Related papers: A category theory approach using preradicals to mo…
It is well-known that biological phenomena are emergent. Emergent phenomena are quite interesting and amazing. However, they are difficult to be understood. Due to this difficulty, we propose a theory to describe emergence based on a…
To investigate the role of information flow in group formation, we introduce a model of communication and social navigation. We let agents gather information in an idealized network society, and demonstrate that heterogeneous groups can…
Understanding human mobility is crucial for applications such as forecasting epidemic spreading, planning transport infrastructure and urbanism in general. While, traditionally, mobility information has been collected via surveys, the…
Many of the essential features of the evolution of scientific research are imprinted in the structure of citation networks. Connections in these networks imply information about the transfer of knowledge among papers, or in other words,…
In this work we consider a generalization of graph flows. A graph flow is, in its simplest formulation, a labeling of the directed edges with real numbers subject to various constraints. A common constraint is conservation in a vertex,…
This work is motivated by the following question in data-driven study of dynamical systems: given a dynamical system that is observed via time series of persistence diagrams that encode topological features of solutions snapshots, what…
The bedrock of persistence theory over a single parameter is decomposition of persistence modules into intervals. In [HLM24], the authors leveraged interval decomposition to produce a cell decomposition of the minimal model of a simply…
In this paper, we consider the temporal pattern in traffic flow time series, and implement a deep learning model for traffic flow prediction. Detrending based methods decompose original flow series into trend and residual series, in which…
In real-world systems, the relationships and connections between components are highly complex. Real systems are often described as networks, where nodes represent objects in the system and edges represent relationships or connections…
Classical path search assumes complete graphs and scalar optimization metrics, yet real infrastructure networks are incomplete and require multi-dimensional evaluation. We introduce the concept of traversal: a generalization of paths that…
Standard methods of using categorical variables as predictors either endow them with an ordinal structure or assume they have no structure at all. However, categorical variables often possess structure that is more complicated than a linear…
Multiparameter persistent homology has emerged as a powerful generalization of topological data analysis, capable of encoding multivariate filtrations. However, the algebraic complexity of multiparameter persistence modules, marked by wild…
Dynamical processes, such as the diffusion of knowledge, opinions, pathogens, "fake news", innovation, and others, are highly dependent on the structure of the social network on which they occur. However, questions on why most social…
We develop a category-theoretic criterion for determining the equivalence of causal models having different but homomorphic directed acyclic graphs over discrete variables. Following Jacobs et al. (2019), we define a causal model as a…
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…
This article advances the prerequisite network as a means to visualize the hidden structure in an academic curriculum. Network technologies have been used for some time now in social analyses and more recently in biology in the areas of…
We introduce priors and algorithms to perform Bayesian inference in Gaussian models defined by acyclic directed mixed graphs. Such a class of graphs, composed of directed and bi-directed edges, is a representation of conditional…
Modeling a sequence of design steps, or a sequence of parameter settings, yields a sequence of dynamical systems. In many cases, such a sequence is intended to approximate a certain limit case. However, formally defining that limit turns…
We show how every stock-flow consistent model of the macroeconomy can be represented as a directed acyclic graph. The advantages of representing the model in this way include graphical clarity, causal inference, and model specification. We…
The correlations that can be observed between a set of variables depend on the causal structure underpinning them. Causal structures can be modeled using directed acyclic graphs, where nodes represent variables and edges denote functional…