Scalar and Spinor Effective Actions in Global de Sitter

In this paper, we compute the effective action of both a scalar field and a Dirac spinor field in the global de Sitter space of any dimension $d$ using the in-/out-state formalism. We show that there is particle production in even dimensions for both scalar field and spinor field. The in-out vacuum amplitude $Z_{in/out}$ is divergent at late times. By using dimensional regularization, we extract the finite part of $\log Z_{in/out}$ for $d$ even and the logarithmically divergent part of $\log Z_{in/out}$ for $d$ odd. We also find that the regularized in-out vacuum amplitude equals the ratio of determinants associated with different quantizations in $AdS_d$ upon the identification of certain parameters in the two theories.Comment: 27 pages; typos correcte

Effects of Home Resources and School Environment on Eighth-Grade Mathematics Achievement in Taiwan

Over the past decades, researchers have explored the relationship among home resources, school environment, and students' mathematics achievement in a large amount of studies. Many of them suggested that rich home resources for learning were related to higher average academic achievement. Some also suggested that the home background was closely associated with the learning environment, and therefore, influenced students' achievements. Thus, this study hypothesized that students who own more home resources would perform better than students who possess fewer resources and that schools that have more socioeconomically advantaged students, located in high-income neighborhoods, and possess more instructional resources would have better mathematics performance. The study focuses on eighth graders in Taiwan and explores the variance in mathematics achievement of students as a function of student and school level differences

Rasch Analysis of the Mathematics Self Concept Questionnaire

TIMSS & PIRLS International Study Center is a research center at Boston College that conducts a series of assessments in a number of countries to measure trends in mathematics and science achievement at the fourth and eighth grades. In general, TIMSS assessments include achievement tests as well as questionnaires for student, parent, teacher, school, and curricular. There are 63 participating countries and 14 benchmarking participants in TIMSS 2011, including 608,641 students, 49,429 teachers, 19,612 school principals, and the National Research Coordinators of each country. TIMSS data are valuable for researchers and analysts from all over the world, especially for those from participating countries, to conduct related studies to improve education

Distribution-Free, Size Adaptive Submatrix Detection with Acceleration

Given a large matrix containing independent data entries, we consider the problem of detecting a submatrix inside the data matrix that contains larger-than-usual values. Different from previous literature, we do not have exact information about the dimension of the potential elevated submatrix. We propose a Bonferroni type testing procedure based on permutation tests, and show that our proposed test loses no first-order asymptotic power compared to tests with full knowledge of potential elevated submatrix. In order to speed up the calculation during the test, an approximation net is constructed and we show that Bonferroni type permutation test on the approximation net loses no power on the first order asymptotically

Stochastic Perron for stochastic target games

We extend the stochastic Perron method to analyze the framework of stochastic target games, in which one player tries to find a strategy such that the state process almost surely reaches a given target no matter which action is chosen by the other player. Within this framework, our method produces a viscosity sub-solution (super-solution) of a Hamilton-Jacobi-Bellman (HJB) equation. We then characterize the value function as a viscosity solution to the HJB equation using a comparison result and a byproduct to obtain the dynamic programming principle.Comment: Published at http://dx.doi.org/10.1214/15-AAP1112 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Long-time asymptotics of the modified KdV equation in weighted Sobolev spaces

The long time behavior of solutions to the defocusing modified Korteweg-de vries (MKdV) equation is established for initial conditions in some weighted Sobolev spaces. Our approach is based on the nonlinear steepest descent method of Deift and Zhou and its reformulation by Dieng and McLaughlin through $\overline{\partial}$-derivatives. To extend the asymptotics to solutions with initial data in lower regularity spaces, we apply a global approximation via PDE techniques.Comment: 51 page

