Multistable behavior above synchronization in a locally coupled Kuramoto model

A system of nearest neighbors Kuramoto-like coupled oscillators placed in a ring is studied above the critical synchronization transition. We find a richness of solutions when the coupling increases, which exists only within a solvability region (SR). We also find that the solutions possess different characteristics, depending on the section of the boundary of the SR where they appear. We study the birth of these solutions and how they evolve when the coupling strength increases, and determine the diagram of solutions in phase space.

Crossover between the extended and localized regimes in stochastic partially self-avoiding walks in one-dimensional disordered systems

Consider N sites randomly and uniformly distributed in a d-dimensional hypercube. A walker explores this disordered medium going to the nearest site, which has not been visited in the last mu (memory) steps. The walker trajectory is composed of a transient part and a periodic part (cycle). For one-dimensional systems, travelers can or cannot explore all available space, giving rise to a crossover between localized and extended regimes at the critical memory mu(1) = log(2) N. The deterministic rule can be softened to consider more realistic situations with the inclusion of a stochastic parameter T (temperature). In this case, the walker movement is driven by a probability density function parameterized by T and a cost function. The cost function increases as the distance between two sites and favors hops to closer sites. As the temperature increases, the walker can escape from cycles that are reminiscent of the deterministic nature and extend the exploration. Here, we report an analytical model and numerical studies of the influence of the temperature and the critical memory in the exploration of one-dimensional disordered systems.

Influence of memory in deterministic walks in random media: Analytical calculation within a mean-field approximation

Consider a random medium consisting of N points randomly distributed so that there is no correlation among the distances separating them. This is the random link model, which is the high dimensionality limit (mean-field approximation) for the Euclidean random point structure. In the random link model, at discrete time steps, a walker moves to the nearest point, which has not been visited in the last mu steps (memory), producing a deterministic partially self-avoiding walk (the tourist walk). We have analytically obtained the distribution of the number n of points explored by the walker with memory mu=2, as well as the transient and period joint distribution. This result enables us to explain the abrupt change in the exploratory behavior between the cases mu=1 (memoryless walker, driven by extreme value statistics) and mu=2 (walker with memory, driven by combinatorial statistics). In the mu=1 case, the mean newly visited points in the thermodynamic limit (N >> 1) is just < n >=e=2.72... while in the mu=2 case, the mean number < n > of visited points grows proportionally to N(1/2). Also, this result allows us to establish an equivalence between the random link model with mu=2 and random map (uncorrelated back and forth distances) with mu=0 and the abrupt change between the probabilities for null transient time and subsequent ones.

An assessment of population structure in eight breeds of cattle using a whole genome SNP panel

Background: Analyses of population structure and breed diversity have provided insight into the origin and evolution of cattle. Previously, these studies have used a low density of microsatellite markers, however, with the large number of single nucleotide polymorphism markers that are now available, it is possible to perform genome wide population genetic analyses in cattle. In this study, we used a high-density panel of SNP markers to examine population structure and diversity among eight cattle breeds sampled from Bos indicus and Bos taurus. Results: Two thousand six hundred and forty one single nucleotide polymorphisms ( SNPs) spanning all of the bovine autosomal genome were genotyped in Angus, Brahman, Charolais, Dutch Black and White Dairy, Holstein, Japanese Black, Limousin and Nelore cattle. Population structure was examined using the linkage model in the program STRUCTURE and Fst estimates were used to construct a neighbor-joining tree to represent the phylogenetic relationship among these breeds. Conclusion: The whole-genome SNP panel identified several levels of population substructure in the set of examined cattle breeds. The greatest level of genetic differentiation was detected between the Bos taurus and Bos indicus breeds. When the Bos indicus breeds were excluded from the analysis, genetic differences among beef versus dairy and European versus Asian breeds were detected among the Bos taurus breeds. Exploration of the number of SNP loci required to differentiate between breeds showed that for 100 SNP loci, individuals could only be correctly clustered into breeds 50% of the time, thus a large number of SNP markers are required to replace the 30 microsatellite markers that are currently commonly used in genetic diversity studies.

