Related papers: Mathematica: A System of Computer Programs
Mathematical information is essential for technical work, but its creation, interpretation, and search are challenging. To help address these challenges, researchers have developed multimodal search engines and mathematical question…
Computational chemistry allows researchers to experiment in sillico: by running a computer simulations of a biological or chemical processes of interest. Molecular dynamics with molecular mechanics model of interactions simulates N-body…
Due to the ubiquity of batch data processing in cloud computing, the related problem of scheduling malleable batch tasks and its extensions have received significant attention recently. In this paper, we consider a fundamental model where a…
Mathematical reasoning---a core ability within human intelligence---presents some unique challenges as a domain: we do not come to understand and solve mathematical problems primarily on the back of experience and evidence, but on the basis…
This paper outlines our ideas on how to teach linear algebra in a mechanized mathematical environment, and discusses some of our reasons for thinking that this is a better way to teach linear algebra than the ``old fashioned way''. We…
We introduce program splicing, a programming methodology that aims to automate the commonly used workflow of copying, pasting, and modifying code available online. Here, the programmer starts by writing a "draft" that mixes unfinished code,…
Concurrent programming often entails meticulous pairing of sends and receives between participants to avoid deadlock. Choreographic programming alleviates this burden by specifying the system as a single program. However, there are more…
Many powerful machine learning models are based on the composition of multiple processing layers, such as deep nets, which gives rise to nonconvex objective functions. A general, recent approach to optimise such "nested" functions is the…
We present an open-source Mathematica importer for CERN ROOT files. Taking advantage of Mathematica's import/export plug-in mechanism, the importer offers a simple, unified interface that cleanly wraps around its MathLink-based core that…
Parallel parameterized complexity theory studies how fixed-parameter tractable (fpt) problems can be solved in parallel. Previous theoretical work focused on parallel algorithms that are very fast in principle, but did not take into account…
Concurrent data structures are the data sharing side of parallel programming. Data structures give the means to the program to store data, but also provide operations to the program to access and manipulate these data. These operations are…
A speculative overview of a future topic of research. The paper is a collection of ideas concerning two related areas: 1) Graph computation machines ("computing with graphs"). This is the class of models of computation in which the state of…
Parallel dataflow systems have become a standard technology for large-scale data analytics. Complex data analysis programs in areas such as machine learning and graph analytics often involve control flow, i.e., iterations and branching.…
The focus of these lecture notes is on abstract models and basic ideas and results that relate to the operational semantics of programming languages largely conceived. The approach is to start with an abstract description of the computation…
There is a growing consensus that physics majors need to learn computational skills, but many departments are still devoid of computation in their physics curriculum. Some departments may lack the resources or commitment to create a…
Neural networks that compute over graph structures are a natural fit for problems in a variety of domains, including natural language (parse trees) and cheminformatics (molecular graphs). However, since the computation graph has a different…
Over the past few years, self-attention is shining in the field of deep learning, especially in the domain of natural language processing(NLP). Its impressive effectiveness, along with ubiquitous implementations, have aroused our interest…
Large language models (LLMs) benefit greatly from prompt engineering, with in-context learning standing as a pivital technique. While former approaches have provided various ways to construct the demonstrations used for in-context learning,…
Nowadays, we are to find out solutions to huge computing problems very rapidly. It brings the idea of parallel computing in which several machines or processors work cooperatively for computational tasks. In the past decades, there are a…
An introduction to applied mathematics written for students in engineering and science. Focus is on a rigorous presentation that also builds understanding by discussion, analogy, and examples. Discussion of concepts involved in modeling…