Related papers: Symbolic representation and classification of inte…
We discuss the use of methods coming from integrable systems to study problems of enumerative and algebraic combinatorics, and develop two examples: the enumeration of Alternating Sign Matrices and related combinatorial objects, and the…
Analysis and manipulation of trained neural networks is a challenging and important problem. We propose a symbolic representation for piecewise-linear neural networks and discuss its efficient computation. With this representation, one can…
We consider the following problem: Given a nested sum expression, find a sum representation such that the nested depth is minimal. We obtain a symbolic summation framework that solves this problem for sums defined, e.g., over…
A key aspect of machine learning models lies in their ability to learn efficient intermediate features. However, the input representation plays a crucial role in this process, and polyphonic musical scores remain a particularly complex type…
An integrable theory is developed for the perturbation equations engendered from small disturbances of solutions. It includes various integrable properties of the perturbation equations: hereditary recursion operators, master symmetries,…
As power systems evolve with the increasing integration of renewable energy sources and smart grid technologies, there is a growing demand for flexible and scalable modeling approaches capable of capturing the complex dynamics of modern…
In this paper, we present our position for a neuralsymbolic integration strategy, arguing in favor of a hybrid representation to promote an effective integration. Such description differs from others fundamentally, since its entities aim at…
Some of the most important compartmental systems, such as irreversible catenary, mamillary and circular systems are symbolically simplified by the method of exact linear lumping. A few symbolically unmanageable systems are numerically…
We propose a novel symbolic modeling framework for decision-making under risk that merges interpretability with the core insights of Prospect Theory. Our approach replaces opaque utility curves and probability weighting functions with…
A new proof of Imprimitivity theorem for transitive systems of covariance is given and a definition of square-integrable representation modulo a subgroup is proposed. This clarifies the relation between coherent states, wavelet transforms…
Symmetry plays a central role in accelerating symbolic computation involving polynomials. This chapter surveys recent developments and foundational methods that leverage the inherent symmetries of polynomial systems to reduce complexity,…
The aim of the present survey paper is to provide an accessible introduction to a new chapter of representation theory - harmonic analysis for noncommutative groups with infinite-dimensional dual space. I omitted detailed proofs but tried…
A complete classification of isotropic vector equations of the geometric type that possess higher symmetries is proposed. New examples of integrable multi-component systems of the geometric type and their auto-Backlund transformations are…
This paper is a review containing new original results on the finite order variational sequence and its different representations with emphasis on applications in the theory of variational symmetries and conservation laws in physics.
Symbolic models have recently spurred the interest of the research community because they offer a correct-by-design approach to the control of embedded and cyber-physical systems. In this paper we address construction of symbolic models for…
We give a short introduction to the methods of representing polynomial and trigonometric series that are often used in Celestial Mechanics. A few applications are also illustrated.
The present paper is a short review of different path integral representations of the partition function of quantum spin systems. To begin with, I consider coherent states for SU(2) algebra. Different parameterizations of the coherent…
Using semi-tensor product of matrices, the structures of several kinds of symmetric games are investigated via the linear representation of symmetric group in the structure vector of games as its representation space. First of all, the…
We classify irreducible representations of the special linear groups in positive characteristic with small weight multiplicities with respect to the group rank and give estimates for the maximal weight multiplicities. For the natural…
For an integrable Hamiltonian system we construct a representation of the phase space symmetry algebra over the space of functions on a Lagrangian manifold. The representation is a result of the canonical quantization of the integrable…