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We computationally implement and experimentally test the behavioral predictions of a dynamic neural model of lexical meaning in the framework of Dynamic Field Theory. We demonstrate the architecture and behavior of the model using as a test…

Syntactic structures used to play a vital role in natural language processing (NLP), but since the deep learning revolution, NLP has been gradually dominated by neural models that do not consider syntactic structures in their design. One…

Many stochastic physical systems evolve smoothly over time in the sense that the distribution of states changes regularly across time steps. The transition from current state to the next state can often be modeled as the combination of a…

This paper introduces a mathematical framework of a stochastic process model as a generalization of diffusion stochastic processes to model latent variables in categorical responses given unobserved random effects and maximum likelihood…

Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics…

We provide a survey on relational models. Relational models describe complete networked {domains by taking into account global dependencies in the data}. Relational models can lead to more accurate predictions if compared to non-relational…

These lecture notes cover basic automata-theoretic concepts and logical formalisms for the modeling and verification of concurrent and distributed systems. Many of these concepts naturally extend the classical automata and logics over…

We develop the foundations of Algebraic Stochastic Calculus, with an aim to replacing what is typically referred to as Stochastic Calculus by a purely categorical version thereof. We first give a sheaf theoretic reinterpretation of…

Recent trends in information management involve the periodic transcription of data onto secondary devices in a networked environment, and the proper scheduling of these transcriptions is critical for efficient data management. To assist in…

Representing token embeddings as probability distributions over learned manifolds allows for more flexible contextual inference, reducing representational rigidity while enhancing semantic granularity. Comparative evaluations demonstrate…

Linear implication can represent state transitions, but real transition systems operate under temporal, stochastic or probabilistic constraints that are not directly representable in ordinary linear logic. We propose a general modal…

Quantum contextuality, a fundamental feature distinguishing quantum theory from classical models, is investigated via algebraic and topological structures inherent in modular tensor categories. This work rigorously demonstrates that braid…

Automation systems are increasingly being used in dynamic and various operating conditions. With higher flexibility demands, they need to promptly respond to surrounding dynamic changes by adapting their operation. Context information…

This work proposes a general framework for capturing noise-driven transitions in spatially extended non-equilibrium systems and explains the emergence of coherent patterns beyond the instability onset. The framework relies on stochastic…

This document develops general concepts useful for extracting knowledge embedded in large graphs or datasets that have pair-wise relationships, such as cause-effect-type relations. Almost no underlying assumptions are made, other than that…

This paper explores the connection between semantic equivalences and preorders for concrete sequential processes, represented by means of labelled transition systems, and formats of transition system specifications using Plotkin's…

The Alexandrov topology affords a well-known semantics of modal necessity and possibility. This paper develops an Alexandrov topological semantics of intuitionistic propositional modal logic internally in any elementary topos. This is done…

This Thesis explores how tools from Statistical Physics and Information Theory can help us describe and understand complex systems. In the first part, we study the interplay between internal interactions, environmental changes, and…

Causal and temporal reasoning about video dynamics is a challenging problem. While neuro-symbolic models that combine symbolic reasoning with neural-based perception and prediction have shown promise, they exhibit limitations, especially in…

This report is an extension of 'A Model of Parametric Dependent Type Theory in Bridge/Path Cubical Sets' (Nuyts, arXiv:1706.04383). The purpose of this text is to prove all technical aspects of our model for dependent type theory with…