Strong stability of Nash equilibria in load balancing games

We study strong stability of Nash equilibria in the load balancing games of m (m >= 2) identical servers, in which every job chooses one of the m servers and each job wishes to minimize its cost, given by the workload of the server it chooses. A Nash equilibrium (NE) is a strategy profile that is resilient to unilateral deviations. Finding an NE in such a game is simple. However, an NE assignment is not stable against coordinated deviations of several jobs, while a strong Nash equilibrium (SNE) is. We study how well an NE approximates an SNE. Given any job assignment in a load balancing game, the improvement ratio (IR) of a deviation of a job is defined as the ratio between the pre-and post-deviation costs. An NE is said to be a ρ-approximate SNE (ρ >= 1) if there is no coalition of jobs such that each job of the coalition will have an IR more than ρ from coordinated deviations of the coalition. While it is already known that NEs are the same as SNEs in the 2-server load balancing game, we prove that, in the m-server load balancing game for any given m >= 3, any NE is a (5=4)-approximate SNE, which together with the lower bound already established in the literature implies that the approximation bound is tight. This closes the final gap in the literature on the study of approximation of general NEs to SNEs in the load balancing games. To establish our upper bound, we apply with novelty a powerful graph-theoretic tool

Phase diagram of Kondo-Heisenberg model on honeycomb lattice with geometrical frustration

We calculated the phase diagram of the Kondo-Heisenberg model on two-dimensional honeycomb lattice with both nearest-neighbor and next-nearest-neighbor antiferromagnetic spin exchanges, to investigate the interplay between RKKY and Kondo interactions at presence of magnetic frustration. Within a mean-field decoupling technology in slave-fermion representation, we derived the zero-temperature phase diagram as a function of Kondo coupling $J_k$ and frustration strength $Q$. The geometrical frustration can destroy the magnetic order, driving the original antiferromagnetic (AF) phase to non-magnetic valence bond state (VBS). In addition, we found two distinct VBS. As $J_k$ is increased, a phase transition from AF to Kondo paramagnetic (KP) phase occurs, without the intermediate phase coexisting AF order with Kondo screening found in square lattice systems. In the KP phase, the enhancement of frustration weakens the Kondo screening effect, resulting in a phase transition from KP to VBS. We also found a process to recover the AF order from VBS by increasing $J_k$ in a wide range of frustration strength. Our work may provide deeper understanding for the phase transitions in heavy-fermion materials, particularly for those exhibiting triangular frustration

Worldwide genetic variation of the IGHV and TRBV immune receptor gene families in humans.

The immunoglobulin heavy variable (IGHV) and T cell beta variable (TRBV) loci are among the most complex and variable regions in the human genome. Generated through a process of gene duplication/deletion and diversification, these loci can vary extensively between individuals in copy number and contain genes that are highly similar, making their analysis technically challenging. Here, we present a comprehensive study of the functional gene segments in the IGHV and TRBV loci, quantifying their copy number and single-nucleotide variation in a globally diverse sample of 109 (IGHV) and 286 (TRBV) humans from over a 100 populations. We find that the IGHV and TRBV gene families exhibit starkly different patterns of variation. In addition to providing insight into the different evolutionary paths of the IGHV and TRBV loci, our results are also important to the adaptive immune repertoire sequencing community, where the lack of frequencies of common alleles and copy number variants is hampering existing analytical pipelines

Polyoxometalate (POM)-layered double hydroxides (LDH) composite materials: design and catalytic applications

Layered double hydroxides (LDHs) are an important large class of two-dimensional (2D) anionic lamellar materials that possess flexible modular structure, facile exchangeability of inter-lamellar guest anions and uniform distribution of metal cations in the layer. Owing to the modular accessible gallery and unique inter-lamellar chemical environment, polyoxometalates (POMs) intercalated with LDHs has shown a vast array of physical properties with applications in environment, energy, catalysis, etc. Here we describe how polyoxometalate clusters can be used as building components for the construction of systems with important catalytic properties. This review article mainly focuses on the discussion of new synthetic approaches developed recently that allow the incorporation of the element of design in the construction of a fundamentally new class of materials with pre-defined functionalities in catalytic applications. Introducing the element of design and taking control over the finally observed functionality we demonstrate the unique opportunity for engineering materials with modular properties for specific catalytic applications

Self-adaptive GA, quantitative semantic similarity measures and ontology-based text clustering

As the common clustering algorithms use vector space model (VSM) to represent document, the conceptual relationships between related terms which do not co-occur literally are ignored. A genetic algorithm-based clustering technique, named GA clustering, in conjunction with ontology is proposed in this article to overcome this problem. In general, the ontology measures can be partitioned into two categories: thesaurus-based methods and corpus-based methods. We take advantage of the hierarchical structure and the broad coverage taxonomy of Wordnet as the thesaurus-based ontology. However, the corpus-based method is rather complicated to handle in practical application. We propose a transformed latent semantic analysis (LSA) model as the corpus-based method in this paper. Moreover, two hybrid strategies, the combinations of the various similarity measures, are implemented in the clustering experiments. The results show that our GA clustering algorithm, in conjunction with the thesaurus-based and the LSA-based method, apparently outperforms that with other similarity measures. Moreover, the superiority of the GA clustering algorithm proposed over the commonly used k-means algorithm and the standard GA is demonstrated by the improvements of the clustering performance

Measurable Concurrence of Mixed States

We show that bipartite concurrence for rank-2 mixed states of qubits is written by an observable which can be exactly and directly measurable in experiment by local projective measurements, provided that four copies of the composite quantum system are available. In addition, for a tripartite quantum pure state of qubits, the 3-tangle is also shown to be measurable only by projective measurements on the reduced density matrices of a pair of qubits conditioned on four copies of the state.Comment: 3 page

Multifractal analysis of weighted networks by a modified sandbox algorithm

Complex networks have attracted growing attention in many fields. As a generalization of fractal analysis, multifractal analysis (MFA) is a useful way to systematically describe the spatial heterogeneity of both theoretical and experimental fractal patterns. Some algorithms for MFA of unweighted complex networks have been proposed in the past a few years, including the sandbox (SB) algorithm recently employed by our group. In this paper, a modified SB algorithm (we call it SBw algorithm) is proposed for MFA of weighted networks.First, we use the SBw algorithm to study the multifractal property of two families of weighted fractal networks (WFNs): "Sierpinski" WFNs and "Cantor dust" WFNs. We also discuss how the fractal dimension and generalized fractal dimensions change with the edge-weights of the WFN. From the comparison between the theoretical and numerical fractal dimensions of these networks, we can find that the proposed SBw algorithm is efficient and feasible for MFA of weighted networks. Then, we apply the SBw algorithm to study multifractal properties of some real weighted networks ---collaboration networks. It is found that the multifractality exists in these weighted networks, and is affected by their edge-weights.Comment: 15 pages, 6 figures. Accepted for publication by Scientific Report