Projects / Programmes
Computationally intensive methods in theoretical computer science, discrete mathematics, combinatorial optimization, and numerical analysis and algebra with applications in natural and social sciences
January 1, 2020
- December 31, 2027
| Code |
Science |
Field |
Subfield |
| 1.07.00 |
Natural sciences and mathematics |
Computer intensive methods and applications |
|
| 1.01.00 |
Natural sciences and mathematics |
Mathematics |
|
| Code |
Science |
Field |
| P170 |
Natural sciences and mathematics |
Computer science, numerical analysis, systems, control |
| Code |
Science |
Field |
| 1.01 |
Natural Sciences |
Mathematics |
large networks, big data, maps, graph representations, configurations, symmetries,
optimization, computability, programming languages, multiparameter eigenvalue problem,
bivariate polynomials, spline, approximation, enumeration, symmetric functions, polytopes
Data for the last 5 years (citations for the last 10 years) on
April 25, 2024;
A3 for period
2018-2022
| Database |
Linked records |
Citations |
Pure citations |
Average pure citations |
| WoS |
644 |
8,478 |
6,944 |
10.78 |
| Scopus |
728 |
11,122 |
9,358 |
12.85 |
Researchers (33)
Organisations (4)
Abstract
In mathematical modeling, scientific computing, and data analysis, increasingly large quantities of data as well as increasing demand for computation capabilities are being encountered. Our research activities and goals will cover a selection of topics which revolve around computationally intensive methods for solving problems, formulating hypotheses, and performing analyses in a variety of domains, ranging from pure mathematics, to natural and social sciences and industry. Our methodology combines the insights provided by deep mathematical and scientific results with their applicability in real-world situations. Our research group, which consists of more than 20 professional researchers, will focus on the following areas:
Representations of graphs, maps, combinatorial configurations and other incidence structures. We will continue research into geometric, topological and combinatorial representations of graphs and combinatorial structures (configurations, maps, maniplexes, polytopes, etc.). This involves the structural analysis and classification of special families of objects.
Databases of highly symmetrical combinatorial objects. We plan to build and upgrade data collections of symmetric objects (symmetric graphs, maps, abstract polytopes, configurations) which will be used for hypotheses forming and testing. Collections are freely available to the scientific community. In the process, the theoretical background will be studied and developed for specific collections.
Big data and network analysis. We will focus on the development of new approaches to network analysis with a focus on linked networks, temporal networks and symbolic networks. We will further develop methodologies for symbolic data analysis on big data. The work on new approaches will address both theoretical and algorithmic points of view.
Computational reasoning. We will work on two main topics. The first is the development of domain-specific methods for reasoning about computational systems. The second is the development of a unified approach to the implementation of configurable dependent type theories. The topics will be synthesized in applications of proof assistants and in the design of bespoke type theories designed around programming applications.
Numerical analysis and algebra. We will study systems of bivariate polynomials and applications, new interpolation and approximation schemes, the inverse eigenvalue problem and cubic splines in the context of computer aided geometric design.
Combinatorics. We will work on hyper-hypergeometric and convolutive solutions of linear recursions with hypergeometric coefficients, representations of the symmetric group related to parking functions, Schur functions and alternating sign matrices and on challenges related to Young tableaux.
Applications in chemistry, synthetic biology and industrial applications. We will address problems in chemical graph theory and polyhedral self-assembly in synthetic biology. Knowledge will be applied in various business domains, such as mobility, fintech, etc.
Significance for science
Our work yields important results in applications of computationally intensive methods in theoretical computer science, analysis of large networks, problems in graph theory, numerical analysis and linear algebra, computer aided geometric design, combinatorial optimization, chemistry, synthetic biology and bioinformatics. The results of this research will also prove very useful for researchers in the area of algebraic combinatorics. Potentially, they can be used in either disproving or providing further evidence for long-standing conjectures. To be more specific, a few of many examples include:
Results on polyhedral self-assembly represent foundations for computation machines based on chemical and biological structures, thus opening up a potentially very important research area.
