1. Nut digraphsNino Bašić, Patrick W. Fowler, Maxine M. McCarthy, Primož Potočnik, 2026, izvirni znanstveni članek Opis: A nut graph is a simple graph whose kernel is spanned by a single full vector (i.e., the adjacency matrix has a single zero eigenvalue and all non-zero kernel eigenvectors have no zero entry). We classify generalisations of nut graphs to nut digraphs: a digraph whose kernel (resp. co-kernel) is spanned by a full vector is dextro-nut (resp. laevo-nut); a bi-nut digraph is both laevo- and dextro-nut; an ambi-nut digraph is a bi-nut digraph where kernel and co-kernel are spanned by the same vector; a digraph is inter-nut if the intersection of the kernel and co-kernel is spanned by a full vector. It is known that a nut graph is connected, leafless and non-bipartite. It is shown here that an ambi-nut digraph is strongly connected, non-bipartite (i.e., has a non-bipartite underlying graph) and has minimum in-degree and minimum out-degree of at least 2. Refined notions of core and core-forbidden vertices apply to singular digraphs. Infinite families of nut digraphs and systematic coalescence, crossover and multiplier constructions are introduced. Relevance of nut digraphs to topological physics is discussed.
Ključne besede: nut graph, core graph, nullity, directed graph, nut digraph, dextro-nut, laevo-nut, bi-nut, ambi-nut, inter-nut, dextro-core vertex, laevo-core vertex, graph spectra
Objavljeno v RUP: 09.01.2026; Ogledov: 92; Prenosov: 3
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2. Nut graphs with a prescribed number of vertex and edge orbitsNino Bašić, Ivan Damnjanović, 2026, izvirni znanstveni članek Opis: A nut graph is a nontrivial graph whose adjacency matrix has a one-dimensional null space spanned by a vector without zero entries. Recently, it was shown that a nut graph has more edge orbits than vertex orbits. It was also shown that for any even $r \geq 2$ and any $k \geq r + 1$, there exist infinitely many nut graphs with r vertex orbits and k edge orbits. Here, we extend this result by finding all the pairs $(r, k)$ for which there exists a nut graph with $r$ vertex orbits and $k$ edge orbits. In particular, we show that for any $k \geq 2$, there are infinitely many Cayley nut graphs with $k$ edge orbits and $k$ arc orbits.
Ključne besede: nut graph, vertex orbit, edge orbit, arc orbit, Cayley graph, automorphism
Objavljeno v RUP: 09.01.2026; Ogledov: 91; Prenosov: 3
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3. Linear bounds on treewidth in terms of excluded planar minorsJ. Pascal Gollin, Kevin Hendrey, Sang-il Oum, Bruce Reed, 2025, izvirni znanstveni članek Opis: One of the fundamental results in graph minor theory is that for every planar graph $H$, there is a minimum integer $f(H)$ such that graphs with no minor isomorphic to $H$ have treewidth at most $f(H)$. A lower bound for $f(H)$ can be obtained by considering the maximum integer $k$ such that $H$ contains $k$ vertex-disjoint cycles. There exists a graph of treewidth $\Omega(k\log k)$ which does not contain $k$ vertex-disjoint cycles, from which it follows that $f(H) = \Omega(k\log k)$. In particular, if $f(H)$ is linear in $\lvert V(H) \rvert$ for graphs $H$ from a subclass of planar graphs, it is necessary that $n$-vertex graphs from the class contain at most $\lvert V(H) \rvert$ vertex-disjoint cycles. We ask whether this is also a sufficient condition, and demonstrate that this is true for classes of planar graphs with bounded component size. For an $n$-vertex graph $H$ which is a disjoint union of $r$ cycles, we show that ${f(H) \leq 3n/2 + O(r^2 \log r)}$, and improve this to $f(H)$≤$n$+O(√$n$) when $r$=2. In particular this bound is linear when $r$=O(√$n$/logn). We present a linear bound for $f(H)$ when $H$ is a subdivision of an $r$-edge planar graph for any constant~$r$. We also improve the best known bounds for $f(H)$ when $H$ is the wheel graph or the 4×4 grid, obtaining a bound of 160 for the latter.