Kinematic analysis and membership status of TWA22 AB

Context. TWA22 was initially regarded as a member of the TW Hydrae association (TWA). In addition to being one of the youngest (approximate to 8 Myr) and nearest (approximate to 20 pc) stars to Earth, TWA22 has proven to be very interesting after being resolved as a tight, very low-mass binary. This binary can serve as a very useful dynamical calibrator for pre-main sequence evolutionary models. However, its membership in the TWA has been recently questioned despite due to the lack of accurate kinematic measurements. Aims. Based on proper motion, radial velocity, and trigonometric parallax measurements, we aim here to re-analyze the membership of TWA22 to young, nearby associations. Methods. Using the ESO NTT/SUSI2 telescope, we observed TWA22 AB during 5 different observing runs over 1.2 years to measure its trigonometric parallax and proper motion. This is a part of a larger project measuring trigonometric parallaxes and proper motions of most known TWA members at a sub-milliarcsec level. HARPS at the ESO 3.6 m telescope was also used to measure the system's radial velocity over 2 years. Results. We report an absolute trigonometric parallax of TWA22 AB, pi = 57.0 +/- 0.7 mas, corresponding to a distance 17.5 +/- 0.2 pc from Earth. Measured proper motions of TWA 22AB are mu(alpha) cos(delta) = -175.8 +/- 0.8 mas/yr and mu delta = -21.3 +/- 0.8 mas/yr. Finally, from HARPS measurements, we obtain a radial velocity V(rad) = 14.8 +/- 2.1 km s(-1). Conclusions. A kinematic analysis of TWA22 AB space motion and position implies that a membership of TWA22 AB to known young, nearby associations can be excluded except for the beta Pictoris and TW Hydrae associations. Membership probabilities based on the system's Galactic space motion and/or the trace-back technique support a higher chance of being a member to the beta Pictoris association. Membership of TWA22 in the TWA cannot be fully excluded because of large uncertainties in parallax measurements and radial velocities and to the uncertain internal velocity dispersion of its members.

The close circumstellar environment of Betelgeuse II. Diffraction-limited spectro-imaging from 7.76 to 19.50 mu m with VLT/VISIR

Context. Mass-loss occurring in red supergiants (RSGs) is a major contributor to the enrichment of the interstellar medium in dust and molecules. The physical mechanism of this mass loss is however relatively poorly known. Betelgeuse is the nearest RSG, and as such a prime object for high angular resolution observations of its surface (by interferometry) and close circumstellar environment. Aims. The goal of our program is to understand how the material expelled from Betelgeuse is transported from its surface to the interstellar medium, and how it evolves chemically in this process. Methods. We obtained diffraction-limited images of Betelgeuse and a calibrator (Aldebaran) in six filters in the N band (7.76 to 12.81 mu m) and two filters in the Q band (17.65 and 19.50 mu m), using the VLT/VISIR instrument. Results. Our images show a bright, extended and complex circumstellar envelope at all wavelengths. It is particularly prominent longwards of approximate to 9-10 mu m, pointing at the presence of O-rich dust, such as silicates or alumina. A partial circular shell is observed between 0.5 and 1.0 '' from the star, and could correspond to the inner radius of the dust envelope. Several knots and filamentary structures are identified in the nebula. One of the knots, located at a distance of 0.9 '' west of the star, is particularly bright and compact. Conclusions. The circumstellar envelope around Betelgeuse extends at least up to several tens of stellar radii. Its relatively high degree of clumpiness indicates an inhomogeneous spatial distribution of the material lost by the star. Its extension corresponds to an important intermediate scale, where most of the dust is probably formed, between the hot and compact gaseous envelope observed previously in the near infrared and the interstellar medium.

Critical behavior of the susceptible-infected-recovered model on a square lattice

By means of numerical simulations and epidemic analysis, the transition point of the stochastic asynchronous susceptible-infected-recovered model on a square lattice is found to be c(0)=0.176 500 5(10), where c is the probability a chosen infected site spontaneously recovers rather than tries to infect one neighbor. This point corresponds to an infection/recovery rate of lambda(c)=(1-c(0))/c(0)=4.665 71(3) and a net transmissibility of (1-c(0))/(1+3c(0))=0.538 410(2), which falls between the rigorous bounds of the site and bond thresholds. The critical behavior of the model is consistent with the two-dimensional percolation universality class, but local growth probabilities differ from those of dynamic percolation cluster growth, as is demonstrated explicitly.

