Persistence in q-state Potts model: A Mean-Field approach

We study the Persistence properties of the T=0 coarsening dynamics of one dimensional $q$-state Potts model using a modified mean-field approximation (MMFA). In this approximation, the spatial correlations between the interfaces separating spins with different Potts states is ignored, but the correct time dependence of the mean density $P(t)$ of persistent spins is imposed. For this model, it is known that $P(t)$ follows a power-law decay with time, $P(t)\sim t^{-\theta(q)}$ where $\theta(q)$ is the $q$-dependent persistence exponent. We study the spatial structure of the persistent region within the MMFA. We show that the persistent site pair correlation function $P_{2}(r,t)$ has the scaling form $P_{2}(r,t)=P(t)^{2}f(r/t^{{1/2}})$ for all values of the persistence exponent $\theta(q)$. The scaling function has the limiting behaviour $f(x)\sim x^{-2\theta}$ ($x\ll 1$) and $f(x)\to 1$ ($x\gg 1$). We then show within the Independent Interval Approximation (IIA) that the distribution $n(k,t)$ of separation $k$ between two consecutive persistent spins at time $t$ has the asymptotic scaling form $n(k,t)=t^{-2\phi}g(t,\frac{k}{t^{\phi}})$ where the dynamical exponent has the form $\phi$=max(${1/2},\theta$). The behaviour of the scaling function for large and small values of the arguments is found analytically. We find that for small separations $k\ll t^{\phi}, n(k,t)\sim P(t)k^{-\tau}$ where $\tau$=max($2(1-\theta),2\theta$), while for large separations $k\gg t^{\phi}$, $g(t,x)$ decays exponentially with $x$. The unusual dynamical scaling form and the behaviour of the scaling function is supported by numerical simulations.Comment: 11 pages in RevTeX, 10 figures, submitted to Phys. Rev.

Persistence in One-dimensional Ising Models with Parallel Dynamics

We study persistence in one-dimensional ferromagnetic and anti-ferromagnetic nearest-neighbor Ising models with parallel dynamics. The probability P(t) that a given spin has not flipped up to time t, when the system evolves from an initial random configuration, decays as P(t) \sim 1/t^theta_p with theta_p \simeq 0.75 numerically. A mapping to the dynamics of two decoupled A+A \to 0 models yields theta_p = 3/4 exactly. A finite size scaling analysis clarifies the nature of dynamical scaling in the distribution of persistent sites obtained under this dynamics.Comment: 5 pages Latex file, 3 postscript figures, to appear in Phys Rev.

An adaptive and flexible brain energized full body exoskeleton with IoT edge for assisting the paralyzed patients

The paralyzed population is increasing worldwide due to stroke, spinal code injury, post-polio, and other related diseases. Different assistive technologies are used to improve the physical and mental health of the affected patients. Exoskeletons have emerged as one of the most promising technology to provide movement and rehabilitation for the paralyzed. But exoskeletons are limited by the constraints of weight, flexibility, and adaptability. To resolve these issues, we propose an adaptive and flexible Brain Energized Full Body Exoskeleton (BFBE) for assisting the paralyzed people. This paper describes the design, control, and testing of BFBE with 15 degrees of freedom (DoF) for assisting the users in their daily activities. The flexibility is incorporated into the system by a modular design approach. The brain signals captured by the Electroencephalogram (EEG) sensors are used for controlling the movements of BFBE. The processing happens at the edge, reducing delay in decision making and the system is further integrated with an IoT module that helps to send an alert message to multiple caregivers in case of an emergency. The potential energy harvesting is used in the system to solve the power issues related to the exoskeleton. The stability in the gait cycle is ensured by using adaptive sensory feedback. The system validation is done by using six natural movements on ten different paralyzed persons. The system recognizes human intensions with an accuracy of 85%. The result shows that BFBE can be an efficient method for providing assistance and rehabilitation for paralyzed patients. © 2013 IEEE. **Please note that there are multiple authors for this article therefore only the name of the first 5 including Federation University Australia affiliate “Venki Balasubramanian” is provided in this record*

