2,837 research outputs found
Stable divisorial gonality is in NP
Divisorial gonality and stable divisorial gonality are graph parameters,
which have an origin in algebraic geometry. Divisorial gonality of a connected
graph can be defined with help of a chip firing game on . The stable
divisorial gonality of is the minimum divisorial gonality over all
subdivisions of edges of .
In this paper we prove that deciding whether a given connected graph has
stable divisorial gonality at most a given integer belongs to the class NP.
Combined with the result that (stable) divisorial gonality is NP-hard by
Gijswijt, we obtain that stable divisorial gonality is NP-complete. The proof
consist of a partial certificate that can be verified by solving an Integer
Linear Programming instance. As a corollary, we have that the number of
subdivisions needed for minimum stable divisorial gonality of a graph with
vertices is bounded by for a polynomial
Level-rank duality of the U(N) WZW model, Chern-Simons theory, and 2d qYM theory
We study the WZW, Chern-Simons, and 2d qYM theories with gauge group U(N).
The U(N) WZW model is only well-defined for odd level K, and this model is
shown to exhibit level-rank duality in a much simpler form than that for SU(N).
The U(N) Chern-Simons theory on Seifert manifolds exhibits a similar duality,
distinct from the level-rank duality of SU(N) Chern-Simons theory on S^3. When
q = e^{2 pi i/(N+K)}, the observables of the 2d U(N) qYM theory can be
expressed as a sum over a finite subset of U(N) representations. When N and K
are odd, the qYM theory exhibits N K duality, provided q = e^{2 pi
i/(N+K)} and theta = 0 mod 2 pi /(N+K).Comment: 19 pages; v2: minor typo corrected, 1 paragraph added, published
versio
Unconventional secretion of α-Crystallin B requires the Autophagic pathway and is controlled by phosphorylation of its serine 59 residue
α-Crystallin B (CRYAB or HspB5) is a chaperone member of the small heat-shock protein family that prevents aggregation of many cytosolic client proteins by means of its ATP-independent holdase activity. Surprisingly, several reports show that CRYAB exerts a protective role also extracellularly, and it has been recently demonstrated that CRYAB is secreted from human retinal pigment epithelial cells by an unconventional secretion pathway that involves multi-vesicular bodies. Here we show that autophagy is crucial for this unconventional secretion pathway and that phosphorylation at serine 59 residue regulates CRYAB secretion by inhibiting its recruitment to the autophagosomes. In addition, we found that autophagosomes containing CRYAB are not able to fuse with lysosomes. Therefore, CRYAB is capable to highjack and divert autophagosomes toward the exocytic pathway, inhibiting their canonical route leading to the lysosomal compartment. Potential implications of these findings in the context of disease-associated mutant proteins turn-over are discussed
Instanton on toric singularities and black hole countings
We compute the instanton partition function for U(N) gauge
theories living on toric varieties, mainly of type
including or O_{\PP_1}(-p) surfaces. The results provide
microscopic formulas for the partition functions of black holes made out of
D4-D2-D0 bound states wrapping four-dimensional toric varieties inside a
Calabi-Yau. The partition function gets contributions from regular and
fractional instantons. Regular instantons are described in terms of symmetric
products of the four-dimensional variety. Fractional instantons are built out
of elementary self-dual connections with no moduli carrying non-trivial fluxes
along the exceptional cycles of the variety. The fractional instanton
contribution agrees with recent results based on 2d SYM analysis. The partition
function, in the large charge limit, reproduces the supergravity macroscopic
formulae for the D4-D2-D0 black hole entropy.Comment: 29 pages, 3 fig Section 5 is improved by the inclusion of a detailed
comparison between the instanton partition function and the D4-D2-D0 black
hole entropy formula coming from supergravit
TopiaryExplorer: visualizing large phylogenetic trees with environmental metadata
Motivation: Microbial community profiling is a highly active area of research, but tools that facilitate visualization of phylogenetic trees and associated environmental data have not kept up with the increasing quantity of data generated in these studies
Strings from Feynman Graph counting : without large N
A well-known connection between n strings winding around a circle and
permutations of n objects plays a fundamental role in the string theory of
large N two dimensional Yang Mills theory and elsewhere in topological and
physical string theories. Basic questions in the enumeration of Feynman graphs
can be expressed elegantly in terms of permutation groups. We show that these
permutation techniques for Feynman graph enumeration, along with the Burnside
counting lemma, lead to equalities between counting problems of Feynman graphs
in scalar field theories and Quantum Electrodynamics with the counting of
amplitudes in a string theory with torus or cylinder target space. This string
theory arises in the large N expansion of two dimensional Yang Mills and is
closely related to lattice gauge theory with S_n gauge group. We collect and
extend results on generating functions for Feynman graph counting, which
connect directly with the string picture. We propose that the connection
between string combinatorics and permutations has implications for QFT-string
dualities, beyond the framework of large N gauge theory.Comment: 55 pages + 10 pages Appendices, 23 figures ; version 2 - typos
correcte
Psi-floor diagrams and a Caporaso-Harris type recursion
Floor diagrams are combinatorial objects which organize the count of tropical
plane curves satisfying point conditions. In this paper we introduce Psi-floor
diagrams which count tropical curves satisfying not only point conditions but
also conditions given by Psi-classes (together with points). We then generalize
our definition to relative Psi-floor diagrams and prove a Caporaso-Harris type
formula for the corresponding numbers. This formula is shown to coincide with
the classical Caporaso-Harris formula for relative plane descendant
Gromov-Witten invariants. As a consequence, we can conclude that in our case
relative descendant Gromov-Witten invariants equal their tropical counterparts.Comment: minor changes to match the published versio
Coupled-Bunch Beam Breakup due to Resistive-Wall Wake
The coupled-bunch beam breakup problem excited by the resistive wall wake is
formulated. An approximate analytic method of finding the asymptotic behavior
of the transverse bunch displacement is developed and solved.Comment: 8 page
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