806 research outputs found
Combinatorial properties of the G-degree
A strong interaction is known to exist between edge-colored graphs (which encode PL pseudo-manifolds of arbitrary dimension) and random tensor models (as a possible approach to the study of Quantum Gravity). The key tool is the "G-degree" of the involved graphs, which drives the 1/N expansion in the tensor models context. In the present paper - by making use of combinatorial properties concerning Hamiltonian decompositions of the complete graph - we prove that, in any even dimension d greater or equal to 4, the G-degree of all bipartite graphs, as well as of all (bipartite or non-bipartite) graphs representing singular manifolds, is an integer multiple of (d-1)!. As a consequence, in even dimension, the terms of the 1/N expansion corresponding to odd powers of 1/N are null in the complex context, and do not involve colored graphs representing singular manifolds in the real context. In particular, in the 4-dimensional case, where the G-degree is shown to depend only on the regular genera with respect to an arbitrary pair of "associated" cyclic permutations, several results are obtained, relating the G-degree or the regular genus of 5-colored graphs and the Euler characteristic of the associated PL 4-manifolds
TOPOLOGY IN COLORED TENSOR MODELS
From a “geometric topology” point of view, the theory of manifold representation by means of edge-colored graphs has been deeply studied since 1975 and many results have been achieved: its great advantage is the possibility of encoding, in any dimension, every PL d-manifold by means of a totally combinatorial tool.
Edge-colored graphs also play an important rĂ´le within colored tensor models theory, considered as a possible approach to the study of Quantum Gravity: the key tool is the G-degree of the involved graphs, which drives the 1/N expansion in the higher dimensional tensor models context, exactly as it happens for the genus of surfaces in the two-dimensional matrix model setting.
Therefore, topological and geometrical properties of the represented PL manifolds, with respect to the G-degree, have specific relevance in the tensor models framework, show- ing a direct fruitful interaction between tensor models and discrete geometry, via edge-colored graphs.
In colored tensor models, manifolds and pseudomanifolds are (almost) on the same footing, since they constitute the class of polyhedra represented by edge-colored Feynman graphs arising in this context; thus, a promising research trend is to look for classification results concerning all pseudomanifolds - or, at least, singular d-manifolds, if d ≥ 4 - represented by graphs of a given G-degree.
In dimension 4, the existence of colored graphs encoding different PL manifolds with the same underlying TOP manifold, suggests also to investigate the ability of ten- sor models to accurately reflect geometric degrees of freedom of Quantum Gravity
Granular Rheology in Zero Gravity
We present an experimental investigation on the rheological behavior of model
granular media made of nearly elastic spherical particles. The experiments are
performed in a cylindrical Couette geometry and the experimental device is
placed inside an airplane undergoing parabolic flights to cancel the effect of
gravity. The corresponding curves, shear stress versus shear rate, are
presented and a comparison with existing theories is proposed. The quadratic
dependence on the shear rate is clearly shown and the behavior as a function of
the solid volume fraction of particles exhibits a power law function. It is
shown that theoretical predictions overestimate the experiments. We observe, at
intermediate volume fractions, the formation of rings of particles regularly
spaced along the height of the cell. The differences observed between
experimental results and theoretical predictions are discussed and related to
the structures formed in the granular medium submitted to the external shear.Comment: 10 pages, 6 figures to be published in Journal of Physics : Condensed
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Trajectory attractors for the Sun-Liu model for nematic liquid crystals in 3D
In this paper we prove the existence of a trajectory attractor (in the sense
of V.V. Chepyzhov and M.I. Vishik) for a nonlinear PDE system coming from a 3D
liquid crystal model accounting for stretching effects. The system couples a
nonlinear evolution equation for the director d (introduced in order to
describe the preferred orientation of the molecules) with an incompressible
Navier-Stokes equation for the evolution of the velocity field u. The technique
is based on the introduction of a suitable trajectory space and of a metric
accounting for the double-well type nonlinearity contained in the director
equation. Finally, a dissipative estimate is obtained by using a proper
integrated energy inequality. Both the cases of (homogeneous) Neumann and
(non-homogeneous) Dirichlet boundary conditions for d are considered.Comment: 32 page
Filling a silo with a mixture of grains: Friction-induced segregation
We study the filling process of a two-dimensional silo with inelastic
particles by simulation of a granular media lattice gas (GMLG) model. We
calculate the surface shape and flow profiles for a monodisperse system and we
introduce a novel generalization of the GMLG model for a binary mixture of
particles of different friction properties where, for the first time, we
measure the segregation process on the surface. The results are in good
agreement with a recent theory, and we explain the observed small deviations by
the nonuniform velocity profile.Comment: 10 pages, 5 figures, to be appear in Europhys. Let
Amphibian peptides for skin protection and healing
BACKGROUND: Amphibians are currently suffering a dramatic decline worldwide, mainly due to chytridiomycosis, a skin infection caused by the pathogenic fungus Batrachochytrium dendrobatidis (Bd). An important natural defense of amphibian skin is the production of antimicrobial peptides (AMPs) by granular glands in the dermis. AMPs collected from several species of frogs successfully inhibit the growth of Bd in vitro. Besides their anti-microbial and anti-fungal activities, AMPs have been shown to exert other biological effects such as anti-viral, anti-tumor, anti-oxidant, immunomodulating and wound healing.
