2,695 research outputs found
Topological transversals to a family of convex sets
Let be a family of compact convex sets in . We say
that has a \emph{topological -transversal of index }
(, ) if there are, homologically, as many transversal
-planes to as -planes containing a fixed -plane in
.
Clearly, if has a -transversal plane, then
has a topological -transversal of index for and . The converse is not true in general.
We prove that for a family of compact convex sets in
a topological -transversal of index implies an
ordinary -transversal. We use this result, together with the
multiplication formulas for Schubert cocycles, the Lusternik-Schnirelmann
category of the Grassmannian, and different versions of the colorful Helly
theorem by B\'ar\'any and Lov\'asz, to obtain some geometric consequences
Fast Evaluation of Interlace Polynomials on Graphs of Bounded Treewidth
We consider the multivariate interlace polynomial introduced by Courcelle
(2008), which generalizes several interlace polynomials defined by Arratia,
Bollobas, and Sorkin (2004) and by Aigner and van der Holst (2004). We present
an algorithm to evaluate the multivariate interlace polynomial of a graph with
n vertices given a tree decomposition of the graph of width k. The best
previously known result (Courcelle 2008) employs a general logical framework
and leads to an algorithm with running time f(k)*n, where f(k) is doubly
exponential in k. Analyzing the GF(2)-rank of adjacency matrices in the context
of tree decompositions, we give a faster and more direct algorithm. Our
algorithm uses 2^{3k^2+O(k)}*n arithmetic operations and can be efficiently
implemented in parallel.Comment: v4: Minor error in Lemma 5.5 fixed, Section 6.6 added, minor
improvements. 44 pages, 14 figure
Vertex Cover Kernelization Revisited: Upper and Lower Bounds for a Refined Parameter
An important result in the study of polynomial-time preprocessing shows that
there is an algorithm which given an instance (G,k) of Vertex Cover outputs an
equivalent instance (G',k') in polynomial time with the guarantee that G' has
at most 2k' vertices (and thus O((k')^2) edges) with k' <= k. Using the
terminology of parameterized complexity we say that k-Vertex Cover has a kernel
with 2k vertices. There is complexity-theoretic evidence that both 2k vertices
and Theta(k^2) edges are optimal for the kernel size. In this paper we consider
the Vertex Cover problem with a different parameter, the size fvs(G) of a
minimum feedback vertex set for G. This refined parameter is structurally
smaller than the parameter k associated to the vertex covering number vc(G)
since fvs(G) <= vc(G) and the difference can be arbitrarily large. We give a
kernel for Vertex Cover with a number of vertices that is cubic in fvs(G): an
instance (G,X,k) of Vertex Cover, where X is a feedback vertex set for G, can
be transformed in polynomial time into an equivalent instance (G',X',k') such
that |V(G')| <= 2k and |V(G')| <= O(|X'|^3). A similar result holds when the
feedback vertex set X is not given along with the input. In sharp contrast we
show that the Weighted Vertex Cover problem does not have a polynomial kernel
when parameterized by the cardinality of a given vertex cover of the graph
unless NP is in coNP/poly and the polynomial hierarchy collapses to the third
level.Comment: Published in "Theory of Computing Systems" as an Open Access
publicatio
Resource Competition on Integral Polymatroids
We study competitive resource allocation problems in which players distribute
their demands integrally on a set of resources subject to player-specific
submodular capacity constraints. Each player has to pay for each unit of demand
a cost that is a nondecreasing and convex function of the total allocation of
that resource. This general model of resource allocation generalizes both
singleton congestion games with integer-splittable demands and matroid
congestion games with player-specific costs. As our main result, we show that
in such general resource allocation problems a pure Nash equilibrium is
guaranteed to exist by giving a pseudo-polynomial algorithm computing a pure
Nash equilibrium.Comment: 17 page
Large scale shell model calculations for odd-odd Mn isotopes
Large scale shell model calculations have been carried out for odd-odd
Mn isotopes in two different model spaces. First set of calculations
have been carried out in full shell valence space with two recently
derived shell interactions namely GXPF1A and KB3G treating Ca
as core. The second set of calculations have been performed in
valence space with the interaction treating Ca as core and
imposing a truncation by allowing up to a total of six particle excitations
from the 0f orbital to the upper orbitals for protons and
from the upper orbitals to the 0g orbital for neutron. For
low-lying states in Mn, the KB3G and GXPF1A both predicts good results
and for Mn, KB3G is much better than GXPF1A. For negative parity and
high-spin positive parity states in both isotopes interaction is
required. Experimental data on Mn is sparse and therefore it is not
possible to make any definite conclusions. More experimental data on negative
parity states is needed to ascertain the importance of 0g and higher
orbitals in neutron rich Mn isotopes.Comment: 5 pages, 4 figures, Submitted to Eur. Phys. J.
