22,912 research outputs found
On C1-robust transitivity of volume-preserving flows
We prove that a divergence-free and C1-robustly transitive vector field has
no singularities. Moreover, if the vector field is C4 then the linear Poincare
flow associated to it admits a dominated splitting over M
Control of complex networks requires both structure and dynamics
The study of network structure has uncovered signatures of the organization
of complex systems. However, there is also a need to understand how to control
them; for example, identifying strategies to revert a diseased cell to a
healthy state, or a mature cell to a pluripotent state. Two recent
methodologies suggest that the controllability of complex systems can be
predicted solely from the graph of interactions between variables, without
considering their dynamics: structural controllability and minimum dominating
sets. We demonstrate that such structure-only methods fail to characterize
controllability when dynamics are introduced. We study Boolean network
ensembles of network motifs as well as three models of biochemical regulation:
the segment polarity network in Drosophila melanogaster, the cell cycle of
budding yeast Saccharomyces cerevisiae, and the floral organ arrangement in
Arabidopsis thaliana. We demonstrate that structure-only methods both
undershoot and overshoot the number and which sets of critical variables best
control the dynamics of these models, highlighting the importance of the actual
system dynamics in determining control. Our analysis further shows that the
logic of automata transition functions, namely how canalizing they are, plays
an important role in the extent to which structure predicts dynamics.Comment: 15 pages, 6 figure
Microwave-Assisted Extraction of Brewers' Spent Grain Arabinoxylans
Brewers´ spent grain (BSG) is a by-product from beer industry that can be exploited as a source of
arabinoxylo-oligosaccharides (AXOS) with prebiotic activity. In this study, microwave-assisted extractions were
performed during 2 min at 140-210°Cin order to evaluate the feasibility of this extraction technology for quantitative
extraction of the arabinoxylans (AX) or AXOS from BSG. The AX yield increasedwith the increase of the temperature
in the range used. The best condition of extraction of the AXwas 210 ºC during 2 min, allowing the extraction of 43%
of total AX. These AX showed structural variability which allow to define specific types of compounds for different
applications and uses depending on the extraction conditions used
Modularity and the spread of perturbations in complex dynamical systems
We propose a method to decompose dynamical systems based on the idea that
modules constrain the spread of perturbations. We find partitions of system
variables that maximize 'perturbation modularity', defined as the
autocovariance of coarse-grained perturbed trajectories. The measure
effectively separates the fast intramodular from the slow intermodular dynamics
of perturbation spreading (in this respect, it is a generalization of the
'Markov stability' method of network community detection). Our approach
captures variation of modular organization across different system states, time
scales, and in response to different kinds of perturbations: aspects of
modularity which are all relevant to real-world dynamical systems. It offers a
principled alternative to detecting communities in networks of statistical
dependencies between system variables (e.g., 'relevance networks' or
'functional networks'). Using coupled logistic maps, we demonstrate that the
method uncovers hierarchical modular organization planted in a system's
coupling matrix. Additionally, in homogeneously-coupled map lattices, it
identifies the presence of self-organized modularity that depends on the
initial state, dynamical parameters, and type of perturbations. Our approach
offers a powerful tool for exploring the modular organization of complex
dynamical systems
Unfolding Physics from the Algebraic Classification of Spinor Fields
After reviewing the Lounesto spinor field classification, according to the
bilinear covariants associated to a spinor field, we call attention and unravel
some prominent features involving unexpected properties about spinor fields
under such classification. In particular, we pithily focus on the new aspects
--- as well as current concrete possibilities. They mainly arise when we deal
with some non-standard spinor fields concerning, in particular, their
applications in physics.Comment: 6 pages, accepted for publication in PL
Braneworld Remarks in Riemann-Cartan Manifolds
We analyze the projected effective Einstein equation in a 4-dimensional
arbitrary manifold embedded in a 5-dimensional Riemann-Cartan manifold. The
Israel-Darmois matching conditions are investigated, in the context where the
torsion discontinuity is orthogonal to the brane. Unexpectedly, the presence of
torsion terms in the connection does not modify such conditions whatsoever,
despite of the modification in the extrinsic curvature and in the connection.