Asynchronous Decentralized Optimization in Directed Networks

A popular asynchronous protocol for decentralized optimization is randomized gossip where a pair of neighbors concurrently update via pairwise averaging. In practice, this creates deadlocks and is vulnerable to information delays. It can also be problematic if a node is unable to response or has only access to its private-preserved local dataset. To address these issues simultaneously, this paper proposes an asynchronous decentralized algorithm, i.e. APPG, with {\em directed} communication where each node updates {\em asynchronously} and independently of any other node. If local functions are strongly-convex with Lipschitz-continuous gradients, each node of APPG converges to the same optimal solution at a rate of $O(\lambda^k)$, where $\lambda\in(0,1)$ and the virtual counter $k$ increases by 1 no matter on which node updates. The superior performance of APPG is validated on a logistic regression problem against state-of-the-art methods in terms of linear speedup and system implementations

Stochastic Perron for Stochastic Target Problems

In this paper, we adapt stochastic Perron's method to analyze a stochastic target problem with unbounded controls in a jump diffusion set-up. With this method, we construct a viscosity sub-solution and super-solution to the associated Hamiltonian-Jacobi-Bellman (HJB) equations. Under comparison principles, uniqueness of the viscosity solutions holds and the value function coincides with the unique solution in the parabolic interior. Since classical control problems can be analyzed under the framework of stochastic target problems (with unbounded controls), we use our results to generalize the results in ArXiv:1212.2170 to problems with controlled jumps.Comment: Final version. To appear in the Journal of Optimization Theory and Applications. Keywords: The stochastic target problem, stochastic Perron's method, jump-diffusion processes, viscosity solutions, unbounded control

MPO: An Efficient and Low-cost Peer-to-Peer Overlay for Autonomic Communications

The term Autonomic Communication (AC) refers to self-managing systems which are capable of supporting self-configuration, self-healing and self-optimization. However, information reflection and collection, lack of centralized control, non-cooperation and so on are just some of the challenges within AC systems. We have considered these problems in theory and practice and reached the following conclusion; in order to build an ideal system for autonomic communication, there are three key problems to be solved. Motivated by the need for AC, we have designed an efficient and low-cost Peer-to-Peer (P2P) overlay called Maya-Pyramid overlay (MPO) and combined merits of unstructured P2P with those of structured P2P overlays. Differing from the traditional hierarchical P2P (i.e. tree-like structure) overlay, (1) MPO is composed of levels and layers, which uses small world characteristic to improve efficiency, and the maintenance cost is decreased because update and backup only take place in two neighboring levels or layers instead of recursively perform in higher levels. (2) Unlike normal redundant mechanisms for solving the single fault problem: Tri-Information Center (Tri-IC) mechanism is presented in order to improve robustness by alleviating the load of cluster heads in a hierarchical P2P overlay. (3) A source ranking mechanism is proposed in order to discourage free riding and whitewashing and to encourage frequent information exchanges between peers. (4) Inspired by Pastry's ID structure for a structured DHT algorithm, a 3D unique ID structure is presented in the unstructured P2P overlay. This will guarantee anonymity in routing, and will be, not only more efficient because it applies the DHT-like routing algorithm in the unstructured P2P overlay, but also more adaptive to suit AC. Evaluation proved that MPO is robust, highly efficient and of a low-cost.Comment: 37 pages,9 figures,37 reference

Hierarchical Attention Generative Adversarial Networks for Cross-domain Sentiment Classification

Cross-domain sentiment classification (CDSC) is an importance task in domain adaptation and sentiment classification. Due to the domain discrepancy, a sentiment classifier trained on source domain data may not works well on target domain data. In recent years, many researchers have used deep neural network models for cross-domain sentiment classification task, many of which use Gradient Reversal Layer (GRL) to design an adversarial network structure to train a domain-shared sentiment classifier. Different from those methods, we proposed Hierarchical Attention Generative Adversarial Networks (HAGAN) which alternately trains a generator and a discriminator in order to produce a document representation which is sentiment-distinguishable but domain-indistinguishable. Besides, the HAGAN model applies Bidirectional Gated Recurrent Unit (Bi-GRU) to encode the contextual information of a word and a sentence into the document representation. In addition, the HAGAN model use hierarchical attention mechanism to optimize the document representation and automatically capture the pivots and non-pivots. The experiments on Amazon review dataset show the effectiveness of HAGAN