Fractal dimension of domain walls in the Edwards-Anderson spin glass model

We study directly the length of the domain walls (DW) obtained by comparing the ground states of the Edwards-Anderson spin glass model subject to periodic and antiperiodic boundary conditions. For the bimodal and Gaussian bond distributions, we have isolated the DW and have calculated directly its fractal dimension $d_f$. Our results show that, even though in three dimensions $d_f$ is the same for both distributions of bonds, this is clearly not the case for two-dimensional (2D) systems. In addition, contrary to what happens in the case of the 2D Edwards-Anderson spin glass with Gaussian distribution of bonds, we find no evidence that the DW for the bimodal distribution of bonds can be described as a Schramm-Loewner evolution processes.Comment: 6 pages, 5 figures. Accepted for publication in PR

Expression of synthetic genes encoding bovine and human basic fibroblast growth factors (bFGFs) in Escherichia coli.

Synthetic genes encoding bovine and human basic fibroblast growth factors (bFGFs) were assembled and cloned using established Escherichia coli expression plasmids. Transformed E. coli cells were able to synthesize either a fusion protein, comprising the first seven amino acids of β-galactosidase, a linker fragment and bovine FGF, or genomic human bFGF. The two growth factors were purified from E. coli lysates by cation exchange and heparin-Sepharose affinity chromatography. The purified recombinant proteins were biologically active as monitored by their mitogenic activity for bovine aortic endothelial cells and their angiogenic capacity in the rabbit cornea

Levy ratchets with dichotomic random flashing

Additive symmetric L\'evy noise can induce directed transport of overdamped particles in a static asymmetric potential. We study, numerically and analytically, the effect of an additional dichotomous random flashing in such L\'evy ratchet system. For this purpose we analyze and solve the corresponding fractional Fokker-Planck equations and we check the results with Langevin simulations. We study the behavior of the current as function of the stability index of the L\'evy noise, the noise intensity and the flashing parameters. We find that flashing allows both to enhance and diminish in a broad range the static L\'evy ratchet current, depending on the frequencies and asymmetry of the multiplicative dichotomous noise, and on the additive L\'evy noise parameters. Our results thus extend those for dichotomous flashing ratchets with Gaussian noise to the case of broadly distributed noises.Comment: 15 pages, 6 figure

Statistical Mechanics of Soft Margin Classifiers

We study the typical learning properties of the recently introduced Soft Margin Classifiers (SMCs), learning realizable and unrealizable tasks, with the tools of Statistical Mechanics. We derive analytically the behaviour of the learning curves in the regime of very large training sets. We obtain exponential and power laws for the decay of the generalization error towards the asymptotic value, depending on the task and on general characteristics of the distribution of stabilities of the patterns to be learned. The optimal learning curves of the SMCs, which give the minimal generalization error, are obtained by tuning the coefficient controlling the trade-off between the error and the regularization terms in the cost function. If the task is realizable by the SMC, the optimal performance is better than that of a hard margin Support Vector Machine and is very close to that of a Bayesian classifier.Comment: 26 pages, 12 figures, submitted to Physical Review

Ground-state topology of the Edwards-Anderson +/-J spin glass model

In the Edwards-Anderson model of spin glasses with a bimodal distribution of bonds, the degeneracy of the ground state allows one to define a structure called backbone, which can be characterized by the rigid lattice (RL), consisting of the bonds that retain their frustration (or lack of it) in all ground states. In this work we have performed a detailed numerical study of the properties of the RL, both in two-dimensional (2D) and three-dimensional (3D) lattices. Whereas in 3D we find strong evidence for percolation in the thermodynamic limit, in 2D our results indicate that the most probable scenario is that the RL does not percolate. On the other hand, both in 2D and 3D we find that frustration is very unevenly distributed. Frustration is much lower in the RL than in its complement. Using equilibrium simulations we observe that this property can be found even above the critical temperature. This leads us to propose that the RL should share many properties of ferromagnetic models, an idea that recently has also been proposed in other contexts. We also suggest a preliminary generalization of the definition of backbone for systems with continuous distributions of bonds, and we argue that the study of this structure could be useful for a better understanding of the low temperature phase of those frustrated models.Comment: 16 pages and 21 figure

The endothelial glycocalyx prefers albumin for evoking shear stress-induced, nitric oxide-mediated coronary dilatation