The Jang equation reduction of the spacetime positive energy theorem in dimensions less than eight
We extend the Jang equation proof of the positive energy theorem due to R.
Schoen and S.-T. Yau from dimension to dimensions . This
requires us to address several technical difficulties that are not present when
. The regularity and decay assumptions for the initial data sets to which
our argument applies are weaker than those of R. Schoen and S.-T. Yau. In
recent joint work with L.-H. Huang, D. Lee, and R. Schoen we have given a
different proof of the full positive mass theorem in dimensions .
We pointed out that this theorem can alternatively be derived from our density
argument and the positive energy theorem of the present paper.Comment: All comments welcome! Final version to appear in Comm. Math. Phy
Top quark associated production of topcolor pions at hadron colliders
We investigate the associated production of a neutral physical pion with top
quarks in the context of topcolor assisted technicolor. We find that single-top
associated production does not yield viable rates at either the Tevatron or
LHC. tt-associated production at the Tevatron is suppressed relative to
Standard Model ttH, but at the LHC is strongly enhanced and would allow for
easy observation of the main decay channels to bottom quarks, and possible
observation of the decay to gluons.Comment: 13 pages, 4 figures, submitted to PR
Black Hole Production at LHC: String Balls and Black Holes from pp and Lead-lead Collisions
If the fundamental planck scale is near a TeV, then parton collisions with
high enough center-of-mass energy should produce black holes. The production
rate for such black holes at LHC has been extensively studied for the case of a
proton-proton collision. In this paper, we extend this analysis to a lead-lead
collision at LHC. We find that the cross section for small black holes which
may in principle be produced in such a collision is either enhanced or
suppressed, depending upon the black hole mass. For example, for black holes
with a mass around 3 TeV we find that the differential black hole production
cross section, d\sigma/dM, in a typical lead-lead collision is up to 90 times
larger than that for black holes produced in a typical proton-proton collision.
We also discuss the cross-sections for `string ball' production in these
collisions. For string balls of mass about 1 (2) TeV, we find that the
differential production cross section in a typical lead-lead collision may be
enhanced by a factor up to 3300 (850) times that of a proton-proton collision
at LHC.Comment: Added some discussion, final version to appear in Phys. Rev. D (rapid
communications
Integrability of Type II Superstrings on Ramond-Ramond Backgrounds in Various Dimensions
We consider type II superstrings on AdS backgrounds with Ramond-Ramond flux
in various dimensions. We realize the backgrounds as supercosets and analyze
explicitly two classes of models: non-critical superstrings on AdS_{2d} and
critical superstrings on AdS_p\times S^p\times CY. We work both in the
Green--Schwarz and in the pure spinor formalisms. We construct a one-parameter
family of flat currents (a Lax connection) leading to an infinite number of
conserved non-local charges, which imply the classical integrability of both
sigma-models. In the pure spinor formulation, we use the BRST symmetry to prove
the quantum integrability of the sigma-model. We discuss how classical
\kappa-symmetry implies one-loop conformal invariance. We consider the addition
of space-filling D-branes to the pure spinor formalism.Comment: LaTeX2e, 56 pages, 1 figure, JHEP style; v2: references added, typos
fixed in some equations; v3: typos fixed to match the published versio
Frictional drag between non-equilibrium charged gases
The frictional drag force between separated but coupled two-dimensional
electron gases of different temperatures is studied using the non-equilibrium
Green function method based on the separation of center-of-mass and relative
dynamics of electrons. As the mechanisms of producing the frictional force we
include the direct Coulomb interaction, the interaction mediated via virtual
and real TA and LA phonons, optic phonons, plasmons, and TA and LA
phonon-electron collective modes. We found that, when the distance between the
two electron gases is large, and at intermediate temperature where plasmons and
collective modes play the most important role in the frictional drag, the
possibility of having a temperature difference between two subsystems modifies
greatly the transresistivity.Comment: 8figure
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