56,852 research outputs found
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
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
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