Can Temporal-Difference and Q-Learning Learn Representation? A
Mean-Field Theory
June 8, 2020
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Computer Science
Mathematics
Statistics
Machine Learning
Optimization and Control
Machine Learning
Temporal-difference and Q-learning play a key role in deep reinforcement
learning, where they are empowered by expressive nonlinear function
approximators such as neural networks. At the core of their empirical successes
is the learned feat...
Generalized Lorenz Systems Family
June 7, 2020
Physics
Chaotic Dynamics
This article briefly introduces the generalized Lorenz systems family, which
includes the classical Lorenz system and the relatively new Chen system as
special cases, with infinitely many related but not topologically equivalent
chaotic sys...
Surgery and Excision for Furuta-Ohta invariants on Homology S1×S3
June 7, 2020
Mathematics
Geometric Topology
We prove a surgery formula and an excision formula for the Furuta-Ohta
invariant λFO defined on homology S1×S3, which provides
more evidence on its equivalence with the Casson-Seiberg-Witten invariant
λSW. T...
Archimedean Zeta Integrals for Unitary Groups
June 7, 2020
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Mathematics
Number Theory
Representation Theory
We derive precise formulas for the archimedean Euler factors occurring in
certain standard Langlands L-functions for unitary groups. In the 1980s, Paul
Garrett, as well as Ilya Piatetski-Shapiro and Stephen Rallis (independently of
Garret...
Gordon decomposition of the magnetizability of a Dirac one-electron atom
in an arbitrary discrete energy state
June 6, 2020
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Physics
Quantum Physics
Quantum Physics
We present a Gordon decomposition of the magnetizability of a Dirac
one-electron atom in an arbitrary discrete energy eigenstate, with a pointlike,
spinless, and motionless nucleus of charge Ze. The external magnetic field,
by which the a...
Vector TSP: A Traveling Salesperson Problem with Racetrack-like
Acceleration Constraints
June 5, 2020
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Computer Science
Mathematics
Data Structures and Algorithms
Computational Complexity
Combinatorics
Data Structures and Algorithms
Computational Complexity
Combinatorics
We study a new version of the Traveling Salesperson Problem, called
\VectorTSP, where the traveler is subject to discrete acceleration constraints,
as defined in the paper-and-pencil game Racetrack (also known as Vector Racer).
In this mode...
The precise regularity of the Lyapunov exponent for C2 Cos-type
quasiperiodic Schr\"odinger cocycles with large couplings
June 5, 2020
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Mathematics
Dynamical Systems
Dynamical Systems
In this paper, we study the regularity of the Lyapunov exponent for
quasiperiodic Schr\"odinger cocycles with C2 cos-type potentials, large
coupling constants, and a fixed Diophantine frequency. We obtain the absolute
continuity of the L...
A tourist's guide to regularity structures and singular stochastic PDEs
June 5, 2020
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Mathematics
Analysis of PDEs
Classical Analysis and ODEs
We give an essentially self-contained treatment of the fundamental analytic
and algebraic features of regularity structures and its applications to the
study of singular stochastic PDEs....
An improved lower bound of Heilbronn's triangle problem
June 5, 2020
Mathematics
Number Theory
Using the method of compression we improve on the current lower bound of
Heilbronn's triangle problem. In particular, by letting Δ(s) denotes the
minimal area of the triangle induced by s points in a unit disc. Then we have
the low...
Multiple ergodic averages along functions from a Hardy field:
convergence, recurrence and combinatorial applications
June 5, 2020
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Mathematics
Combinatorics
Dynamical Systems
We obtain new results pertaining to convergence and recurrence of multiple
ergodic averages along functions from a Hardy field. Among other things, we
confirm some of the conjectures posed by Frantzikinakis in [Fra10; Fra16] and
obtain comb...