Beclin 1 Phosphorylation – at the Center of Autophagy Regulation

Autophagy is a tightly regulated catabolic process wherein cells under stress sequester cytosolic constituents like damaged proteins and organelles in double-membrane vesicles called autophagosomes. The autophagosomes degrade their cargo by lysosomal proteolysis generating raw materials for the biosynthesis of vital macromolecules. One of the initial steps in the assembly of autophagosomes from pre-autophagic structures is the recruitment and activation of the class III phosphatidylinositol 3-kinase complex consisting of Beclin 1 (BECN1), VPS34, VPS15, and ATG14 proteins. Several pieces of evidence indicate that the phosphorylation and ubiquitination of BECN1 at an array of residues fine-tune the responses to diverse autophagy modulating stimuli and helps in maintaining the balance between pro-survival autophagy and pro-apoptotic responses. In this mini-review, we will discuss the importance of distinct BECN1 phosphorylation events, the diverse signaling pathways and kinases involved and their role in the regulation of autophagy

Genetic Deletion of SEPT7 Reveals a Cell Type-Specific Role of Septins in Microtubule Destabilization for the Completion of Cytokinesis

Cytokinesis terminates mitosis, resulting in separation of the two sister cells. Septins, a conserved family of GTP-binding cytoskeletal proteins, are an absolute requirement for cytokinesis in budding yeast. We demonstrate that septin-dependence of mammalian cytokinesis differs greatly between cell types: genetic loss of the pivotal septin subunit SEPT7 in vivo reveals that septins are indispensable for cytokinesis in fibroblasts, but expendable in cells of the hematopoietic system. SEPT7-deficient mouse embryos fail to gastrulate, and septin-deficient fibroblasts exhibit pleiotropic defects in the major cytokinetic machinery, including hyperacetylation/stabilization of microtubules and stalled midbody abscission, leading to constitutive multinucleation. We identified the microtubule depolymerizing protein stathmin as a key molecule aiding in septin-independent cytokinesis, demonstrated that stathmin supplementation is sufficient to override cytokinesis failure in SEPT7-null fibroblasts, and that knockdown of stathmin makes proliferation of a hematopoietic cell line sensitive to the septin inhibitor forchlorfenuron. Identification of septin-independent cytokinesis in the hematopoietic system could serve as a key to identify solid tumor-specific molecular targets for inhibition of cell proliferation

Persistence Exponents and Scaling In Two Dimensional XY model and A Nematic Model

The persistence exponents associated with the T=0 quenching dynamics of the two dimensional XY model and a two dimensional uniaxial spin nematic model have been evaluated using a numerical simulation. The site persistence or the probability that the sign of a local spin component does not change starting from initial time t=0 up to certain time t, is found to decay as L(t)^-theta, (L(t) is the linear domain length scale), with theta =0.305 for the two dimensional XY model and 0.199 for the two dimensional uniaxial spin nematic model. We have also investigated the scaling (at the late time of phase ordering) associated with the correlated persistent sites in both models. The persistence correlation length was found to grow in same way as L(t).Comment: 8 figures, only three new references are included in this version. (ref. 18 and ref. 32

Fraction of uninfected walkers in the one-dimensional Potts model

The dynamics of the one-dimensional q-state Potts model, in the zero temperature limit, can be formulated through the motion of random walkers which either annihilate (A + A -> 0) or coalesce (A + A -> A) with a q-dependent probability. We consider all of the walkers in this model to be mutually infectious. Whenever two walkers meet, they experience mutual contamination. Walkers which avoid an encounter with another random walker up to time t remain uninfected. The fraction of uninfected walkers is investigated numerically and found to decay algebraically, U(t) \sim t^{-\phi(q)}, with a nontrivial exponent \phi(q). Our study is extended to include the coupled diffusion-limited reaction A+A -> B, B+B -> A in one dimension with equal initial densities of A and B particles. We find that the density of walkers decays in this model as \rho(t) \sim t^{-1/2}. The fraction of sites unvisited by either an A or a B particle is found to obey a power law, P(t) \sim t^{-\theta} with \theta \simeq 1.33. We discuss these exponents within the context of the q-state Potts model and present numerical evidence that the fraction of walkers which remain uninfected decays as U(t) \sim t^{-\phi}, where \phi \simeq 1.13 when infection occurs between like particles only, and \phi \simeq 1.93 when we also include cross-species contamination.Comment: Expanded introduction with more discussion of related wor