State of Rosa acicularis L. coenopopulations in forest park zone of Ekaterinburg

The experiments revealed that the studied fragments of Rosa acicularis L. coenopopulation were normal and full-fledged with single-vertex ontogenetic spectra. They are able to form self-sustaining habitats for several generations and spread over a significant territory. Three periods and six ontogenetic states were distinguished in the ontogenesis of Rosa acicularis L. The age structure had three types of spectrum - left-sided, centered, and right-sided. The difference in the ontogenetic structure depends on influence of anthropogenic factor, ecological and coenotic conditions of rose habitats, and variations in climatic conditions. When analyzing the parameters of coenopopulations, we found that the best conditions for existence of Rosa acicularis L. were in the berry pine forest (FCP5) in the park named after Foresters of Russia and reed grass pine forest (FCP1) in Uktus forest park, where the habitats were characterized by high morphological indicators, numbers and high values of the pregenerative fraction.

Exact and Approximate Algorithms for Computing Betweenness Centrality in Directed Graphs

Graphs (networks) are an important tool to model data in different domains. Realworld graphs are usually directed, where the edges have a direction and they are not symmetric. Betweenness centrality is an important index widely used to analyze networks. In this paper, first given a directed network G and a vertex r ∈ V (G), we propose an exact algorithm to compute betweenness score of r. Our algorithm pre-computes a set ℛ𝒱(r), which is used to prune a huge amount of computations that do not contribute to the betweenness score of r. Time complexity of our algorithm depends on |ℛ𝒱(r)| and it is respectively Θ(|ℛ𝒱(r)| · |E(G)|) and Θ(|ℛ𝒱(r)| · |E(G)| + |ℛ𝒱(r)| · |V(G)| log |V(G)|) for unweighted graphs and weighted graphs with positive weights. |ℛ𝒱(r)| is bounded from above by |V(G)| – 1 and in most cases, it is a small constant. Then, for the cases where ℛ𝒱(r) is large, we present a simple randomized algorithm that samples from ℛ𝒱(r) and performs computations for only the sampled elements. We show that this algorithm provides an (ɛ, δ)-approximation to the betweenness score of r. Finally, we perform extensive experiments over several real-world datasets from different domains for several randomly chosen vertices as well as for the vertices with the highest betweenness scores. Our experiments reveal that for estimating betweenness score of a single vertex, our algorithm significantly outperforms the most efficient existing randomized algorithms, in terms of both running time and accuracy. Our experiments also reveal that our algorithm improves the existing algorithms when someone is interested in computing betweenness values of the vertices in a set whose cardinality is very small.

Sufficient Conditions for the Global Rigidity of Periodic Graphs

Tanigawa (2016) showed that vertex-redundant rigidity of a graph implies its global rigidity in arbitrary dimension. We extend this result to periodic frameworks under fixed lattice representations. That is, we show that if a generic periodic framework is vertex-redundantly rigid, in the sense that the deletion of a single vertex orbit under the periodicity results in a periodically rigid framework, then it is also periodically globally rigid. Our proof is similar to the one of Tanigawa, but there are some added difficulties. First, it is not known whether periodic global rigidity is a generic property in dimension $$d>2$$ d > 2 . We work around this issue by using slight modifications of recent results of Kaszanitzky et al. (2021). Secondly, while the rigidity of finite frameworks in $${\mathbb {R}}^d$$ R d on at most d vertices obviously implies their global rigidity, it is non-trivial to prove a similar result for periodic frameworks. This is accomplished by extending a result of Bezdek and Connelly (2002) on the existence of a continuous motion between two equivalent d-dimensional realisations of a single graph in $${\mathbb {R}}^{2d}$$ R 2 d to periodic frameworks. As an application of our result, we give a necessary and sufficient condition for the global rigidity of generic periodic body-bar frameworks in arbitrary dimension. This provides a periodic counterpart to a result of Connelly et al. (2013) regarding the global rigidity of generic finite body-bar frameworks.

On Factors of Independent Transversals in $k$-Partite Graphs

A $[k,n,1]$-graph is a $k$-partite graph with parts of order $n$ such that the bipartite graph induced by any pair of parts is a matching. An independent transversal in such a graph is an independent set that intersects each part in a single vertex. A factor of independent transversals is a set of $n$ pairwise-disjoint independent transversals. Let $f(k)$ be the smallest integer $n_0$ such that every $[k,n,1]$-graph has a factor of independent transversals assuming $n \geqslant n_0$. Several known conjectures imply that for $k \geqslant 2$, $f(k)=k$ if $k$ is even and $f(k)=k+1$ if $k$ is odd. While a simple greedy algorithm based on iterating Hall's Theorem shows that $f(k) \leqslant 2k-2$, no better bound is known and in fact, there are instances showing that the bound $2k-2$ is tight for the greedy algorithm. Here we significantly improve upon the greedy algorithm bound and prove that $f(k) \leqslant 1.78k$ for all $k$ sufficiently large, answering a question of MacKeigan.

