@article{MTMT:37075955, title = {On the logarithmic calculus and Sidorenko's conjecture}, url = {https://m2.mtmt.hu/api/publication/37075955}, author = {Li, X. and Szegedy, Balázs}, doi = {10.1007/s10474-026-01582-2}, journal-iso = {ACTA MATH HUNG}, journal = {ACTA MATHEMATICA HUNGARICA}, volume = {Accepted: 2025}, unique-id = {37075955}, issn = {0236-5294}, abstract = {We study a type of calculus for proving inequalities between subgraph densities that is based on Jensen's inequality for the logarithmic function.As a demonstration of the method we verify the conjecture of Erdös-Simonovits and Sidorenko for various families of graphs.In particular we give a short analytic proof for a result by Conlon, Fox and Sudakov. Using this, we prove the forcing conjecture for bipartite graphs in which one vertex is complete to the other side.}, year = {2026}, eissn = {1588-2632}, pages = {&}, orcid-numbers = {Szegedy, Balázs/0009-0009-6682-3361} } @article{MTMT:36103030, title = {Mesterséges intelligencia témájú kutatások Magyarországon}, url = {https://m2.mtmt.hu/api/publication/36103030}, author = {Benczúr, András, ifj and Gyimóthy, Tibor and Szegedy, Balázs}, doi = {10.1556/2065.186.2025.4.7}, journal-iso = {MAGYAR TUDOMÁNY}, journal = {MAGYAR TUDOMÁNY}, volume = {186}, unique-id = {36103030}, issn = {0025-0325}, year = {2025}, eissn = {1588-1245}, pages = {663-675}, orcid-numbers = {Benczúr, András, ifj/0000-0002-9392-0986; Gyimóthy, Tibor/0000-0002-2123-7387; Szegedy, Balázs/0009-0009-6682-3361} } @article{MTMT:36294977, title = {Logarithmic kinetics and bundling in random packings of elongated 3D physical links}, url = {https://m2.mtmt.hu/api/publication/36294977}, author = {Bonamassa, Ivan and Ráth, Balázs and Pósfai, Márton and Abért, Miklós and Keliger, Dániel and Szegedy, Balázs and Kertész, János and Lovász, László and Barabási, Albert-László}, doi = {10.1073/pnas.2427145122}, journal-iso = {P NATL ACAD SCI USA}, journal = {PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA}, volume = {122}, unique-id = {36294977}, issn = {0027-8424}, abstract = {We explore the impact of excluded volume interactions on the local assembly of linear physical networks, where nodes are spheres and links are rigid cylinders with varying length. To focus on the effect of elongated links, we introduce a minimal 3D model that helps us zoom into confined regions of these networks whose distant parts are sequentially connected by the random deposition of physical links with a very large aspect ratio. We show that the nonequilibrium kinetics at which these elongated links, or spaghetti, adhere to the available volume without mutual crossings is logarithmic in time, as opposed to the algebraic growth in lower dimensions for needle-like packings. We attribute this qualitatively different behavior to a delay in the activation of depletion forces caused by the 3D nature of the problem. Equally important, we find that this slow kinetics is metastable, allowing us to analytically predict the kinetic scaling characterizing an algebraic growth due to the nucleation of local bundles. Our findings offer a theoretical benchmark to study the local assembly of physical networks, with implications for the modeling of nest-like packings far from equilibrium.}, keywords = {Male; ARTICLE; KINETICS; controlled study; Physical networks; needle; RANDOM PACKINGS; Benchmarking; nonequilibrium kinetics; bird-nest materials}, year = {2025}, eissn = {1091-6490}, orcid-numbers = {Szegedy, Balázs/0009-0009-6682-3361; Lovász, László/0000-0001-6596-0465} } @article{MTMT:36318073, title = {On measure-preserving \mathbb{F}_{p}^{\omega}-systems of order k}, url = {https://m2.mtmt.hu/api/publication/36318073}, author = {Candela, Pablo and Gonzalez Sanchez, Diego and Szegedy, Balázs}, doi = {10.1007/s11854-025-0381-4}, journal-iso = {J ANAL MATH}, journal = {JOURNAL D ANALYSE MATHEMATIQUE}, volume = {Published: 13 July 2025}, unique-id = {36318073}, issn = {0021-7670}, abstract = {Building on previous work in the nilspace-theoretic approach to the study of Host–Kra factors of measure-preserving systems, we prove that every ergodic \mathbb{F}_{p}^{\omega} F p ω -system of order k is a factor of an Abramov \mathbb{F}_{p}^{\omega} F p ω -system of order k . This answers a question of Jamneshan, Shalom and Tao.