On implicational bases of closure systems with unique critical sets

We show that every optimum basis of a finite closure system, in D.Maier's sense, is also right-side optimum, which is a parameter of a minimum CNF representation of a Horn Boolean function. New parameters for the size of the binary part are also established. We introduce a K-basis of a general closure system, which is a refinement of the canonical basis of Duquenne and Guigues, and discuss a polynomial algorithm to obtain it. We study closure systems with the unique criticals and some of its subclasses, where the K-basis is unique. A further refinement in the form of the E-basis is possible for closure systems without D-cycles. There is a polynomial algorithm to recognize the D-relation from a K-basis. Thus, closure systems without D-cycles can be effectively recognized. While E-basis achieves an optimum in one of its parts, the optimization of the others is an NP-complete problem.Comment: Presented on International Symposium of Artificial Intelligence and Mathematics (ISAIM-2012), Ft. Lauderdale, FL, USA Results are included into plenary talk on conference Universal Algebra and Lattice Theory, June 2012, Szeged, Hungary 29 pages and 2 figure

Formation of color-singlet gluon-clusters and inelastic diffractive scattering

This is the extensive follow-up report of a recent Letter in which the existence of self-organized criticality (SOC) in systems of interacting soft gluons is proposed, and its consequences for inelastic diffractive scattering processes are discussed. It is pointed out, that color-singlet gluon-clusters can be formed in hadrons as a consequence of SOC in systems of interacting soft gluons, and that the properties of such spatiotemporal complexities can be probed experimentally by examing inelastic diffractive scattering. Theoretical arguments and experimental evidences supporting the proposed picture are presented --- together with the result of a systematic analysis of the existing data for inelastic diffractive scattering processes performed at different incident energies, and/or by using different beam-particles. It is shown in particular that the size- and the lifetime-distributions of such gluon-clusters can be directly extracted from the data, and the obtained results exhibit universal power-law behaviors --- in accordance with the expected SOC-fingerprints. As further consequences of SOC in systems of interacting soft gluons, the $t$-dependence and the $(M_x^2/s)$-dependence of the double differential cross-sections for inelastic diffractive scattering off proton-target are discussed. Here $t$ stands for the four-momentum-transfer squared, $M_x$ for the missing mass, and $\sqrt{s}$ for the total c.m.s. energy. It is shown, that the space-time properties of the color-singlet gluon-clusters due to SOC, discussed above, lead to simple analytical formulae for $d^2\sigma/dt d(M_x^2/s)$ and for $d\sigma/dt$, and that the obtained results are in good agreement with the existing data. Further experiments are suggested.Comment: 67 pages, including 11 figure

Characterization of the Vertices and Extreme Directions of the Negative Cycles Polyhedron and Hardness of Generating Vertices of 0/1-Polyhedra

Given a graph $G=(V,E)$ and a weight function on the edges w:E\mapsto\RR, we consider the polyhedron $P(G,w)$ of negative-weight flows on $G$, and get a complete characterization of the vertices and extreme directions of $P(G,w)$. As a corollary, we show that, unless $P=NP$, there is no output polynomial-time algorithm to generate all the vertices of a 0/1-polyhedron. This strengthens the NP-hardness result of Khachiyan et al. (2006) for non 0/1-polyhedra, and comes in contrast with the polynomiality of vertex enumeration for 0/1-polytopes \cite{BL98} [Bussieck and L\"ubbecke (1998)]

Development of an optimized processing method for Withania frutescens

Withania somnifera (L.) Dunal originates mainly from Northern and Southern India. Primarily the roots are used in the Ayurvedic medicine as tonic, sedative hypnotic, adstringent, diuretic, emetic, and aphrodisiac. In Europe, it is widely used in food supplements. Due to the many effects and uses of this plant, the analysis of the Withania somnifera and optimization of industrial processing is nowadays an important issue. In Europe W. frutescens is native, and may be interesting for industrial preparation due to its similar phytochemical profile to W. somnifera. The point of our research was to develop an effective extraction and hydrolysis method of the Withania frutescens leaves to optimize the industrial processing

