arXiv subjects

T. Antal

Publications and source records attributed to T. Antal.

At least 19 recordsLinked to original sources

arXiv2010

Dynamics of Microtubule Instabilities

We investigate the dynamics of an idealized model of microtubule growth that evolves by: (i) attachment of guanosine triphosphate (GTP) at rate lambda, (ii) conversion of GTP to guanosine diphosphate (GDP) at rate 1, and (iii) detachment of GDP at rate mu. As a function of these rates, a microtubule can grow steadily or its length can fluctuate wildly. For mu=0, we find the exact tubule and GTP cap length distributions, and power-law length distributions of GTP and GDP islands. For mu=infinity, we argue that the time between catastrophes, where the microtubule shrinks to zero length, scales as exp(lambda). We also find the phase boundary between a growing and shrinking microtubule.

q-bio.QM↗

arXiv2009

Shepherd Model for Knot-Limited Polymer Ejection from a Capsid

We construct a tractable model to describe the rate at which a knotted polymer is ejected from a spherical capsid via a small pore. Knots are too large to fit through the pore and must reptate to the end of the polymer for ejection to occur. The reptation of knots is described by symmetric exclusion on the line, with the internal capsid pressure represented by an additional biased particle that drives knots to the end of the chain. We compute the exact ejection speed for a finite number of knots L and find that it scales as 1/L. We also construct a continuum theory for many knots that matches the exact discrete theory for large L.

q-bio.QM↗

arXiv2008

Front Propagation with Rejuvenation in Flipping Processes

We study a directed flipping process that underlies the performance of the random edge simplex algorithm. In this stochastic process, which takes place on a one-dimensional lattice whose sites may be either occupied or vacant, occupied sites become vacant at a constant rate and simultaneously cause all sites to the right to change their state. This random process exhibits rich phenomenology. First, there is a front, defined by the position of the left-most occupied site, that propagates at a nontrivial velocity. Second, the front involves a depletion zone with an excess of vacant sites. The total excess D_k increases logarithmically, D_k ~ ln k, with the distance k from the front. Third, the front exhibits rejuvenation -- young fronts are vigorous but old fronts are sluggish. We investigate these phenomena using a quasi-static approximation, direct solutions of small systems, and numerical simulations.

cond-mat.stat-mech↗

arXiv2008

Exciting Hard Spheres

We investigate the collision cascade that is generated by a single moving incident particle on a static hard-sphere gas. We argue that the number of moving particles at time t grows as t^{xi} and the number collisions up to time t grows as t^{eta}, with xi=2d/(d+2) and eta=2(d+1)/(d+2) and d the spatial dimension. These growth laws are the same as those from a hydrodynamic theory for the shock wave emanating from an explosion. Our predictions are verified by molecular dynamics simulations in d=1 and 2. For a particle incident on a static gas in a half-space, the resulting backsplatter ultimately contains almost all the initial energy.

physics.flu-dyn↗

arXiv2008

Aging and Immortality in a Cell Proliferation Model

We investigate a model of cell division in which the length of telomeres within the cell regulate their proliferative potential. At each cell division the ends of linear chromosomes change and a cell becomes senescent when one or more of its telomeres become shorter than a critical length. In addition to this systematic shortening, exchange of telomere DNA between the two daughter cells can occur at each cell division. We map this telomere dynamics onto a biased branching diffusion process with an absorbing boundary condition whenever any telomere reaches the critical length. As the relative effects of telomere shortening and cell division are varied, there is a phase transition between finite lifetime and infinite proliferation of the cell population. Using simple first-passage ideas, we quantify the nature of this transition.

q-bio.CB↗

arXiv2008

Dynamics of Microtubule Growth and Catastrophe

We investigate a simple model of microtubule dynamics in which a microtubule evolves by: (i) attachment of guanosine triphosphate (GTP) to its end at rate lambda, (ii) GTP converting irreversibly to guanosine diphosphate (GDP) at rate 1, and (iii) detachment of GDP from the end of a microtubule at rate mu. As a function of these elemental rates, the microtubule can grow steadily or its length can fluctuate wildly. A master equation approach is developed to characterize these intriguing features. For mu=0, we find exact expressions for tubule and GTP cap length distributions, as well as a power-law length distributions of GTP and GDP islands. For mu=oo, we find the average time between catastrophes, where the microtubule shrinks to zero length, and extend this approach to also determine the size distribution of avalanches (sequence of consecutive GDP detachment events). We obtain the phase diagram for general rates and verify our predictions by numerical simulations.

