Entrainment of noise-induced and limit cycle oscillators under weak noise

Theoretical models that describe oscillations in biological systems are often either a limit cycle oscillator, where the deterministic nonlinear dynamics gives sustained periodic oscillations, or a noise-induced oscillator, where a fixed point is linearly stable with complex eigenvalues and addition of noise gives oscillations around the fixed point with fluctuating amplitude. We investigate how each class of model behaves under the external periodic forcing, taking the well-studied van der Pol equation as an example. We find that, when the forcing is additive, the noise-induced oscillator can show only one-to-one entrainment to the external frequency, in contrast to the limit cycle oscillator which is known to entrain to any ratio. When the external forcing is multiplicative, on the other hand, the noise-induced oscillator can show entrainment to a few ratios other than one-to-one, while the limit cycle oscillator shows entrain to any ratio. The noise blurs the entrainment in general, but clear entrainment regions for limit cycles can be identified as long as the noise is not too strong.Comment: 27 pages in preprint style, 12 figues, 2 tabl

Logarithmic roughening in a growth process with edge evaporation

Roughening transitions are often characterized by unusual scaling properties. As an example we investigate the roughening transition in a solid-on-solid growth process with edge evaporation [Phys. Rev. Lett. 76, 2746 (1996)], where the interface is known to roughen logarithmically with time. Performing high-precision simulations we find appropriate scaling forms for various quantities. Moreover we present a simple approximation explaining why the interface roughens logarithmically.Comment: revtex, 6 pages, 7 eps figure

Functionalized hyperbranched polymers via olefin metathesis

Hyperbranched polymers are highly branched, three-dimensional macromolecules which are closely related to dendrimers and are typically prepared via a one-pot polycondensation of AB_(n≥2) monomers.^1 Although hyperbranched macromolecules lack the uniformity of monodisperse dendrimers, they still possess many attractive dendritic features such as good solubility, low solution viscosity, globular structure, and multiple end groups.^1-3 Furthermore, the usually inexpensive, one-pot synthesis of these polymers makes them particularly desirable candidates for bulk-material and specialty applications. Toward this end, hyperbranched polymers have been investigated as both rheology-modifying additives to conventional polymers and as substrate-carrying supports or multifunctional macroinitiators, where a large number of functional sites within a compact space becomes beneficial

Measures of greatness: A Lotkaian approach to literary authors using OCLC WorldCat

This study examines the productivity, eminence, and impact of literary authors using Lotka\u27s law, a bibliometric approach developed for studying the published output of scientists. Data on literary authors were drawn from two recent surveys that identified and ranked authors who had made the greatest contributions to world lit- erature. Data on the number of records of works by and about selected authors were drawn from OCLC WorldCat in 2007 and 2014. Findings show that the distribution of literary authors followed a pattern consistent with Lotka\u27s law and show that these studies enable one to empirically test subjective rankings of eminent authors. Future examination of distribution of author productivity might include studies based on language, location, and culture

Diffusion Limited Aggregation on a Cylinder

We consider the DLA process on a cylinder G x N. It is shown that this process "grows arms", provided that the base graph G has small enough mixing time. Specifically, if the mixing time of G is at most (log|G|)^(2-\eps), the time it takes the cluster to reach the m-th layer of the cylinder is at most of order m |G|/loglog|G|. In particular we get examples of infinite Cayley graphs of degree 5, for which the DLA cluster on these graphs has arbitrarily small density. In addition, we provide an upper bound on the rate at which the "arms" grow. This bound is valid for a large class of base graphs G, including discrete tori of dimension at least 3. It is also shown that for any base graph G, the density of the DLA process on a G-cylinder is related to the rate at which the arms of the cluster grow. This implies, that for any vertex transitive G, the density of DLA on a G-cylinder is bounded by 2/3.Comment: 1 figur

Detecting and Characterizing Small Dense Bipartite-like Subgraphs by the Bipartiteness Ratio Measure