Isotropic and anisotropic spin-spin interactions and a quantum phase transition in a dinuclear Cu(II) compound

We report electron-paramagnetic resonance (EPR) studies at similar to 9.5 GHz (X band) and similar to 34 GHz (Q band) of powder and single-crystal samples of the compound Cu(2)[TzTs](4) [N-thiazol-2-yl-toluenesulfonamidatecopper(II)], C(40)H(36)Cu(2)N(8)O(8)S(8), having copper(II) ions in dinuclear units. Our data allow determining an antiferromagnetic interaction J(0)=(-113 +/- 1) cm(-1) (H(ex)=-J(0)S(1)center dot S(2)) between Cu(II) ions in the dinuclear unit and the anisotropic contributions to the spin-spin coupling matrix D (H(ani)=S(1)center dot D center dot S(2)), a traceless symmetric matrix with principal values D/4=(0.198 +/- 0.003) cm(-1) and E/4=(0.001 +/- 0.003) cm(-1) arising from magnetic dipole-dipole and anisotropic exchange couplings within the units. In addition, the single-crystal EPR measurements allow detecting and estimating very weak exchange couplings between neighbor dinuclear units, with an estimated magnitude parallel to J(')parallel to=(0.060 +/- 0.015) cm(-1). The interactions between a dinuclear unit and the ""environment"" of similar units in the structure of the compound produce a spin dynamics that averages out the intradinuclear dipolar interactions. This coupling with the environment leads to decoherence, a quantum phase transition that collapses the dipolar interaction when the isotropic exchange coupling with neighbor dinuclear units equals the magnitude of the intradinuclear dipolar coupling. Our EPR experiments provide a new procedure to follow the classical exchange-narrowing process as a shift and collapse of the line structure (not only as a change of the resonance width), which is described with general (but otherwise simple) theories of magnetic resonance. Using complementary procedures, our EPR measurements in powder and single-crystal samples allow measuring simultaneously three types of interactions differing by more than three orders of magnitude (between 113 cm(-1) and 0.060 cm(-1)).

Social interaction as a heuristic for combinatorial optimization problems

We investigate the performance of a variant of Axelrod's model for dissemination of culture-the Adaptive Culture Heuristic (ACH)-on solving an NP-Complete optimization problem, namely, the classification of binary input patterns of size F by a Boolean Binary Perceptron. In this heuristic, N agents, characterized by binary strings of length F which represent possible solutions to the optimization problem, are fixed at the sites of a square lattice and interact with their nearest neighbors only. The interactions are such that the agents' strings (or cultures) become more similar to the low-cost strings of their neighbors resulting in the dissemination of these strings across the lattice. Eventually the dynamics freezes into a homogeneous absorbing configuration in which all agents exhibit identical solutions to the optimization problem. We find through extensive simulations that the probability of finding the optimal solution is a function of the reduced variable F/N(1/4) so that the number of agents must increase with the fourth power of the problem size, N proportional to F(4), to guarantee a fixed probability of success. In this case, we find that the relaxation time to reach an absorbing configuration scales with F(6) which can be interpreted as the overall computational cost of the ACH to find an optimal set of weights for a Boolean binary perceptron, given a fixed probability of success.

Statistics of opinion domains of the majority-vote model on a square lattice

The existence of juxtaposed regions of distinct cultures in spite of the fact that people's beliefs have a tendency to become more similar to each other's as the individuals interact repeatedly is a puzzling phenomenon in the social sciences. Here we study an extreme version of the frequency-dependent bias model of social influence in which an individual adopts the opinion shared by the majority of the members of its extended neighborhood, which includes the individual itself. This is a variant of the majority-vote model in which the individual retains its opinion in case there is a tie among the neighbors' opinions. We assume that the individuals are fixed in the sites of a square lattice of linear size L and that they interact with their nearest neighbors only. Within a mean-field framework, we derive the equations of motion for the density of individuals adopting a particular opinion in the single-site and pair approximations. Although the single-site approximation predicts a single opinion domain that takes over the entire lattice, the pair approximation yields a qualitatively correct picture with the coexistence of different opinion domains and a strong dependence on the initial conditions. Extensive Monte Carlo simulations indicate the existence of a rich distribution of opinion domains or clusters, the number of which grows with L(2) whereas the size of the largest cluster grows with ln L(2). The analysis of the sizes of the opinion domains shows that they obey a power-law distribution for not too large sizes but that they are exponentially distributed in the limit of very large clusters. In addition, similarly to other well-known social influence model-Axelrod's model-we found that these opinion domains are unstable to the effect of a thermal-like noise.

