Random Sampling in Computational Algebra: Helly Numbers and Violator Spaces

This paper transfers a randomized algorithm, originally used in geometric optimization, to computational problems in commutative algebra. We show that Clarkson's sampling algorithm can be applied to two problems in computational algebra: solving large-scale polynomial systems and finding small generating sets of graded ideals. The cornerstone of our work is showing that the theory of violator spaces of G\"artner et al.\ applies to polynomial ideal problems. To show this, one utilizes a Helly-type result for algebraic varieties. The resulting algorithms have expected runtime linear in the number of input polynomials, making the ideas interesting for handling systems with very large numbers of polynomials, but whose rank in the vector space of polynomials is small (e.g., when the number of variables and degree is constant).Comment: Minor edits, added two references; results unchange

Models of spin-orbit coupled oligomers

We address the stability and dynamics of eigenmodes in linearly-shaped strings (dimers, trimers, tetramers, and pentamers) built of droplets of a binary Bose-Einstein condensate (BEC). The binary BEC is composed of atoms in two pseudo-spin states with attractive interactions, dressed by properly arranged laser fields, which induce the (pseudo-) spin-orbit (SO) coupling. We demonstrate that the SO-coupling terms help to create eigenmodes of particular types in the strings. Dimer, trimer, and pentamer eigenmodes of the linear system, which correspond to the zero eigenvalue (EV, alias chemical potential) extend into the nonlinear ones, keeping an exact analytical form, while tetramers do not admit such a continuation, because the respective spectrum does not contain a zero EV. Stability areas of these modes shrink with the increasing nonlinearity. Besides these modes, other types of nonlinear states, which are produced by the continuation of their linear counterparts corresponding to some nonzero EVs, are found in a numerical form (including ones for the tetramer system). They are stable in nearly entire existence regions in trimer and pentamer systems, but only in a very small area for the tetramers. Similar results are also obtained, but not displayed in detail, for hexa- and septamers.Comment: Chaos, in pres

Interface solitons in locally linked two-dimensional lattices

Existence, stability and dynamics of soliton complexes, centered at the site of a single transverse link connecting two parallel 2D (two-dimensional) lattices, are investigated. The system with the on-site cubic self-focusing nonlinearity is modeled by the pair of discrete nonlinear Schr\"{o}dinger equations linearly coupled at the single site. Symmetric, antisymmetric and asymmetric complexes are constructed by means of the variational approximation (VA) and numerical methods. The VA demonstrates that the antisymmetric soliton complexes exist in the entire parameter space, while the symmetric and asymmetric modes can be found below a critical value of the coupling parameter. Numerical results confirm these predictions. The symmetric complexes are destabilized via a supercritical symmetry-breaking pitchfork bifurcation, which gives rise to stable asymmetric modes. The antisymmetric complexes are subject to oscillatory and exponentially instabilities in narrow parametric regions. In bistability areas, stable antisymmetric solitons coexist with either symmetric or asymmetric ones.Comment: 9 figure

Investigation of gene pool and genealogical links between sheep breeds of southern Russia by blood groups and DNA microsatellites

To study the gene pool and the establishment of genealogical relationships between breeds of sheep of different directions productivity bred in Russia, were used two classes of genetic markers - blood and DNA microsatellites. The included sample sheep are fine-wool Merino breeds: Grozny (GR), Caucasian (CA), Manychskij merino (MM), the Soviet Merino (SM), Stavropol (ST) and coarse wool breeds: Edilbaevskaya (ED), Karakul (CR) and Romanov (RO). For the study of erythrocyte, were selected antigens (blood group) in 1159 samples from 11 breeding farms. For microsatellite DNA study - 598 from 10 breeding farms. Microsatellite analysis revealed that the most polymorphic were Stavropol breed sheep that have identified an average of 18.27 alleles per locus were relatively conservative Romanov breed sheep - 9.7 alleles per locus. The minimum genetic distances established between Grozny and Soviet Merino - 0.0569 (for microsatellites) and 0.0741 (blood groups - later in the same sequence). The rocks of the Stavropol - Grozny were 0.0861 and 0, 0810. Whereas Stavropol and Soviet Merino 0.0861 and 0.1094. Also relatively close between Grozny - Edilbaevskoy, Grozny Karakul, Edilbaevskoy - Karakul: 0.1364 and 0.0851, respectively; 0.1620 and 0.1208; 0.1875 and 0.1192. The highest genetic distances were between Stavropol and Karakul 0.2664 and 0.1804, as well as between the Romanov and all studied species - 0.2491 ... 0.3211 and 0.1734 ... 0.2235

Guided Graph Spectral Embedding: Application to the C. elegans Connectome

Graph spectral analysis can yield meaningful embeddings of graphs by providing insight into distributed features not directly accessible in nodal domain. Recent efforts in graph signal processing have proposed new decompositions-e.g., based on wavelets and Slepians-that can be applied to filter signals defined on the graph. In this work, we take inspiration from these constructions to define a new guided spectral embedding that combines maximizing energy concentration with minimizing modified embedded distance for a given importance weighting of the nodes. We show these optimization goals are intrinsically opposite, leading to a well-defined and stable spectral decomposition. The importance weighting allows to put the focus on particular nodes and tune the trade-off between global and local effects. Following the derivation of our new optimization criterion and its linear approximation, we exemplify the methodology on the C. elegans structural connectome. The results of our analyses confirm known observations on the nematode's neural network in terms of functionality and importance of cells. Compared to Laplacian embedding, the guided approach, focused on a certain class of cells (sensory, inter- and motoneurons), provides more biological insights, such as the distinction between somatic positions of cells, and their involvement in low or high order processing functions.Comment: 43 pages, 7 figures, submitted to Network Neuroscienc

