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This article may be seen as a summary and a final discussion of the work that the author has done in recent years on the foundation of quantum theory. It is shown that quantum mechanics as a model follows under certain specific conditions…
Intelligent agent naturally learns from motion. Various self-supervised algorithms have leveraged motion cues to learn effective visual representations. The hurdle here is that motion is both ambiguous and complex, rendering previous works…
A statistical, path-dependent framework to describe time-dependent macroscopic theories using the Principle of Maximum Caliber is presented. By means of this procedure, it is possible to infer predictive non-equilibrium statistical…
In the present work we discuss a third alternative to explain the latest observational data concerning the accelerating Universe and its different stages. The particle creation mechanism in the framework of non-equilibrium thermodynamics is…
Mining genuine mechanisms underlying the complex data generation process in real-world systems is a fundamental step in promoting interpretability of, and thus trust in, data-driven models. Therefore, we propose a variation-based cause…
The transition from reversible microdynamics to irreversible transport can be studied very efficiently with the help of the so-called projection method. We give a concise introduction to that method, illustrate its power by using it to…
We propose a framework for studying predictability of extreme events in complex systems. Major conceptual elements -- hierarchical structure, spatial dynamics, and external driving -- are combined in a classical branching diffusion with…
We consider the orbital motion of a test particle in the gravitational field of a massive body (that might be a black hole) with mass $m$ placed on the expanding cosmological manifold described by the McVittie metric. We introduce the local…
We consider symmetries and reduction in non-relativistic many-body quantum mechanics, with the aim of identifying physically meaningful observables in systems such as molecules and crystalline solids. To this end, we propose a unified…
A time-dependent vibrational electronic coupled-cluster (VECC) approach is proposed to simulate photoelectron/ UV-VIS absorption spectra, as well as time-dependent properties for non-adiabatic vibronic models, going beyond the…
A construction of covariant quantum phase observables, for Hamiltonians with a finite number of energy eigenvalues, has been recently given by D. Arsenovic et al. [Phys. Rev. A 85, 044103 (2012)]. For Hamiltonians generating periodic…
The paper presents a multidimensional model for nonlinear Markovian random walks that generalizes one we developed previously (Phys. Rev. E v.79, 011110, 2009) in order to describe the Levy type stochastic processes in terms of continuous…
We propose a new classical approach for describing a system composed of $n$ interacting particles with variable mass connected by a single field with no predefined form ($n$-VMVF systems). Instead of assuming any particular nature or…
Recent advances in electron, scanning probe, optical, and chemical imaging and spectroscopy yield bespoke data sets containing the information of structure and functionality of complex systems. In many cases, the resulting data sets are…
Bayesian Inference is a powerful approach to data analysis that is based almost entirely on probability theory. In this approach, probabilities model {\it uncertainty} rather than randomness or variability. This thesis is composed of a…
Multimodal VAEs seek to model the joint distribution over heterogeneous data (e.g.\ vision, language), whilst also capturing a shared representation across such modalities. Prior work has typically combined information from the modalities…
1. Understanding the mechanisms underlying biological systems, and ultimately, predicting their behaviours in a changing environment requires overcoming the gap between mathematical models and experimental or observational data.…
Bayesian methods have proved powerful in many applications for the inference of model parameters from data. These methods are based on Bayes' theorem, which itself is deceptively simple. However, in practice the computations required are…
In this PhD thesis, we explore and apply methods inspired by the free energy principle to two important areas in machine learning and neuroscience. The free energy principle is a general mathematical theory of the necessary…
It is hypothesised, following Conrad et al. (1988) (http://www.tcm.phy.cam.ac.uk/~bdj10/papers/urbino.html) that quantum physics is not the ultimate theory of nature, but merely a theoretical account of the phenomena manifested in nature…