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In observational studies, the true causal model is typically unknown and needs to be estimated from available observational and limited experimental data. In such cases, the learned causal model is commonly represented as a partially…
Comprehending and elucidating the purpose of code is often cited as being a key learning objective within introductory programming courses. To address this objective ``Explain-in-Plain-English'' questions, in which students are shown a…
We present a process algebra aimed at describing interactions that are multiparty, i.e. that may involve more than two processes and that are open, i.e. the number of the processes they involve is not fixed or known a priori. Here we focus…
Datalogo is an extension of Datalog that allows for aggregation and recursion over an arbitrary commutative semiring. Like Datalog, Datalogo programs can be evaluated via the natural iterative algorithm until a fixed point is reached.…
We prove that the number of parameters defining a complex of projective modules over a finite dimensional algebra is upper semi-continuous in families of algebras. Supposing that every algebra is either derived tame or derived wild, we get…
Answer set programming - the most popular problem solving paradigm based on logic programs - has been recently extended to support uninterpreted function symbols. All of these approaches have some limitation. In this paper we propose a…
Let $P$ be a unital subsemigroup of a group $G$. We propose an approach to $\mathrm{C}^*$-algebras associated to product systems over $P$. We call the $\mathrm{C}^*$-algebra of a given product system $\mathcal{E}$ its covariance algebra and…
Several popular language models represent local contexts in an input text $x$ as bags of words. Such representations are naturally encoded by a sequence graph whose vertices are the distinct words occurring in $x$, with edges representing…
Multiplicative gating is widely used in neural architectures and has recently been applied to attention layers to improve performance and training stability in large language models. Despite the success of gated attention, the mathematical…
Standard architectures used in instruction following often struggle on novel compositions of subgoals (e.g. navigating to landmarks or picking up objects) observed during training. We propose a modular architecture for following natural…
Automata expressiveness is an essential feature in understanding which of the formalisms available should be chosen for modelling a particular problem. Probabilistic and stochastic automata are suitable for modelling systems exhibiting…
Program source code contains complex structure information, which can be represented in structured data forms like trees or graphs. To acquire the structural information in source code, most existing researches use abstract syntax trees…
Motivated by old and new applications, we investigate Datalog as a language for sequence databases. We reconsider classical features of Datalog programs, such as negation, recursion, intermediate predicates, and relations of higher arities.…
The class of Gaussian Process (GP) methods for Temporal Difference learning has shown promise for data-efficient model-free Reinforcement Learning. In this paper, we consider a recent variant of the GP-SARSA algorithm, called Sparse…
A sequence of nonnegative integers $\pi$ is {\it graphic} if it is the degree sequence of some graph $G$. In this case we say that $G$ is a \textit{realization} of $\pi$, and we write $\pi=\pi(G)$. A graphic sequence $\pi$ is {\it…
We show that if $T$ is any of four semigroups of two elements that are not groups, there exists a finite dimensional associative $T$-graded algebra over a field of characteristic $0$ such that the codimensions of its graded polynomial…
We propose to consider non confluence with respect to implicit complexity. We come back to some well known classes of first-order functional program, for which we have a characterization of their intentional properties, namely the class of…
Scott's graph model is a lambda-algebra based on the observation that continuous endofunctions on the lattice of sets of natural numbers can be represented via their graphs. A graph is a relation mapping finite sets of input values to…
Software for the resolution of certain kind of problems, those that rate high in the Stringent Performance Objectives adjustment factor (IFPUG scheme), can be described using a combination of game theory and autonomous systems. From this…
Geometry constitutes a core set of intuitions present in all humans, regardless of their language or schooling [1]. Could brain's built in machinery for processing geometric information take part in uncertainty representation? For decades…