5,519 research outputs found
Covariant canonical formalism for four-dimensional BF theory
The covariant canonical formalism for four-dimensional BF theory is
performed. The aim of the paper is to understand in the context of the
covariant canonical formalism both the reducibility that some first class
constraints have in Dirac's canonical analysis and also the role that
topological terms play. The analysis includes also the cases when both a
cosmological constant and the second Chern character are added to the pure BF
action. In the case of the BF theory supplemented with the second Chern
character, the presymplectic 3-form is different to the one of the BF theory in
spite of the fact both theories have the same equations of motion while on the
space of solutions they both agree to each other. Moreover, the analysis of the
degenerate directions shows some differences between diffeomorphisms and
internal gauge symmetries.Comment: Latex file, 22 pages (due to the macro). Revised version to match
published versio
Unitary Chern-Simons matrix model and the Villain lattice action
We use the Villain approximation to show that the Gross-Witten model, in the
weak- and strong-coupling limits, is related to the unitary matrix model that
describes U(N) Chern-Simons theory on S^3. The weak-coupling limit corresponds
to the q->1 limit of the Chern-Simons theory while the strong-coupling regime
is related to the q->0 limit. In the latter case, there is a logarithmic
relationship between the respective coupling constants. We also show how the
Chern-Simons matrix model arises by considering two-dimensional Yang-Mills
theory with the Villain action. This leads to a U(1)^N theory which is the
Abelianization of 2d Yang-Mills theory with the heat-kernel lattice action. In
addition, we show that the character expansion of the Villain lattice action
gives the q deformation of the heat kernel as it appears in q-deformed 2d
Yang-Mills theory. We also study the relationship between the unitary and
Hermitian Chern-Simons matrix models and the rotation of the integration
contour in the corresponding integrals.Comment: 17 pages, Minor corrections to match the published versio
Multiple-event probability in general-relativistic quantum mechanics
We discuss the definition of quantum probability in the context of "timeless"
general--relativistic quantum mechanics. In particular, we study the
probability of sequences of events, or multi-event probability. In conventional
quantum mechanics this can be obtained by means of the ``wave function
collapse" algorithm. We first point out certain difficulties of some natural
definitions of multi-event probability, including the conditional probability
widely considered in the literature. We then observe that multi-event
probability can be reduced to single-event probability, by taking into account
the quantum nature of the measuring apparatus. In fact, by exploiting the
von-Neumann freedom of moving the quantum classical boundary, one can always
trade a sequence of non-commuting quantum measurements at different times, with
an ensemble of simultaneous commuting measurements on the joint
system+apparatus system. This observation permits a formulation of quantum
theory based only on single-event probability, where the results of the "wave
function collapse" algorithm can nevertheless be recovered. The discussion
bears also on the nature of the quantum collapse
Anomalous Hall effect in the coplanar antiferromagnetic coloring-triangular lattice
We study the anomalous Hall effect on the antiferromagnetic coloring-triangular lattice with a coplanar magnetic configuration in the presence of a spin-orbit interaction. The effect of the spin-orbit coupling is included at an effective level as a rotation of the electronic spin as the electrons hop from site to site. Our result reveals that a finite Hall conductivity in the planar 120 structure takes place if a finite spin-orbit coupling is present. A quantized Hall conductivity occurs at global band gaps resulting from the topologically nontrivial band structure.Fil: Duran, A. C.. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas. Centro CientĂfico TecnolĂłgico Conicet - La Plata. Instituto de FĂsica de LĂquidos y Sistemas BiolĂłgicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de FĂsica de LĂquidos y Sistemas BiolĂłgicos; ArgentinaFil: Osorio, Santiago Antonio. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas. Oficina de CoordinaciĂłn Administrativa Ciudad Universitaria. Unidad Ejecutora Instituto de Nanociencia y NanotecnologĂa. Unidad Ejecutora Instituto de Nanociencia y NanotecnologĂa - Nodo Bariloche | ComisiĂłn Nacional de EnergĂa AtĂłmica. Unidad Ejecutora Instituto de Nanociencia y NanotecnologĂa. Unidad Ejecutora Instituto de Nanociencia y NanotecnologĂa - Nodo Bariloche; ArgentinaFil: Sturla, Mauricio Bernardo. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas. Centro CientĂfico TecnolĂłgico Conicet - La Plata. Instituto de FĂsica de LĂquidos y Sistemas BiolĂłgicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de FĂsica de LĂquidos y Sistemas BiolĂłgicos; Argentin
Encoding dynamics for multiscale community detection: Markov time sweeping for the Map equation
The detection of community structure in networks is intimately related to
finding a concise description of the network in terms of its modules. This
notion has been recently exploited by the Map equation formalism (M. Rosvall
and C.T. Bergstrom, PNAS, 105(4), pp.1118--1123, 2008) through an
information-theoretic description of the process of coding inter- and
intra-community transitions of a random walker in the network at stationarity.
However, a thorough study of the relationship between the full Markov dynamics
and the coding mechanism is still lacking. We show here that the original Map
coding scheme, which is both block-averaged and one-step, neglects the internal
structure of the communities and introduces an upper scale, the `field-of-view'
limit, in the communities it can detect. As a consequence, Map is well tuned to
detect clique-like communities but can lead to undesirable overpartitioning
when communities are far from clique-like. We show that a signature of this
behavior is a large compression gap: the Map description length is far from its
ideal limit. To address this issue, we propose a simple dynamic approach that
introduces time explicitly into the Map coding through the analysis of the
weighted adjacency matrix of the time-dependent multistep transition matrix of
the Markov process. The resulting Markov time sweeping induces a dynamical
zooming across scales that can reveal (potentially multiscale) community
structure above the field-of-view limit, with the relevant partitions indicated
by a small compression gap.Comment: 10 pages, 6 figure
Linear models of activation cascades: analytical solutions and coarse-graining of delayed signal transduction
Cellular signal transduction usually involves activation cascades, the
sequential activation of a series of proteins following the reception of an
input signal. Here we study the classic model of weakly activated cascades and
obtain analytical solutions for a variety of inputs. We show that in the
special but important case of optimal-gain cascades (i.e., when the
deactivation rates are identical) the downstream output of the cascade can be
represented exactly as a lumped nonlinear module containing an incomplete gamma
function with real parameters that depend on the rates and length of the
cascade, as well as parameters of the input signal. The expressions obtained
can be applied to the non-identical case when the deactivation rates are random
to capture the variability in the cascade outputs. We also show that cascades
can be rearranged so that blocks with similar rates can be lumped and
represented through our nonlinear modules. Our results can be used both to
represent cascades in computational models of differential equations and to fit
data efficiently, by reducing the number of equations and parameters involved.
In particular, the length of the cascade appears as a real-valued parameter and
can thus be fitted in the same manner as Hill coefficients. Finally, we show
how the obtained nonlinear modules can be used instead of delay differential
equations to model delays in signal transduction.Comment: 18 pages, 7 figure
- …