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Recent research has demonstrated that quantum computers can solve certain types of problems substantially faster than the known classical algorithms. These problems include factoring integers and certain physics simulations. Practical…
The study of mereology (parts and wholes) in the context of formal approaches to vagueness can be approached in a number of ways. In the context of rough sets, mereological concepts with a set-theoretic or valuation based ontology acquire…
The goal of this thesis is twofold; introduce the fundamentals of Bayesian inference and computation focusing on astronomical and cosmological applications, and present recent advances in probabilistic computational methods developed by the…
How do neural network image classifiers respond to simpler and simpler inputs? And what do such responses reveal about the learning process? To answer these questions, we need a clear measure of input simplicity (or inversely, complexity),…
State estimation or filtering serves as a fundamental task to enable intelligent decision-making in applications such as autonomous vehicles, robotics, healthcare monitoring, smart grids, intelligent transportation, and predictive…
In this paper we study a new approach to classify mathematical theorems according to their computational content. Basically, we are asking the question which theorems can be continuously or computably transferred into each other? For this…
I am most honoured to have the privilege to present the Foreword to this fascinating and wonderfully varied collection of contributions, concerning the nature of computation and of its deep connection with the operation of those basic laws,…
What is computable with limited resources? How can we verify the correctness of computations? How to measure computational power with precision? Despite the immense scientific and engineering progress in computing, we still have only…
This paper focuses on greedy expansions, one possible representation of numbers, and on arithmetical operations with them. Performing addition or multiplication some additional digits can appear. We study bounds on the number of such digits…
We study a broad class of algorithmic problems with an "additive flavor" such as computing sumsets, 3SUM, Subset Sum and geometric pattern matching. Our starting point is that these problems can often be solved efficiently for integers,…
The use of simulation-based methods for introducing inference is growing in popularity for the Stat 101 course, due in part to increasing evidence of the methods ability to improve students' statistical thinking. This impact comes from…
For the first time in history, we are seeing a branching point in computing paradigms with the emergence of quantum processing units (QPUs). Extracting the full potential of computation and realizing quantum algorithms with a…
We provide explicit, finite-sample guarantees for learning causal representations from data with a sublinear number of environments. Causal representation learning seeks to provide a rigourous foundation for the general representation…
Modern machine learning applications should be able to address the intrinsic challenges arising over inference on massive real-world datasets, including scalability and robustness to outliers. Despite the multiple benefits of Bayesian…
While machine learning is traditionally a resource intensive task, embedded systems, autonomous navigation and the vision of the Internet-of-Things fuel the interest in resource efficient approaches. These approaches require a carefully…
For several years, students visit us on different occasions at the university. But how to bridge from the school curriculum to the contents of the university mathematics? And how to find a focal point at which an active contribute, despite…
The goal of this paper is to explore the basic Approximate Bayesian Computation (ABC) algorithm via the lens of information theory. ABC is a widely used algorithm in cases where the likelihood of the data is hard to work with or…
The computational complexity of reasoning within the Dempster-Shafer theory of evidence is one of the main points of criticism this formalism has to face. To overcome this difficulty various approximation algorithms have been suggested that…
A new Approximate Bayesian Computation (ABC) algorithm for Bayesian updating of model parameters is proposed in this paper, which combines the ABC principles with the technique of Subset Simulation for efficient rare-event simulation, first…
Quantum computing is an emerging field with growing implications across science and industry, making early educational exposure increasingly important. This paper examines how quantum computing concepts can be introduced into high-school…