Sampling Algebra Structures on Minimal Free Resolutions
March 23, 2023
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Mathematics
Commutative Algebra
Ideals in the ring of power series in three variables can be classified based
on algebra structures on their minimal free resolutions. The classification is
incomplete in the sense that it remains open which algebra structures actually
occu...
Medical diffusion on a budget: Textual Inversion for medical image
generation
March 23, 2023
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Computer Science
Electrical Engineering and Systems Science
Computer Vision and Pattern Recognition
Image and Video Processing
Diffusion models for text-to-image generation, known for their efficiency,
accessibility, and quality, have gained popularity. While inference with these
systems on consumer-grade GPUs is increasingly feasible, training from scratch
require...
Search for an Immobile Hider on a Binary Tree with Unreliable Locational
Information
March 23, 2023
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Computer Science
Discrete Mathematics
Adversarial search of a network for an immobile Hider (or target) was
introduced and solved for rooted trees by Gal (1979). In this zero-sum game, a
Hider picks a point to hide on the tree and a Searcher picks a unit speed
trajectory starti...
On the minimal power of q in a Kazhdan-Lusztig polynomial
March 23, 2023
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Mathematics
Combinatorics
Representation Theory
For w in the symmetric group, we provide an exact formula for the smallest
positive power qh(w) appearing in the Kazhdan-Lusztig polynomial
Pe,w(q). We also provide a tight upper bound on h(w) in simply-laced
types, resolving ...
The families of Hamiltonians sharing common symmetry structure
March 23, 2023
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Physics
Mathematics
Mathematical Physics
Mathematical Physics
We describe a general procedure which allows to construct, starting from a
given Hamiltonian, the whole family of new ones sharing the same set of
unparameterized trajectories in phase space. The symmetry structure of this
family can be com...
Arrested on heating: controlling the motility of active droplets by
temperature
March 23, 2023
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Physics
Fluid Dynamics
Soft Condensed Matter
Self-propelling active matter relies on the conversion of energy from the
undirected, nanoscopic scale to directed, macroscopic motion. One of the
challenges in the design of synthetic active matter lies in the control of
dynamic states, or...
Persuaded Search
March 23, 2023
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Economics
Theoretical Economics
We consider sequential search by an agent who cannot observe the quality of
goods but can acquire information by buying signals from a profit-maximizing
principal with limited commitment power. The principal can charge higher prices
for mor...
Optimization Dynamics of Equivariant and Augmented Neural Networks
March 23, 2023
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Computer Science
Mathematics
Machine Learning
Optimization and Control
Machine Learning
Optimization and Control
We investigate the optimization of neural networks on symmetric data, and
compare the strategy of constraining the architecture to be equivariant to that
of using data augmentation. Our analysis reveals that that the relative
geometry of th...
An Optimization Model for Offline Scheduling Policy of Low-density
Parity-check Codes
March 23, 2023
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Computer Science
Mathematics
Information Theory
Information Theory
In this study, an optimization model for offline scheduling policy of
low-density parity-check (LDPC) codes is proposed to improve the decoding
efficiency of the belief propagation (BP). The optimization model uses the
number of messages pa...
Controlled Lagrangians and Stabilization of Euler--Poincar\'e Equations
with Symmetry Breaking Nonholonomic Constraints
March 23, 2023
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Mathematics
Optimization and Control
We extend the method of Controlled Lagrangians to nonholonomic
Euler--Poincar\'e equations with advected parameters, specifically to those
mechanical systems on Lie groups whose symmetry is broken not only by a
potential force but also by n...