Defects and multistability in eutectic solidification patterns

We use three-dimensional phase-field simulations to investigate the dynamics of the two-phase composite patterns formed upon during solidification of eutectic alloys. Besides the spatially periodic lamellar and rod patterns that have been widely studied, we find that there is a large number of additional steady-state patterns which exhibit stable defects. The defect density can be so high that the pattern is completely disordered, and that the distinction between lamellar and rod patterns is blurred. As a consequence, the transition from lamellae to rods is not sharp, but extends over a finite range of compositions and exhibits strong hysteresis. Our findings are in good agreement with experiments.Comment: 6 pages, 8 figure

Numerical estimate of the Kardar Parisi Zhang universality class in (2 + 1) dimensions

We study the Restricted Solid on Solid model for surface growth in spatial dimension $d=2$ by means of a multi-surface coding technique that allows to produce a large number of samples of samples in the stationary regime in a reasonable computational time. Thanks to: (i) a careful finite-size scaling analysis of the critical exponents, (ii) the accurate estimate of the first three moments of the height fluctuations, we can quantify the wandering exponent with unprecedented precision: $\chi_{d=2} = 0.3869(4)$. This figure is incompatible with the long-standing conjecture due to Kim and Koesterlitz that hypothesized $\chi_{d=2}=2/5$.Comment: 4 pages, 4 figure

Multi-surface coding simulations of the restricted solid-on-solid model in four dimensions

We study the Restricted Solid on Solid (RSOS) model for surface growth in spatial dimension d=4 by means of a multi-surface coding technique that allows to analyze samples to analyze samples of size up to $256^4$ in the steady state regime. For such large systems we are able to achieve a controlled asymptotic regime where the typical scale of the fluctuations are larger than the lattice spacing used in the simulations. A careful finite-size scaling analysis of the critical exponents clearly indicate that d=4 is not the upper critical dimension of the model.Comment: 6 pages, 3 pdf figures, changed title and minor changes in the abstract, added some references. This is the published versio

Detecting and Describing Dynamic Equilibria in Adaptive Networks

We review modeling attempts for the paradigmatic contact process (or SIS model) on adaptive networks. Elaborating on one particular proposed mechanism of topology change (rewiring) and its mean field analysis, we obtain a coarse-grained view of coevolving network topology in the stationary active phase of the system. Introducing an alternative framework applicable to a wide class of adaptive networks, active stationary states are detected, and an extended description of the resulting steady-state statistics is given for three different rewiring schemes. We find that slight modifications of the standard rewiring rule can result in either minuscule or drastic change of steady-state network topologies.Comment: 14 pages, 10 figures; typo in the third of Eqs. (1) correcte

Supersymmetric quenched complexity in the Sherrington-Kirkpatrick model

By using the BRST supersymmetry we compute the quenched complexity of the TAP states in the SK model. We prove that the BRST complexity is equal to the Legendre transform of the static free energy with respect to the largest replica symmetry breaking point of its overlap matrix

Ictal epileptic headache. an old story with courses and appeals

The term "ictal epileptic headache" has been recently proposed to classify the clinical picture in which headache is the isolated ictal symptom of a seizure. There is emerging evidence from both basic and clinical neurosciences that cortical spreading depression and an epileptic focus may facilitate each other, although with a different degree of efficiency. This review address the long history which lead to the 'migralepsy' concept to the new emerging pathophysiological aspects, and clinical and electroencephalography evidences of ictal epileptic headache. Here, we review and discuss the common physiopathology mechanisms and the historical aspects underlying the link between headache and epilepsy. Either experimental or clinical measures are required to better understand this latter relationship: the development of animal models, molecular studies defining more precise genotype/phenotype correlations as well as multicenter clinical studies with revision of clinical criteria for headache-/epilepsy-related disorders represent the start of future research. Therefore, the definition of ictal epileptic headache should be used to classify the rare events in which headache is the only manifestation of a seizure. Finally, using our recently published criteria, we will be able to clarify if ictal epileptic headache represents an underestimated phenomenon or not

What does it take to evolve behaviorally complex organisms?

What genotypic features explain the evolvability of organisms that have to accomplish many different tasks? The genotype of behaviorally complex organisms may be more likely to encode modular neural architectures because neural modules dedicated to distinct tasks avoid neural interference, i.e., the arrival of conflicting messages for changing the value of connection weights during learning. However, if the connection weights for the various modules are genetically inherited, this raises the problem of genetic linkage: favorable mutations may fall on one portion of the genotype encoding one neural module and unfavorable mutations on another portion encoding another module. We show that this can prevent the genotype from reaching an adaptive optimum. This effect is different from other linkage effects described in the literature and we argue that it represents a new class of genetic constraints. Using simulations we show that sexual reproduction can alleviate the problem of genetic linkage by recombining separate modules all of which incorporate either favorable or unfavorable mutations. We speculate that this effect may contribute to the taxonomic prevalence of sexual reproduction among higher organisms. In addition to sexual recombination, the problem of genetic linkage for behaviorally complex organisms may be mitigated by entrusting evolution with the task of finding appropriate modular architectures and learning with the task of finding the appropriate connection weights for these architectures