AIM: We intended to test the efficacy of AMPs as cutaneous defenses in frog species either resistant or susceptible to Bd.
METHODS: 3 frog species (Gastrotheca nebulanastes (GN), G. excubitor (GE) and Hypsiboas gladiator (HG), were collected in montane scrub, cloud forest and high elevation grassland habitats near Manu National Park in southeastern Peru. AMP secretion was stimulated by injection of norepinephrine into the dorsal lymph sacks. AMPs were then purified by chromatographic techniques. The human endothelial cell line HECV was treated with AMP concentrations ranging from 0.005 to 50 \ub5g/mL. Cell viability was verified by MTT test. Wound healing properties were analyzed by scratch wound assay. AMP inhibition strength against Bd growth was measured in vitro by incubating Bd zoospores with different concentrations of AMPs.
RESULTS: Treatment with AMPs secreted from GN, GE and HG did not affect HECV cell viability at any concentration tested. No significant differences in cell migration rate were observed in HECV cells scratched and treated with GN and GE AMPs. Only HG peptides showed wound healing properties as well as strong Bd growth inhibiting ability.
CONCLUSIONS: Stimulation of wound healing mechanisms and inhibition of Bd growth by skin AMPs might both contribute to HG resistance to chytridiomycosis. Understanding the role of skin defenses may lead to the development of novel Bd mitigation strategies. Possible applications of amphibian AMPs in skin medicine deserve attention and further studies.
This work was funded by the European Commission (Tender ENV.B.3/SER/2016/0028, Mitigating a new infectious disease in salamanders to counteract the loss of European biodiversity) and by Parco Nazionale delle Cinque Terre
Granular Elasticity without the Coulomb Condition
An self-contained elastic theory is derived which accounts both for
mechanical yield and shear-induced volume dilatancy. Its two essential
ingredients are thermodynamic instability and the dependence of the elastic
moduli on compression.Comment: 4pages, 2 figure
Robustness of Local Predictions in Atomistic Machine Learning Models
Machine learning (ML) models for molecules and materials commonly rely on a
decomposition of the global target quantity into local, atom-centered
contributions. This approach is convenient from a computational perspective,
enabling large-scale ML-driven simulations with a linear-scaling cost, and also
allow for the identification and post-hoc interpretation of contributions from
individual chemical environments and motifs to complicated macroscopic
properties. However, even though there exist practical justifications for these
decompositions, only the global quantity is rigorously defined, and thus it is
unclear to what extent the atomistic terms predicted by the model can be
trusted. Here, we introduce a quantitative metric, which we call the local
prediction rigidity (LPR), that allows one to assess how robust the locally
decomposed predictions of ML models are. We investigate the dependence of LPR
on the aspects of model training, particularly the composition of training
dataset, for a range of different problems from simple toy models to real
chemical systems. We present strategies to systematically enhance the LPR,
which can be used to improve the robustness, interpretability, and
transferability of atomistic ML models
A Hedged Monte Carlo Approach to Real Option Pricing
In this work we are concerned with valuing optionalities associated to invest
or to delay investment in a project when the available information provided to
the manager comes from simulated data of cash flows under historical (or
subjective) measure in a possibly incomplete market. Our approach is suitable
also to incorporating subjective views from management or market experts and to
stochastic investment costs. It is based on the Hedged Monte Carlo strategy
proposed by Potters et al (2001) where options are priced simultaneously with
the determination of the corresponding hedging. The approach is particularly
well-suited to the evaluation of commodity related projects whereby the
availability of pricing formulae is very rare, the scenario simulations are
usually available only in the historical measure, and the cash flows can be
highly nonlinear functions of the prices.Comment: 25 pages, 14 figure
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