q-bio.QM↗

arXiv2006

Flows on Graphs with Random Capacities

We investigate flows on graphs whose links have random capacities. For binary trees we derive the probability distribution for the maximal flow from the root to a leaf, and show that for infinite trees it vanishes beyond a certain threshold that depends on the distribution of capacities. We then examine the maximal total flux from the root to the leaves. Our methods generalize to simple graphs with loops, e.g., to hierarchical lattices and to complete graphs.

cond-mat.stat-mech↗

arXiv2006

Social Balance on Networks: The Dynamics of Friendship and Enmity

How do social networks evolve when both friendly and unfriendly relations exist? Here we propose a simple dynamics for social networks in which the sense of a relationship can change so as to eliminate imbalanced triads--relationship triangles that contains 1 or 3 unfriendly links. In this dynamics, a friendly link changes to unfriendly or vice versa in an imbalanced triad to make the triad balanced. Such networks undergo a dynamic phase transition from a steady state to "utopia"--all friendly links--as the amount of network friendliness is changed. Basic features of the long-time dynamics and the phase transition are discussed.

physics.gen-ph↗

arXiv2006

Evolutionary dynamics on degree-heterogeneous graphs

The evolution of two species with different fitness is investigated on degree-heterogeneous graphs. The population evolves either by one individual dying and being replaced by the offspring of a random neighbor (voter model (VM) dynamics) or by an individual giving birth to an offspring that takes over a random neighbor node (invasion process (IP) dynamics). The fixation probability for one species to take over a population of N individuals depends crucially on the dynamics and on the local environment. Starting with a single fitter mutant at a node of degree k, the fixation probability is proportional to k for VM dynamics and to 1/k for IP dynamics.

q-bio.PE↗

arXiv2005

Escape of a Uniform Random Walk from an Interval

We study the first-passage properties of a random walk in the unit interval in which the length of a single step is uniformly distributed over the finite range [-a,a]. For a of the order of one, the exit probabilities to each edge of the interval and the exit time from the interval exhibit anomalous properties stemming from the change in the minimum number of steps to escape the interval as a function of the starting point. As a decreases, first-passage properties approach those of continuum diffusion, but non-diffusive effects remain because of residual discreteness effects

physics.data-an↗

arXiv2005

Dynamics of Social Balance on Networks

We study the evolution of social networks that contain both friendly and unfriendly pairwise links between individual nodes. The network is endowed with dynamics in which the sense of a link in an imbalanced triad--a triangular loop with 1 or 3 unfriendly links--is reversed to make the triad balanced. With this dynamics, an infinite network undergoes a dynamic phase transition from a steady state to "paradise"--all links are friendly--as the propensity p for friendly links in an update event passes through 1/2. A finite network always falls into a socially-balanced absorbing state where no imbalanced triads remain. If the additional constraint that the number of imbalanced triads in the network does not increase in an update is imposed, then the network quickly reaches a balanced final state.

cond-mat.stat-mech↗

arXiv2005

A "Burnt Bridge'' Brownian Ratchet

Motivated by a biased diffusion of molecular motors with the bias dependent on the state of the substrate, we investigate a random walk on a one-dimensional lattice that contains weak links (called "bridges'') which are affected by the walker. Namely, a bridge is destroyed with probability p when the walker crosses it; the walker is not allowed to cross it again and this leads to a directed motion. The velocity of the walker is determined analytically for equidistant bridges. The special case of p=1 is more tractable -- both the velocity and the diffusion constant are calculated for uncorrelated locations of bridges, including periodic and random distributions.

