Reinterpreting the Middle-Levels Theorem via Natural Enumeration of
Ordered Trees
November 5, 2019
Mathematics
Combinatorics
Let 0<k∈Z. A reinterpretation of the proof of existence of
Hamilton cycles in the middle-levels graph Mk induced by the vertices of the
(2k+1)-cube representing the k- and (k+1)-subsets of {0,…,2k} is
given vi...
Intriguing Properties of Adversarial ML Attacks in the Problem Space
[Extended Version]
November 5, 2019
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Computer Science
Cryptography and Security
Machine Learning
Recent research efforts on adversarial machine learning (ML) have
investigated problem-space attacks, focusing on the generation of real evasive
objects in domains where, unlike images, there is no clear inverse mapping to
the feature space...
Strichartz estimates and low-regularity solutions to multiplicative
stochastic NLS
November 5, 2019
Mathematics
Analysis of PDEs
Probability
We study Strichartz estimates with very rough potentials, the spatial white
noise on the 2 dimensional torus being of particular interest. Applications
include solving the multiplicative stochastic NLS with general integer powers
in a low-r...
Sarnak's conjecture in quantum computing, cyclotomic unitary group
coranks, and Shimura curves
November 5, 2019
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Mathematics
Number Theory
Group Theory
Sarnak's conjecture in quantum computing concerns when the groups
PU2 and PSU2 over cyclotomic rings
Z[ζn,1/2] with ζn=e2πi/n, 4∣n, are generated by
the Clifford-cyclotomic...
Controllability and Vector Potential
November 4, 2019
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Mathematics
Computer Science
Electrical Engineering and Systems Science
Optimization and Control
Systems and Control
Systems and Control
Optimization and Control
Systems and Control
Systems and Control
Kalman's fundamental notion of a controllable state space system \cite{k} has
been generalised to higher order systems by Willems \cite{w}, and further to
distributed systems defined by partial differential equations \cite{ps}. It
turns out...
A discrete version of Liouville's theorem on conformal maps
November 3, 2019
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Mathematics
Differential Geometry
Combinatorics
Complex Variables
Geometric Topology
Differential Geometry
Combinatorics
Complex Variables
Geometric Topology
Liouville's theorem says that in dimension greater than two, all conformal
maps are M\"obius transformations. We prove an analogous statement about
simplicial complexes, where two simplicial complexes are considered discretely
conformally e...
Homotopy of product systems and K-theory of Cuntz-Nica-Pimsner algebras
November 3, 2019
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Mathematics
Operator Algebras
We introduce the notion of a homotopy of product systems, and show that the
Cuntz-Nica-Pimsner algebras of homotopic product systems over N^k have
isomorphic K-theory. As an application, we give a new proof that the K-theory
of a 2-graph C*...
Continuous and coherent actions on wrapped Fukaya categories
November 1, 2019
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Mathematics
Symplectic Geometry
Algebraic Topology
We establish the continuous functoriality of wrapped Fukaya categories with
respect to Liouville automorphisms, yielding a way to probe the homotopy type
of the automorphism group of a Liouville sector. These methods prove Liouville
and mon...
Convergence of a damped Newton's method for discrete Monge-Ampere
functions with a prescribed asymptotic cone
November 1, 2019
Mathematics
Computer Science
Numerical Analysis
Numerical Analysis
We prove the convergence of a damped Newton's method for the nonlinear system
resulting from a discretization of the second boundary value problem for the
Monge-Ampere equation. The boundary condition is enforced through the use of
the noti...
Entropy-stable positivity-preserving DG schemes for Boltzmann-Poisson
models of collisional electronic transport along energy bands
November 1, 2019
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Mathematics
Computer Science
Physics
Numerical Analysis
Numerical Analysis
Computational Physics
This work is related to developing entropy-stable positivity-preserving
Discontinuous Galerkin (DG) methods as a computational scheme for
Boltzmann-Poisson systems modeling the probability density of collisional
electronic transport along s...