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Dynamical systems theory is especially well-suited for determining the possible asymptotic states (at both early and late times) of cosmological models, particularly when the governing equations are a finite system of autonomous ordinary…
A variety of complex fluids under shear exhibit complex spatio-temporal behaviour, including what is now termed rheological chaos, at moderate values of the shear rate. Such chaos associated with rheological response occurs in regimes where…
Cellular automata are fully-discrete, spatially-extended dynamical systems that evolve by simultaneously applying a local update function. Despite their simplicity, the induced global dynamic produces a stunning array of richly-structured,…
Reasoning about security properties involves reasoning about where the information of a system is located, and how it evolves over time. While most security analysis techniques need to cope with some notions of information locality and…
In this article, we develop fully Bayesian, copula-based, spatial-statistical models for large, noisy, incomplete, and non-Gaussian spatial data. Our approach includes novel constructions of copulas that accommodate a spatial-random-effects…
We define a class of probabilistic models in terms of an operator algebra of stochastic processes, and a representation for this class in terms of stochastic parameterized grammars. A syntactic specification of a grammar is mapped to…
Cells exhibit a wide variety of different shapes. This diversity poses a challenge for computational approaches that attempt to shed light on the role cell geometry plays in regulating cell physiology and behavior. The simulation platform…
A high activity of reactions can be confined in a model cell with a semipermeable membrane in the Schl\"ogl model. It is interpreted as a model of primitive metabolism in a cell. We study two generalized models to understand the creation of…
Since its foundations, more than one hundred years ago, the field of structural biology has strived to understand and analyze the properties of molecules and their interactions by studying the structure that they take in 3D space. However,…
This study presents a mathematical model describing cloned hematopoiesis in chronic myeloid leukemia (CML) through a nonlinear system of differential equations. The primary objective is to understand the progression from healthy…
We study the Scalar Field Cosmology (SFC) using the geometric language of the phase space. We define and study an ensemble of dynamical systems as a Banach space with a Sobolev metric. The metric in the ensemble is used to measure a…
Over the past year, the development of large language models (LLMs) has brought spatial intelligence into focus, with much attention on vision-based embodied intelligence. However, spatial intelligence spans a broader range of disciplines…
The use of Domain-Specific Languages (DSLs) is a promising field for the development of tools tailored to specific problem spaces, effectively diminishing the complexity of hand-made software. With the goal of making models as precise,…
We develop a latent variable model and an efficient spectral algorithm motivated by the recent emergence of very large data sets of chromatin marks from multiple human cell types. A natural model for chromatin data in one cell type is a…
We explore developing rich semantic models of systems. Specifically, we consider structured causal explanations about state changes in those systems. Essentially, we are developing process-based dynamic knowledge graphs. As an example, we…
We introduce a novel approach for parallelizing MCMC inference in models with spatially determined conditional independence relationships, for which existing techniques exploiting graphical model structure are not applicable. Our approach…
Self-similar, spherically symmetric cosmological models with a perfect fluid and a scalar field with an exponential potential are investigated. New variables are defined which lead to a compact state space, and dynamical systems methods are…
Semantic context is an important and useful cue for scene parsing in complicated natural images with a substantial amount of variations in objects and the environment. This paper proposes Spatially Constrained Location Prior (SCLP) for…
Recently, recurrent models based on linear state space models (SSMs) have shown promising performance in language modeling (LM), competititve with transformers. However, there is little understanding of the in-principle abilities of such…
Binary decision diagrams can compactly represent vast sets of states, mitigating the state space explosion problem in model checking. Probabilistic systems, however, require multi-terminal diagrams storing rational numbers. They are…