arXiv subjects

Mateusz Iskrzyński

Publications and source records attributed to Mateusz Iskrzyński.

3 recordsLinked to original sources

arXiv2026

Symmetries of weighted networks: weight approximation method and its application to food webs

Graph symmetries identify structural regularities and reduce the computational complexity of network analysis. In weighted graphs, however, exact automorphisms are rare because real-valued weights seldom coincide. We introduce a general framework for detecting approximate symmetries by aggregating weights into discrete categories, generating a sequence of coarser graphs on which classical automorphism analysis applies. The approximation path is fully configurable, based on interaction magnitudes, and can be matched to the empirical weight distribution. Applied to 250 empirical food webs using logarithmic aggregation, the method reveals that automorphisms emerge even at low approximation levels and almost always form small orbits. Orbit sizes rarely exceed two or three vertices, reflecting the combinatorial fragility of larger symmetric sets. Even so, symmetric vertices occupy diverse structural positions in the network and high connectivity does not imply asymmetry. The observation of just local permutations confirms the conclusions of trophic species and niche analysis. A case study demonstrates that automorphisms can also recover latent ecological structure. The minimal aggregation level at which two vertices become substitutable provides a quantitative measure of role similarity. The framework offers a principled, automorphism-based approach for quantifying similarity and redundancy in weighted complex networks.

physics.soc-ph↗

arXiv2025

Pangraphs as models of higher-order interactions

Graphs depict pairwise relationships between objects within a system. Higher-order interactions (HOIs), which involve more than two objects simultaneously, are common in nature. Such interactions can change the stability of a complex system. Hypergraphs can represent an HOI as an arbitrary subset of vertices. However, they fail to capture the specific roles of the vertices involved, which can be highly asymmetric, particularly in the case of interaction modifications. We introduce pangraphs, a robust and quantitative generalisation of graphs that accurately captures arbitrarily complex higher-order interactions. We demonstrate that several higher-order representations proposed in the literature are specific instances of pangraphs. Additionally, we introduce an incidence multilayer digraph representation of a pangraph, referred to as Levi digraph. We adapt degree and Katz centrality measures to the pangraph framework and show that a consistent generalisation of recursive graph measures cannot be simplified to a Levi digraph of a pangraph. We construct a pangraph for a real-world coffee agroecosystem and compare Katz centrality between its dihypergraph and pangraph representations, both analytically and numerically. The choice of representation significantly affects centrality values and alters vertex ranks. Additionally, we emphasise the use of real-valued incidence matrices to quantify interaction strengths and the roles of vertices within the system.

physics.soc-ph↗

arXiv2015

Yukawa matrix unification in the Minimal Supersymmetric Standard Model

In this dissertation, the Minimal Supersymmetric Standard Model (MSSM) is studied as a low-energy theory stemming from the $SU(5)$ Grand Unified Theory (GUT). We investigate the possibility of satisfying the minimal $SU(5)$ boundary condition $\mathbf{Y}^d=\mathbf{Y}^{e\,T}$ for the full $3\!\times\!3$ down-quark and lepton Yukawa matrices at the GUT scale within the $R$-parity conserving MSSM. We give numerical evidence in favour of the statement: There exist regions in the parameter space of the R-parity conserving MSSM for which the unification of the down-quark and lepton Yukawa matrices takes place, while the predicted values of flavour, electroweak and other collider observables are consistent with experimental constraints. Furthermore, we find evidence that the bottom-tau and strange-muon Yukawa unification is possible with a stable MSSM vacuum in the standard form. We investigate two separate scenarios of the soft supersymmetry breaking terms at the GUT scale. In the first one, it is assumed that the soft terms are flavour-diagonal in the super-CKM basis. In such a case, the trilinear Higgs-squark-squark $A$-terms can generate large threshold corrections to $\mathbf{Y}^d$ at the superpartner decoupling scale. In effect, the condition $\mathbf{Y}^d=\mathbf{Y}^{e\,T}$ imposed at the GUT scale can be satisfied. However, the large trilinear terms make the usual Higgs vacuum metastable (though sufficiently long-lived). In the second scenario, we consider non-vanishing flavour off-diagonal entries in the soft SUSY-breaking mass matrices. We show that a non-trivial flavour structure of the soft SUSY-breaking sector can allow a precise bottom-tau and strange-muon Yukawa coupling unification, while satisfying all phenomenological constraints.

hep-ph↗