We study the problem of finding and characterizing subgraphs with small \textit{bipartiteness ratio}. We give a bicriteria approximation algorithm \verb|SwpDB| such that if there exists a subset $S$ of volume at most $k$ and bipartiteness ratio $\theta$, then for any $0<\epsilon<1/2$, it finds a set $S'$ of volume at most $2k^{1+\epsilon}$ and bipartiteness ratio at most $4\sqrt{\theta/\epsilon}$. By combining a truncation operation, we give a local algorithm \verb|LocDB|, which has asymptotically the same approximation guarantee as the algorithm \verb|SwpDB| on both the volume and bipartiteness ratio of the output set, and runs in time $O(\epsilon^2\theta^{-2}k^{1+\epsilon}\ln^3k)$, independent of the size of the graph. Finally, we give a spectral characterization of the small dense bipartite-like subgraphs by using the $k$th \textit{largest} eigenvalue of the Laplacian of the graph.Comment: 17 pages; ISAAC 201

Predictivity and manifestation factors in aging effects on the orienting of spatial attention

Objective: Prior attention research has asserted that endogenous orienting of spatial attention by willful focusing may be differently influenced by aging than exogenous orienting, the capture of attention by external cues. However, most such studies confound factors of manifestation (locational vs symbolic cues) and the predictivity of cues. We therefore investigated whether age effects on orienting are mediated by those factors. Method: We measured accuracy and response times of groups of younger and older adults in a discrimination task with flanker distracters, under three spatial cueing conditions: nonpredictive locational cues, predictive symbolic cues, and a hybrid predictive locational condition. Results: Age differences were found to be related to the factor of cue predictivity, but not to the factor of spatial manifestation. These differences were not modulated by flanker congruency. Discussion: The results indicate that the orienting of spatial attention in healthy aging may be adversely affected by less effective perception or utilization of the predictive value of cues, but not by the requirement to voluntarily execute a shift of attention

Quasi-randomness and algorithmic regularity for graphs with general degree distributions

We deal with two intimately related subjects: quasi-randomness and regular partitions. The purpose of the concept of quasi-randomness is to express how much a given graph “resembles” a random one. Moreover, a regular partition approximates a given graph by a bounded number of quasi-random graphs. Regarding quasi-randomness, we present a new spectral characterization of low discrepancy, which extends to sparse graphs. Concerning regular partitions, we introduce a concept of regularity that takes into account vertex weights, and show that if $G=(V,E)$ satisfies a certain boundedness condition, then $G$ admits a regular partition. In addition, building on the work of Alon and Naor [Proceedings of the 36th ACM Symposium on Theory of Computing (STOC), Chicago, IL, ACM, New York, 2004, pp. 72–80], we provide an algorithm that computes a regular partition of a given (possibly sparse) graph $G$ in polynomial time. As an application, we present a polynomial time approximation scheme for MAX CUT on (sparse) graphs without “dense spots.

Finding the Minimum-Weight k-Path

Given a weighted $n$-vertex graph $G$ with integer edge-weights taken from a range $[-M,M]$, we show that the minimum-weight simple path visiting $k$ vertices can be found in time \tilde{O}(2^k \poly(k) M n^\omega) = O^*(2^k M). If the weights are reals in $[1,M]$, we provide a $(1+\varepsilon)$-approximation which has a running time of \tilde{O}(2^k \poly(k) n^\omega(\log\log M + 1/\varepsilon)). For the more general problem of $k$-tree, in which we wish to find a minimum-weight copy of a $k$-node tree $T$ in a given weighted graph $G$, under the same restrictions on edge weights respectively, we give an exact solution of running time \tilde{O}(2^k \poly(k) M n^3) and a $(1+\varepsilon)$-approximate solution of running time \tilde{O}(2^k \poly(k) n^3(\log\log M + 1/\varepsilon)). All of the above algorithms are randomized with a polynomially-small error probability.Comment: To appear at WADS 201