Related papers: Spatio-temporal c\`adl\`ag functional marked point…
Many very large-scale systems are networks of cyber-physical systems in which humans and autonomous software agents cooperate. To make the cooperation safe for the humans involved, the systems have to follow protocols with rigid real-time…
Many real-world processes are trajectories that may be regarded as continuous-time "functional data". Examples include patients' biomarker concentrations, environmental pollutant levels, and prices of stocks. Corresponding advances in data…
Spatio-temporal point processes (STPPs) model discrete events distributed in time and space, with important applications in areas such as criminology, seismology, epidemiology, and social networks. Traditional models often rely on…
Categorical Message Passing Language (CaMPL) is a functional-style concurrent programming language whose semantics is in category theory, more specifically, linear actegories. Its core programming feature is message passing along typed…
Many image-based perception tasks can be formulated as detecting, associating and tracking semantic keypoints, e.g., human body pose estimation and tracking. In this work, we present a general framework that jointly detects and forms…
Randomized Numerical Linear Algebra (RandNLA) uses randomness to develop improved algorithms for matrix problems that arise in scientific computing, data science, machine learning, etc. Determinantal Point Processes (DPPs), a seemingly…
Markov branching systems form a fundamental class of stochastic models that are extensively applied in biology, physics, finance, and other domains. These systems are distinguished by their continuous-time evolution and inherent branching…
We describe a computational framework for modeling and statistical inference on high-dimensional stochastic dynamic systems. Our primary motivation is the investigation of metapopulation dynamics arising from a collection of spatially…
In this paper we study time-inhomogeneous affine processes beyond the common assumption of stochastic continuity. In this setting times of jumps can be both inaccessible and predictable. To this end we develop a general theory of finite…
The space-time fractional Poisson process (STFPP), defined by Orsingher and Poilto in \cite{sfpp}, is a generalization of the time fractional Poisson process (TFPP) and the space fractional Poisson process (SFPP). We study the fractional…
We study Markov-modulated affine processes (abbreviated MMAPs), a class of Markov processes that are created from affine processes by allowing some of their coefficients to be a function of an exogenous Markov process. MMAPs allow for…
The spatial and temporal aspects of system properties are crucial for many types of systems. In this short paper, we present a TopFunST framework to analyse topological dependencies among features of the system, covering also spatial and…
Determinantal point processes (DPPs) are repulsive point processes where the interaction between points depends on the determinant of a positive-semi definite matrix. In this paper, we study the limiting process of L-ensembles based on…
Determinantal point processes (DPPs) offer an elegant tool for encoding probabilities over subsets of a ground set. Discrete DPPs are parametrized by a positive semidefinite matrix (called the DPP kernel), and estimating this kernel is key…
We propose a unified mathematical framework for classifying phases of matter. The framework is based on different types of combinatorial structures with a notion of locality called lattices. A tensor lattice is a local prescription that…
Spatio-temporal point processes (STPPs) are potent mathematical tools for modeling and predicting events with both temporal and spatial features. Despite their versatility, most existing methods for learning STPPs either assume a restricted…
Individual mobility prediction is an essential task for transportation demand management and traffic system operation. There exist a large body of works on modeling location sequence and predicting the next location of users; however,…
Classification is a vital tool that is important for modelling many complex numerical models. A model or system may be such that, for certain areas of input space, the output either does not exist, or is not in a quantifiable form. Here, we…
In this research paper, the relationship between finite / countable state space stochastic processes and point processes is explored. Utilizing the known relationship between Poisson processes and continuous time Markov chains, finite /…
Thank you very much for the attention and concern of colleagues and scholars in this work. With the comments and guidance of experts, editors, and reviewers, this work has been accepted for publishing in the journal "Process Safety and…