Related papers: Learning families of algebraic structures from inf…

We study automorphic Lie algebras and their applications to integrable systems. Automorphic Lie algebras are a natural generalisation of celebrated Kac-Moody algebras to the case when the group of automorphisms is not cyclic. They are…

We propose a set theory strong enough to interpret powerful type theories underlying proof assistants such as LEGO and also possibly Coq, which at the same time enables program extraction from its constructive proofs. For this purpose, we…

Structural information of phylogenetic tree topologies plays an important role in phylogenetic inference. However, finding appropriate topological structures for specific phylogenetic inference tasks often requires significant design effort…

We investigate exponential families of random graph distributions as a framework for systematic quantification of structure in networks. In this paper we restrict ourselves to undirected unlabeled graphs. For these graphs, the counts of…

Three classes of algorithms to learn the structure of Bayesian networks from data are common in the literature: constraint-based algorithms, which use conditional independence tests to learn the dependence structure of the data; score-based…

We investigate the complexity of isomorphisms of computable structures on cones in the Turing degrees. We show that, on a cone, every structure has a strong degree of categoricity, and that degree of categoricity is $\bf{0^{(\alpha)}}$ for…

Using new techniques for controlling the categoricity spectrum of a structure, we construct a structure with degree of categoricity but infinite spectral dimension, answering a question of Bazhenov, Kalimulin and Yamaleev. Using the same…

We consider the relationship between learnability of a "base class" of functions on a set $X$, and learnability of a class of statistical functions derived from the base class. For example, we refine results showing that learnability of a…

This paper describes a family of probabilistic architectures designed for online learning under the logarithmic loss. Rather than relying on non-linear transfer functions, our method gains representational power by the use of data…

A novel algebra underlying integrable systems is shown to generate and unify a large class of quantum integrable models with given $R$-matrix, through reductions of an ancestor Lax operator and its different realizations. Along with known…

In this paper we investigate the derivations of filiform Leibniz algebras. Recall that the set of filiform Leibniz algebras of fixed dimension is decomposed into three non-intersected families. We found sufficient conditions under which…

We introduce a new class of possibly infinite dimensional Lie algebras and study their structural properties. Examples of this new class of Lie algebras are finite dimensional simple Lie algebras containing a nonzero split torus, affine and…

Parametrised quantum circuits are a central framework for near term quantum machine learning. However, it remains challenging to determine in advance how architectural choices, such as encoding strategies, gate placement, and entangling…

We study a new class of infinite dimensional Lie algebras, which has important applications to the theory of integrable equations. The construction of these algebras is very similar to the one for automorphic functions and this motivates…

We determine the isomorphism classes of the first family of infinite dimensional simple Lie algebras recently introduced by Xu. The structure space of these algebras is given explicitly. The derivations of these algebras are also…

In algebraic number theory, the finiteness of the Picard group of an order in a number field is generally proved via a lattice argument: the order forms a lattice and every ideal class contains an integral ideal with a small enough non-zero…

In this paper, we examine a time-dependent family of two-dimensional algebras. We investigate the conditions under which any two algebras from this family, formed at different times, are isomorphic. Our findings reveal that the flow…

This work explores the deformation theory of algebraic structures in a very general setting. These structures include commutative, associative algebras, Lie algebras, and the infinity versions of these structures, the strongly homotopy…

We revisit G. Elek's notion of amenable representation type, where algebras are characterised by every indecomposable module being "almost" the direct sum of modules of bounded dimension. We give a new proof of his result that string…

We provide time- and sample-efficient algorithms for learning and testing latent-tree Ising models, i.e. Ising models that may only be observed at their leaf nodes. On the learning side, we obtain efficient algorithms for learning a…