The network analysis tool Pajek co-authored by Batagelj is globally recognized as the top large network analysis tool for research. Similarly, new approaches to temporal and bibliographic networks and software implemented provide important results and stepping stones in the highly interdisciplinary and active field of complex networks (and systems).
Computer reasoning deals with ensuring mathematically proven correctness in software development. Our researchers provide important contributions to this very promising field.
The graph databases produced on the project, beside representing an ordered catalogue, can be used to discover previously unobserved phenomena of the objects in question and thus inspire new direction of research.
Symmetric functions play an important role in statistics and theoretical physics, k-Schur functions are also important in the theory of Schubert polynomials, Macdonald polynomials, cohomology etc.
Polytopes are important in linear programming, statistics, graph theory and elsewhere.
B-spline representations of splines on general triangulations are applicable in geometric modeling and numerical approximation, which makes them a perfect tool for modern approaches to solving partial differential equations on irregular domains.
The high quality of the results of our research is due in large part to the sustained support our professional activities receive. Here human-resource development, dissemination and networking all play crucial roles. Our research is well positioned within the global research community through our decades long cooperation with USA, UK, and various EU countries, to name a few. We provide our junior researchers with connections to leading international researchers, and we educate them on how to participate in the scientific community. It is part of our long term strategy to invest both in young researchers and in highly educated engineers with PhDs. This has resulted in obtaining several alternative funding sources (other than ARRS/SRA) to fund doctoral students and postdocs. Our research group is one of the key engines behind the foundation and running the of first Slovenian mathematical international-SCI-indexed journal Ars Mathematica Contemporanea, established in 2008, reaching top 25% rank in 2015. We have accumulated extensive experience from decades of organizing networking events and journal publishing, and have developed the IT infrastructure to support this. Our group members held leading roles in the successful bid for the 8th European Mathematical Congress (2020) in Slovenia, and now hold leading roles in its organization.
Significance for the country
Importance for economic development
Many results not only have theoretical value, but can be applied in practice, more often by applying methodologies developed than as direct consequences of the results. We use this approach in the transfer of knowledge from the scientific world into industry. For users outside the scientific community, the methodology of problem solving, mathematical modeling and the design of computer algorithms and their implementation are of particular importance. Through cooperation with industry and knowledge transfer, we take care that the applicative value of our research is utilized.
Our research program is the only mathematical program in Slovenia which has its own spin-off company, Abelium, the program partner, established in 2009 by young PhDs coming from within the research group. The company Abelium currently employs 10 PhDs of mathematics and computer science. To see a high impact example of an application of knowledge and optimization methods studied within the program, there is a successful demand-responsive shared transportation company GoOpti, deemed “Slovenian Uber”, receiving multiple innovation awards, of which some members of Abelium are co-founders, responsible for complete information IT infrastructure development, optimizations, etc. The company transfers each year several hundreds of thousands of passengers to and from airports around Slovenia. In such and similar cases, Abelium acts as a kind of “technology accelerator” and digital transformation enabler for promising startups receiving significant foreign investments. Since the Slovenian economy is involved in international activities, it is extremely important that applicable research knowledge is available to our companies, enhancing a faster and a more successful development.
Members of the group cooperate with important national and international companies and institutions, such as Port of Koper (environmental modeling), European office of aerospace research and development, European Space Agency, Air Force Office of Scientific Research (USA), etc.
Importance for social and cultural development
The members of our program are in majority employed at Slovenian universities, where they are active in teaching topics related to the program. This represents a channel for reaching to promising students and help them in developing their careers. We participate in publishing educational material (lecture notes) and are constantly active in providing publicly available e-learning content. Notable examples include the web services Tomo (www.tomo.si) for learning to code and Nauk (www.nauk.si) for e-learning content for primary and secondary schools.
The respect for mathematical tradition is an important aspect of our program, shown through several cultural heritage supporting projects in past. We also organize a weekly Seminar on history of mathematical sciences.
