1,078 research outputs found
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 -dependence and the -dependence of the double
differential cross-sections for inelastic diffractive scattering off
proton-target are discussed. Here stands for the four-momentum-transfer
squared, for the missing mass, and 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 and for , 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 and a weight function on the edges w:E\mapsto\RR, we consider the polyhedron of negative-weight flows on , and get a complete characterization of the vertices and extreme directions of . As a corollary, we show that, unless , 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)]
Analyzing powers in inclusive pion production at high energy and the nucleon spin structure
Analyzing powers in inclusive pion production in high energy transversely
polarized proton-proton collisions are studied theoretically in the framework
of the quark recombination model. Calculations by assuming the SU(6)
spin-flavor symmetry for the nucleon structure disagree with the experiments.
We solve this difficulty by taking into account the %We overcome this
difficulty by taking into account the realistic spin distribution functions of
the nucleon, which differs from the SU(6) expectation at large , %but
coincides with a perturbative QCD constraint on the ratio of the unpolarized
valence distributions, as . We also discuss the kaon spin
asymmetry and find in the polarized proton-proton
collisions at large .Comment: 13 pages, 4 figures, late
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 - and - 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 and 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 He and extraction of the neutron spin structure function
We consider the effect of the transitions and in deep inelastic scattering on polarized He on the extraction
of the neutron spin structure function . 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 increases by % in the range , where our considerations are applicable
and most of the data for 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
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