Related papers: Data linkage algebra, data linkage dynamics, and p…
We explore contemporary, data-driven techniques for solving math word problems over recent large-scale datasets. We show that well-tuned neural equation classifiers can outperform more sophisticated models such as sequence to sequence and…
We present a computational implementation of diagrammatic sets, a model of higher-dimensional diagram rewriting that is "topologically sound": diagrams admit a functorial interpretation as homotopies in cell complexes. This has potential…
In many massively parallel data management platforms, programs are represented as small imperative pieces of code connected in a data flow. This popular abstraction makes it hard to apply algebraic reordering techniques employed by…
Natural systems are typically nonlinear and complex, and it is of great interest to be able to reconstruct a system in order to understand its mechanism, which can not only recover nonlinear behaviors but also predict future dynamics. Due…
Dynamical systems are a broad class of mathematical tools used to describe the evolution of physical and computational processes. Traditionally these processes model changing entities in a static world. Picture a ball rolling on an empty…
We provide a computational definition of the notions of vector space and bilinear functions. We use this result to introduce a minimal language combining higher-order computation and linear algebra. This language extends the Lambda-calculus…
The web of data has brought forth the need to preserve and sustain evolving information within linked datasets; however, a basic requirement of data preservation is the maintenance of the datasets' structural characteristics as well. As…
Interconnected dynamic systems are a pervasive component of our modern infrastructures. The complexity of such systems can be staggering, which motivates simplified representations for their manipulation and analysis. This work introduces…
Data processing systems roughly group into families such as relational, array, graph, and key-value. Many data processing tasks exceed the capabilities of any one family, require data stored across families, or run faster when partitioned…
Data-based decisionmaking must account for the manipulation of data by agents who are aware of how decisions are being made and want to affect their allocations. We study a framework in which, due to such manipulation, data becomes less…
The paper addresses problem of data allocation in two-layer computer storage while taking into account dynamic digraph(s) over computing tasks. The basic version of data file allocation on parallel hard magnetic disks is considered as…
Neural circuits are able to perform computations under very diverse conditions and requirements. The required computations impose clear constraints on their fine-tuning: a rapid and maximally informative response to stimuli in general…
This paper presents general syntactic conditions ensuring the strong normalization and the logical consistency of the Calculus of Algebraic Constructions, an extension of the Calculus of Constructions with functions and predicates defined…
These lecture notes are derived from a graduate-level course in dynamic optimization, offering an introduction to techniques and models extensively used in management science, economics, operations research, engineering, and computer…
To answer database queries over incomplete data the gold standard is finding certain answers: those that are true regardless of how incomplete data is interpreted. Such answers can be found efficiently for conjunctive queries and their…
Large scale neural recordings have established that the transformation of sensory stimuli into motor outputs relies on low-dimensional dynamics at the population level, while individual neurons exhibit complex selectivity. Understanding how…
Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical…
Text analytical tasks like word embedding, phrase mining, and topic modeling, are placing increasing demands as well as challenges to existing database management systems. In this paper, we provide a novel algebraic approach based on…
The Circular Economy framework emphasizes sustainability by reducing resource consumption and waste through the reuse of components and materials. This paper presents ReLink, a computational framework for the circular design of planar…
A linkage is a finite graph with lengths assigned to each edge. A planar realization is a map to the plane which preserves edge lengths. It can be thought of as a mechanical device formed from stiff rods and rotating joints. We look at the…