Searcharxiv⌕ Search

arXiv subjects

Peteris Daugulis

Publications and source records attributed to Peteris Daugulis.

17 recordsLinked to original sources
arXiv2025

A PCA-based Data Prediction Method

The problem of choosing appropriate values for missing data is often encountered in the data science. We describe a novel method containing both traditional mathematics and machine learning elements for prediction (imputation) of missing data. This method is based on the notion of distance between shifted linear subspaces representing the existing data and candidate sets. The existing data set is represented by the subspace spanned by its first principal components. Solutions for the case of the Euclidean metric are given.

cs.LG↗
arXiv2025

Optimizing Administrative Divisions: A Vertex $k$-Center Approach for Edge-Weighted Road Graphs

Efficient and equitable access to municipal services hinges on well-designed administrative divisions. It requires ongoing adaptation to changing demographics, infrastructure, and economic factors. This article proposes a novel transparent data-driven method for territorial division based on the Voronoi partition of edge-weighted road graphs and the vertex $k$-center problem as a special case of the minimax facility location problem. By considering road network structure and strategic placement of administrative centers, this method seeks to minimize travel time disparities and ensure a more balanced distribution of administrative time burden for the population. We show implementations of this approach in the context of Latvia, a country with complex geographical features and diverse population distribution.

cs.DS↗
arXiv2019

$16$-vertex graphs with automorphism groups $A_{4}$ and $A_{5}$ from icosahedron

The article deals with the problem of finding vertex-minimal graphs with a given automorphism group. We exhibit two undirected $16$-vertex graphs having automorphism groups $A_{4}$ and $A_{5}$. It improves the Babai's bound for $A_{4}$ and the graphical regular representation bound for $A_{5}$. The graphs are constructed using projectivisation of the vertex-face graph of icosahedron.

math.CO↗
arXiv2019

Classifying presentations of finite groups -- the case of dicyclic groups

The problem of classifying equivalence classes of presentations up to isomorphism of Cayley graphs is considered in this article in the case of dicyclic groups. The number of equivalence classes of presentations is uniformly bounded - it is a "finite presentation type" case. We find all equivalence classes of presentations of dicyclic groups having two generators. For the dicyclic group of order $4n$ apart from the classical presentation with order multiset $\{\{2n,4\}\}$ for all $n$ there are presentations with order multiset $\{\{4,4\}\}$. If $n$ is odd there is an additional presentation having elements with order multiset $\{\{n,4\}\}$. These results may be used in characterizing group structure and properties.

math.GR↗
arXiv2018

On coordinatization of mathematics

The problem of advancing coordinatization of mathematics is considered. The need to develop a theory for measuring value and complexity of mathematical implications and proofs is discussed including motivations, benefits and implementation problems. Examples of mathematical considerations for such a theory are given. Arguments supporting such an advance related to applications in mathematical research guidance, publication standards and education are given.

math.HO↗
arXiv2016

Strong connectivity and its applications

Directed graphs are widely used in modelling of nonsymmetric relations in various sciences and engineering disciplines. We discuss invariants of strongly connected directed graphs - minimal number of vertices or edges necessary to remove to make remaining graphs not strongly connected. By analogy with undirected graphs these invariants are called strong vertex/edge connectivities. We review some properties of these invariants. Computational results for some publicly available connectome graphs used in neuroscience are described.

cs.DM↗
arXiv2016

A note on a generalization of eigenvector centrality for bipartite graphs and applications

Eigenvector centrality is a linear algebra based graph invariant used in various rating systems such as webpage ratings for search engines. A generalization of the eigenvector centrality invariant is defined which is motivated by the need to design rating systems for bipartite graph models of time-sensitive and other processes. The linear algebra connection and some applications are described.

math.CO↗
arXiv2016

Nonuniqueness of semidirect decompositions for semidirect products with directly decomposable factors and applications for dihedral groups

Nonuniqueness of semidirect decompositions of groups is an insufficiently studied question in contrast to direct decompositions. We obtain some results about semidirect decompositions for semidirect products with factors which are nontrivial direct products. We deal with a special case of semidirect product when the twisting homomorphism acts diagonally on a direct product, as well as for the case when the extending group is a direct product. We give applications of these results in the case of generalized dihedral groups and classic dihedral groups $D_{2n}$. For $D_{2n}$ we give a complete description of semidirect decompositions and values of minimal permutation degrees.

math.GR↗
arXiv2015

Graphs with $2^n+6$ vertices and cyclic automorphism group of order $2^n$

The problem of finding upper bounds for minimal vertex number of graphs with a given automorphism group is addressed in this article for the case of cyclic $2$-groups. We show that for any natural $n\ge 2$ there is an undirected graph having $2^n+6$ vertices and automorphism group cyclic of order $2^n$. This confirms an upper bound claimed by other authors for minimal number of vertices of undirected graphs having automorphism group $\mathbb{Z}/2^n\mathbb{Z}$.

math.CO↗
arXiv2015

Normal forms of triangles and quadrilaterals up to similarity

In this paper the problem of finding a normal form of triangles and plane quadrilaterals up to similarity is considered. Several normal forms for triangles and a normal form for quadrilaterals of special case are described. Normal forms of simple plane objects such as triangles can be used in mathematics teaching.

math.MG↗
arXiv2015

Graph structure of commuting functions

The problem of finding graph structure of functions commuting with a given function in terms of their functional graphs is considered. Structure of functional graphs of commuting functions is described. The problem is reduced to describing graph homomorphisms of weakly connected components of functional graphs. Four subcases with finite sets are considered: permutations commuting with permutation, permutations commuting with a function, functions commuting with a permutation and functions commuting with a function. For finite sets the number of functions commuting with a given one and functions with extremal properties are found. Results for finite sets are generalized to the case of arbitrary sets where there are additional types of functional graph components.

math.CO↗
arXiv2014

Connectome graphs and maximum flow problems

We propose to study maximum flow problems for connectome graphs. We suggest a few computational problems: finding vertex pairs with maximal flow, finding new edges which would increase the maximal flow. Initial computation results for some publicly available connectome graphs are described.

q-bio.NC↗
arXiv2014

Homomorphisms of connectome graphs

We propose to study homomorphisms of connectome graphs. Homomorphisms can be studied as sequences of elementary homomorphisms - folds, which identify pairs of vertices. Several fold types are defined. Initial computation results for some connectome graphs are described.

q-bio.NC↗
arXiv2011

Coarsifications of the module isomorphism relation

In this paper new equivalence relations on the category $Mod(A)$ for any associative algebra $A$ and several related results are given. The new equivalence relations are defined using restrictions to subalgebras and the action of algebra automorphisms on modules.

math.RT↗