Related papers: Algebraic analysis of multiple social networks wit…
We present a form of algebraic reasoning for computational objects which are expressed as graphs. Edges describe the flow of data between primitive operations which are represented by vertices. These graphs have an interface made of…
Real networks often form interacting parts of larger and more complex systems. Examples can be found in different domains, ranging from the Internet to structural and functional brain networks. Here, we show that these multiplex systems are…
Directed acyclic graphs (DAGs) are a popular framework to express multivariate probability distributions. Acyclic directed mixed graphs (ADMGs) are generalizations of DAGs that can succinctly capture much richer sets of conditional…
A network can be analyzed at different topological scales, ranging from single nodes to motifs, communities, up to the complete structure. We propose a novel intermediate-level topological analysis that considers non-overlapping subgraphs…
Data depth concept offers a variety of powerful and user friendly tools for robust exploration and inference for multivariate socio-economic phenomena. The offered techniques may be successfully used in cases of lack of our knowledge on…
We present probabilistic neural programs, a framework for program induction that permits flexible specification of both a computational model and inference algorithm while simultaneously enabling the use of deep neural networks.…
We introduce the Macaulay2 package GradedLieAlgebras for doing computations in graded Lie algebras presented by generators and relations.
We shortly describe the algorithms behind some of the functions provided by the Macaulay2 package MultiprojectiveVarieties, a package for multi-projective varieties and rational maps between them.
Due to the advent of the expressions of data other than tabular formats, the topological compositions which make samples interrelated came into prominence. Analogically, those networks can be interpreted as social connections, dataflow…
Complex networks are frequently employed to model physical or virtual complex systems. When certain entities exist across multiple systems simultaneously, unveiling their corresponding relationships across the networks becomes crucial. This…
An arithmetical structure on a graph is given by a labeling of the vertices which satisfies certain divisibility properties. In this note, we look at several families of graphs and attempt to give counts on the number of arithmetical…
With the advent of high-throughput sequencing (HTS) in molecular biology and medicine, the need for scalable statistical solutions for modeling complex biological systems has become of critical importance. The increasing number of platforms…
Graph signal processing (GSP) has become an important tool in image processing because of its ability to reveal underlying data structures. Many real-life multimedia datasets, however, exhibit heterogeneous structures across frames.…
Recently, distributed processing of large dynamic graphs has become very popular, especially in certain domains such as social network analysis, Web graph analysis and spatial network analysis. In this context, many distributed/parallel…
In this paper we describe the main featuress of the Bergm package for the open-source R software which provides a comprehensive framework for Bayesian analysis for exponential random graph models: tools for parameter estimation, model…
We present the $\textit{NumericalImplicitization}$ package for $\textit{Macaulay2}$, which allows for user-friendly computation of the invariants of the image of a polynomial map, such as dimension, degree, and Hilbert function values. This…
This paper describes a novel Python package, named causalgraph, for modeling and saving causal graphs embedded in knowledge graphs. The package has been designed to provide an interface between causal disciplines such as causal discovery…
Laplacian matrices of graphs arise in large-scale computational applications such as machine learning; spectral clustering of images, genetic data and web pages; transportation network flows; electrical resistor circuits; and elliptic…
We introduce the \verb|Macaulay2| package \verb|RepHomology| for the computations of representation homology of certain spaces. The main methods implement computing the representation homology of surfaces (with group coefficients, and…
In this paper we propose an algebraic formalization of connectors in the quantitative setting, in order to address their non-functional features in architectures of component-based systems. We firstly present a weighted Algebra of…