Related papers: Analyzing the topological structure of composite d…
Many real-world processes evolve in cascades over complex networks, whose topologies are often unobservable and change over time. However, the so-termed adoption times when blogs mention popular news items, individuals in a community catch…
Networked structures arise in a wide array of different contexts such as technological and transportation infrastructures, social phenomena, and biological systems. These highly interconnected systems have recently been the focus of a great…
This article surveys the mathematics of the cut and project method as applied to point sets, called here {\em model sets}. It covers the geometric, arithmetic, and analytical sides of this theory as well as diffraction and the connection…
As a first step toward realizing a dynamical system that evolves while spontaneously determining its own rule for time evolution, function dynamics (FD) is analyzed. FD consists of a functional equation with a self-referential term, given…
It is common for people to access multiple social networks, for example, using phone, email, and social media. Together, the multi-layer social interactions form a "integrated social network." How can we extend well developed knowledge…
Some of the basic properties of any dynamical system can be summarized by a graph. The dynamical systems in our theory run from maps like the logistic map to ordinary differential equations to dissipative partial differential equations. Our…
Persistent homology has recently emerged as a powerful technique in topological data analysis for analyzing the emergence and disappearance of topological features throughout a filtered space, shown via persistence diagrams. Additionally,…
Data collection at a massive scale is becoming ubiquitous in a wide variety of settings, from vast offline databases to streaming real-time information. Learning algorithms deployed in such contexts must rely on single-pass inference, where…
Scientific visualization tools tend to be flexible in some ways (e.g., for exploring isovalues) while restricted in other ways, such as working only on regular grids, or only on unstructured meshes (as used in the finite element method,…
Many natural systems, such as neurons firing in the brain or basketball teams traversing a court, give rise to time series data with complex, nonlinear dynamics. We can gain insight into these systems by decomposing the data into segments…
Bayesian networks are a versatile and powerful tool to model complex phenomena and the interplay of their components in a probabilistically principled way. Moving beyond the comparatively simple case of completely observed, static data,…
In contrast to dyadic interactions, higher-order interactions may contain one another, with subgroups naturally embedded within larger groups. These containment patterns arise empirically in ecology, sociology, computer science and the…
We discuss the problems of modeling, control, and decision support in complex dynamic systems from a general system theoretic point of view. The main characteristics of complex systems and of system approach to complex system study are…
We introduce structured prediction energy networks (SPENs), a flexible framework for structured prediction. A deep architecture is used to define an energy function of candidate labels, and then predictions are produced by using…
Recently, data exchange platforms have emerged in the digital economy to enable better resource allocation in a data-driven society, which requires cross-organizational data collaborations. Understanding the characteristics of the data on…
Differential equations based on physical principals are used to represent complex dynamic systems in all fields of science and engineering. Through repeated use in both academics and industry, these equations have been shown to represent…
Climate models play a crucial role in understanding the effect of environmental and man-made changes on climate to help mitigate climate risks and inform governmental decisions. Large global climate models such as the Community Earth System…
What is a time-varying graph, a time-varying topological space, or, more generally, a mathematical structure that evolves over time? In this work, we lay the foundations for a general theory of temporal data by introducing categories of…
In the present paper, we propose the model of {\it structural information learning machines} (SiLeM for short), leading to a mathematical definition of learning by merging the theories of computation and information. Our model shows that…
This short paper presents an abstract, tunable model of genomic structural change within the cell lifecycle and explores its use with simulated evolution. A well-known Boolean model of genetic regulatory networks is extended to include…