Sharp and rigid isoperimetric inequality in metric measure spaces with
non-negative Ricci curvature
December 22, 2022
Mathematics
Metric Geometry
Functional Analysis
By using optimal transport theory, we prove a sharp dimension-free
isoperimetric inequality involving the volume entropy, in metric measure spaces
with non-negative Ricci curvature in the sense of Lott--Sturm--Villani. We show
that this iso...
An introduction to variational quantum algorithms for combinatorial
optimization problems
December 22, 2022
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Mathematics
Physics
Optimization and Control
Quantum Physics
Noisy intermediate-scale quantum computers (NISQ computers) are now readily
available, motivating many researchers to experiment with Variational Quantum
Algorithms (VQAs). Among them, the Quantum Approximate Optimization Algorithm
(QAOA) i...
Sum and Tensor of Quantitative Effects
December 22, 2022
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Computer Science
Logic in Computer Science
Inspired by the seminal work of Hyland, Plotkin, and Power on the combination
of algebraic computational effects via sum and tensor, we develop an analogous
theory for the combination of quantitative algebraic effects. Quantitative
algebrai...
Channel Simulation: Finite Blocklengths and Broadcast Channels
December 22, 2022
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Computer Science
Mathematics
Physics
Information Theory
Information Theory
Quantum Physics
We study channel simulation under common randomness assistance in the
finite-blocklength regime and identify the smooth channel max-information as a
linear program one-shot converse on the minimal simulation cost for fixed error
tolerance. ...
Modeling Heat Conduction with Dual-Dissipative Variables: A
Mechanism-Data Fusion Method
December 22, 2022
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Physics
Computational Physics
Many macroscopic non-Fourier heat conduction models have been developed in
the past decades based on Chapman-Enskog, Hermite or other small perturbation
expansion methods. These macroscopic models have made great success on
capturing non-Fo...
Frequency Stability-Constrained Unit Commitment: Tight Approximation
using Bernstein Polynomials
December 22, 2022
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Electrical Engineering and Systems Science
Computer Science
Mathematics
Systems and Control
Systems and Control
Optimization and Control
Systems and Control
Systems and Control
Optimization and Control
As we replace conventional synchronous generators with renewable energy, the
frequency security of power systems is at higher risk. This calls for a more
careful consideration of unit commitment (UC) and primary frequency response
(PFR) res...
Global Kuranishi charts and a product formula in symplectic
Gromov-Witten theory
December 22, 2022
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Mathematics
Symplectic Geometry
Algebraic Geometry
Symplectic Geometry
Algebraic Geometry
We construct global Kuranishi charts for the moduli spaces of stable
pseudoholomorphic maps to a closed symplectic manifold in all genera. This is
used to prove a product formula for symplectic Gromov-Witten invariants. As a
consequence we ...
Stability via closure relations with applications to dissipative and
port-Hamiltonian systems
December 22, 2022
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Mathematics
Functional Analysis
Optimization and Control
We consider differential operators A that can be represented by means of a
so-called closure relation in terms of a simpler operator
Aext defined on a larger space. We analyze how the spectral
properties of A and $A_...
Potential Singularity of the Axisymmetric Euler Equations with
Cα Initial Vorticity for A Large Range of α. Part II: the
N-Dimensional Case
December 22, 2022
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Mathematics
Computer Science
Analysis of PDEs
Numerical Analysis
Numerical Analysis
In Part II of this sequence to our previous paper for the 3-dimensional Euler
equations \cite{zhang2022potential}, we investigate potential singularity of
the n-diemnsional axisymmetric Euler equations with Cα initial
vorticity fo...
Potential Singularity of the Axisymmetric Euler Equations with
Cα Initial Vorticity for A Large Range of α
December 22, 2022
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Mathematics
Computer Science
Analysis of PDEs
Numerical Analysis
Numerical Analysis
We provide numerical evidence for a potential finite-time self-similar
singularity of the 3D axisymmetric Euler equations with no swirl and with
Cα initial vorticity for a large range of α. We employ a highly
effective adapti...