Related papers: Model theory and Ultrapower Embedding Problems in …
The notion of embedding tensors and the associated tensor hierarchies form an effective tool for the construction of supergravity and higher gauge theories. Embedding tensors and related structures are extensively studied also in the…
Knowledge bases are employed in a variety of applications from natural language processing to semantic web search; alas, in practice their usefulness is hurt by their incompleteness. Embedding models attain state-of-the-art accuracy in…
We study the representation theory of graded Hecke algebras, starting from scratch and focusing on representations that are obtained with induction from a discrete series representation of a parabolic subalgebra. We determine all…
One approach to parametric and adaptive model reduction is via the interpolation of orthogonal bases, subspaces or positive definite system matrices. In all these cases, the sampled inputs stem from matrix sets that feature a geometric…
We continue our study of operator algebras with and contractive approximate identities (cais). In earlier papers we have introduced and studied a new notion of positivity in operator algebras, with an eye to extending certain C*-algebraic…
The goal of this paper is to set up an obstruction theory in the context of algebras over an operad and in the framework of differential graded modules over a field. Precisely, the problem we consider is the following: Suppose given two…
Pre-trained word embeddings are the primary method for transfer learning in several Natural Language Processing (NLP) tasks. Recent works have focused on using unsupervised techniques such as language modeling to obtain these embeddings. In…
Recent work in machine learning shows that deep neural networks can be used to solve a wide variety of inverse problems arising in computational imaging. We explore the central prevailing themes of this emerging area and present a taxonomy…
Traditional wireless network design relies on optimization algorithms derived from domain-specific mathematical models, which are often inefficient and unsuitable for dynamic, real-time applications due to high complexity. Deep learning has…
Families of operator identities appeared as a consequence of an existence of finite-dimensional representation of (super) Lie algebras of first-order differential operators and $q$-deformed (quantum) algebras of first-order…
In this paper, the notion of unitary vertex operator superalgebra is introduced. It is proved that the vertex operator superalgebras associated to the unitary highest weight representations for the Neveu-Schwarz Lie superalgebra, Heisenberg…
The thesis is devoted to abstract, geometric and symmetric aspects of modern elementary particle theories. A new direction in constructing supersymmetric and superstring models based on consequent and strong consideration and inclusion of…
We construct integrable generalised models in a systematic way exploring different representations of the gl(N) algebra. The models are then interpreted in the context of atomic and molecular physics, most of them related to different types…
Part I of this paper embeds the AC power flow problem with voltage control and exponential load model in the complex plane. Modeling the action of network controllers that regulate the magnitude of voltage phasors is a challenging task in…
We prove a variant of the so-called bilinear embedding theorem for operators in divergence form with complex coefficients and with nonnegative locally integrable potentials, subject to mixed boundary conditions, and acting on arbitrary open…
We examine general properties of superembeddings, i.e., embeddings of supermanifolds into supermanifolds. The connection between an embedding procedure and the method of non-linearly realised supersymmetry is clarified, and we demonstrate…
In this short note, we establish an operator theoretic version of the Wiener-Ikehara tauberian theorem, and point out how this leads to a new proof of the Prime number theorem that should be accessible to anyone with a basic knowledge of…
We introduce two mirror constructions of Vertex Operator Algebras associated to special boundary conditions in 3d N=4 gauge theories. We conjecture various relations between these boundary VOA's and properties of the (topologically twisted)…
We construct the intertwining operator superalgebras and vertex tensor categories for the N=2 superconformal unitary minimal models and other related models.
The paper provides a coherent presentation of an operator scheme, which is used in an approach to inverse problems of mathematical physics (the boundary control method). The scheme is based on the triangular factorization of operators. It…