Related papers: LazySets.jl: Scalable Symbolic-Numeric Set Computa…
Set systems are used to model data that naturally arises in many contexts: social networks have communities, musicians have genres, and patients have symptoms. Visualizations that accurately reflect the information in the underlying set…
The Julia library TSSOS aims at helping polynomial optimizers to solve large-scale problems with sparse input data. The underlying algorithmic framework is based on exploiting correlative and term sparsity to obtain a new moment-SOS…
We introduce Dionysos.jl, a modular package for solving optimal control problems for complex dynamical systems using state-of-the-art and experimental techniques from symbolic control, optimization, and learning. More often than not with…
We present MultiObjectiveAlgorithms.jl, an open-source Julia library for solving multi-objective optimization problems written in JuMP. MultiObjectiveAlgorithms.jl implements a number of different solution algorithms, which all rely on an…
This paper investigates reachability analysis for max-plus linear systems (MPLS), an important class of dynamical systems that model synchronization and delay phenomena in timed discrete-event systems. We specifically focus on backward…
Point processes model the occurrence of a countable number of random points over some support. They can model diverse phenomena, such as chemical reactions, stock market transactions and social interactions. We show that JumpProcesses.jl is…
Advanced applied mathematics problems are underrepresented in existing Large Language Model (LLM) benchmark datasets. To address this, we introduce HARDMath, a dataset inspired by a graduate course on asymptotic methods, featuring…
In this paper, we present Insertus.jl, the Julia package that can help the user generate a randomization sequence of a given length for a multi-arm trial with a pre-specified target allocation ratio and assess the operating characteristics…
The study of dynamical systems involves analyzing how functions behave under iteration in different mathematical spaces. In the context of complex dynamics, tools such as Julia sets and filled Julia sets are used to understand the long-term…
Proprietary closed-source software is still the norm in advanced process control. Transparency and reproducibility are key aspects of scientific research. Free and open-source toolkit can contribute to the development, sharing and…
Jupyter Scatter is a scalable, interactive, and interlinked scatterplot widget for exploring datasets in Jupyter Notebook/Lab, Colab, and VS Code. Its goal is to simplify the visual exploration, analysis, and comparison of large-scale…
In the nonlinear timeseries analysis literature, countless quantities have been presented as new ``entropy'' or ``complexity'' measures, often with similar roles. The ever-increasing pool of such measures makes creating a sustainable and…
We present a Julia package HypersurfaceRegions.jl for computing all connected components in the complement of an arrangement of real algebraic hypersurfaces in $\mathbb{R}^n$.
Bridging cultures that have often been distant, Julia combines expertise from the diverse fields of computer science and computational science to create a new approach to numerical computing. Julia is designed to be easy and fast. Julia…
With the advent of Transformers, large language models (LLMs) have saturated well-known NLP benchmarks and leaderboards with high aggregate performance. However, many times these models systematically fail on tail data or rare groups not…
SymBoltz is a new Julia package for solving the linear Einstein-Boltzmann equations in cosmology. It features a symbolic-numeric interface for specifying equations, is free of approximation switching schemes, and is compatible with…
Large Language Models (LLM) exhibit zero-shot mathematical reasoning capacity as a behavior emergent with scale, commonly manifesting as chain-of-thoughts (CoT) reasoning. However, multiple empirical findings suggest that this prowess is…
Scientific software relies on high-precision computation, yet finite floating-point representations can introduce precision errors that propagate in safety-critical domains. Despite the growing use of large language models (LLMs) in…
Agent-based models capture heterogeneity among individuals in a population and are widely used in studies of multi-cellular systems, disease, epidemics and demography to name a few. However, existing frameworks consider discrete time-step…
Many uncertainty propagation software exist, written in different programming languages, but not all of them are able to handle functional correlation between quantities. In this paper we review one strategy to deal with uncertainty…