5,389 research outputs found
Kauffman Knot Invariant from SO(N) or Sp(N) Chern-Simons theory and the Potts Model
The expectation value of Wilson loop operators in three-dimensional SO(N)
Chern-Simons gauge theory gives a known knot invariant: the Kauffman
polynomial. Here this result is derived, at the first order, via a simple
variational method. With the same procedure the skein relation for Sp(N) are
also obtained. Jones polynomial arises as special cases: Sp(2), SO(-2) and
SL(2,R). These results are confirmed and extended up to the second order, by
means of perturbation theory, which moreover let us establish a duality
relation between SO(+/-N) and Sp(-/+N) invariants. A correspondence between the
firsts orders in perturbation theory of SO(-2), Sp(2) or SU(2) Chern-Simons
quantum holonomies and the partition function of the Q=4 Potts Model is built.Comment: 20 pages, 7 figures; accepted for publication on Phys. Rev.
Production of a Higgs pseudoscalar plus two jets in hadronic collisions
We consider the production of a Higgs pseudoscalar accompanied by two jets in
hadronic collisions. We work in the limit that the top quark is much heavier
than the Higgs pseudoscalar and use an effective Lagrangian for the
interactions of gluons with the pseudoscalar. We compute the amplitudes
involving: 1) four gluons and the pseudoscalar, 2) two quarks, two gluons and
the pseudoscalar and 3) four quarks and the pseudoscalar. We find that the
pseudoscalar amplitudes are nearly identical to those for the scalar case, the
only differences being the overall size and the relative signs between terms.
We present numerical cross sections for proton-proton collisions with
center-of-mass energy 14 TeV.Comment: 12 pages, LaTeX, 4 Postscript figures, submitted to Phys. Rev.
Residue network in protein native structure belongs to the universality class of three dimensional critical percolation cluster
A single protein molecule is regarded as a contact network of amino-acid
residues. Some studies have indicated that this network is a small world
network (SWN), while other results have implied that this is a fractal network
(FN). However, SWN and FN are essentially different in the dependence of the
shortest path length on the number of nodes. In this paper, we investigate this
dependence in the residue contact networks of proteins in native structures,
and show that the networks are not SWN but FN. FN is generally characterized by
several dimensions. Among them, we focus on three dimensions; the network
topological dimension , the fractal dimension , and the spectral
dimension . We find that proteins universally yield ,
and . These values are in surprisingly good
coincidence with those in three dimensional critical percolation cluster. Hence
the residue contact networks in the protein native structures belong to the
universality class of three dimensional percolation cluster. The criticality is
relevant to the ambivalent nature of the protein native structures, i.e., the
coexistence of stability and instability, both of which are necessary for a
protein to function as a molecular machine or an allosteric enzyme.Comment: 4 pages, 3 figure
Unsolved Problems in Virtual Knot Theory and Combinatorial Knot Theory
This paper is a concise introduction to virtual knot theory, coupled with a
list of research problems in this field.Comment: 65 pages, 24 figures. arXiv admin note: text overlap with
arXiv:math/040542
Quantum entanglement: The unitary 8-vertex braid matrix with imaginary rapidity
We study quantum entanglements induced on product states by the action of
8-vertex braid matrices, rendered unitary with purely imaginary spectral
parameters (rapidity). The unitarity is displayed via the "canonical
factorization" of the coefficients of the projectors spanning the basis. This
adds one more new facet to the famous and fascinating features of the 8-vertex
model. The double periodicity and the analytic properties of the elliptic
functions involved lead to a rich structure of the 3-tangle quantifying the
entanglement. We thus explore the complex relationship between topological and
quantum entanglement.Comment: 4 pages in REVTeX format, 2 figure
Complex-network analysis of combinatorial spaces: The NK landscape case
We propose a network characterization of combinatorial fitness landscapes by
adapting the notion of inherent networks proposed for energy surfaces. We use
the well-known family of NK landscapes as an example. In our case the inherent
network is the graph whose vertices represent the local maxima in the
landscape, and the edges account for the transition probabilities between their
corresponding basins of attraction. We exhaustively extracted such networks on
representative NK landscape instances, and performed a statistical
characterization of their properties. We found that most of these network
properties are related to the search difficulty on the underlying NK landscapes
with varying values of K.Comment: arXiv admin note: substantial text overlap with arXiv:0810.3492,
arXiv:0810.348
Self-organized Networks of Competing Boolean Agents
A model of Boolean agents competing in a market is presented where each agent
bases his action on information obtained from a small group of other agents.
The agents play a competitive game that rewards those in the minority. After a
long time interval, the poorest player's strategy is changed randomly, and the
process is repeated. Eventually the network evolves to a stationary but
intermittent state where random mutation of the worst strategy can change the
behavior of the entire network, often causing a switch in the dynamics between
attractors of vastly different lengths.Comment: 4 pages, 3 included figures. Some text revision and one new figure
added. To appear in PR
Living on the edge of chaos: minimally nonlinear models of genetic regulatory dynamics
Linearized catalytic reaction equations modeling e.g. the dynamics of genetic
regulatory networks under the constraint that expression levels, i.e. molecular
concentrations of nucleic material are positive, exhibit nontrivial dynamical
properties, which depend on the average connectivity of the reaction network.
In these systems the inflation of the edge of chaos and multi-stability have
been demonstrated to exist. The positivity constraint introduces a nonlinearity
which makes chaotic dynamics possible. Despite the simplicity of such minimally
nonlinear systems, their basic properties allow to understand fundamental
dynamical properties of complex biological reaction networks. We analyze the
Lyapunov spectrum, determine the probability to find stationary oscillating
solutions, demonstrate the effect of the nonlinearity on the effective in- and
out-degree of the active interaction network and study how the frequency
distributions of oscillatory modes of such system depend on the average
connectivity.Comment: 11 pages, 5 figure
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Cre/lox generation of a novel whole-body Kiss1r KO mouse line recapitulates a hypogonadal, obese, and metabolically-impaired phenotype.
Kisspeptin and its receptor, Kiss1r, act centrally to stimulate reproduction. Recent evidence indicates that kisspeptin is also important for body weight and metabolism, as whole-body Kiss1r KO mice, developed with gene trap technology, display obesity and reduced metabolism. Kiss1r is expressed in brain and multiple peripheral tissues, but it is unknown which is responsible for the metabolic phenotype. Here, we sought to confirm that 1) the metabolic phenotype of the gene trap Kiss1r KOs is due to disruption of kisspeptin signaling and not off-target effects of viral mutagenesis, and 2) the Kiss1r flox line is suitable for creating conditional KOs to study the metabolic phenotype. We used Cre/lox technology (Zp3-Cre/Kiss1r flox) to develop a new global Kiss1r KO ("Kiss1r gKO") to compare with the original gene trap KO phenotype. We confirmed that deleting exon 2 of Kiss1r from the entire body induces hypogonadism in both sexes. Moreover, global deletion of Kiss1r induced obesity in females, but not males, along with increased adiposity and impaired glucose tolerance, similar to the gene trap Kiss1r KOs. Likewise, Kiss1r gKO females had decreased VO2 and VCO2, likely underlying their obesity. These findings support that our previous results in gene trap Kiss1r KOs are due to disrupted kisspeptin signaling, and further highlight a role for Kiss1r signaling in energy expenditure and metabolism besides controlling reproduction. Moreover, given Kiss1r expression in multiple cell-types, our findings indicate that the Kiss1r flox line is viable for future investigations to isolate specific target cells of kisspeptin's metabolic effects
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