Ključne besede: graph minor, treewidth, cycle packing
Objavljeno v RUP: 05.01.2026; Ogledov: 164; Prenosov: 2
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4. Tracking pyrethroid resistance in arbovirus mosquito vectors : mutations I1532T and F1534C in Aedes albopictus across EuropeVerena Pichler, Vera Valadas, Mustafa M. Akiner, Georgios Balatsos, Carlos Barceló, Maria-Louise Borg, Jeremy Bouyer, Daniel Bravo-Barriga, Ruben Bueno, Beniamino Caputo, Katja Adam, 2025, izvirni znanstveni članek Opis: Background With the worldwide spread of the Asian tiger mosquito, Aedes albopictus, the number of autochtho‑ nous cases of exotic arboviral diseases, such as dengue or chikungunya, is increasing in temperate regions. In Europe, pyrethroids are the only insecticides allowed for the abatement of adult mosquitoes and are thus crucial for limiting ongoing arbovirus transmission. Despite this and the report of resistance rising in vector populations worldwide, information on the pyrethroid resistance status of vector populations and knowledge on resistance mechanisms is widely lacking. Genotyping of knockdown resistance (kdr) mutations situated within the target site of pyrethroids, i.e., the voltage‑gated sodium channel (VGSC), and associated with pyrethroid resistance, is a cost‑effective approach to investigate the spread of resistance in a population. Herein, we describe the European‑wide distribution of two kdr mutations, i.e., I1532T and F1534C, in Ae. albopictus and evaluate their co‑occurrence with another well‑characterized kdr mutation, V1016G. Methods Genotyping of the kdr mutation F1534C was performed by allele‑specific PCR for 1732 Ae. albopictus specimens sampled in 19 European countries; for a subset of 419 specimens mutation I1532T was also genotyped by sequencing. For all samples, information on mutation V1016G was available, allowing evaluation of the co‑occur‑ rence of kdr alleles. Results Mutation 1534C was detected in nine sites from six countries at an overall frequency close to 5%. High‑ est frequencies per site were detected in Cyprus (84%) and Greece (45%). Allele 1532 T was identified in 11 sites from 7 countries at frequencies ranging from 4% to 25% per site. Co‑occurrence of different kdr alleles (1534C, 1532 T and 1016G) was observed in nine sampling sites from seven countries. Conclusions The present study offers the first map of the occurrence of the major Ae. albopictus kdr alleles across Europe and highlights a differential distribution of the two alleles most strongly associated with pyrethroid resistance, 1016G and 1534C. Our findings also point to the need for enhancing resistance monitoring in the East‑ ern Mediterranean region, where the two mutations are shown to exist in geographically close areas, with the risk of emergence of highly resistant double mutants.
Ključne besede: mosquito, Aedes albopictus, insecticide resistance, Kdr, arbovirus vector, vector control, Europe
Objavljeno v RUP: 05.01.2026; Ogledov: 170; Prenosov: 3
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6. Permutations satisfying (▫$P_1$▫) and (▫$P_2$▫) properties and ▫$\ell$▫-optimal bent functionsSadmir Kudin, Enes Pašalić, Alexandr Polujan, Fengrong Zhang, Haixia Zhao, 2026, izvirni znanstveni članek Opis: An important classification of permutations over Fm 2 , suitable for construct- ing Maiorana-McFarland bent functions on Fm 2 × Fm 2 with the unique M-subspace of maximal dimension, was recently considered in Pasalic et al (IEEE Trans Inf Theory 70:4464–4477, 2024). More precisely, two properties called (P1) and (P2) were in- troduced and a generic method of constructing permutations having the property (P1) was presented, whereas no such results were provided related to the (P2) property. In this article, we provide a deeper insight on these properties, their mutual relationship, and specify some explicit classes of permutations having these properties. Such per- mutations are then employed to generate a large variety of bent functions outside the completed Maiorana-McFarland class M# . We also introduce -optimal bent functions as bent functions with the lowest possible linearity index; such functions can be consid- ered as opposite to Maiorana-McFarland bent functions. We give explicit constructions of -optimal bent functions within the D0 class, which in turn can be employed in cer- tain secondary constructions of bent functions (Zhang et al in Inf Comput 297:105149, 2024) for providing even more classes of bent functions that are provably outside M# . Moreover, we demonstrate that a certain subclass of D0 has an additional property of having only 5-valued spectra decompositions, similarly to the only result in this direction concerning monomial bent functions (Canteaut and Charpin in IEEE Trans Inf Theory 498:2004–2019, 2003). Finally, we generalize the so-called swapping variables method introduced in Pasalic et al. (IEEE Trans Inf Theory 70:4464–4477, 2024) which then allows us to specify much larger families of bent functions outside M# compared to Pasalic et al (IEEE Trans Inf Theory 70:4464–4477, 2024). In this way, we give a better explanation of the origin of bent functions in dimension eight, since the vast majority of them is outside M# , as indicated in Langevin and Leander (Designs Codes Cryptogr 59:193–205, 2011).
