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Predicting protein-protein interactions (PPIs) by learning informative representations from amino acid sequences is a challenging yet important problem in biology. Although various deep learning models in Siamese architecture have been…
This paper introduces a novel method for compact representation of sets of n-dimensional binary sequences in a form of compact triplets structures (CTS), supposing both logic and arithmetic interpretations of data. Suitable illustration of…
We develop a unified categorical theory of substructural abstract syntax with variable binding and single-variable (capture-avoiding) substitution. This is done for the gamut of context structural rules given by exchange (linear theory)…
In sequent calculi, cut elimination is a property that guarantees that any provable formula can be proven analytically. For example, Gentzen's classical and intuitionistic calculi LK and LJ enjoy cut elimination. The property is less…
Any set of truth-functional connectives has sequent calculus rules that can be generated systematically from the truth tables of the connectives. Such a sequent calculus gives rise to a multi-conclusion natural deduction system and to a…
In this review, we discuss approaches for learning causal structure from data, also called causal discovery. In particular, we focus on approaches for learning directed acyclic graphs (DAGs) and various generalizations which allow for some…
Structural learning, which aims to learn directed acyclic graphs (DAGs) from observational data, is foundational to causal reasoning and scientific discovery. Recent advancements formulate structural learning into a continuous optimization…
A rapidly growing body of research on compositional generalization investigates the ability of a semantic parser to dynamically recombine linguistic elements seen in training into unseen sequences. We present a systematic comparison of…
One of the central open questions in bounded arithmetic is whether Buss' hierarchy of theories of bounded arithmetic collapses or not. In this paper, we reformulate Buss' theories using free logic and conjecture that such theories are…
We introduce a functional calculus with simple syntax and operational semantics in which the calculi introduced so far in the Curry-Howard correspondence for Classical Logic can be faithfully encoded. Our calculus enjoys confluence without…
We present an algebraic construction of trace-based De Bruijn tori over finite fields, focusing on the nonzero variant that omits the all-zero pattern. The construction arranges nonzero field elements on a toroidal grid using two…
Continuous-time Bayesian Networks (CTBNs) represent a compact yet powerful framework for understanding multivariate time-series data. Given complete data, parameters and structure can be estimated efficiently in closed-form. However, if…
We present a calculus that models a simple sort of process interaction. Our calculus consists of a collection of terms together with a rewrite relation, parameterised by an arbitrary multicategory whose morphisms we understand as…
We provide a general and syntactically-defined family of sequent calculi, called \emph{semi-analytic}, to formalize the informal notion of a "nice" sequent calculus. We show that any sufficiently strong (multimodal) substructural logic with…
The intrinsic treatment of binding in the lambda calculus makes it an ideal data structure for representing syntactic objects with binding such as formulas, proofs, types, and programs. Supporting such a data structure in an implementation…
The popular view according to which Category theory provides a support for Mathematical Structuralism is erroneous. Category-theoretic foundations of mathematics require a different philosophy of mathematics. While structural mathematics…
Inspired by the ideas and techniques used in the study of cluster algebras we construct a new class of algebras, called bistellar cluster algebras, from closed oriented triangulated even-dimensional manifolds by performing…
The distribution of a given sequence in the set of all sequences with n ones and m = M - n zeros are found by relating the problem to the partitions of a natural number in m natural summands, taking into account the order. The formulas…
Grid computing (GC) systems are large-scale virtual machines, built upon a massive pool of resources (processing time, storage, software) that often span multiple distributed domains. Concurrent users interact with the grid by adding new…
A *-algebraic indefinite structure of quantum stochastic (QS) calculus is introduced and a continuity property of generalized nonadapted QS integrals is proved under the natural integrability conditions in an infinitely dimensional nuclear…