Related papers: Algorithmic randomness and stochastic selection fu…
In this review we establish various connections between complex networks and symmetry. While special types of symmetries (e.g., automorphisms) are studied in detail within discrete mathematics for particular classes of deterministic graphs,…
There are good motivations for considering some type of quantum histories formalism. Several possible formalisms are known, defined by different definitions of event and by different selection criteria for sets of histories. These…
We develop a behavioural theory of reflective parallel algorithms (RAs), i.e. synchronous parallel algorithms that can modify their own behaviour. The theory comprises a set of postulates defining the class of RAs, an abstract machine…
This dissertation investigates questions arising in the consistent histories formulation of the quantum mechanics of closed systems. Various criteria for approximate consistency are analysed. The connection between the Dowker-Halliwell…
We use algorithmic methods from online learning to explore some important objects at the intersection of model theory and combinatorics, and find natural ways that algorithmic methods can detect and explain (and improve our understanding…
Natural numbers can be divided in two non-overlapping infinite sets, primes and composites, with composites factorizing into primes. Despite their apparent simplicity, the elucidation of the architecture of natural numbers with primes as…
Quantum machine learning (QML) aims to accelerate machine learning tasks by exploiting quantum computation. Previous work studied a QML algorithm for selecting sparse subnetworks from large shallow neural networks. Instead of directly…
In classical probability theory, the convergence of empirical frequencies to theoretical probabilities: as captured by the Law of Large Numbers (LLN): is treated as axiomatic and emergent from statistical assumptions such as independence…
Classic machine learning algorithms have been reviewed and studied mathematically on its performance and properties in detail. This paper intends to review the empirical functioning of widely used classical supervised learning algorithms…
Algorithmic theories of randomness can be related to theories of probabilistic sequence prediction through the notion of a predictor, defined as a function which supplies lower bounds on initial-segment probabilities of infinite sequences.…
This paper derives a unifying theorem establishing consistency results for a broad class of tree-based algorithms. It improves current results in two aspects. First of all, it can be applied to algorithms that vary from traditional Random…
In this paper, we consider robust control using randomized algorithms. We extend the existing order statistics distribution theory to the general case in which the distribution of population is not assumed to be continuous and the order…
Theoretical analyses of stochastic search algorithms, albeit few, have always existed since these algorithms became popular. Starting in the nineties a systematic approach to analyse the performance of stochastic search heuristics has been…
We begin by reiterating that common neural network activation functions have simple Bayesian origins. In this spirit, we go on to show that Bayes's theorem also implies a simple recurrence relation; this leads to a Bayesian recurrent unit…
Stochastic approximation algorithms are iterative procedures which are used to approximate a target value in an environment where the target is unknown and direct observations are corrupted by noise. These algorithms are useful, for…
Power-law distributions are typical macroscopic features occurring in almost all complex systems observable in nature. As a result, researchers in quantitative analyses must often generate random synthetic variates obeying power-law…
Many statistical problems involve mixture models and the need for computationally efficient methods to estimate the mixing distribution has increased dramatically in recent years. Newton [Sankhya Ser. A 64 (2002) 306--322] proposed a fast…
Randomized search algorithms for hard combinatorial problems exhibit a large variability of performances. We study the different types of rare events which occur in such out-of-equilibrium stochastic processes and we show how they cooperate…
This paper investigates the randomness properties of a function of the divisor pairs of a natural number. This function, the antecedents of which go to very ancient times, has randomness properties that can find applications in…
Previously referred to as `miraculous' in the scientific literature because of its powerful properties and its wide application as optimal solution to the problem of induction/inference, (approximations to) Algorithmic Probability (AP) and…