Lambda Polarization in Polarized Proton-Proton Collisions at RHIC

We discuss Lambda polarization in semi-inclusive proton-proton collisions, with one of the protons longitudinally polarized. The hyperfine interaction responsible for the $\Delta$-$N$ and $\Sigma$-$\Lambda$ mass splittings gives rise to flavor asymmetric fragmentation functions and to sizable polarized non-strange fragmentation functions. We predict large positive Lambda polarization in polarized proton-proton collisions at large rapidities of the produced Lambda, while other models, based on SU(3) flavor symmetric fragmentation functions, predict zero or negative Lambda polarization. The effect of $\Sigma^0$ and $\Sigma^*$ decays is also discussed. Forthcoming experiments at RHIC will be able to differentiate between these predictions.Comment: 18 pages, 5 figure

Deep inelastic scattering on asymmetric nuclei

We study deep inelastic scattering on isospin asymmetric nuclei. In particular, the difference of the nuclear structure functions and the Gottfried sum rule for the lightest mirror nuclei, 3He and 3H, are investigated. It is found that such systems can provide significant information on charge symmetry breaking and flavor asymmetry in the nuclear medium. Furthermore, we propose a new method to extract the neutron structure function from radioactive isotopes far from the line of stability. We also discuss the flavor asymmetry in the Drell-Yan process with isospin asymmetric nuclei

Polynomial Delay Algorithm for Listing Minimal Edge Dominating sets in Graphs

The Transversal problem, i.e, the enumeration of all the minimal transversals of a hypergraph in output-polynomial time, i.e, in time polynomial in its size and the cumulated size of all its minimal transversals, is a fifty years old open problem, and up to now there are few examples of hypergraph classes where the problem is solved. A minimal dominating set in a graph is a subset of its vertex set that has a non empty intersection with the closed neighborhood of every vertex. It is proved in [M. M. Kant\'e, V. Limouzy, A. Mary, L. Nourine, On the Enumeration of Minimal Dominating Sets and Related Notions, In Revision 2014] that the enumeration of minimal dominating sets in graphs and the enumeration of minimal transversals in hypergraphs are two equivalent problems. Hoping this equivalence can help to get new insights in the Transversal problem, it is natural to look inside graph classes. It is proved independently and with different techniques in [Golovach et al. - ICALP 2013] and [Kant\'e et al. - ISAAC 2012] that minimal edge dominating sets in graphs (i.e, minimal dominating sets in line graphs) can be enumerated in incremental output-polynomial time. We provide the first polynomial delay and polynomial space algorithm that lists all the minimal edge dominating sets in graphs, answering an open problem of [Golovach et al. - ICALP 2013]. Besides the result, we hope the used techniques that are a mix of a modification of the well-known Berge's algorithm and a strong use of the structure of line graphs, are of great interest and could be used to get new output-polynomial time algorithms.Comment: proofs simplified from previous version, 12 pages, 2 figure

Role of the Delta (1232) in DIS on polarized 3^3He and extraction of the neutron spin structure function g1n(x,Q2)g_{1}^{n}(x,Q^2)

We consider the effect of the transitions $n \to \Delta^{0}$ and $p \to \Delta^{+}$ in deep inelastic scattering on polarized $^3$He on the extraction of the neutron spin structure function $g_{1}^{n}(x,Q^2)$. Making the natural assumption that these transitions are the dominant non-nucleonic contributions to the renormalization of the axial vector coupling constant in the A=3 system, we find that the effect of $\Delta$ increases $g_{1}^{n}(x,Q^2)$ by $10 \div 40$% in the range $0.05 \le x \le 0.6$, where our considerations are applicable and most of the data for $g_{1}^{n}(x,Q^2)$ exist.Comment: 23 pages, 6 figures, revte

Second moment of the Husimi distribution as a measure of complexity of quantum states

We propose the second moment of the Husimi distribution as a measure of complexity of quantum states. The inverse of this quantity represents the effective volume in phase space occupied by the Husimi distribution, and has a good correspondence with chaoticity of classical system. Its properties are similar to the classical entropy proposed by Wehrl, but it is much easier to calculate numerically. We calculate this quantity in the quartic oscillator model, and show that it works well as a measure of chaoticity of quantum states.Comment: 25 pages, 10 figures. to appear in PR