An Interpretable Approach to Load Profile Forecasting in Power Grids
using Galerkin-Approximated Koopman Pseudospectra
April 16, 2023
| | | | |
Computer Science
Mathematics
Physics
Machine Learning
Functional Analysis
Data Analysis, Statistics and Probability
Machine Learning
Functional Analysis
Data Analysis, Statistics and Probability
This paper presents an interpretable machine learning approach that
characterizes load dynamics within an operator-theoretic framework for
electricity load forecasting in power grids. We represent the dynamics of load
data using the Koopman...
Even Stiefel-Whitney invariants for anti-hermitian quaternionic forms
April 16, 2023
|
Mathematics
K-Theory and Homology
K-Theory and Homology
We extend all cohomological invariants of similarity classes of quadratic
forms to anti-hermitian forms over a quaternion algebra. This uses the fact
that such invariants can be lifted to Witt invariants, which can be described
as combinati...
Graphical constructions of simple exclusion processes with applications
to random environments
April 16, 2023
Mathematics
Physics
Probability
Mathematical Physics
Mathematical Physics
We show that the symmetric simple exclusion process (SSEP) on a countable set
is well defined by the stirring graphical construction as soon as the dynamics
of a single particle is. The resulting process is Feller, its Markov generator
is d...
Linkage and translation for tensor products of representations of simple
algebraic groups and quantum groups
April 16, 2023
Mathematics
Representation Theory
Let G be either a simple linear algebraic group over an
algebraically closed field of characteristic ℓ>0 or a quantum group at an
ℓ-th root of unity. We define a tensor ideal of singular
G-modules in the cate...
On modeling NP-Complete problems as polynomial-sized linear programs:
Escaping/Side-stepping the "barriers"
April 16, 2023
| |
Computer Science
Mathematics
Computational Complexity
Data Structures and Algorithms
Optimization and Control
In view of the extended formulations (EFs) developments (e.g. "Fiorini, S.,
S. Massar, S. Pokutta, H.R. Tiwary, and R. de Wolf [2015]. Exponential Lower
Bounds for Polytopes in Combinatorial Optimization. Journal of the ACM 62:2"),
we focus...
Ng\^o support theorem and polarizability of quasi-projective commutative
group schemes
April 16, 2023
|
Mathematics
Algebraic Geometry
We prove that any commutative group scheme over an arbitrary base scheme of
finite type over a field with connected fibers and admitting a relatively ample
line bundle is polarizable in the sense of Ng\^o. This extends the
applicability of ...
First characterization of the scattering length distribution of vector
meson interaction with deuteron
April 16, 2023
| |
Physics
High Energy Physics - Phenomenology
Nuclear Theory
Under the framework of the vector meson dominance model (VMD), the absolute
scattering lengths of light vector mesons (ϕ, ω, and ρ) with
the deuteron are calculated from the cross sections of vector meson
photoproduction of...
Sidon sets, sum-free sets and linear codes
April 16, 2023
|
Mathematics
Computer Science
Combinatorics
Information Theory
Information Theory
Finding the maximum size of a Sidon set in F2t is of research
interest for more than 40 years. In order to tackle this problem we recall a
one-to-one correspondence between sum-free Sidon sets and linear codes with
minimum dist...
TeAAL: A Declarative Framework for Modeling Sparse Tensor Accelerators
April 16, 2023
| | | | |
Computer Science
Hardware Architecture
Over the past few years, the explosion in sparse tensor algebra workloads has
led to a corresponding rise in domain-specific accelerators to service them.
Due to the irregularity present in sparse tensors, these accelerators employ a
wide v...
Velocity Obstacle for Polytopic Collision Avoidance for Distributed
Multi-robot Systems
April 16, 2023
| | | | |
Computer Science
Electrical Engineering and Systems Science
Mathematics
Robotics
Systems and Control
Systems and Control
Optimization and Control
Obstacle avoidance for multi-robot navigation with polytopic shapes is
challenging. Existing works simplify the system dynamics or consider it as a
convex or non-convex optimization problem with positive distance constraints
between robots,...