GPIomics: global analysis of glycosylphosphatidylinositol-anchored molecules of Trypanosoma cruzi

Glycosylphosphatidylinositol (GPI) anchoring is a common, relevant posttranslational modification of eukaryotic surface proteins. Here, we developed a fast, simple, and highly sensitive (high attomole-low femtomole range) method that uses liquid chromatography-tandem mass spectrometry (LC-MS(n)) for the first large-scale analysis of GPI-anchored molecules (i.e., the GPIome) of a eukaryote, Trypanosoma cruzi, the etiologic agent of Chagas disease. Our genome-wise prediction analysis revealed that approximately 12% of T. cruzi genes possibly encode GPI-anchored proteins. By analyzing the GPIome of T. cruzi insect-dwelling epimastigote stage using LC-MS(n), we identified 90 GPI species, of which 79 were novel. Moreover, we determined that mucins coded by the T. cruzi small mucin-like gene (TcSMUG S) family are the major GPI-anchored proteins expressed on the epimastigote cell surface. TcSMUG S mucin mature sequences are short (56-85 amino acids) and highly O-glycosylated, and contain few proteolytic sites, therefore, less likely susceptible to proteases of the midgut of the insect vector. We propose that our approach could be used for the high throughput GPIomic analysis of other lower and higher eukaryotes. Molecular Systems Biology 7 April 2009; doi:10.1038/msb.2009.13

An opinion dynamics model for the diffusion of innovations

We study the dynamics of the adoption of new products by agents with continuous opinions and discrete actions (CODA). The model is such that the refusal in adopting a new idea or product is increasingly weighted by neighbor agents as evidence against the product. Under these rules, we study the distribution of adoption times and the final proportion of adopters in the population. We compare the cases where initial adopters are clustered to the case where they are randomly scattered around the social network and investigate small world effects on the final proportion of adopters. The model predicts a fat tailed distribution for late adopters which is verified by empirical data. (C) 2009 Elsevier B.V. All rights reserved.

Analytical calculation of the transition to complete phase synchronization in coupled oscillators

Here we present a system of coupled phase oscillators with nearest neighbors coupling, which we study for different boundary conditions. We concentrate at the transition to the total synchronization. We are able to develop exact solutions for the value of the coupling parameter when the system becomes completely synchronized, for the case of periodic boundary conditions as well as for a chain with fixed ends. We compare the results with those calculated numerically.

COMPETITION AMONG EUCALYPTUS TREES DEPENDS ON GENETIC VARIATION AND RESOURCE SUPPLY

Genetic variation and environmental heterogeneity fundamentally shape the interactions between plants of the same species. According to the resource partitioning hypothesis, competition between neighbors intensifies as their similarity increases. Such competition may change in response to increasing supplies of limiting resources. We tested the resource partitioning hypothesis in stands of genetically identical (clone-origin) and genetically diverse (seed-origin) Eucalyptus trees with different water and nutrient supplies, using individual-based tree growth models. We found that genetic variation greatly reduced competitive interactions between neighboring trees, supporting the resource partitioning hypothesis. The importance of genetic variation for Eucalyptus growth patterns depended strongly on local stand structure and focal tree size. This suggests that spatial and temporal variation in the strength of species interactions leads to reversals in the growth rank of seed-origin and clone-origin trees. This study is one of the first to experimentally test the resource partitioning hypothesis for intergenotypic vs. intragenotypic interactions in trees. We provide evidence that variation at the level of genes, and not just species, is functionally important for driving individual and community-level processes in forested ecosystems.

Multilabeled classification approach to find a plaint source for terpenoids

Recently, we have built a classification model that is capable of assigning a given sesquiterpene lactone (STL) into exactly one tribe of the plant family Asteraceae from which the STL has been isolated. Although many plant species are able to biosynthesize a set of peculiar compounds, the occurrence of the same secondary metabolites in more than one tribe of Asteraceae is frequent. Building on our previous work, in this paper, we explore the possibility of assigning an STL to more than one tribe (class) simultaneously. When an object may belong to more than one class simultaneously, it is called multilabeled. In this work, we present a general overview of the techniques available to examine multilabeled data. The problem of evaluating the performance of a multilabeled classifier is discussed. Two particular multilabeled classification methods-cross-training with support vector machines (ct-SVM) and multilabeled k-nearest neighbors (M-L-kNN)were applied to the classification of the STLs into seven tribes from the plant family Asteraceae. The results are compared to a single-label classification and are analyzed from a chemotaxonomic point of view. The multilabeled approach allowed us to (1) model the reality as closely as possible, (2) improve our understanding of the relationship between the secondary metabolite profiles of different Asteraceae tribes, and (3) significantly decrease the number of plant sources to be considered for finding a certain STL. The presented classification models are useful for the targeted collection of plants with the objective of finding plant sources of natural compounds that are biologically active or possess other specific properties of interest.