Then, by imposing the Z_2-symmetry, the Einstein equation obtained via
Gauss-Codazzi formalism is extended, in order to now encompass the torsion
terms. We also show that the factors involving contorsion change drastically
the effective Einstein equation on the brane, as well as the effective
cosmological constant.Comment: 7 pages. A corrected misprint in def.(18), and the respective terms
in Eqs.(20-23). All physical consequences remain unchange
Gravitational constraints of dS branes in AdS Einstein-Brans-Dicke bulk
We derive the full projected Einstein-Brans-Dicke gravitational equations
associated with a n-dimensional brane embedded in a (n+1)-dimensional bulk. By
making use of general conditions, as the positivity of the Brans-Dicke
parameter and the effective Newton gravitational constant as well, we are able
to constrain the brane cosmological constant in terms of the brane tension, the
Brans-Dicke scalar field, and the trace of the stress tensor on the brane, in
order to achieve a brane. Applying these constraints to a specific
five-dimensional model, a lower bound for the scalar field on the brane is
elicited without solving the full equations. It is shown under which conditions
the brane effective cosmological constant can be ignored in the brane projected
gravitational field equations, suggesting a different fine tuning between the
brane tension and the bulk cosmological.Comment: 9 pages, revTe
Eisenstein Series and String Thresholds
We investigate the relevance of Eisenstein series for representing certain
-invariant string theory amplitudes which receive corrections from BPS
states only. may stand for any of the mapping class, T-duality and
U-duality groups , or respectively.
Using -invariant mass formulae, we construct invariant modular functions
on the symmetric space of non-compact type, with the
maximal compact subgroup of , that generalize the standard
non-holomorphic Eisenstein series arising in harmonic analysis on the
fundamental domain of the Poincar\'e upper half-plane. Comparing the
asymptotics and eigenvalues of the Eisenstein series under second order
differential operators with quantities arising in one- and -loop string
amplitudes, we obtain a manifestly T-duality invariant representation of the
latter, conjecture their non-perturbative U-duality invariant extension, and
analyze the resulting non-perturbative effects. This includes the and
couplings in toroidal compactifications of M-theory to any
dimension and respectively.Comment: Latex2e, 60 pages; v2: Appendix A.4 extended, 2 refs added, thms
renumbered, plus minor corrections; v3: relation (1.7) to math Eis series
clarified, eq (3.3) and minor typos corrected, final version to appear in
Comm. Math. Phys; v4: misprints and Eq C.13,C.24 corrected, see note adde
ELKO, flagpole and flag-dipole spinor fields, and the instanton Hopf fibration
In a previous paper we explicitly constructed a mapping that leads Dirac
spinor fields to the dual-helicity eigenspinors of the charge conjugation
operator (ELKO spinor fields). ELKO spinor fields are prime candidates for
describing dark matter, and belong to a wider class of spinor fields, the
so-called flagpole spinor fields, corresponding to the class-(5), according to
Lounesto spinor field classification, based on the relations and values taken
by their associated bilinear covariants. Such a mapping between Dirac and ELKO
spinor fields was obtained in an attempt to extend the Standard Model in order
to encompass dark matter. Now we prove that such a mapping, analogous to the
instanton Hopf fibration map , prevents ELKO to describe the
instanton, giving a suitable physical interpretation to ELKO. We review ELKO
spinor fields as type-(5) spinor fields under the Lounesto spinor field
classification, explicitly computing the associated bilinear covariants. This
paper is also devoted to investigate some formal aspects of the flag-dipole
spinor fields, which correspond to the class-(4) under the Lounesto spinor
field classification. In addition, we prove that type-(4) spinor fields
(corresponding to flag-dipoles) and ELKO spinor fields (corresponding to
flagpoles) can also be entirely described in terms of the Majorana and Weyl
spinor fields. After all, by choosing a projection endomorphism of the
spacetime algebra Cl(1,3) it is shown how to obtain ELKO, flagpole, Majorana
and Weyl spinor fields, respectively corresponding to type-(5) and -(6) spinor
fields, uniquely from limiting cases of a type-(4) (flag-dipole) spinor field,
in a similar result obtained by Lounesto.Comment: 17 Pages, RevTeX, accepted for publication in Adv. Appl. Clifford Al
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