}, year = {2025}, eissn = {1565-8538}, pages = {&}, orcid-numbers = {Szegedy, Balázs/0009-0009-6682-3361} } @CONFERENCE{MTMT:36436058, title = {Higher-order Fourier analysis via spectral algorithms}, url = {https://m2.mtmt.hu/api/publication/36436058}, author = {Candela, P. and Gonzalez Sanchez, Diego and Szegedy, Balázs}, booktitle = {Proceedings of the 13th European Conference on Combinatorics, Graph Theory and Applications, EUROCOMB'25}, unique-id = {36436058}, year = {2025}, pages = {&}, orcid-numbers = {Szegedy, Balázs/0009-0009-6682-3361} } @article{MTMT:33678606, title = {Random homomorphisms into the orthogonality graph}, url = {https://m2.mtmt.hu/api/publication/33678606}, author = {Kunszenti-Kovács, Dávid and Lovász, László and Szegedy, Balázs}, doi = {10.1016/j.jctb.2024.03.007}, journal-iso = {J COMB THEORY B}, journal = {JOURNAL OF COMBINATORIAL THEORY SERIES B}, volume = {167}, unique-id = {33678606}, issn = {0095-8956}, abstract = {Subgraph densities have been defined, and served as basic tools, both in the case of graphons (limits of dense graph sequences) and graphings (limits of bounded-degree graph sequences). While limit objects have been described for the "middle ranges", the notion of subgraph densities in these limit objects remains elusive. We define subgraph densities in the orthogonality graphs on the unit spheres in dimension d, under appropriate sparsity condition on the subgraphs. These orthogonality graphs exhibit the main difficulties of defining subgraphs the "middle" range, and so we expect their study to serve as a key example to defining subgraph densities in more general Markov spaces. The problem can also be formulated as defining and computing random orthogonal representations of graphs. Orthogonal representations have played a role in information theory, optimization, rigidity theory and quantum physics, so to study random ones may be of interest from the point of view of these applications as well.}, year = {2024}, eissn = {1096-0902}, pages = {392-444}, orcid-numbers = {Kunszenti-Kovács, Dávid/0000-0002-1314-8528; Lovász, László/0000-0001-6596-0465; Szegedy, Balázs/0009-0009-6682-3361} } @article{MTMT:34479868, title = {Subgraph densities in Markov spaces}, url = {https://m2.mtmt.hu/api/publication/34479868}, author = {Kunszenti-Kovács, Dávid and Lovász, László and Szegedy, Balázs}, doi = {10.1016/j.aim.2023.109414}, journal-iso = {ADV MATH}, journal = {ADVANCES IN MATHEMATICS}, volume = {437}, unique-id = {34479868}, issn = {0001-8708}, abstract = {We generalize subgraph densities, arising in dense graph limit theory, to Markov spaces (symmetric measures on the square of a standard Borel space). More generally, we define an analogue of the set of homomorphisms in the form of a measure on maps of a finite graph into a Markov space. The existence of such homomorphism measures is not always guaranteed, but can be established under rather natural smoothness conditions on the Markov space and sparseness conditions on the graph. This continues a direction in graph limit theory in which such measures are viewed as limits of graph sequences. © 2023 Elsevier Inc.}, keywords = {Graph limit; Subgraph density; Markov space}, year = {2024}, eissn = {1090-2082}, orcid-numbers = {Kunszenti-Kovács, Dávid/0000-0002-1314-8528; Lovász, László/0000-0001-6596-0465; Szegedy, Balázs/0009-0009-6682-3361} } @article{MTMT:34686162, title = {Impact of physicality on network structure}, url = {https://m2.mtmt.hu/api/publication/34686162}, author = {Pósfai, M. and Szegedy, Balázs and Bačić, I. and Blagojević, L. and Abért, Miklós and Kertész, János and Lovász, László and Barabási, A.-L.