Tuesday, 22 March 2022 As many as 11 new projects of bilateral scientific research cooperation with the USA at UP FAMNIT and UP IAM
The Departments of Mathematics UP IAM and UP FAMNIT were once again successful in the public tender announced by the Research Agency of the Republic of Slovenia (ARRS) for co-financing scientific research cooperation between the Republic of Slovenia and the United States of America in the period 2022-2024.
The University of Primorska has received a total of 12 new projects, 11 of which are in the field of mathematics. In addition, another bilateral cooperation project was acquired by Michael Mrissa, who works at the InnoRenew CoE Institute and the University of Primorska. At the Faculty of Management, the project was acquired by Tina Vukasović.
The ARRS public tender co-finances mutual visits of Slovenian researchers from the United States, which carry out joint scientific research projects aimed at strengthening cooperation with the USA and increasing mobility of Slovenian researchers as well as top US researchers coming to Slovenia. Additionally, the aim is to increase the number of submitted projects from Slovenian researchers, both for proposals of the EU Framework Programs, as well as other international calls in research and innovation programmes.
The co-funded projects led by UP FAMNIT and UP IAM employees are:
Title: Matroids with Transitive Automorphism Group
Institutions: UP Faculty of Mathematics, Natural Sciences and Information Technologies and University of Mississippi
UP project leader: Edward Taucher Dobson
Field: Mathematics
Questions regarding the symmetry of combinatorial objects have a long history and are still very active research topics. Usually, these questions are asked about digraphs and graphs, sometimes about designs such as Steiner triple systems, and occasionally about error-correcting codes. We propose to consider these, and related questions, for matroids, a combinatorial object which is a joint generalization of graphs and linear algebra.
Title: Certain structural properties of Cayley graphs
Institutions: UP Faculty of Mathematics, Natural Sciences and Information Technologies and Kennesaw State University
UP project leader: Ademir Hujdurović
Field: Mathematics
We plan to investigate strong independent sets and strong cliques in Cayley graphs. Cliques in Cayley graphs are also interesting from the point of view of studying the intersection density of permutation groups, namely intersecting sets of a permutation group G correspond to cliques of the Cayley graph on G with the connection set S being the union of all point stabilizers.
Title: Computer Algorithm Development for Molecular Dynamics Simulation of Macromolecules
Institutions: UP Faculty of Mathematics, Natural Sciences and Information Technologies and Kennesaw State University and National Institutes of Health (NIH)
UP project leader: Dušanka Janežič
Field: Mathematics
The goal of the proposed research is to introduce new improvements in molecular dynamics simulation of macromolecules that increase the accuracy and efficiency of present-day simulation approaches. Our goal is to develop new methodological solutions for prediction and study of protein binding sites, based on graph theoretical approaches, combined with molecular dynamics simulations. One of the goals of this project is to combine ProBiS web server with molecular dynamics methods into a new freely available web tool: ProBiS-ATLAS: Protein interaction atlas for prediction of genetic variations involved in drug interactions and disease development enabling the discovery of molecules, relevant to pharmaceutical research.
Title: Certain problems in hypergraphs, graphs, and games
Institutions: UP Faculty of Mathematics, Natural Sciences and Information Technologies and Rutgers University, MSIS Department, RUTCOR
UP project leader: Matjaž Krnc
Field: Mathematics
In the course of this project, we plan to focus on the following: Problem 1: The Bi-SP conjecture. Problem 2: On the avoidable paths. A path is called avoidable if every linear extension may be extended to an induced cycle. Problem 3: An efficient characterization of threshold 3-uniform hypergraphs. A hypergraph is said to be threshold if there exists a linear weight function on the vertices separating the independent sets from the dependent ones. Problem 4: Deterministic graphical games with no Nash equilibria. We plan to analyze the existence of deterministic graphical games that have no Nash equilibria in pure stationary strategies, with respect to additive effective payoffs. Problem 5: Exact transversals in graphs and hypergraphs. We plan to study the related exact transversal hypergraph operator, study conditions under which it is involutive, and examine connections with strong cliques in graphs and related concepts.
Title: Preserver problems in quantum mechanics
Institutions: UP Faculty of Mathematics, Natural Sciences and Information Technologies and the Department of Mathematics, Embry–Riddle Aeronautical University
UP project leader: Bojan Kuzma
Field: Mathematics
Spectrum preservers on unbounded operators. In a mathematical formulation, quantum-mechanical observables (i.e., things that can be observed and measured) are modelled with (unbounded) self-adjoint operators acting on a complex separable Hilbert space. As part of the project, we intend to classify all additive transformations that map (unbounded) self-adjoint operators into themselves and preserve their spectrum. Isometries of complexified norms. Any real vector space can be complexified, ie. made into a complex vector space by extending the scalars; the procedure is unique. In contrast to this, for a given norm on a real space, we can define several different complex norms on the complexified space, all of which extend the initial real norm. Preserver problems in quantum information sciences. Tensor products play a key role in quantum mechanics and quantum information theory: In mathematical terminology, a quantum state is described by a positive-semidefinite matrix of trace-one; the tensor product of two (or more) states describes a joint bipartite (or multipartite) system.
