We study the three dimensional stochastic Zakharov system in the energy
space, where the Schr\"odinger equation is driven by linear multiplicative
noise and the wave equation is driven by additive noise. We prove the
well-posedness of the s...
Monotonicity of the period and positive periodic solutions of a
quasilinear equation
January 5, 2023
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Mathematics
Analysis of PDEs
Classical Analysis and ODEs
We investigate the monotonicity of the minimal period of the periodic
solutions of some quasilinear differential equations involving the p-Laplace
operator. The monotonicity is obtained as a function of a Hamiltonian energy in
two cases. ...
EPR-Net: Constructing non-equilibrium potential landscape via a
variational force projection formulation
January 5, 2023
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Physics
Computer Science
Biological Physics
Statistical Mechanics
Artificial Intelligence
Computational Physics
We present EPR-Net, a novel and effective deep learning approach that tackles
a crucial challenge in biophysics: constructing potential landscapes for
high-dimensional non-equilibrium steady-state (NESS) systems. EPR-Net leverages
a nice ma...
Beyond Inverted Pendulums: Task-optimal Simple Models of Legged
Locomotion
January 5, 2023
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Computer Science
Robotics
Reduced-order models (ROM) are popular in online motion planning due to their
simplicity. A good ROM for control captures critical task-relevant aspects of
the full dynamics while remaining low dimensional. However, planning within the
redu...
A Streamline upwind Petrov-Galerkin Reduced Order Method for
Advection-Dominated Partial Differential Equations under Optimal Control
January 5, 2023
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Mathematics
Computer Science
Numerical Analysis
Numerical Analysis
In this paper we will consider distributed Linear-Quadratic Optimal Control
Problems dealing with Advection-Diffusion PDEs for high values of the P\'eclet
number. In this situation, computational instabilities occur, both for steady
and uns...
Lessons from Formally Verified Deployed Software Systems (Extended
version)
January 5, 2023
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Computer Science
Software Engineering
The technology of formal software verification has made spectacular advances,
but how much does it actually benefit the development of practical software?
Considerable disagreement remains about the practicality of building systems
with mec...
On 1/2 estimate for global Newlander-Nirenberg theorem
January 5, 2023
Mathematics
Complex Variables
Differential Geometry
Given a formally integrable almost complex structure X defined on the
closure of a bounded domain D⊂Cn, and provided that X is
sufficiently close to the standard complex structure, the global
Newlander-Nirenberg probl...
Linear response due to singularities
January 5, 2023
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Mathematics
Physics
Dynamical Systems
Chaotic Dynamics
It is well known that a family of tent-like maps with bounded derivatives has
no linear response for typical deterministic perturbations changing the value
of the turning point. In this note we prove the following result: if we
consider a t...
Generalized Symmetries and Anomalies of 3d N=4 SCFTs
January 5, 2023
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Physics
High Energy Physics - Theory
We study generalized global symmetries and their 't Hooft anomalies in 3d N=4
superconformal field theories (SCFTs). Following some general considerations,
we focus on good quiver gauge theories, comprised of balanced unitary nodes and
unba...
Optimal lower bounds for Quantum Learning via Information Theory
January 5, 2023
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Mathematics
Computer Science
Physics
Information Theory
Machine Learning
Information Theory
Computational Complexity
Quantum Physics
Although a concept class may be learnt more efficiently using quantum samples
as compared with classical samples in certain scenarios, Arunachalam and de
Wolf (JMLR, 2018) proved that quantum learners are asymptotically no more
efficient th...