Mirror symmetry for parabolic Higgs bundles via p-adic integration
February 6, 2023
Mathematics
Algebraic Geometry
Representation Theory
Applying the technique of p-adic integration, we prove the topological
mirror symmetry conjecture of Hausel-Thaddeus for the moduli spaces of
(strongly) parabolic Higgs bundles for the structure groups SLn and
PGLn, bu...
Emergent Causality and the Foundation of Consciousness
February 6, 2023
Computer Science
Artificial Intelligence
To make accurate inferences in an interactive setting, an agent must not
confuse passive observation of events with having intervened to cause them. The
do operator formalises interventions so that we may reason about their
effect. Yet th...
Matrix factorizations and pentagon maps
February 6, 2023
Physics
Mathematics
Exactly Solvable and Integrable Systems
Mathematical Physics
Mathematical Physics
We propose a specific class of matrices which participate in factorization
problems that turn to be equivalent to constant and entwining (non-constant)
pentagon, reverse-pentagon or Yang-Baxter maps, expressed in non-commutative
variables. ...
Random Forests for time-fixed and time-dependent predictors: The
DynForest R package
February 6, 2023
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Statistics
Computer Science
Machine Learning
Machine Learning
The R package DynForest implements random forests for predicting a
continuous, a categorical or a (multiple causes) time-to-event outcome based on
time-fixed and time-dependent predictors. The main originality of DynForest is
that it handle...
Short proofs of ideal membership
February 6, 2023
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Computer Science
Symbolic Computation
A cofactor representation of an ideal element, that is, a representation in
terms of the generators, can be considered as a certificate for ideal
membership. Such a representation is typically not unique, and some can be a
lot more complica...
Limiting distributions of conjugate algebraic integers
February 6, 2023
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Mathematics
Number Theory
Let Σ⊂C be a compact subset of the complex plane, and
μ be a probability distribution on Σ. We give necessary and
sufficient conditions for μ to be the weak* limit of a sequence of uniform
probability ...
Less is More: Understanding Word-level Textual Adversarial Attack via
n-gram Frequency Descend
February 6, 2023
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Computer Science
Computation and Language
Artificial Intelligence
Cryptography and Security
Machine Learning
Word-level textual adversarial attacks have demonstrated notable efficacy in
misleading Natural Language Processing (NLP) models. Despite their success, the
underlying reasons for their effectiveness and the fundamental characteristics
of a...
Congruence classes for modular forms over small sets
February 6, 2023
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Mathematics
Number Theory
J.P. Serre showed that for any integer m,a(n)≡0(modm) for almost
all n, where a(n) is the nth Fourier coefficient of any modular
form with rational coefficients. In this article, we consider a certain class
of cus...
Phase transitions induced by standard and predetermined measurements in
transmon arrays
February 6, 2023
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Physics
Quantum Physics
The confluence of unitary dynamics and non-unitary measurements gives rise to
intriguing and relevant phenomena, generally referred to as measurement-induced
phase transitions. These transitions have been observed in quantum systems
compose...
An Implicit GNN Solver for Poisson-like problems
February 6, 2023
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Computer Science
Mathematics
Machine Learning
Artificial Intelligence
Analysis of PDEs
This paper presents Ψ-GNN, a novel Graph Neural Network (GNN) approach
for solving the ubiquitous Poisson PDE problems with mixed boundary conditions.
By leveraging the Implicit Layer Theory, Ψ-GNN models an "infinitely" deep
netw...