}, doi = {10.1038/s41567-023-02267-1}, journal-iso = {NAT PHYS}, journal = {NATURE PHYSICS}, volume = {20}, unique-id = {34686162}, issn = {1745-2473}, abstract = {The emergence of detailed maps of physical networks, such as the brain connectome, vascular networks or composite networks in metamaterials, whose nodes and links are physical entities, has demonstrated the limits of the current network science toolset. Link physicality imposes a non-crossing condition that affects both the evolution and the structure of a network, in a way that the adjacency matrix alone—the starting point of all graph-based approaches—cannot capture. Here, we introduce a meta-graph that helps us to discover an exact mapping between linear physical networks and independent sets, which is a central concept in graph theory. The mapping allows us to analytically derive both the onset of physical effects and the emergence of a jamming transition, and to show that physicality affects the network structure even when the total volume of the links is negligible. Finally, we construct the meta-graphs of several real physical networks, which allows us to predict functional features, such as synapse formation in the brain connectome, that agree with empirical data. Overall, our results show that, to understand the evolution and behaviour of real complex networks, the role of physicality must be fully quantified. © 2023, The Author(s), under exclusive licence to Springer Nature Limited.}, keywords = {complex networks; Graph theory; Mapping; Toolsets; Network structures; Network science; condition; Nodes and links; VASCULAR NETWORK; connectomes; Meta-graph; 'current; Physical network}, year = {2024}, eissn = {1745-2481}, pages = {142-149}, orcid-numbers = {Szegedy, Balázs/0009-0009-6682-3361; Kertész, János/0000-0003-4957-5406; Lovász, László/0000-0001-6596-0465} } @misc{MTMT:34760336, title = {On measure-preserving Fωp-systems of order k}, url = {https://m2.mtmt.hu/api/publication/34760336}, author = {Pablo, Candela and Gonzalez Sanchez, Diego and Szegedy, Balázs}, unique-id = {34760336}, abstract = {Building on previous work in the nilspace-theoretic approach to the study of Host-Kra factors of measure-preserving systems, we prove that every ergodic Fωp-system of order k is a factor of an Abramov Fωp-system of order k. This answers a question of Jamneshan, Shalom and Tao.}, year = {2024} } @misc{MTMT:35447049, title = {On Fω2-affine-exchangeable probability measures}, url = {https://m2.mtmt.hu/api/publication/35447049}, author = {Pablo, Candela and Gonzalez Sanchez, Diego and Szegedy, Balázs}, unique-id = {35447049}, abstract = {For any standard Borel space B, let P(B) denote the space of Borel probability measures on B. In relation to a difficult problem of Aldous in exchangeability theory, and in connection with arithmetic combinatorics, Austin raised the question of describing the structure of affine-exchangeable probability measures on product spaces indexed by the vector space Fω2, i.e., the measures in P(BFω2) that are invariant under the coordinate permutations on BFω2 induced by all affine automorphisms of Fω2. We answer this question by describing the extreme points of the space of such affine-exchangeable measures. We prove that there is a single structure underlying every such measure, namely, a random infinite-dimensional cube (sampled using Haar measure adapted to a specific filtration) on a group that is a countable power of the 2-adic integers. Indeed, every extreme affine-exchangeable measure in P(BFω2) is obtained from a P(B)-valued function on this group, by a vertex-wise composition with this random cube. The consequences of this result include a description of the convex set of affine-exchangeable measures in P(BFω2) equipped with the vague topology (when B is a compact metric space), showing that this convex set is a Bauer simplex. We also obtain a correspondence between affine-exchangeability and limits of convergent sequences of (compact-metric-space valued) functions on vector spaces Fn2 as n→∞. Via this correspondence, we establish the above-mentioned group as a general limit domain valid for any such sequence.}, year = {2024} }