Related papers: Complete Boolean Algebra for Memristive and Spintr…
Multimodal MRI offers complementary multi-scale information to characterize the brain structure. However, it remains challenging to effectively integrate multimodal MRI while achieving neuroscience interpretability. Here we propose to use…
Second-order superintegrable systems in dimensions two and three are essentially classified. With increasing dimension, however, the non-linear partial differential equations employed in current methods become unmanageable. Here we propose…
In recent years, there has been considerable interest in the transformative potential of additive manufacturing (AM) since it allows for producing highly customizable and complex components while reducing lead times and costs. The rise of…
Bialgebrae provide an abstract framework encompassing the semantics of different kinds of computational models. In this paper we propose a bialgebraic approach to the semantics of logic programming. Our methodology is to study logic…
We present the sliding basis computational framework to automatically synthesize heterogeneous (graded or discrete) material fields for parts designed using constrained optimization. Our framework uses the fact that any spatially varying…
State-of-the-art inference approaches in probabilistic logic programming typically start by computing the relevant ground program with respect to the queries of interest, and then use this program for probabilistic inference using knowledge…
The construction of superintegrable systems based on Lie algebras and their universal enveloping algebras has been widely studied over the past decades. However, most constructions rely on explicit differential operator realisations and…
Spatial (dataflow) computer architectures can mitigate the control and performance overhead of classical von Neumann architectures such as traditional CPUs. Driven by the popularity of Machine Learning (ML) workloads, spatial devices are…
The application of Large Language Models (LLMs) for Automated Algorithm Discovery (AAD), particularly for optimisation heuristics, is an emerging field of research. This emergence necessitates robust, standardised benchmarking practices to…
The description of symmetry breaking proposed by K. Symanzik within the framework of renormalizable theories is generalized from the geometrical point of view. For an arbitrary compact Lie group, a soft breaking of arbitrary covariance, and…
We address the problem of unambiguous reconstruction of rational functions of many variables. This is particularly relevant for recovery of exact expansion coefficients in integration-by-parts identites (IBPs) based on modular arithmetic.…
Partition logics -- non-Boolean event structures obtained by pasting Boolean algebras -- provide a natural language for situations in which a system has a definite latent state but can be accessed and resolved only through mutually…
Algebraic and fast algebraic attacks are power tools to analyze stream ciphers. A class of symmetric Boolean functions with maximum algebraic immunity were found vulnerable to fast algebraic attacks at EUROCRYPT'06. Recently, the notion of…
Rotation symmetric Boolean functions represent an interesting class of Boolean functions as they are relatively rare compared to general Boolean functions. At the same time, the functions in this class can have excellent properties, making…
We propose a new framework for constructing geometric and physical models on nonholonomic manifolds provided both with Clifford -- Lie algebroid symmetry and nonlinear connection structure. Explicit parametrizations of generic off-diagonal…
Idempotent Boolean functions form a highly structured subclass of Boolean functions that is closely related to rotation symmetry under a normal-basis representation and to invariance under a fixed linear map in a polynomial basis. These…
Meshless methods are often used in numerical simulations of systems of partial differential equations (PDEs), particularly those which involve complex geometries or free surfaces. Here we present a novel compact scheme based on the local…
We apply the BRST approach, previously developed for higher spin field theories, to gauge invariant Lagrangian construction for antisymmetric massive and massless bosonic fields in arbitrary d-dimensional curved space. The obtained theories…
The advent of memristive devices offers a promising avenue for efficient and scalable analog computing, particularly for linear algebra operations essential in various scientific and engineering applications. This paper investigates the…
Nonhamiltonian interaction of hamiltonian systems is considered. Dynamical equations are constructed by use of symmetric designs on Lie algebras. The results of analysis of these equations show that some class of symmetric designs on Lie…