Hogyan befolyásolja a villamosenergia-hálózatról rendelkezésre álló információ a fizikai támadások által okozott sérülékenységről alkotott képet?

Összefoglaló. A villamosenergia-rendszerek fizikai támadásokkal szembeni ellenálló képessége a közelmúltban világszerte történt események ismeretében egyre nagyobb hangsúlyt kap a tématerület kutatásaiban. Az ilyen eseményekre való megfelelő felkészüléshez elengedhetetlen az üzemeltetett infrastruktúrának, elsősorban annak gyengeségeinek pontos ismerete. A cikkben Magyarország villamosenergia-hálózatának adatai alapján készített súlyozatlan és súlyozott gráfokon végzünk vizsgálatokat, hogy megértsük a különböző stratégia mentén kiválasztott célpontok elleni támadások milyen mértékben csökkentik a topológiai hatékonyságot. A cikk célja egyben a magyar hálózat sérülékenységének általános bemutatása is, mely hasznos bemeneti információ lehet a kockázati tervek elkészítésekor. Summary. Tolerance of the power grid against physical intrusions has gained importance in the light of various attacks that have taken place around the world. To adequately prepare for such events, grid operators have to possess a deep understanding of their infrastructure, more specifically, of its weaknesses. A graph representation of the Hungarian power grid was created in a way that the vertices are generators, transformers, and substations and the edges are high-voltage transmission lines. All transmission and sub-transmission elements were considered, including the 132 kV network as well. The network is subjected to various types of single and double element attacks, objects of which are selected according to different aspects. The vulnerability of the network is measured as a relative drop in efficiency when a vertex or an edge is removed from the network. Efficiency is a measure of the network’s performance, assuming that the efficiency for transmitting electricity between vertices i and j is proportional to the reciprocal of their distance. In this paper, simultaneous removals were considered, arranged into two scenarios (single or double element removal) and a total of 5 cases were carried out (single vertex removal, single edge removal, double vertex removal, double edge removal, single vertex and single edge removal). During the examinations, all possible removal combinations were simulated, thus the 5 cases represent 385, 504, 73920, 128271 and 193797 runs, respectively. After all runs were performed, damage values were determined for random and targeted attacks, and attacks causing maximal damage were also identified. In all cases, damage was calculated for unweighted and weighted networks as well, to enable the comparison of those two models. The aims of this paper are threefold: to perform a general assessment on the vulnerability of the Hungarian power grid against random and targeted attacks; to compare the damage caused by different attack strategies; and to highlight the differences between using unweighted and weighted graphs representations. Random removal of a single vertex or a single edge caused 0.3–0.4% drop in efficiency, respectively, which indicates a high tolerance against such attacks. Damage for random double attacks was still only in the range of 0.6–0.8%, which is acceptable. It was shown that if targets are selected by the attacker based on the betweenness rank of the element, damage would be below the maximal possible values. Comparison of the damage measured in the unweighted and the weighted network representations has shown that damage to the weighted network tends to be bigger for vertex attacks, but the contrary is observed for edge attacks. Numerical differences between the two representations do not show any trend that could be generalised, but in the case of the most vulnerable elements significant differences were found in damage measures, which underlines the importance of using weighted models.

The structure in diameter and sanitary condition of geographical cultures of Scots pine

The study of geographical forest cultures is the scientific basis for forest-seed zoning and selection of tree species. This research identifies the structural features of the diameter of middle-aged stands of different ecotypes of Scots pine (Pinus sylvestris L.) in geographic cultures, as an assessment of its current sanitary state. We studied the stands of 18 forest-steppe and 14 steppe ecotypes. We laid test areas with measuring the diameters of trees with a measuring fork at a height of 1.3 m. Trees with a continuous count were divided into six categories of sanitary status: no signs of weakening, weakened, strongly weakened, shrinking, fresh dead wood and dead wood of past years. Based on the results of continuous recounts, the distribution rows of trees were constructed according to 2- and 4-cm thickness steps. In forest-steppe ecotypes, the distribution of trees along 2-and 4-centimeter-thick steps is single-vertex, but with right asymmetry. The distribution of trees of steppe ecotypes over 2-cm steps of thickness is asymmetric and two-peaked. The distribution of trees of steppe ecotypes by 2-cm thickness steps is asymmetric and two-vertex. The average score of the sanitary state of stands of forest-steppe ecotypes is 1.5 (healthy), in steppe – 1.7 (weakened).

