Related papers: Modular Localization and the Bootstrap-Formfactor …
We examine the proof of a classical localization theorem of Bousfield and Friedlander and we remove the assumption that the underlying model category be right proper. The key to the argument is a lemma about factoring in morphisms in the…
Based on the concepts of $\mathbb{R}$-factorizable topological groups and $\mathcal{M}$-factorizable topological groups, we introduce four classes of factorizabilities on topological groups, named $P\mathcal{M}$-factorizabilities,…
The module theorem by Janhunen et al. demonstrates how to provide a modular structure in answer set programming, where each module has a well-defined input/output interface which can be used to establish the compositionality of answer sets.…
Human beings learn causal models and constantly use them to transfer knowledge between similar environments. We use this intuition to design a transfer-learning framework using object-oriented representations to learn the causal…
The feasibility of a classification-by-rank program for modular categories follows from the Rank-Finiteness Theorem. We develop arithmetic, representation theoretic and algebraic methods for classifying modular categories by rank. As an…
We present an example of a homotopical localization functor which is not a localization with respect to any set of maps. Our example arises from equivariant homotopy theory. The technique of equivariant cellularization is developed and…
We compare modular forms of characteristic $p>0$ (i.e. Drinfeld's modular forms) and automorphic forms. We prove that spaces of these modular forms (which are of characteristic $p$) can be described by function spaces of characteristic…
The identification of relevant collective coordinates is crucial for the interpretation of coherent nonlinear spectroscopies of complex molecules and liquids. Using an $\hbar$ expansion of Liouville space generating functions, we show how…
This paper establishes a rigorous connection between circuit representations and tensor factorizations, two seemingly distinct yet fundamentally related areas. By connecting these fields, we highlight a series of opportunities that can…
Value factorization is a popular and promising approach to scaling up multi-agent reinforcement learning in cooperative settings, which balances the learning scalability and the representational capacity of value functions. However, the…
We introduce the concept of multiplicatively closed subsets of a commutative ring $R$ which split an $R$-module $M$ and study factorization properties of elements of $M$ with respect to such a set. Also we demonstrate how one can utilize…
This paper is a complement to our earlier work \cite{BCSS10b}. With the help of the multi-scale analysis, we derive, from estimates obtained in \cite{BCSS10b}, dynamical localization for a multi-particle Anderson model in a Euclidean space…
Given labeled data represented by a binary matrix, we consider the task to derive a Boolean matrix factorization which identifies commonalities and specifications among the classes. While existing works focus on rank-one factorizations…
Oftentimes, patterns can be represented through different modalities. For example, leaf data can be in the form of images or contours. Handwritten characters can also be either online or offline. To exploit this fact, we propose the use of…
Recent progress on a constructive approach to QFT which is based on modular theory is reviewed and compared with the standard quantization approaches. Talk given at ``Quantum Theory and Symmetries'', Goslar, Germany, July 1999
We define the stack of $G$-local systems with restricted variation on the formal puntured disc and study its properties. We embed sheaves of categories over this stack into the category of factorization module categories over…
Integrable Quantum Field Theories can be solved exactly using bootstrap techniques based on their elastic and factorisable S-matrix. While knowledge of the scattering amplitudes reveals the exact spectrum of particles and their on-shell…
In this paper, we characterize rank one preserving module maps on a Hilbert $C^\ast-$module and study its applications on free probability theory.
In these lecture notes, we give a brief introduction to some elements of category theory. The choice of topics is guided by applications to functional programming. Firstly, we study initial algebras, which provide a mathematical…
Let X be an algebraic curve. We study the problem of parametrizing geometric data over X, which is only generically defined. E.g., parametrizing generically defined (aka rational) maps from X to a fixed target scheme Y. There are three…