Localization of Rota-Baxter algebras

A commutative Rota-Baxter algebra can be regarded as a commutative algebra that carries an abstraction of the integral operator. With the motivation of generalizing the study of algebraic geometry to Rota-Baxter algebra, we extend the central concept of localization for commutative algebras to commutative Rota-Baxter algebras. The existence of such a localization is proved and, under mild conditions, its explicit constructions are obtained. The existence of tensor products of commutative Rota-Baxter algebras is also proved and the compatibility of localization and tensor product of Rota-Baxter algebras is established. We further study Rota-Baxter coverings and show that they form a Gr\"othendieck topology.Comment: 19 page

The simplified weighted sum function and its average sensitivity

In this paper we simplify the definition of the weighted sum Boolean function which used to be inconvenient to compute and use. We show that the new function has essentially the same properties as the previous one. In particular, the bound on the average sensitivity of the weighted sum Boolean function remains unchanged after the simplification.Comment: 9 page

On the Asymptotic Behavior of the Kernel Function in the Generalized Langevin Equation: A One-dimensional lattice model

We present some estimates for the memory kernel function in the generalized Langevin equation, derived using the Mori-Zwanzig formalism from a one-dimensional lattice model, in which the particles interactions are through nearest and second nearest neighbors. The kernel function can be explicitly expressed in a matrix form. The analysis focuses on the decay properties, both spatially and temporally, revealing a power-law behavior in both cases. The dependence on the level of coarse-graining is also studied

The Mori-Zwanzig formalism for the derivation of a fluctuating heat conduction model from molecular dynamics

Energy transport equations are derived directly from full molecular dynamics models as coarse-grained description. With the local energy chosen as the coarse-grained variables, we apply the Mori-Zwanzig formalism to derive a reduced model, in the form of a generalized Langevin equation. A Markovian embedding technique is then introduced to eliminate the history dependence. In sharp contrast to conventional energy transport models, this derivation yields {\it stochastic} dynamics models for the spatially averaged energy. We discuss the approximation of the random force using both additive and multiplicative noises, to ensure the correct statistics of the solution

Small generators of cocompact arithmetic Fuchsian groups

In the study of Fuchsian groups, it is a nontrivial problem to determine a set of generators. Using a dynamical approach we construct for any cocompact arithmetic Fuchsian group a fundamental region in $\mathbf{SL}_2(\mathbb{R})$ from which we determine a set of small generators.Comment: added references and some minor change

Nonlinear Constitutive Models for Nano-scale Heat Conduction

We present a rigorous approach that leads, from a many-particle description, to a nonlinear, stochastic constitutive relation for the modeling of transient heat conduction processes at nanoscale. By enforcing statistical consistency, in that the statistics of the local energy is consistent with that from an all-atom description, we identify the driving force as well as the model parameters in these generalized constitutive models

A Learning based Branch and Bound for Maximum Common Subgraph Problems

Branch-and-bound (BnB) algorithms are widely used to solve combinatorial problems, and the performance crucially depends on its branching heuristic.In this work, we consider a typical problem of maximum common subgraph (MCS), and propose a branching heuristic inspired from reinforcement learning with a goal of reaching a tree leaf as early as possible to greatly reduce the search tree size.Extensive experiments show that our method is beneficial and outperforms current best BnB algorithm for the MCS.Comment: 6 pages, 4 figures, uses ijcai19.st

Optimal Transmit Beamforming for Secure SWIPT in Heterogeneous Networks

This letter investigates the artificial noise aided beamforming design for secure simultaneous wireless information and power transfer (SWIPT) in a two-tier downlink heterogeneous network, where one femtocell is overlaid with one macrocell in co-channel deployment. Each energy receiver (ER) in femtocell can be considered as a potential eaves- dropper for messages intended for information receiver (IR). Our objective is to maximize the secrecy rate at IR subject to the signal-to-interference-plus noise ratio (SINR) requirements of macro users (MUs), transmit power constraint and energy harvesting constraint. Due to the non-convexity of the formulated problem, it cannot be solved directly. Thus, we propose a novel reformulation by using first-order Taylor expansion and successive convex approximation (SCA) techniques. Furthermore, an SCA-based algorithm with low complexity is proposed to arrive at provably convergent solution. Finally, numerical results evaluate the performance of the proposed algorithm.Comment: single column, 10 pages, 3 figure

A Face-to-Face Neural Conversation Model

Neural networks have recently become good at engaging in dialog. However, current approaches are based solely on verbal text, lacking the richness of a real face-to-face conversation. We propose a neural conversation model that aims to read and generate facial gestures alongside with text. This allows our model to adapt its response based on the "mood" of the conversation. In particular, we introduce an RNN encoder-decoder that exploits the movement of facial muscles, as well as the verbal conversation. The decoder consists of two layers, where the lower layer aims at generating the verbal response and coarse facial expressions, while the second layer fills in the subtle gestures, making the generated output more smooth and natural. We train our neural network by having it "watch" 250 movies. We showcase our joint face-text model in generating more natural conversations through automatic metrics and a human study. We demonstrate an example application with a face-to-face chatting avatar.Comment: Published at CVPR 201

MG-WFBP: Efficient Data Communication for Distributed Synchronous SGD Algorithms

Distributed synchronous stochastic gradient descent has been widely used to train deep neural networks on computer clusters. With the increase of computational power, network communications have become one limiting factor on system scalability. In this paper, we observe that many deep neural networks have a large number of layers with only a small amount of data to be communicated. Based on the fact that merging some short communication tasks into a single one may reduce the overall communication time, we formulate an optimization problem to minimize the training iteration time. We develop an optimal solution named merged-gradient WFBP (MG-WFBP) and implement it in our open-source deep learning platform B-Caffe. Our experimental results on an 8-node GPU cluster with 10GbE interconnect and trace-based simulation results on a 64-node cluster both show that the MG-WFBP algorithm can achieve much better scaling efficiency than existing methods WFBP and SyncEASGD.Comment: 9 pages, INFOCOM 201