Title: Computational aspects of some combinatorial games on Ferrer's diagrams
Institutions: UP Faculty of Mathematics, Natural Sciences and Information Technologies and Rhodes College
UP project leader: Riste Škrekovski
Field: Mathematics
Combinatorial game theory is a large and growing field that includes in its scope a wide range of game types, generally focusing on two-player games in which both players have perfect information and there are no moves of chance. Sprague and Grundy introduced a method of quantifying game positions for impartial normal-play games, i.e., those in which both players have the same possible moves in each position. These Sprague-Grundy values are a generalization of winning and losing positions.
Title: Chemical graphs on steroids
Institutions: UP Institute Andrej Marušič and University and The Massachusetts College of Liberal Arts (MCLA)
UP project leader: Nino Bašić
Field: Mathematics
Fullerenes and benzenoids are important chemical compounds. In mathematical chemistry, they are modelled by fullerene graphs and benzenoid graphs. Much of the mathematical chemistry literature is concerned with their mathematical properties. The research will proceed in several directions. In the present project we will refine the notion of the Pentagonal Incidence Partition. Both of the topics will also be considered in relation to Clar and Fries numbers, two graph invariants of fullerenes and benzenoids. We also plan to investigate the computational complexity of determining the Clar number (and several associated values) in fullerenes and nanotubes.
Title: New bounds in extremal graph theory
Institutions: UP Institute Andrej Marušič and University and Mississippi State University
UP project leader: Slobodan Filipovski
Field: Mathematics
In this project we will establish new bounds on the maximum number of edges in K_r - free graphs in terms of the order n and the maximum degree d_1, in terms of the order n and the minimum degree d_n, and in terms of n and both d_1 and d_n. Moreover, we will show that the bounds obtained in this project are better than the corresponding bounds of Mantel and Turán. More precisely, we show that the upper bounds on the maximum sizes of K_r -free graphs of specified maximum or minimum degrees given by our theorems are smaller than or equal to the upper bounds on the maximum sizes among all K_r -free graphs.
Title: Distance-regular graphs with exactly three irreducible T-modules with endpoint 1, all of which are thin
Institutions: UP Institute Andrej Marušič and University and Seattle University
UP project leader: Štefko Miklavič
Field: Mathematics
Our research concerns a combinatorial object known as a graph. A graph is a finite set of vertices, together with a set of undirected arcs or edges, each of which connects a pair of distinct vertices. We say that vertices x, y are adjacent whenever x, y are connected by an edge. The concept of a graph is useful because mathematical, as well as intuitive notions, can be formulated in terms of adjacency. Our research concerns a type of graph said to be distance-regular.
Title: Studies in duality: graphs on surfaces and conformal hypergraphs
Institutions: UP Institute Andrej Marušič and Rutgers University, MSIS Department, RUTCOR
UP project leader: Martin Milanič
Field: Mathematics
The project will focus on the study of selected open problems in graph and hypergraph theory. Graph theory is a young branch of discrete mathematics that has developed rapidly in recent decades, largely due to many applications in the modern world in such diverse fields as computer science, sociology, biology, logistics, and so on. A graph is a combinatorial object consisting of a finite set of vertices and a set of edges each connecting two vertices. A hypergraph is a generalization of a graph where an edge can be formed by any subset of vertices. The project will address two central research topics related to two types of duality.
Title: Combinatorial structure and algebraic properties of a Q-polynomial graph for which the adjacency algebra is closed
Institutions: UP Institute Andrej Marušič and University of Wisconsin
UP project leader: Safet Penjić
Field: Mathematics
The alternating central extension of q-Onsager is generated by q-Onsager along with some extra central elements. This raises a question that the project leader plan to work on. Our problem is: Can we find any elements in our algebra \T, that are not in T, but commute with everything in \T? Such elements might be the missing generators for the alternating central extension of Q-Onsager or U^+_q.
Title: Decentralized communities for building monitoring
Institutions: InnoRenew CoE and Oregon State University
Project Leader: Michael Mrissa
Field: Computer Science
Nowadays, due to low cost sensors, mature data infrastructure and internet, monitoring data of mass timber buildings built in different parts of the world are made available. There is a huge potential in these data, especially if they are used in a federated way. However, there are multiple challenges. This project looks into some of the challenges and aims at developing a methodological framework to realize this potential. The objectives of this project are:
- To define lifecycle activities of mass timber buildings, decisions on which they depend, and the information required to support these decisions and the organizations in charge of them.
- To identify requirements and characteristics of an Information Management Framework (IMF) to ensure that (federated) monitoring data can provide needed information at the right time, to the right people with high-quality information.
- To define monitoring/measurement methodology/strategy (what sensors, what to measure, how to select spots for measurement, the required frequency of measurements, what the distance between sensors should be, how to communicate data, etc,) which would provide data with sufficient granularity in location as well as in time to be further used in IMF.
Congratulations to all our researchers!
