Related papers: Practical Exploration of Polyhedral Model Checking
We give an elementary introduction to some recent polyhedral techniques for understanding and solving systems of multivariate polynomial equations. We provide numerous concrete examples and illustrations, and assume no background in…
We describe a scheme of constructing classical integrable models in 2+1-dimensional discrete space-time, based on the functional tetrahedron equation - equation that makes manifest the symmetries of a model in local form. We construct a…
In this article, we survey the primary research on polyhedral computing methods for constrained linear control systems. Our focus is on the modeling power of convex optimization, featured to design set-based robust and optimal controllers.…
This article describes a volumetric approach for procedural shape modeling and a new Procedural Shape Modeling Language (PSML) that facilitates the specification of these models. PSML provides programmers the ability to describe shapes in…
Most engineering models contain several parameters, and the map from input parameters to model output can be viewed as a multivariate function. An active subspace is a low-dimensional subspace of the space of inputs that explains the…
Multimodal large language models (MLLMs) have achieved significant progress in image and language tasks due to the strong reasoning capability of large language models (LLMs). Nevertheless, most MLLMs suffer from limited spatial reasoning…
The use of reduced models for investigating the self-assembly dynamics underlying protein shell formation in spherical viruses is described. The spontaneous self-assembly of these polyhedral, supramolecular structures, in which icosahedral…
Although neural models have performed impressively well on various tasks such as image recognition and question answering, their reasoning ability has been measured in only few studies. In this work, we focus on spatial reasoning and…
Polyhedral meshes (PM) - meshes having planar faces - have enjoyed a rise in popularity in recent years due to their importance in architectural and industrial design. However, they are also notoriously difficult to generate and manipulate.…
Many classical geometric inequalities on functionals of convex bodies depend on the dimension of the ambient space. We show that this dimension dependence may often be replaced (totally or partially) by different symmetry measures of the…
It is well-known that the convex and concave envelope of a multilinear polynomial over a box are polyhedral functions. Exponential-sized extended and projected formulations for these envelopes are also known. We consider the convexification…
We present a method for the efficient processing of contact and collision in volumetric elastic models simulated using the Projective Dynamics paradigm. Our approach enables interactive simulation of tetrahedral meshes with more than half a…
This chapter provides a brief introduction to the theory and practice of spatial stochastic simulations. It begins with an overview of different methods available for biochemical simulations highlighting their strengths and limitations.…
Research in cell biology is steadily contributing new knowledge about many different aspects of physiological processes like polymerization, both with respect to the involved molecular structures as well as their related function.…
A stochastic model checker is presented for analysing the performance of game-theoretic learning algorithms. The method enables the comparison of short-term behaviour of learning algorithms intended for practical use. The procedure of…
Large Multimodal Models (LMMs) have achieved strong performance across a range of vision and language tasks. However, their spatial reasoning capabilities are under-investigated. In this paper, we construct a novel VQA dataset, Spatial-MM,…
Molecular dynamics (MD) simulations enable the description of ma- terial properties and processes with atomistic detail by numerically solv- ing the time evolution of every atom in the system. We introduce Poly- merModeler, a…
Polynomial functions are a usual choice to model the nonlinearity of lenses. Typically, these models are obtained through physical analysis of the lens system or on purely empirical grounds. The aim of this work is to facilitate an…
Bounded model checking of pointer programs is a debugging technique for programs that manipulate dynamically allocated pointer structures on the heap. It is based on the following four observations. First, error conditions like dereference…
While the particle-in-cell (PIC) method is quite mature, verification and validation of both newly developed methods and individual codes has largely focused on an idiosyncratic choice of a few test cases. Many of these test cases involve…