Ključne besede: bent functions, Maiorana-McFarland class, permutations
Objavljeno v RUP: 30.12.2025; Ogledov: 264; Prenosov: 2
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7. Almost Maiorana-McFarland bent functionsSadmir Kudin, Enes Pašalić, Alexandr Polujan, Fengrong Zhang, Haixia Zhao, 2025, izvirni znanstveni članek Opis: In this article, we study bent functions on F2m 2 of the form f (x, y) = x·φ(y)+h(y), where x ∈ Fm−1 2 and y ∈ Fm+1 2 , which form the generalized Maiorana-McFarland class (denoted by GMMm+1) and are referred to as almost Maiorana-McFarland bent functions. We provide a complete characterization of the bent property for such functions and determine their duals. Specifically, we show that f is bent if and only if the mapping φ partitions Fm+1 2 into 2-dimensional affine subspaces, on each of which the function h has odd weight. While the partition of Fm+1 2 into 2-dimensional affine subspaces is crucial for the bentness, we demonstrate that the algebraic structure of these subspaces plays an even greater role in ensuring that the constructed bent func- tions f are excluded from the completed Maiorana-McFarland class M# (the set of bent functions that are extended-affine equivalent to bent functions from the Maiorana-McFarland class M). Consequently, we investigate which properties of mappings φ : Fm+1 2 → Fm−1 2 lead to bent functions of the form f (x, y) = x · φ(y) + h(y) both inside and outside M# and provide construction methods for suitable Boolean functions h on Fm+1 2 . As part of this framework, we present a simple algorithm for constructing partitions of the vector space Fm+1 2 together with appropriate Boolean functions h that generate bent functions outside M#. When 2m = 8, we explicitly identify many such partitions that produce at least 278 distinct bent functions on F8 2 that do not belong to M#, thereby generating more bent functions outside M# than the total number of 8-variable bent functions in M# (whose cardinality is approximately 277). Additionally, we demonstrate that concatenating four almost Maiorana-McFarland bent functions outside M#, i.e., defining f = f1|| f2|| f3|| f4 where fi < M#, can result in a bent function f ∈ M#. This finding essentially answers an open problem posed recently in Kudin et al. (IEEE Trans. Inf. Theory 71(5): 3999- 4011, 2025). Conversely, using a similar approach to concatenate our functions f1|| f2|| f3|| f4, where each fi ∈ M#, we generate bent functions that are provably outside M#.
Ključne besede: bent functions, Maiorana-McFarland class, M-subspaces
Objavljeno v RUP: 29.12.2025; Ogledov: 186; Prenosov: 2
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8. Population genomics and the environmental drivers of population structure in a cosmopolitan marine predator, Tursiops truncatusDaniel M. Moore, André E. Moura, Ada Natoli, Elena Papale, Mónica A. Silva, Tilen Genov, Stefania Gaspari, Giuseppa Buscaino, Per Berggren, A. Rus Hoelzel, 2025, izvirni znanstveni članek Opis: The marine environment comprises vast regions without physical barriers to movement, making the understanding of population isolation and the evolution of diversity challenging. This is especially the case for highly mobile marine species. Here we investigate populations of the common bottlenose dolphin (Tursiops truncatus) across the Mediterranean Sea and adjacent North Atlantic using high-resolution genomic markers (RADseq) and stable isotope analyses to better understand the evolution of population structure in this system. High-resolution genomic data and broad geographic sampling revealed patterns of structure not previously identified, and integration with stable isotope data suggests that prey choice varies across this region. Unexpected patterns included genetic and isotopic similarity between the North Atlantic and the region around Sicily (but not including the medially located Gulf of Cádiz and surrounding regions). The regional habitat within and beyond the Mediterranean Sea is structured with ocean frontal systems including thermal and halocline transitions, several of which show alignment with genetic transitions within our data. Our data help to distinguish among possible drivers of population differentiation for a marine predator that has the potential for long-distance dispersion. 1 Introduction
Ključne besede: genomics, phylogeography, population structure, stable isotopes, Tursiops truncatus
Objavljeno v RUP: 27.12.2025; Ogledov: 235; Prenosov: 0
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10. General interaction battery : simple object navigation and affordances (GIBSONA)Danaja Rutar, Alva Markelius, Wout Schellaert, José Hernández-Orallo, Lucy Cheke, 2025, izvirni znanstveni članek Opis: Perception of affordances is an agent’s capability to identify what action-possibilities exist with a particular object or set of objects, based on its own physical properties and capacities. This capability has been well explored in psychology because perception of affordances provides the basis for understanding and interacting with the world. For the same reason, affordance perception is also crucial for AI research. Most approaches to evaluating AI are task-oriented which means that they are geared towards evaluating aggregate performance on a specific set of tasks, rather than focusing on the nature and degree of underlying capabilities that drive task performance. An alternative approach to measuring performance in AI is capability-oriented evaluation, which aims to measure robust, task-independent capabilities across different conditions and difficulties. This approach allows not only measurement of performance but also prediction of performance on novel challenges that share the same fundamental demands. In the context of affordances, there are currently no clear guidelines as to how such capability-oriented approach should best be implemented; for example, there is much variation in what perception of affordances entails. Perhaps for this reason, no comprehensive battery of affordances tasks for AI currently exists. Building on this gap, the aims of this paper are to first, lay out some candidate guidelines for the construction of capability-oriented task batteries for embodied AI and second, to construct and present a battery GIBSONA that takes a step towards this goal: Assessing perception of a set of affordances in AI, directly following these guidelines.
Ključne besede: perception of affordances, capability-oriented AI evaluation, animal AI, capability-oriented task battery
Objavljeno v RUP: 24.12.2025; Ogledov: 482; Prenosov: 2
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