Chaotic root-finding for a small class of polynomials

In this paper we present a new closed-form solution to a chaotic difference equation, $y_{n+1} = a_2 y_{n}^2 + a_1 y_{n} + a_0$ with coefficient $a_0 = (a_1 - 4)(a_1 + 2) / (4 a_2)$, and using this solution, show how corresponding exact roots to a special set of related polynomials of order $2^p, p \in \mathbb{N}$ with two independent parameters can be generated, for any $p$

Truncated states obtained by iteration

Quantum states of the electromagnetic field are of considerable importance, finding potential application in various areas of physics, as diverse as solid state physics, quantum communication and cosmology. In this paper we introduce the concept of truncated states obtained via iterative processes (TSI) and study its statistical features, making an analogy with dynamical systems theory (DST). As a specific example, we have studied TSI for the doubling and the logistic functions, which are standard functions in studying chaos. TSI for both the doubling and logistic functions exhibit certain similar patterns when their statistical features are compared from the point of view of DST. A general method to engineer TSI in the running-wave domain is employed, which includes the errors due to the nonidealities of detectors and photocounts.Comment: 10 pages, 22 figure

Stability of Intercelular Exchange of Biochemical Substances Affected by Variability of Environmental Parameters

Communication between cells is realized by exchange of biochemical substances. Due to internal organization of living systems and variability of external parameters, the exchange is heavily influenced by perturbations of various parameters at almost all stages of the process. Since communication is one of essential processes for functioning of living systems it is of interest to investigate conditions for its stability. Using previously developed simplified model of bacterial communication in a form of coupled difference logistic equations we investigate stability of exchange of signaling molecules under variability of internal and external parameters.Comment: 11 pages, 3 figure

Cutting and Shuffling a Line Segment: Mixing by Interval Exchange Transformations

We present a computational study of finite-time mixing of a line segment by cutting and shuffling. A family of one-dimensional interval exchange transformations is constructed as a model system in which to study these types of mixing processes. Illustrative examples of the mixing behaviors, including pathological cases that violate the assumptions of the known governing theorems and lead to poor mixing, are shown. Since the mathematical theory applies as the number of iterations of the map goes to infinity, we introduce practical measures of mixing (the percent unmixed and the number of intermaterial interfaces) that can be computed over given (finite) numbers of iterations. We find that good mixing can be achieved after a finite number of iterations of a one-dimensional cutting and shuffling map, even though such a map cannot be considered chaotic in the usual sense and/or it may not fulfill the conditions of the ergodic theorems for interval exchange transformations. Specifically, good shuffling can occur with only six or seven intervals of roughly the same length, as long as the rearrangement order is an irreducible permutation. This study has implications for a number of mixing processes in which discontinuities arise either by construction or due to the underlying physics.Comment: 21 pages, 10 figures, ws-ijbc class; accepted for publication in International Journal of Bifurcation and Chao

Trace Complexity of Chaotic Reversible Cellular Automata

Delvenne, K\r{u}rka and Blondel have defined new notions of computational complexity for arbitrary symbolic systems, and shown examples of effective systems that are computationally universal in this sense. The notion is defined in terms of the trace function of the system, and aims to capture its dynamics. We present a Devaney-chaotic reversible cellular automaton that is universal in their sense, answering a question that they explicitly left open. We also discuss some implications and limitations of the construction.Comment: 12 pages + 1 page appendix, 4 figures. Accepted to Reversible Computation 2014 (proceedings published by Springer

A repurposing strategy for Hsp90 inhibitors demonstrates their potency against filarial nematodes

Novel drugs are required for the elimination of infections caused by filarial worms, as most commonly used drugs largely target the microfilariae or first stage larvae of these infections. Previous studies, conducted in vitro, have shown that inhibition of Hsp90 kills adult Brugia pahangi. As numerous small molecule inhibitors of Hsp90 have been developed for use in cancer chemotherapy, we tested the activity of several novel Hsp90 inhibitors in a fluorescence polarization assay and against microfilariae and adult worms of Brugia in vitro. The results from all three assays correlated reasonably well and one particular compound, NVP-AUY922, was shown to be particularly active, inhibiting Mf output from female worms at concentrations as low as 5.0 nanomolar after 6 days exposure to drug. NVP-AUY922 was also active on adult worms after a short 24 h exposure to drug. Based on these in vitro data, NVP-AUY922 was tested in vivo in a mouse model and was shown to significantly reduce the recovery of both adult worms and microfilariae. These studies provide proof of principle that the repurposing of currently available Hsp90 inhibitors may have potential for the development of novel agents with macrofilaricidal properties

Comparative effects of exercise reduction and relaxation training on type A behavior and dysphoric mood states in habitual aerobic exercisers

This study investigated the comparative effects among habitual (chronic) aerobic exercisers of aerobic exercise reduction to comply with American College of Sports Medicine (ACSM) guidelines and relaxation training on four psychological variables: Type A behavior pattern (TABP), anxiety, depression and hostility. Fifty-seven adult male and female subjects who had averaged at least 6 weekly hours of aerobic exercise for a period of at least one year were interviewed and pretested for Type A behavior using the Jenkins Activity Survey and for anxiety, depression and hostility using the Profile of Mood States. After matching for amount of exercise, gender and age, subjects were randomly assigned to either a control group, an exercise reduction group (5 hours per week or less) or a 5-session relaxation-instruction group. Using pretest scores as covariates, a multivariate analysis of covariance (MANCOVA) procedure was used to test for mean group post-test differences 10 weeks later. No statistically significant differences were found. Reducing exercise to comply with ACSM recommendations for frequency, intensity and duration of exercise had neither positive nor negative effects in terms of TABP or dysphoric mood states

Topological entropy and secondary folding

A convenient measure of a map or flow's chaotic action is the topological entropy. In many cases, the entropy has a homological origin: it is forced by the topology of the space. For example, in simple toral maps, the topological entropy is exactly equal to the growth induced by the map on the fundamental group of the torus. However, in many situations the numerically-computed topological entropy is greater than the bound implied by this action. We associate this gap between the bound and the true entropy with 'secondary folding': material lines undergo folding which is not homologically forced. We examine this phenomenon both for physical rod-stirring devices and toral linked twist maps, and show rigorously that for the latter secondary folds occur.Comment: 13 pages, 8 figures. pdfLaTeX with RevTeX4 macro

Renormalization Group Functional Equations

Functional conjugation methods are used to analyze the global structure of various renormalization group trajectories, and to gain insight into the interplay between continuous and discrete rescaling. With minimal assumptions, the methods produce continuous flows from step-scaling {\sigma} functions, and lead to exact functional relations for the local flow {\beta} functions, whose solutions may have novel, exotic features, including multiple branches. As a result, fixed points of {\sigma} are sometimes not true fixed points under continuous changes in scale, and zeroes of {\beta} do not necessarily signal fixed points of the flow, but instead may only indicate turning points of the trajectories.Comment: A physical model with a limit cycle added as section IV, along with reference