Related papers: A Logical Product Approach to Zonotope Intersectio…
We consider a general class of (intersecting) loop models in D dimensions, including those related to high-temperature expansions of well-known spin models. We find that the loop models exhibit some interesting features - often in the…
We introduce a new multiplication for the polytope algebra, defined via the intersection of polytopes. After establishing the foundational properties of this intersection product, we investigate finite-dimensional subalgebras that arise…
We continue the study of intersection bodies of polytopes, focusing on the behavior of $IP$ under translations of $P$. We introduce an affine hyperplane arrangement and show that the polynomials describing the boundary of $I(P+t)$ can be…
Superposition or Neuron Polysemanticity are important concepts in the field of interpretability and one might say they are these most intricately beautiful blockers in our path of decoding the Machine Learning black-box. The idea behind…
In the discrete Tempotron learning problem a neuron receives time varying inputs and for a set of such input sequences ($\mathcal S_-$ set) the neuron must be sub-threshold for all times while for some other sequences ($\mathcal S_+$ set)…
Regular transition systems (RTS) are a popular formalism for modeling infinite-state systems in general, and parameterised systems in particular. In a CONCUR 22 paper, Esparza et al. introduce a novel approach to the verification of RTS,…
We give an interpretation of a class of discrete-to-continuum results for Ising systems using the theory of zonoids. We define the classes of rational zonotopes and zonoids, as those of the Wulff shapes of perimeters obtained as limits of…
We prove convergence for the nonoverlapping Robin-Robin method applied to nonlinear elliptic equations with a $p$-structure, including degenerate diffusion equations governed by the $p$-Laplacian. This nonoverlapping domain decomposition is…
We present a parametric abstract domain for array content analysis. The method maintains invariants for contiguous regions of the array, similar to the methods of Gopan, Reps and Sagiv, and of Halbwachs and Peron. However, it introduces a…
In this work, we derive conditions under which compositional abstractions of networks of stochastic hybrid systems can be constructed using the interconnection topology and joint dissipativity-type properties of subsystems and their…
In this paper, we present an improved numerical algorithm for computing the intersection area of multiple circles and a complex polygon efficiently. This geometric problem is fundamental to applications such as wireless sensor networks and…
We show how geometric methods from the general theory of fractal dimensions and iterated function systems can be deployed to study symbolic dynamics in the zero entropy regime. More precisely, we establish a dimensional characterization of…
We study two-dimensional conformal field theories (CFTs) with boundaries via the conformal bootstrap. We derive a positive semi-definite program from crossing symmetry of three observables: the annulus partition function, the two-point…
The weakly relational domain of Octagons offers a decent compromise between precision and efficiency for numerical properties. Here, we are concerned with the construction of non-numerical relational domains. We provide a general…
Graph-based signal processing techniques have become essential for handling data in non-Euclidean spaces. However, there is a growing awareness that these graph models might need to be expanded into `higher-order' domains to effectively…
In context of efforts of composing category-theoretic and logical methods in the area of knowledge representation we propose the notion of conceptory. We consider intersection/union and other constructions in conceptories as expressive…
Pair production of massive coloured particles in hadron collisions is accompanied by potentially large radiative corrections related to the suppression of soft gluon emission and enhanced Coulomb exchange near the production threshold. We…
We present a general framework for exemplar-based image translation, which synthesizes a photo-realistic image from the input in a distinct domain (e.g., semantic segmentation mask, or edge map, or pose keypoints), given an exemplar image.…
Recently, their has been development of an abstract approach to the Robin--Robin method, enabling the treatment of linear and nonlinear elliptic and parabolic equations on Lipschitz domains within one framework. However, previously this…
Building a semantic parser quickly in a new domain is a fundamental challenge for conversational interfaces, as current semantic parsers require expensive supervision and lack the ability to generalize to new domains. In this paper, we…