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We introduce a new class of computationally tractable scattering problems in unbounded domains, which we call decomposable problems. In these decomposable problems, the computational domain can be split into a finite collection of…
We present a systematic procedure for analyzing cumulants to arbitrary order in the context of heavy-ion collisions. It generalizes and improves existing procedures in many respects. In particular, particles which are correlated are allowed…
Category theory provides a means through which many far-ranging fields of mathematics can be related by their similar structure. In a paper by Robinson [2], this interconnectivity afforded by categorical perspectives allowed for the…
Intersection distribution and non-hitting index are concepts introduced recently by Li and Pott as a new way to view the behaviour of a collection of finite field polynomials. With both an algebraic interpretation via the intersection of a…
Monotonic abstraction is a technique introduced in model checking parameterized distributed systems in order to cope with transitions containing global conditions within guards. The technique has been re-interpreted in a declarative setting…
In the analysis of logic programs, abstract domains for detecting sharing and linearity information are widely used. Devising abstract unification algorithms for such domains has proved to be rather hard. At the moment, the available…
We study the mixed formulation of the abstract Hodge Laplacian on axisymmetric domains with general data through Fourer-finite-element-methods in weighted functions spaces. Closed Hilbert complexes and commuting projectors are used through…
A central challenge for cognitive science is to explain how abstract concepts are acquired from limited experience. This has often been framed in terms of a dichotomy between connectionist and symbolic cognitive models. Here, we highlight a…
We define and study geometric versions of the Benoist limit cone and matrix joint spectrum, which we call the translation cone and the joint translation spectrum, respectively. These new notions allow us to generalize the study of…
In predicate abstraction, exact image computation is problematic, requiring in the worst case an exponential number of calls to a decision procedure. For this reason, software model checkers typically use a weak approximation of the image.…
Neural networks often pack many unrelated concepts into a single neuron - a puzzling phenomenon known as 'polysemanticity' which makes interpretability much more challenging. This paper provides a toy model where polysemanticity can be…
Over-approximating the reachable sets of dynamical systems is a fundamental problem in safety verification and robust control synthesis. The representation of these sets is a key factor that affects the computational complexity and the…
Hybrid systems - more precisely, their mathematical models - can exhibit behaviors, like Zeno behaviors, that are absent in purely discrete or purely continuous systems. First, we observe that, in this context, the usual definition of…
Recent deep learning methods for object detection rely on a large amount of bounding box annotations. Collecting these annotations is laborious and costly, yet supervised models do not generalize well when testing on images from a different…
The success of Conflict Driven Clause Learning (CDCL) for Boolean satisfiability has inspired adoption in other domains. We present a novel lifting of CDCL to program analysis called Abstract Conflict Driven Learning for Programs (ACDLP).…
We suggest a short review of literature on various solitonic lattices and individual solitons in quasi one-dimensional conductors. This information seems to be quite relevant to topics of stripes and their melted phases correspondingly. We…
This paper presents a brand new methodology to deal with isotopic fine structure calculations. By using the Poisson approximation in an entirely novel way, we introduce mathematical elegance into the discussion on the trade-off between…
This manuscript introduces a finite collection of generalized permutohedra associated to a simple graph. The first polytope of this collection is the graphical zonotope of the graph and the last is the graph-associahedron associated to it.…
Correspondence identifies relationships among objects via similarities among their components; it is ubiquitous in the analysis of spatial datasets, including images, weather maps, and computational simulations. This paper develops a novel…
Abstract separation systems provide a simple general framework in which both tree-shape and high cohesion of many combinatorial structures can be expressed, and their duality proved. Applications range from tangle-type duality and tree…