Primena molekularnih markera u napretku stočarstva

With recent developments in DNA technologies, a large number of genetic polymorphisms at DNA sequence level has been introduced over the last decades as named DNA-based markers. The discovery of new class of DNA profiling markers has facilitated the development of marker-based gene tags, mapbased cloning of livestock important genes, variability studies, phylogenetic analysis, synteny mapping, marker-assisted selection of favourable genotypes, etc. The most commonly used DNA-based markers have advantages over the traditional phenotypic and biochemical markers since they provide data that can be analyzed objectively. In this article the main applications of molecular markers in present-day breeding strategies for livestock improvement - parentage determination, genetic distance estimation, genetic diversity, gene mapping and marker-assisted selection have been reviewed.Sa razvojem DNK tehnologija, veliki broj genetskih polimorfizama na nivou DNK sekvence su predstavljene poseldnjih godina pod nazivom DNK markeri. Otkriće novih klasa DNK markera je olakšalo razvoj marker gena, kloniranja gena od važnosti u stočarstvu i to na bazi mapa, ispitivanje varijabilnosti, filogenetske analize, mapiranja, selekcije poželjnih genotipova pomoću markera, itd. Markeri na bazi DNK koji se najčešće koriste imaju prednost u odnosu na tradicionalne fenotiske i biohemijske markere jer obezbeđuju podatke koji se mogu objektivno analizirati. U ovom radu su predstavljeni načini korišćenja i aplikacija molekularnih markera u postojećim odgajivačkim strategijama odn. napretku stočarstva - određivanje porekla, ocena genetske distance, genetskog diverziteta, mapiranje gena i selekcija pomoću markera

Study of the growth traits relationship of lambs in the postnatal development

Data from the Pirot improved sheep were use to estimate postnatal development and growth traits relationship of lambs from birth to weaning. The experiment included 360 lambs, divided into three groups (I, II, III). Lamb traits included BW at birth and approximately 30d, 60d and 90d (weaning). Lambs managed under conditions typical of the area. Male lambs in-group I had a total gain of 22.97 kg (0.255 kg/d), in group II 25.97 kg (0.286 kg/d) (P (lt) 0.01). Lambs in-group III the total gain was 24.64 kg (0.274 kg/d), which was lower than lambs of group II (P>0.05). On the other side, III group of lambs had a higher gain than the I group (P (lt) 0.01). Development of female lambs in the postnatal period was slightly weaker. Lambs of I group, from birth to weaning had a total gain of 21.27 kg, (0.236 kg/d), II group was 23.32 kg (0.259 kg/d). The difference was statistically very significant (P (lt) 0.01). Lambs of group III had a total gain of 23.54 kg (0.261kg/d) and higher growth rate then lambs of group II, but not significant (P>0.05). From the other side, the difference in comparison with the groups III and I was very significant (P (lt) 0.01). Correlations between BWB and BW30, 60, 90 are ranged from low to moderate among the respective traits and ranged between positive from 0.001 to 0.365 and negative from -0.005 to -0.279. Can conclude that the selection should direct towards producing lambs with intermediate birth weight

Uticaj genotipa i perioda laktacije na količinu, fizičke i hemijske osobine ovčijeg mleka

Two genotype of sheep have been utilized in the conduct of the experiment composed of 60 ewes from Pirot x Virtemberg as genotype 1 and 60 ewes of Improved Pirot as genotype 2. All the ewes were reared under identical conditions and without any differences in nutrition and management during the whole period under study. The collection of Milk sampling was done in morning and evening during periods (1, 2, 3) of lactation duration. The average lactation duration and average total milk of the two genotypes were very close and has a minimal difference of 0.467 day and 1.562 kg, in favor of genotype 2. The differences between genotypes were not significant (P>0,05). Regarding physical and chemical properties of milk for both genotypes, the difference were very minimal such as follows; viscosity Pa x s - 0.006, electrical conductivity Ω - 0.018, density kg/m3 -0,001, freezing, t 0C - 0.013, LD number - 0.028 total solids, % - 0.014, fat,% - 0,026, protein,% - 0.085, lactose,% - 0.038, ash,% - 0,021, acidity, 0SH - 0.209. The results indicated that the properties of milk for both genotypes were very near to each other. It can be interpreted that the breeds utilized in the experiment were comparable due to similar characteristics perhaps. The effect of genotype was very significant only for the % protein of the milk. The lactation periods were highly significant in all physical and chemical properties of milk.Istraživanja su obavljena kod dve rase ovaca i to 60 grla Pirotska x Virtemberg kao genotip 1 i 60 ovaca pirotske oplemenjene populacije, kao genotip 2. Sve životinje su držane u istim proizvodnim uslovima na farmi u Vrnjačkoj Banji. Prosečne vrednosti trajanja laktacije i mleka dobijenog u periodu laktacije su bile vrlo ujednačene, tako da nije utvrđen uticaj genotipa na ova svojstva. Takođe, razlike između fizičko hemijskih osobina mleka, u većini slučajeva su bile nesignifikantne. Uticaj genotipa kao fiksnog faktora je bio vrlo signifikantan samo kod sadržaja proteina u mleku ovaca (P (lt) 0.01). Međutim utvrđeno je da period laktacije ima vrlo signifikantan uticaj na sva posmatrana fizička i hemijska svojstva mleka