Related papers: On the likelihood of normalisation in combinatory …

We give theorems about asymptotic normality of general additive functionals on patricia tries in an i.i.d. setting, derived from results on tries by Janson (2022). These theorems are applied to show asymptotic normality of the distribution…

We describe a combinatorial approach for investigating properties of rational numbers. The overall approach rests on structural bijections between rational numbers and familiar combinatorial objects, namely rooted trees. We emphasize that…

We study a very large family of graphs, the members of which comprise disjoint paths of cliques with extremal cliques identified. This broad characterisation naturally generalises those of various smaller families of graphs having…

Linear thresholding models postulate that the conditional distribution of a response variable in terms of covariates differs on the two sides of a (typically unknown) hyperplane in the covariate space. A key goal in such models is to learn…

Asymptotic analysis on some statistical properties of the random binary-tree model is developed. We quantify a hierarchical structure of branching patterns based on the Horton-Strahler analysis. We introduce a transformation of a binary…

We prove that in characteristic zero the multiplication of sections of dominant line bundles on a complete symmetric variety $X=\bar{G/H}$ is a surjective map. As a consequence the cone defined by a complete linear system over $X$, or over…

We provide results on the smoothness of normalisers in connected reductive algebraic groups $G$ over fields $k$ of positive characteristic $p$. Specifically we we give bounds on $p$ which guarantee that normalisers of subalgebras of…

Consider a random recusive tree with n vertices. We show that the number of vertices with even depth is asymptotically normal as n tends to infinty. The same is true for the number of vertices of depth divisible by m for m=3, 4 or 5; in all…

An interesting result by T. Kato and A. Pazy says that a contractive semigroup (T(t)) on a uniformly convex space X is holomorphic iff limsup_{t \downarrow 0} ||T(t)-Id|| < 2. We study extensions of this result which are valid on arbitrary…

Hybrid logic with binders is an expressive specification language. Its satisfiability problem is undecidable in general. If frames are restricted to N or general linear orders, then satisfiability is known to be decidable, but of…

This work investigates the algorithmic complexity of non-classical logics, focusing on superintuitionistic and modal systems. It is shown that propositional logics are usually polynomial-time reducible to their fragments with at most two…

Polynomial multiplication is known to have quasi-linear complexity in both the dense and the sparse cases. Yet no truly linear algorithm has been given in any case for the problem, and it is not clear whether it is even possible. This…

In this article we survey the development of generic and coarse computability and the main results on how classical asymptotic density interacts with the theory of computability.

Representing a proof tree by a combinator term that reduces to the tree lets subtle forms of duplication within the tree materialize as duplicated subterms of the combinator term. In a DAG representation of the combinator term these…

The success of machine learning solutions for reasoning about discrete structures has brought attention to its adoption within combinatorial optimization algorithms. Such approaches generally rely on supervised learning by leveraging…

The number of embeddings of a partially ordered set $S$ in a partially ordered set $T$ is the number of subposets of $T$ isomorphic to $S$. If both, $S$ and $T$, have only one unique maximal element, we define good embeddings as those in…

We study the complexity of finding an optimal hierarchical clustering of an unweighted similarity graph under the recently introduced Dasgupta objective function. We introduce a proof technique, called the normalization procedure, that…

We prove that the rational elliptic curve y^2 = x^3 - n^2x satisfies the full Birch and Swinnerton-Dyer conjecture for at least 41.9% of positive squarefree integers n equal to 1, 2, or 3 mod 8, and that it satisfies the regular BSD…

Deep neural networks generalize well despite being exceedingly overparameterized and being trained without explicit regularization. This curious phenomenon has inspired extensive research activity in establishing its statistical principles:…

Adapting a result of Bazhenov, Kalimullin, and Yamaleev, we show that if a Turing degree $\textbf{d}$ is the degree of categoricity of a computable structure $\mathcal{M}$ and is not the strong degree of categoricity of any computable…