A duality transform for realizing convex polytopes with small integer coordinates

Wir entwickeln eine Dualitätstransformation für Polyeder, die eine Einbettung auf dem polynomiellen Gitter berechnet, wenn das ursprüngliche Polyeder auf einem polynomiellen Gitter gegeben ist. Die Konstruktion erfordert einen beschränkten Knotengrad des Polytop-Graphen, funktioniert aber im allgemeinen Fall für die Klasse der Stapelpolytope. Als Konsequenz können wir zeigen, dass sich die "Truncated Polytopes" auf einem polynomiellen Gitter realisieren lassen. Dieses Ergebnis gilt für jede (feste) Dimension.We study realizations of convex polytopes with small integer coordinates. We develop an efficient duality transform, that allows us to go from an efficient realization of a convex polytope to an efficient realization of its dual.Our methods prove to be especially efficient for realizing the class of polytopes dual to stacked polytopes, known as truncated polytopes. We show that every 3d truncated polytope with n vertices can be realized on an integer grid of size O(n^(9lg(6)+1)), and in R^d the required grid size is n^(O(d^2*lg(d))). The class of truncated polytopes is only the second nontrivial class of polytopes, the first being the class of stacked polytopes, for which realizations on a polynomial size integer grid are known to exists

Drawing Planar Graphs with Few Geometric Primitives

We define the \emph{visual complexity} of a plane graph drawing to be the number of basic geometric objects needed to represent all its edges. In particular, one object may represent multiple edges (e.g., one needs only one line segment to draw a path with an arbitrary number of edges). Let $n$ denote the number of vertices of a graph. We show that trees can be drawn with $3n/4$ straight-line segments on a polynomial grid, and with $n/2$ straight-line segments on a quasi-polynomial grid. Further, we present an algorithm for drawing planar 3-trees with $(8n-17)/3$ segments on an $O(n)\times O(n^2)$ grid. This algorithm can also be used with a small modification to draw maximal outerplanar graphs with $3n/2$ edges on an $O(n)\times O(n^2)$ grid. We also study the problem of drawing maximal planar graphs with circular arcs and provide an algorithm to draw such graphs using only $(5n - 11)/3$ arcs. This is significantly smaller than the lower bound of $2n$ for line segments for a nontrivial graph class.Comment: Appeared at Proc. 43rd International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2017

ОБОСНОВАНИЕ ТЕХНОЛОГИЧЕСКИХ И КОНСТРУКТИВНЫХ ПАРАМЕТРОВ СОШНИКА

About 80 percent of winter wheat is cultivated in cotton plants interrow spacings under the conditions of Uzbekistan. But commercial cotton cultivators for surface sowing of wheat into interrows are not equipped with special coulter. To create a new design of this tool for cotton plants row-spacings it is necessary to study their profile. The pilot field studies showed that soil bulldozing before a coulter increases at humidity of the soil less than 8-11 percent and hardness more than 1.6-2.0 MPas, and at humidity of 16-20 percent the building-up decreases. The depth of furrows in row-spacings should be 12-16 cm, nonuniformity in longitudinal sections is 3-5 cm for 14-18 cm optimum height of the soil layer at coulter operation. A geometrical form of a scoulter was designed, its technological and geometrical parameters are proved. For high-quality crops and formation of a seedbed the coulter should be 2-4 cm downward pulled. The optimum angle of the coulter wings placed in the longitudinal direction of the movement is equal 47 degrees, and between the wings it is 69 degrees. For row-spacings of 60 cm At the outer diameter of a seed tube of 3 cm, sowing depth of 5, a side spalling angle of 50 degrees 5 tines are recommended for row-spacings of 60 cm, and 9 units are optimal for row-spacings of 90 cm.В условиях Узбекистана около 80 процентов озимой пшеницы возделывают в междурядьях хлопчатника. Для выполнения этой операции в настоящее время у серийных хлопковых культиваторов для осуществления сева разбросным способом и заделки семян пшеницы в междурядья отсутствуют специальные сошники. Отметили, что для создания новой конструкции специальных сошников для междурядий хлопчатника необходимо изучить их профиль. Проведенные в полевых условиях экспериментальные исследования показали, что при влажности почвы менее 8-11 процентов и твердости более 1,6-2,0 МПа объем сгруживания перед сошником возрастает, а при влажности 16-20 процентов - уменьшается. Определили, что глубина борозд в междурядьях должна быть 12-16 см, неравномерность в продольных разрезах - 3-5 см, для обеспечения оптимальной работы сошника высота почвы должна быть 14-18 см. Разработали геометрическую форму сошника, обосновали его технологические и геометрические параметры. Показали, что для качественного посева и формирования грядки сошник должен заглубляться в почву на 2-4 см. Получили, что оптимальный угол установки крыльев сошника в продольном направлении движения равен 47 градусам, а раствор крыльев - 69 градусам. Определили, что для междурядий 60 см при наружном диаметре семяпровода 3 см, глубине посева 5 см, угле бокового скалывания 50 градусов рекомендуемое количество ножей должно составить 5 ед., а для междурядий 90 см - 9 ед

