[Li0.2Mn0.8]O2 with pure ARR. Unique structural characteristics, rather than prevailing knowledge of covalency of metal-oxygen, enable the stabilization of the crystal structure of Na0.6[Li0.2Mn0.8]O2 along with the ARR. This work suggests that reversible ARR can be manipulated by proper structure designs, thus to achieve high lithium or sodium storage in layered oxide cathodes. For P3-type Na0.6[Li0.2Mn0.8]O2 with relatively weak Mn-O covalent bonding, crystal structure factors play an important role in stabilizing the oxidized species, inhibiting the irreversible transformation of the oxidized species to O2 gas. The finding is important for better design of layered oxide positive materials with higher reversible capacity via the introduction of a reversible anionic redox reaction

The Maximum-Weight Stable Matching Problem: Duality and Efficiency

Given a preference system (G,≺) and an integral weight function defined on the edge set of G (not necessarily bipartite), the maximum-weight stable matching problem is to find a stable matching of (G,≺) with maximum total weight. In this paper we study this NP-hard problem using linear programming and polyhedral approaches. We show that the Rothblum system for defining the fractional stable matching polytope of (G,≺) is totally dual integral if and only if this polytope is integral if and only if (G,≺) has a bipartite representation. We also present a combinatorial polynomial-time algorithm for the maximum-weight stable matching problem and its dual on any preference system with a bipartite representation. Our results generalize Király and Pap's theorem on the maximum-weight stable-marriage problem and rely heavily on their work. © 2012 Society for Industrial and Applied Mathematics.published_or_final_versio

A system for learning statistical motion patterns

Analysis of motion patterns is an effective approach for anomaly detection and behavior prediction. Current approaches for the analysis of motion patterns depend on known scenes, where objects move in predefined ways. It is highly desirable to automatically construct object motion patterns which reflect the knowledge of the scene. In this paper, we present a system for automatically learning motion patterns for anomaly detection and behavior prediction based on a proposed algorithm for robustly tracking multiple objects. In the tracking algorithm, foreground pixels are clustered using a fast accurate fuzzy k-means algorithm. Growing and prediction of the cluster centroids of foreground pixels ensure that each cluster centroid is associated with a moving object in the scene. In the algorithm for learning motion patterns, trajectories are clustered hierarchically using spatial and temporal information and then each motion pattern is represented with a chain of Gaussian distributions. Based on the learned statistical motion patterns, statistical methods are used to detect anomalies and predict behaviors. Our system is tested using image sequences acquired, respectively, from a crowded real traffic scene and a model traffic scene. Experimental results show the robustness of the tracking algorithm, the efficiency of the algorithm for learning motion patterns, and the encouraging performance of algorithms for anomaly detection and behavior prediction