Related papers: A computational framework for connection matrix th…
In many areas of applied geometric/numeric computational mathematics, including geo-mapping, computer vision, computer graphics, finite element analysis, medical imaging, geometric design, and solid modeling, one has to compute incidences,…
The Theory of Functional Connections (TFC) is a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The functionals derived from this method, called \emph{constrained expressions},…
We introduce a framework for generating, organizing, and reasoning with computational knowledge. It is motivated by the observation that most problems in Computational Sciences and Engineering (CSE) can be formulated as that of completing…
In this work, we present a new approach for constructing models for correlation matrices with a user-defined graphical structure. The graphical structure makes correlation matrices interpretable and avoids the quadratic increase of…
We present a systematic, algebraically based, design methodology for efficient implementation of computer programs optimized over multiple levels of the processor/memory and network hierarchy. Using a common formalism to describe the…
We present a categorical framework for relating causal models that represent the same system at different levels of abstraction. We define a causal abstraction as natural transformations between appropriate Markov functors, which concisely…
While topological data analysis has emerged as a powerful paradigm for structural inference, its foundational tools, notably persistent homology and the persistent Laplacian, are frequently insensitive to localized structural fluctuations…
We continue the study of the quantum marginal independence problem, namely the question of which faces of the subadditivity cone are achievable by quantum states. We introduce a new representation of the patterns of marginal independence…
As data structures and mathematical objects used for complex systems modeling, hypergraphs sit nicely poised between on the one hand the world of network models, and on the other that of higher-order mathematical abstractions from algebra,…
We develop a novel framework that aims to create bridges between the computational social choice and the database management communities. This framework enriches the tasks currently supported in computational social choice with relational…
In many scenarios, especially biomedical applications, the correct delineation of complex fine-scaled structures such as neurons, tissues, and vessels is critical for downstream analysis. Despite the strong predictive power of deep learning…
We describe a Martin-L\"of style dependent type theory, called Cocon, that allows us to mix the intensional function space that is used to represent higher-order abstract syntax (HOAS) trees with the extensional function space that…
The aim of this paper is to extend the Morse theory for geodesics to the conical manifolds. We define these manifolds as submanifolds of $\R^n$ with a finite number of conical singularities. To formulate a good Morse theory we must use an…
This paper presents meta-logical investigations based on category theory using the proof assistant Isabelle/HOL. We demonstrate the potential of a free logic based shallow semantic embedding of category theory by providing a formalization…
Matrices and more generally multidimensional arrays, form the backbone of computational studies. In this paper we demonstrate increases in computational efficiency by performing partial-tracing/tensor-contractions on sparse-arrays. It was…
We study the connection between discrete Morse theory and persistent homology in the context of shape reconstruction methods. Specifically, we consider the construction of Wrap complexes, introduced by Edelsbrunner as a subcomplex of the…
The homotopy theory of representations of nets of algebras over a (small) category with values in a closed symmetric monoidal model category is developed. We illustrate how each morphism of nets of algebras determines a change-of-net…
Graph-based representations underlie a wide range of scientific problems. Graph connectivity is typically represented as a sparse matrix in the Compressed Sparse Row format. Large-scale graphs rely on distributed storage, allocating…
Many real-world systems can be modeled as interconnected multilayer networks, namely a set of networks interacting with each other. Here we present a perturbative approach to study the properties of a general class of interconnected…
This work establishes a robust mathematical foundation for compositional System Dynamics modeling, leveraging category theory to formalize and enhance the representation, analysis, and composition of system models. Here, System Dynamics…