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The analysis of complex nonlinear systems is often carried out using simpler piecewise linear representations of them. A principled and practical technique is proposed to linearize and evaluate arbitrary continuous nonlinear functions using…
SEAL is a static analyser for the verification of programs that manipulate unbounded linked data structures. It is based on separation logic to represent abstract memory states and, unlike other separation-logic-based approaches, it employs…
Differentiating through constrained optimization problems is increasingly central to learning, control, and large-scale decision-making systems, yet practical integration remains challenging due to solver specialization and interface…
We provide a user's guide to version 1.0 of the software package CYTools, which we designed to compute the topological data of Calabi-Yau hypersurfaces in toric varieties. CYTools has strong capabilities in analyzing and triangulating…
A representative set of fault diagnosis problems is formulated for linear time-invariant systems with additive faults. For all formulated problems, general existence conditions of their solutions are given. An overview of recent…
Medical image analysis using deep learning frameworks has advanced healthcare by automating complex tasks, but many existing frameworks lack flexibility, modularity, and user-friendliness. To address these challenges, we introduce Yucca, an…
Combustion kinetic modeling is an integral part of combustion simulation, and extensive studies have been devoted to developing both high fidelity and computationally affordable models. Despite these efforts, modeling combustion kinetics is…
ParaSail is a language specifically designed to simplify the construction of programs that make full, safe use of parallel hardware even while manipulating potentially irregular data structures. As parallel hardware has proliferated, there…
We introduce Metatheory.jl: a lightweight and performant general purpose symbolics and metaprogramming framework meant to simplify the act of writing complex Julia metaprograms and to significantly enhance Julia with a native term rewriting…
We present IncompressibleNavierStokes.jl, an open-source Julia package for solving the incompressible Navier--Stokes equations on staggered Cartesian grids. The package features matrix-free, hardware-agnostic kernels that are compiled from…
Implementing and executing numerical algorithms to solve fractional differential equations has been less straightforward than using their integer-order counterparts, posing challenges for practitioners who wish to incorporate fractional…
Biological systems with intertwined feedback loops pose a challenge to mathematical modeling efforts. Moreover, rare events, such as mutation and extinction, complicate system dynamics. Stochastic simulation algorithms are useful in…
Condition monitoring subsea pipelines in low-visibility underwater environments poses significant challenges due to turbidity, light distortion, and image degradation. Traditional visual-based inspection systems often fail to provide…
This paper introduces the TulipaProfileFitting.jl package, a tool developed in Julia for generating renewable energy profiles that fit a specified capacity factor. It addresses the limitations of naive methods in adjusting existing profiles…
The iotools package provides a set of tools for Input/Output (I/O) intensive datasets processing in R (R Core Team, 2014). Efficent parsing methods are included which minimize copying and avoid the use of intermediate string representations…
To address intricate real-world tasks, there has been a rising interest in tool utilization in applications of large language models (LLMs). To develop LLM-based agents, it usually requires LLMs to understand many tool functions from…
Concurrent functional languages that are endowed with symbolic reasoning capabilities such as Maude offer a high-level, elegant, and efficient approach to programming and analyzing complex, highly nondeterministic software systems. Maude's…
It is well known that the nonlinear filtering problem has important applications in both military and civil industries. The central problem of nonlinear filtering is to solve the Duncan-Mortensen-Zakai (DMZ) equation in real time and in a…
Linear systems of equations can be found in various mathematical domains, as well as in the field of machine learning. By employing noisy intermediate-scale quantum devices, variational solvers promise to accelerate finding solutions for…
Most numerical solvers used to determine free variables of dynamical systems rely on first-order derivatives of the state of the system w.r.t. the free variables. The number of the free variables can be fairly large. One of the approaches…