Background: Shear stress induces coronary dilatation via production of nitric oxide ( NO). This should involve the endothelial glycocalyx ( EG). A greater effect was expected of albumin versus hydroxyethyl starch ( HES) perfusion, because albumin seals coronary leaks more effectively than HES in an EG-dependent way. Methods: Isolated hearts ( guinea pigs) were perfused at constant pressure with Krebs-Henseleit buffer augmented with 1/3 volume 5% human albumin or 6% HES ( 200/0.5 or 450/0.7). Coronary flow was also determined after EG digestion ( heparinase) and with nitro-L-arginine ( NO-L-Ag). Results: Coronary flow ( 9.50 +/- 1.09, 5.10 +/- 0.49, 4.87 +/- 1.19 and 4.15 +/- 0.09 ml/ min/ g for `albumin', `HES 200', `HES 450' and `control', respectively, n = 5-6) did not correlate with perfusate viscosity ( 0.83, 1.02, 1.24 and 0.77 cP, respectively). NO-L-Ag and heparinase diminished dilatation by albumin, but not additively. Alone NO-L-Ag suppressed coronary flow during infusion of HES 450. Electron microscopy revealed a coronary EG of 300 nm, reduced to 20 nm after heparinase. Cultured endothelial cells possessed an EG of 20 nm to begin with. Conclusions: Albumin induces greater endothelial shear stress than HES, despite lower viscosity, provided the EG contains negative groups. HES 450 causes some NO-mediated dilatation via even a rudimentary EG. Cultured endothelial cells express only a rudimentary glycocalyx, limiting their usefulness as a model system. Copyright (c) 2007 S. Karger AG, Basel

Multiscale modelling of vascular tumour growth in 3D: the roles of domain size & boundary condition

We investigate a three-dimensional multiscale model of vascular tumour growth, which couples blood flow, angiogenesis, vascular remodelling, nutrient/growth factor transport, movement of, and interactions between, normal and tumour cells, and nutrient-dependent cell cycle dynamics within each cell. In particular, we determine how the domain size, aspect ratio and initial vascular network influence the tumour's growth dynamics and its long-time composition. We establish whether it is possible to extrapolate simulation results obtained for small domains to larger ones, by constructing a large simulation domain from a number of identical subdomains, each subsystem initially comprising two parallel parent vessels, with associated cells and diffusible substances. We find that the subsystem is not representative of the full domain and conclude that, for this initial vessel geometry, interactions between adjacent subsystems contribute to the overall growth dynamics. We then show that extrapolation of results from a small subdomain to a larger domain can only be made if the subdomain is sufficiently large and is initialised with a sufficiently complex vascular network. Motivated by these results, we perform simulations to investigate the tumour's response to therapy and show that the probability of tumour elimination in a larger domain can be extrapolated from simulation results on a smaller domain. Finally, we demonstrate how our model may be combined with experimental data, to predict the spatio-temporal evolution of a vascular tumour

Ground states of 2d +-J Ising spin glasses via stationary Fokker-Planck sampling

We investigate the performance of the recently proposed stationary Fokker-Planck sampling method considering a combinatorial optimization problem from statistical physics. The algorithmic procedure relies upon the numerical solution of a linear second order differential equation that depends on a diffusion-like parameter D. We apply it to the problem of finding ground states of 2d Ising spin glasses for the +-J-Model. We consider square lattices with side length up to L=24 with two different types of boundary conditions and compare the results to those obtained by exact methods. A particular value of D is found that yields an optimal performance of the algorithm. We compare this optimal value of D to a percolation transition, which occurs when studying the connected clusters of spins flipped by the algorithm. Nevertheless, even for moderate lattice sizes, the algorithm has more and more problems to find the exact ground states. This means that the approach, at least in its standard form, seems to be inferior to other approaches like parallel tempering.Comment: v1: 13 pages, 7 figures; v2: extended tex

Dynamic Analysis of Vascular Morphogenesis Using Transgenic Quail Embryos

Background: One of the least understood and most central questions confronting biologists is how initially simple clusters or sheet-like cell collectives can assemble into highly complex three-dimensional functional tissues and organs. Due to the limits of oxygen diffusion, blood vessels are an essential and ubiquitous presence in all amniote tissues and organs. Vasculogenesis, the de novo self-assembly of endothelial cell (EC) precursors into endothelial tubes, is the first step in blood vessel formation [1]. Static imaging and in vitro models are wholly inadequate to capture many aspects of vascular pattern formation in vivo, because vasculogenesis involves dynamic changes of the endothelial cells and of the forming blood vessels, in an embryo that is changing size and shape. Methodology/Principal Findings: We have generated Tie1 transgenic quail lines Tg(tie1:H2B-eYFP) that express H2B-eYFP in all of their endothelial cells which permit investigations into early embryonic vascular morphogenesis with unprecedented clarity and insight. By combining the power of molecular genetics with the elegance of dynamic imaging, we follow the precise patterning of endothelial cells in space and time. We show that during vasculogenesis within the vascular plexus, ECs move independently to form the rudiments of blood vessels, all while collectively moving with gastrulating tissues that flow toward the embryo midline. The aortae are a composite of somatic derived ECs forming its dorsal regions and the splanchnic derived ECs forming its ventral region. The ECs in the dorsal regions of the forming aortae exhibit variable mediolateral motions as they move rostrally; those in more ventral regions show significant lateral-to-medial movement as they course rostrally. Conclusions/Significance: The present results offer a powerful approach to the major challenge of studying the relative role(s) of the mechanical, molecular, and cellular mechanisms of vascular development. In past studies, the advantages of the molecular genetic tools available in mouse were counterbalanced by the limited experimental accessibility needed for imaging and perturbation studies. Avian embryos provide the needed accessibility, but few genetic resources. The creation of transgenic quail with labeled endothelia builds upon the important roles that avian embryos have played in previous studies of vascular development