On the Symbol Length of Fields with finite Square Class Number
January 29, 2021
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Mathematics
Number Theory
Let F be a field of characteristic not 2 with finitely many square
classes. Using combinatorial arguments applied to objects related to vector
spaces over finite fields, we deduce an upper bound for the number of Pfister
forms over F....
Private DNA Sequencing: Hiding Information in Discrete Noise
January 28, 2021
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Computer Science
Mathematics
Information Theory
Cryptography and Security
Information Theory
When an individual's DNA is sequenced, sensitive medical information becomes
available to the sequencing laboratory. A recently proposed way to hide an
individual's genetic information is to mix in DNA samples of other individuals.
We assum...
New notions of simultaneous diagonalizability of quadratic forms with
applications to QCQPs
January 28, 2021
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Mathematics
Optimization and Control
A set of quadratic forms is simultaneously diagonalizable via congruence
(SDC) if there exists a basis under which each of the quadratic forms is
diagonal. This property appears naturally when analyzing quadratically
constrained quadratic p...
Diagonal flow detects topology of strata
January 28, 2021
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Mathematics
Dynamical Systems
We study the interplay between the diagonal flow on, and the topology of, a
stratum component of a space of rooted quadratic differentials. We prove that
the flow group -- the subgroup of the fundamental group generated by
almost-flow loops...
Approximation Theory of Tree Tensor Networks: Tensorized Multivariate
Functions
January 28, 2021
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Mathematics
Computer Science
Functional Analysis
Machine Learning
Numerical Analysis
Numerical Analysis
We study the approximation of multivariate functions with tensor networks
(TNs). The main conclusion of this work is an answer to the following two
questions: ``What are the approximation capabilities of TNs?" and "What is an
appropriate mo...
Characterization of Non-Deterministic Chaos in Two-Dimensional
Non-Smooth Vector Fields
January 28, 2021
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Mathematics
Dynamical Systems
Our context is Filippov systems defined on two-dimensional manifolds having a
finite number of tangency points. We prove that topological transitivity is a
necessary and sufficient condition for the occurrence of non-deterministic
chaos whe...
Asmptotic of the eigenvalues of Toeplitz matrices with even symbol
January 27, 2021
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Mathematics
Classical Analysis and ODEs
Operator Algebras
Spectral Theory
Classical Analysis and ODEs
Operator Algebras
Spectral Theory
In this paper we consider an interval [θ1,θ2]⊂[0,π] and f a differentiable, periodic and even function sufficiently smooth
such that $f(\theta) \in [f(\theta_{1}, f(\theta_{2})] \iff \theta \in
[\theta_{1}, \...
Geometric Satake equivalence in mixed characteristic and Springer
correspondence
January 27, 2021
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Mathematics
Number Theory
Algebraic Geometry
Representation Theory
Number Theory
Algebraic Geometry
Representation Theory
The geometric Satake equivalence and the Springer correspondence are closely
related when restricting to small representations of the Langlands dual group.
We prove this result for \'etale sheaves, including the case of the mixed
characteri...
Monodromy methods for torus conformal blocks and entanglement entropy at
large central charge
January 27, 2021
Physics
High Energy Physics - Theory
We compute the entanglement entropy in a two dimensional conformal field
theory at finite size and finite temperature in the large central charge limit
via the replica trick. We first generalize the known monodromy method for the
calculatio...
The local weak limit of k-dimensional hypertrees
January 27, 2021
Mathematics
Combinatorics
Probability
Let C(n,k) be the set of k-dimensional simplicial complexes C
over a fixed set of n vertices such that:
(1) C has a complete k−1-skeleton;
(2) C has precisely (kn−1)k-faces;
(3) the homology gr...