We introduce the concept of b-suprametric spaces and establish a fixed
point result for mappings satisfying a nonlinear contraction in such spaces.
The obtained result generalizes a fixed point theorem of Czerwik and a recent
result of th...
Non-diversified portfolios with subjective expected utility
April 17, 2023
|
Economics
Theoretical Economics
Diversification is the typical investment strategy of risk-averse agents.
However, non-diversified positions that allocate all resources to a single
asset, state of the world or revenue stream are common too. We show that
whenever finitely ...
On the integrality of locally algebraic representations of
GL2(D)
April 17, 2023
|
Mathematics
Representation Theory
Number Theory
Emerton's theory of Jacquet modules for locally analytic representations
provides necessary conditions for the existence of integral structures in
locally analytic representations. These conditions are also expected to be
sufficient for the...
Star-shaped trajectories of certain billiards around a triangle
April 17, 2023
| |
Mathematics
Dynamical Systems
We explore the triangle outer billiards map in points at infinity in the
hyperbolic plane, focusing on the rotation number. Building on Dogru and
Tabachnikov's work, which established the conditions for triangles where the
rotation number o...
LongForm: Effective Instruction Tuning with Reverse Instructions
April 17, 2023
| | |
Computer Science
Computation and Language
Artificial Intelligence
Machine Learning
Instruction tuning enables language models to more effectively generalize and
better follow user intent. However, obtaining instruction data is costly and
challenging. Prior work employs methods such as expensive human annotation,
crowd-sou...
About the Expressive Power and Complexity of Order-Invariance with Two
Variables
April 17, 2023
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Computer Science
Logic in Computer Science
Order-invariant first-order logic is an extension of first-order logic (FO)
where formulae can make use of a linear order on the structures, under the
proviso that they are order-invariant, i.e. that their truth value is the same
for all li...
Enhancing accuracy with an adaptive discretization for the non-local
integro-partial differential equations involving initial time singularities
April 17, 2023
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Mathematics
Computer Science
Numerical Analysis
Numerical Analysis
This work aims to construct an efficient and highly accurate numerical method
to address the time singularity at t=0 involved in a class of time-fractional
parabolic integro-partial differential equations in one and two dimensions. The
$L...
Two coniveau filtrations and algebraic equivalence over finite fields
April 17, 2023
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Mathematics
Algebraic Geometry
We extend the basic theory of the coniveau and strong coniveau filtrations to
the ℓ-adic setting. By adapting the examples of Benoist--Ottem to the
ℓ-adic context, we show that the two filtrations differ over any
algebraically clo...
Equivariant Tensor Network Potentials
April 17, 2023
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Physics
Computational Physics
Machine-learning interatomic potentials (MLIPs) have made a significant
contribution to the recent progress in the fields of computational materials
and chemistry due to the MLIPs' ability of accurately approximating energy
landscapes of qu...
Preservation of elementarity by tensor products of tracial von Neumann
algebras
April 17, 2023
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Mathematics
Logic
Operator Algebras
Tensoring with type I algebras preserves elementary equivalence in the
category of tracial von Neumann algebras. The proof involves a novel and
general Feferman--Vaught-type theorem for direct integrals of metric
structures....