ON THE WIENER INDEX OF F_H SUMS OF GRAPHS

Wiener index is the first among the long list of topological indices which was used to correlate structural and chemical properties of molecular graphs. In \cite{Eli} M. Eliasi, B. Taeri defined four new sums of graphs based on the subdivision of edges with regard to the cartesian product and computed their Wiener index. In this paper, we define a new class of sums called $F_H$ sums and compute the Wiener index of the resulting graph in terms of the Wiener indices of the component graphs so that the results in \cite{Eli} becomes a particular case of the Wiener index of $F_H$ sums for $H = K_1$, the complete graph on a single vertex.

LITHOLOGY AND HYDRODYNAMICS OF THE BLACK SEA ODESSA COAST UNDERWATER PART

Problem Statement and Purpose. The results of lithological studies, including granulometric analysis, are needed to identify the conditions of sedimentation and distribution of rock fragments by size. They are an indicator of the sedimentation processes dynamic structure peculiarities. The study of the sediment regime is important for the development of measures related to the protection of shores from erosion. The aim of the work is to identify the lithological features of the bottom sediment types distribution on the protected section of the Odessa coast near Cape Maly Fontan. Data & Methods. The materials for this work were obtained in the field research in the summer 2019 in the coastal zone between the hydrobiological station of Odessa I. I. Mechnikov National University, and Cape Malyj Fountain. Three measuring profiles were made perpendicular to the shoreline at 1200 m towards the sea to a depth of 18 m. 35 samples were taken from the upper layer of bottom sediments. Field samples processing was performed in the Problem Research Laboratory of Engineering Geology of the Sea Coast, Reservoirs and Mountain Slopes of Odessa I. I. Mechnikov National University. Granulometric classification was performed. Excel, Statistica, Golden Software Surfer programs were used to process the results. Results. Underwater relief analysis showed that the coastal part is an abrasive terrace, on which ancient landslides relics are widespread. There are 7 main lithological types of bottom sediments detected. The largest areas covered by fine-grained loamy sands and shell detritus with gravel, pebbles and sand. Analysis of distribution curves and cumulative curves of granulometric distribution showed that coarse sediments are characterized by multi-vertex distribution curves and stepwise stretched cumulative curves, which indicates the heterogeneity of sediments in granulometric distribution. For fine-grained material, which is well sorted, the distribution curves are almost single-vertex, and the cumulative curves have a large steepness and a simple, non-stepped shape. There are three hydrodynamic detected in bottom sediments lithology according on statistical parameters of grain size. Outer marine part with depth more than 15 meters characterized by low hydrodynamic processes and presented by good-sorted sands and silt. The central part of polygon in 4–15 meters depth covered by shell detritus with gravel and pebble of carbonate rocks and connected with rocky extrusions after coastal landslides. The feature of this part is active hydrodynamic processes. The rocky extrusions presented like natural breakwater and due to waves braking and collection of different types of sediments. The coastal part in 2–4 m depth in front of constructed breakwater leads to decreasing of wave energy and sedimentation of good-sorted sands.

Sensitivity to geometric shape regularity in humans and baboons: A putative signature of human singularity

Among primates, humans are special in their ability to create and manipulate highly elaborate structures of language, mathematics, and music. Here we show that this sensitivity to abstract structure is already present in a much simpler domain: the visual perception of regular geometric shapes such as squares, rectangles, and parallelograms. We asked human subjects to detect an intruder shape among six quadrilaterals. Although the intruder was always defined by an identical amount of displacement of a single vertex, the results revealed a geometric regularity effect: detection was considerably easier when either the base shape or the intruder was a regular figure comprising right angles, parallelism, or symmetry rather than a more irregular shape. This effect was replicated in several tasks and in all human populations tested, including uneducated Himba adults and French kindergartners. Baboons, however, showed no such geometric regularity effect, even after extensive training. Baboon behavior was captured by convolutional neural networks (CNNs), but neither CNNs nor a variational autoencoder captured the human geometric regularity effect. However, a symbolic model, based on exact properties of Euclidean geometry, closely fitted human behavior. Our results indicate that the human propensity for symbolic abstraction permeates even elementary shape perception. They suggest a putative signature of human singularity and provide a challenge for nonsymbolic models of human shape perception.