Crossover critical behavior of Ga1-xMnxAs

The critical behavior of Ga1-xMnxAs in a close vicinity of the Curie temperature was experimentally studied by using the thermal diffusivity measurements. Taking into account that the inverse of the thermal diffusivity has the same critical behavior as the specific heat, the critical exponent {\alpha} for the samples investigated has been determined. With approaching close to the critical temperature, the crossover from the mean-field-like to the Ising-like critical behavior has been observed. From the crossover behavior the values of the Ginzburg number and the exchange interaction length in Ga1-xMnxAs with different concentrations of Mn were determined.Comment: 17 pages, 5 figure

Quantum probability in decision making from quantum information representation of neuronal states

The recent wave of interest to modeling the process of decision making with the aid of the quantum formalism gives rise to the following question: ‘How can neurons generate quantum-like statistical data?’ (There is a plenty of such data in cognitive psychology and social science.) Our model is based on quantum-like representation of uncertainty in generation of action potentials. This uncertainty is a consequence of complexity of electrochemical processes in the brain; in particular, uncertainty of triggering an action potential by the membrane potential. Quantum information state spaces can be considered as extensions of classical information spaces corresponding to neural codes; e.g., 0/1, quiescent/firing neural code. The key point is that processing of information by the brain involves superpositions of such states. Another key point is that a neuronal group performing some psychological function F is an open quantum system. It interacts with the surrounding electrochemical environment. The process of decision making is described as decoherence in the basis of eigenstates of F. A decision state is a steady state. This is a linear representation of complex nonlinear dynamics of electrochemical states. Linearity guarantees exponentially fast convergence to the decision state

Mild reductions in cytosolic NADP-dependent isocitrate dehydrogenase activity result in lower amino acid contents and pigmentation without impacting growth

Transgenic tomato (Solanum lycopersicum) plants were generated targeting the cytosolic NADP-dependent isocitrate dehydrogenase gene (SlICDH1) via the RNA interference approach. The resultant transformants displayed a relatively mild reduction in the expression and activity of the target enzyme in the leaves. However, biochemical analyses revealed that the transgenic lines displayed a considerable shift in metabolism, being characterized by decreases in the levels of the TCA cycle intermediates, total amino acids, photosynthetic pigments, starch and NAD(P)H. The plants showed little change in photosynthesis with the exception of a minor decrease in maximum photosynthetic efficiency (Fv/Fm), and a small decrease in growth compared to the wild type. These results reveal that even small changes in cytosolic NADP-dependent isocitrate dehydrogenase activity lead to noticeable alterations in the activities of enzymes involved in primary nitrate assimilation and in the synthesis of 2-oxoglutarate derived amino acids. These data are discussed within the context of current models for the role of the various isoforms of isocitrate dehydrogenase within plant amino acid metabolism

NO Dioxygenase Activity in Hemoglobins Is Ubiquitous In Vitro, but Limited by Reduction In Vivo

Genomics has produced hundreds of new hemoglobin sequences with examples in nearly every living organism. Structural and biochemical characterizations of many recombinant proteins reveal reactions, like oxygen binding and NO dioxygenation, that appear general to the hemoglobin superfamily regardless of whether they are related to physiological function. Despite considerable attention to “hexacoordinate” hemoglobins, which are found in nearly every plant and animal, no clear physiological role(s) has been assigned to them in any species. One popular and relevant hypothesis for their function is protection against NO. Here we have tested a comprehensive representation of hexacoordinate hemoglobins from plants (rice hemoglobin), animals (neuroglobin and cytoglobin), and bacteria (Synechocystis hemoglobin) for their abilities to scavenge NO compared to myoglobin. Our experiments include in vitro comparisons of NO dioxygenation, ferric NO binding, NO-induced reduction, NO scavenging with an artificial reduction system, and the ability to substitute for a known NO scavenger (flavohemoglobin) in E. coli. We conclude that none of these tests reveal any distinguishing predisposition toward a role in NO scavenging for the hxHbs, but that any hemoglobin could likely serve this role in the presence of a mechanism for heme iron re-reduction. Hence, future research to test the role of Hbs in NO scavenging would benefit more from the identification of cognate reductases than from in vitro analysis of NO and O2 binding

Influence of mitochondrial genome rearrangement on cucumber leaf carbon and nitrogen metabolism

The MSC16 cucumber (Cucumis sativus L.) mitochondrial mutant was used to study the effect of mitochondrial dysfunction and disturbed subcellular redox state on leaf day/night carbon and nitrogen metabolism. We have shown that the mitochondrial dysfunction in MSC16 plants had no effect on photosynthetic CO2 assimilation, but the concentration of soluble carbohydrates and starch was higher in leaves of MSC16 plants. Impaired mitochondrial respiratory chain activity was associated with the perturbation of mitochondrial TCA cycle manifested, e.g., by lowered decarboxylation rate. Mitochondrial dysfunction in MSC16 plants had different influence on leaf cell metabolism under dark or light conditions. In the dark, when the main mitochondrial function is the energy production, the altered activity of TCA cycle in mutated plants was connected with the accumulation of pyruvate and TCA cycle intermediates (citrate and 2-OG). In the light, when TCA activity is needed for synthesis of carbon skeletons required as the acceptors for NH4+ assimilation, the concentration of pyruvate and TCA intermediates was tightly coupled with nitrate metabolism. Enhanced incorporation of ammonium group into amino acids structures in mutated plants has resulted in decreased concentration of organic acids and accumulation of Glu