cond-mat.stat-mech↗

arXiv2004

Excited Random Walk in One Dimension

We study the excited random walk, in which a walk that is at a site that contains cookies eats one cookie and then hops to the right with probability p and to the left with probability q=1-p. If the walk hops onto an empty site, there is no bias. For the 1-excited walk on the half-line (one cookie initially at each site), the probability of first returning to the starting point at time t scales as t^{-(2-p)}. Although the average return time to the origin is infinite for all p, the walk eats, on average, only a finite number of cookies until this first return when p<1/2. For the infinite line, the probability distribution for the 1-excited walk has an unusual anomaly at the origin. The positions of the leftmost and rightmost uneaten cookies can be accurately estimated by probabilistic arguments and their corresponding distributions have power-law singularities near the origin. The 2-excited walk on the infinite line exhibits peculiar features in the regime p>3/4, where the walk is transient, including a mean displacement that grows as t^{nu}, with nu>1/2 dependent on p, and a breakdown of scaling for the probability distribution of the walk.

math.PR↗

arXiv2004

Weight-driven growing networks

We study growing networks in which each link carries a certain weight (randomly assigned at birth and fixed thereafter). The weight of a node is defined as the sum of the weights of the links attached to the node, and the network grows via the simplest weight-driven rule: A newly-added node is connected to an already existing node with the probability which is proportional to the weight of that node. We show that the node weight distribution n(w) has a universal, that is independent on the link weight distribution, tail: n(w) ~ w^-3 as w->oo. Results are particularly neat for the exponential link weight distribution when n(w) is algebraic over the entire weight range.

cond-mat.dis-nn↗

arXiv2003

Probability distribution of magnetization in the one-dimensional Ising model: Effects of boundary conditions

Finite-size scaling functions are investigated both for the mean-square magnetization fluctuations and for the probability distribution of the magnetization in the one-dimensional Ising model. The scaling functions are evaluated in the limit of the temperature going to zero (T -> 0), the size of the system going to infinity (N -> oo) while N[1-tanh(J/k_BT)] is kept finite (J being the nearest neighbor coupling). Exact calculations using various boundary conditions (periodic, antiperiodic, free, block) demonstrate explicitly how the scaling functions depend on the boundary conditions. We also show that the block (small part of a large system) magnetization distribution results are identical to those obtained for free boundary conditions.

cond-mat.stat-mech↗

arXiv2002

Repeated bond traversal probabilities for the simple random walk

We consider the average number B_m(t) of bonds traversed exactly m times by a t step simple random walk. We determine B_m(t) explicitly in the scaling limit t -> oo with m/sqrt(t) fixed in dimension d=1 and m/log(t) fixed in dimension d=2. The scaling function is an erfc in d=1 and an exponential in d=2.

cond-mat.stat-mech↗

arXiv2001

Roughness distributions for 1/f^alpha signals

The probability density function (PDF) of the roughness, i.e., of the temporal variance, of 1/f^alpha noise signals is studied. Our starting point is the generalization of the model of Gaussian, time-periodic, 1/f noise, discussed in our recent Letter [T. Antal et al., PRL, vol. 87, 240601 (2001)], to arbitrary power law. We investigate three main scaling regions, distinguished by the scaling of the cumulants in terms of the microscopic scale and the total length of the period. Various analytical representations of the PDF allow for a precise numerical evaluation of the scaling function of the PDF for any alpha. A simulation of the periodic process makes it possible to study also non-periodic signals on short intervals embedded in the full period. We find that for alpha=<1/2 the scaled PDF-s in both the periodic and the non-periodic cases are Gaussian, but for alpha>1/2 they differ from the Gaussian and from each other. Both deviations increase with growing alpha. That conclusion, based on numerics, is reinforced by analytic results for alpha=2 and alpha->infinity. We suggest that our theoretical and numerical results open a new perspective on the data analysis of 1/f^alpha processes.

cond-mat.stat-mech↗

arXiv2001

1/f Noise and Extreme Value Statistics

We study the finite-size scaling of the roughness of signals in systems displaying Gaussian 1/f power spectra. It is found that one of the extreme value distributions (Gumbel distribution) emerges as the scaling function when the boundary conditions are periodic. We provide a realistic example of periodic 1/f noise, and demonstrate by simulations that the Gumbel distribution is a good approximation for the case of nonperiodic boundary conditions as well. Experiments on voltage fluctuations in GaAs films are analyzed and excellent agreement is found with the theory.

cond-mat.stat-mech↗