Quantitative fluctuation analysis of multiscale diffusion systems via
Malliavin calculus
January 21, 2023
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Mathematics
Probability
We study fluctuations of small noise multiscale diffusions around their
homogenized deterministic limit. We derive quantitative rates of convergence of
the fluctuation processes to their Gaussian limits in the appropriate
Wasserstein metric...
Inference for Two-stage Experiments under Covariate-Adaptive
Randomization
January 21, 2023
Economics
Statistics
Econometrics
Methodology
This paper studies inference in two-stage randomized experiments under
covariate-adaptive randomization. In the initial stage of this experimental
design, clusters (e.g., households, schools, or graph partitions) are
stratified and randomly...
CodeScore: Evaluating Code Generation by Learning Code Execution
January 21, 2023
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Computer Science
Software Engineering
A proper code evaluation metric (CEM) profoundly impacts the evolution of
code generation, which is an important research field in NLP and software
engineering. Prevailing match-based CEMs (e.g., BLEU, Accuracy, and CodeBLEU)
suffer from tw...
Infinite-dimensional port-Hamiltonian systems with a stationary
interface
January 21, 2023
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Mathematics
Analysis of PDEs
Optimization and Control
We consider two systems of two conservation laws that are defined on
complementary spatial intervals and coupled by an interface as a single
port-Hamiltonian system. In case of a fixed interface position, we characterize
the boundary and in...
A high order unfitted finite element method for time-Harmonic Maxwell
interface problems
January 21, 2023
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Mathematics
Computer Science
Numerical Analysis
Numerical Analysis
We propose a high order unfitted finite element method for solving
timeharmonic Maxwell interface problems. The unfitted finite element method is
based on a mixed formulation in the discontinuous Galerkin framework on a
Cartesian mesh with ...
Improving Signed Propagation of Graph Neural Network Under Multiple
Classes
January 21, 2023
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Computer Science
Machine Learning
Social and Information Networks
Message-passing Graph Neural Networks (GNNs), which collect information from
adjacent nodes achieve dismal performance on heterophilic graphs. Various
schemes have been proposed to solve this problem, and propagating signed
information on h...
The Euler Characteristic of Finite Categories
January 21, 2023
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Mathematics
Category Theory
We associate a rational number χ(A) to every category
A whose object and morphism sets are finite. We show that the
assignment χ is additive under disjoint union and it preserves products.
Hence we consider $...
The Conditional Cauchy-Schwarz Divergence with Applications to
Time-Series Data and Sequential Decision Making
January 21, 2023
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Computer Science
Mathematics
Statistics
Machine Learning
Information Theory
Information Theory
Machine Learning
The Cauchy-Schwarz (CS) divergence was developed by Pr\'{i}ncipe et al. in
2000. In this paper, we extend the classic CS divergence to quantify the
closeness between two conditional distributions and show that the developed
conditional CS d...
The Gysin braid for S3-actions on manifolds
January 21, 2023
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Mathematics
Algebraic Topology
Given a smooth action of the sphere S3 on a manifold M, we have
previously constructed a Gysin sequence relating the cohomology of the manifold
M and that of the orbit space M/S3. This sequence involves an
exotic t...
A central limit theorem for a sequence of conditionally centered and
α-mixing random fields
January 21, 2023
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Mathematics
Statistics
Probability
Statistics Theory
Statistics Theory
A central limit theorem is established for a sum of random variables
belonging to a sequence of random fields. The fields are assumed to have zero
mean conditional on the past history and to satisfy certain conditional
α-mixing condi...