Related papers: Towards Better: A motivated introduction to better…
Higher-order probabilistic programming languages allow programmers to write sophisticated models in machine learning and statistics in a succinct and structured way, but step outside the standard measure-theoretic formalization of…
Networks are a fundamental tool for understanding and modeling complex systems in physics, biology, neuroscience, engineering, and social science. Many networks are known to exhibit rich, lower-order connectivity patterns that can be…
Rankings are a fact of life. Whether or not one likes them, they exist and are influential. Within academia, and in computer science in particular, rankings not only capture our attention but also widely influence people who have a limited…
The notion of quasicrossed product is introduced in the setting of G-graded quasialgebras, i.e., algebras endowed with a grading by a group G, satisfying a "quasiassociative" law. The equivalence between quasicrossed products and…
The aim of these notes is to provide a succinct, accessible introduction to some of the basic ideas of category theory and categorical logic. The notes are based on a lecture course given at Oxford over the past few years. They contain…
We provide a method of constructing better-quasi-orders by generalising a technique for constructing operator algebras that was developed by Pouzet. We then generalise the notion of $\sigma$-scattered to partial orders, and use our method…
We consider partially ordered sets of combinatorial structures under consecutive orders, meaning that two structures are related when one embeds in the other such that `consecutive' elements remain consecutive in the image. Given such a…
It is usually assumed that a quantum computation is performed by applying gates in a specific order. One can relax this assumption by allowing a control quantum system to switch the order in which the gates are applied. This provides a more…
These notes provide a quick introduction to the Coq system and show how it can be used to define logical concepts and functions and reason about them. It is designed as a tutorial, so that readers can quickly start their own experiments,…
The famous theorem of Higman states that for any well-quasi-order (wqo) $Q$ the embeddability order on finite sequences over $Q$ is also wqo. In his celebrated 1965 paper, Nash-Williams established that the same conclusion holds even for…
The unrivaled robustness of topologically ordered states of matter against perturbations has immediate applications in quantum computing and quantum metrology, yet their very existence poses a challenge to our understanding of phase…
We are interested in characterizing which classes of finite graphs are well-quasi-ordered by the induced subgraph relation. To that end, we devise an algorithm to decide whether a class of finite graphs well-quasi-ordered by the induced…
In applied game theory the motivation of players is a key element. It is encoded in the payoffs of the game form and often based on utility functions. But there are cases were formal descriptions in the form of a utility function do not…
We show that Nash-Williams' theorem asserting that the countable transfinite sequences of elements of a better-quasi-ordering ordered by embeddability form a better-quasi-ordering is provable in the subsystem of second order arithmetic…
The most successful unfolding rules used nowadays in the partial evaluation of logic programs are based on well quasi orders (wqo) applied over (covering) ancestors, i.e., a subsequence of the atoms selected during a derivation. Ancestor…
In recent years, quantum mechanics has been actively used in areas outside of physics, such as psychology, sociology, theory of decision-making, game theory, and others. In particular, quantum mechanics is used to explain the paradoxes…
Q-learning can be described as an all-purpose automaton that provides estimates (Q-values) of the continuation values associated with each available action and follows the naive policy of almost always choosing the action with highest…
The quadratic unconstrained binary optimization (QUBO) problem arises in diverse optimization applications ranging from Ising spin problems to classical problems in graph theory and binary discrete optimization. The use of preprocessing to…
For processes involving structure functions and/or fragmentation functions, arguments that, over a range of a proper kinematic variable, there is a part that dominates the next-to-leading order (NLO) corrections are briefly reviewed. The…
The juxtaposition of permutation classes $\mathcal{C}$ and $\mathcal{D}$ is the class of all permutations formed by concatenations $\sigma\tau$, such that $\sigma$ is order isomorphic to a permutation in $\mathcal{C}$, and $\tau$ to a…