Polyhedral characteristics of balanced and unbalanced bipartite subgraph problems

We study the polyhedral properties of three problems of constructing an optimal complete bipartite subgraph (a biclique) in a bipartite graph. In the first problem we consider a balanced biclique with the same number of vertices in both parts and arbitrary edge weights. In the other two problems we are dealing with unbalanced subgraphs of maximum and minimum weight with nonnegative edges. All three problems are established to be NP-hard. We study the polytopes and the cone decompositions of these problems and their 1-skeletons. We describe the adjacency criterion in 1-skeleton of the polytope of the balanced complete bipartite subgraph problem. The clique number of 1-skeleton is estimated from below by a superpolynomial function. For both unbalanced biclique problems we establish the superpolynomial lower bounds on the clique numbers of the graphs of nonnegative cone decompositions. These values characterize the time complexity in a broad class of algorithms based on linear comparisons

Nanoskyrmion engineering with spsp-electron materials: Sn monolayer on SiC(0001) surface

Materials with $sp$-magnetism demonstrate strongly nonlocal Coulomb interactions, which opens a way to probe correlations in the regimes not achievable in transition metal compounds. By the example of Sn monolayer on SiC(0001) surface, we show that such systems exhibit unusual but intriguing magnetic properties at the nanoscale. Physically, this is attributed to the presence of a significant ferromagnetic coupling, the so-called direct exchange, which fully compensates ubiquitous antiferromagnetic interactions of the superexchange origin. Having a nonlocal nature, the direct exchange was previously ignored because it cannot be captured within the conventional density functional methods and significantly challenges ground state models earlier proposed for Sn/SiC(0001). Furthermore, heavy adatoms induce strong spin-orbit coupling, which leads to a highly anisotropic form of the spin Hamiltonian, in which the Dzyaloshinskii-Moriya interaction is dominant. The latter is suggested to be responsible for the formation of a nanoskyrmion state at realistic magnetic fields and temperatures.Comment: 4 pages, supplemental materia

Pollen and Isotope Investigations of an Ice Core from Vavilov Ice Cap, October Revolution Island, Severnaya Zemlya Archipelago, Russia

The Vavilov Ice Cap (79°27'N, 95° 21'E) was cored during February and March of 1988. The corer passed through 457.18 m of glacier ice, 2.15 m of moraine-containing ice, and 2.28 m of underlying rocks. Structural-stratigraphical and isotope analysis show the glacier ice is of Holocene in age; the ice layer covered by frozen deposits is Pleistocene glacier ice; and the ground (ice wedge?) ice from underlying sediments was formed during the Last Interglacial. Palynological studies of this core, carried out for the first time in the Russian Arctic demonstrate that the pollen spectra have a unique pattern. It reduces the possibility of correlation between the Vavilov Ice Cape spectra and pollen spectra from other surficial deposits, because the ice retains pollen and spores brought from enormous distances. Only the upper 65 m of the core is easily dated, to the last millennium, by the presence of cereals, Plantago lanceolata, Centaurea cyanus, Cannabis pollen. That is in good agreement with the model of age distribution based upon depth. The presence of considerable amounts of Tilia cordifolia pollen, a West-European species in the upper layers suggests that summer air masses have been dominantly from the southwest during the last 500 years. The pollen data do not contradict the conclusion the Vavilov ice core is composed of a section of Holocene ice, moraine-containing ice representing the Pleistocene episode, and a ground ice formed during an earlier warm period (Last Interglacial?).Une carotte de glace prélevée en 1988 au sein de la calotte glaciaire de Vavilov (79°27'N, 95°21'E) a fait l'objet d'analyses isotopiques et palynologiques. Le sondage comprend 457,18 m de glace « pure », suivis de 2,15 m de glace chargée de sédiments et 2,28 m de roches gelés du socle. Les résultats des analyses structurales, stratigraphiques et isotopiques sont les suivants : la glace pure datée de l'Holocène, les 2,15 de la couche chargée de sédiments datent du Pléistocène, tandis que la glace présente dans les fentes du socle s'est formée au cours du dernier interglaciaire. Les spectres polliniques de cette carotte sont caractérisés par des grains de pollen d'origine lointaine préservés dans la glace. Cette constatation réduit grandement les possibilités de corrélation avec les données sédimentaires de la région, qui reflètent la composition de la végétation locale. Un âge inférieur à 1000 ans peut être attribué aux 65 m supérieurs de la carotte en raison de la présence de pollen de céréales, de Plantago lanceolata, Centaurea cyanus et de Cannabis. Cette interprétation concorde avec le modèle du taux d'accumulation de la glace. Dans la partie supérieure de la carotte, la présence en quantité considérable de Tilia cordifolia, une espèce de tilleul d'Europe de l'Ouest, laisse supposer que les masses d'air en provenance du sud-ouest ont prédominé au cours des étés des 500 dernières années. En conclusion, les données palynologiques ne contredisent pas les résultats antérieurs selon lesquels la carotte glaciaire étudiée couvre une partie de l'Holocène, que la glace contenant la moraine représente l'épisode du Pléistocène et que la glace du socle se soit formée pendant une période chaude (le dernier interglaciaire?)

Complex numerical-experimental investigations of combustion in model high-speed combustor ducts

International audienceFast technologies for numerical simulation of high-speed flows in ducts, developed in TsAGI, are described. The examples are presented of the application of experimental data, obtained at T-131 wind tunnel, for validation of the developed numerical technologies: 1) validation of 2.5D and 3D calculations of flow in the elliptic combustor with hydrogen supersonic combustion that was studied within HEXAFLY-INT international project; 2) validation of 2D and 2.5D calculations of flow in high-speed model combustor duct with step-like expansion. Preparation of new series of experiments, oriented on validation of turbulent combustion models, is described

HoughNet: neural network architecture for vanishing points detection

In this paper we introduce a novel neural network architecture based on Fast Hough Transform layer. The layer of this type allows our neural network to accumulate features from linear areas across the entire image instead of local areas. We demonstrate its potential by solving the problem of vanishing points detection in the images of documents. Such problem occurs when dealing with camera shots of the documents in uncontrolled conditions. In this case, the document image can suffer several specific distortions including projective transform. To train our model, we use MIDV-500 dataset and provide testing results. The strong generalization ability of the suggested method is proven with its applying to a completely different ICDAR 2011 dewarping contest. In previously published papers considering these dataset authors measured the quality of vanishing point detection by counting correctly recognized words with open OCR engine Tesseract. To compare with them, we reproduce this experiment and show that our method outperforms the state-of-the-art result.Comment: 6 pages, 6 figures, 2 tables, 28 references, conferenc