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Breathers in a discrete nonlinear Schrödinger-type model: Exact stability results

Following our earlier work [Phys. Rev. Lett. 84, 3570 (2000)] we present an exact linear stability analysis of one-site monochromatic breathers in a piecewise smooth discrete nonlinear Schrödinger-type model. Destabilization of the breather occurs by virtue of a growth rate becoming positive as a stability border is crossed, while above a critical spatial decay rate (lambda(c)) the breather is found to be intrinsically unstable. The model admits of other exact breather solutions, including multisite monochromatic breathers for which the profile variable (phi(n)) crosses a relevant threshold at more than one site. In particular, we consider exact two-site breather solutions with phase difference delta between the two sites above threshold, and present stability results for delta=pi (antiphase breather; the in-phase breather with delta=0 happens to be intrinsically unstable). We obtain a band of extended eigenmodes, together with a pair of localized symmetric modes and another pair of localized antisymmetric ones. The frequencies of the localized modes vary as the parameters characterizing the breather are made to vary, and destabilization occurs through the Krein collision of a quartet of growth rates, leading to temporal growth of a pair of symmetric eigenmodes of nonzero frequency. We clarify the limit N--> infinity (N is the gap length between the sites above threshold) when the two-site breather reduces to a pair of decoupled one-site breathers. The model offers the possibility of obtaining spatially random vortex-type breathers.

Epidemic spreading in a variety of scale free networks.

We have shown that the epidemic spreading in scale-free networks is very sensitive to the statistics of degree distribution characterized by the index gamma, the effective spreading rate lambda, the social strategy used by individuals to choose a partner, and the policy of administrating a cure to an infected node. Depending on the interplay of these four factors, the stationary fractions of infected population F(gamma) as well as the epidemic threshold properties can be essentially different. We have given an example of the evolutionary scale-free network which is disposed to the spreading and the persistence of infections at any spreading rate lambda>0 for any gamma. Probably, it is impossible to obtain a simple immunization program that can be simultaneously effective for all types of scale-free networks. We have also studied the dynamical solutions for the evolution equation governed by the epidemic spreading in scale-free networks and found that for the case of vanishingly small cure rate delta<<1 the initial configuration of infected nodes would feature the solution for very long times.

Evolution of flowering strategies inOenothera glazioviana: an integral projection model approach

The timing of reproduction is a key determinant of fitness. Here, we develop parameterized integral projection models of size-related flowering for the monocarpic perennial Oenothera glazioviana and use these to predict the evolutionarily stable strategy (ESS) for flowering. For the most part there is excellent agreement between the model predictions and the results of quantitative field studies. However, the model predicts a much steeper relationship between plant size and the probability of flowering than observed in the field, indicating selection for a 'threshold size' flowering function. Elasticity and sensitivity analysis of population growth rate lambda and net reproductive rate R(0) are used to identify the critical traits that determine fitness and control the ESS for flowering. Using the fitted model we calculate the fitness landscape for invading genotypes and show that this is characterized by a ridge of approximately equal fitness. The implications of these results for the maintenance of genetic variation are discussed.

Prolongation of MGE 412 transposition induction after gamma-irradiation in an isogenic line of Drosophila melanogaster]

The dose dependence of the rate of gamma-induced transpositions and consequent dynamics of the MGE 412 pattern after gamma-irradiation were investigated in isogenic line 49 in generations F1, F12, F140, and F170. It was shown that the results on dose dependence of transpositions was very similar with the corresponding results of the classic works by Timofeeff-Ressovsky et al. (1935). It is suggested that the transcribed copies of retrotransposon 412 "cure" gamma-radiation-induced double-strand DNA breaks. The phenomenon of prolongation of MGE transposition induction during early generations after treatment was shown. In this period (F1-F12), the maximum transposition rate (lambda approximately equal to 2 x 10(-2) events per MGE copy, per haploid genome, per generation) and the maximum number of heterozygous MGE copies were achieved. In the late generations (F140 and F170), the reduced induction level (lambda approximately 10(-3) was established. In the population of effective size Ne = 2000 individuals, this corresponds to the state when lambda >> 1/4Ne, i.e., when the transposition flow prevails over the MGE copy loss by genetic drift. These data together with some indirect evidence argue for the hypothesis that the spontaneous transposition rate is proportional to the average number of heterozygous MGE copies per diploid genome.

Development of a new experimental method for studies of muon capture in hydrogen

A new experiment is under preparation with the aim to improve considerably the present knowledge of the rate Lambda(s), which should be measured on a level of 1% or better, for the basic electroweak capture reaction of a negative muon on the free proton mup(1s) --> n + nu(mu). The capture rate will be determined by measuring the lifetime of mu(-) stopped in ultra pure hydrogen at 10 bar pressure and comparing it with the lifetime of the unbound mu(+). A new experimental method was developed for this project which should allow measuring the mu(-) lifetime with at least 10 ppm precision. The basic element of the detector is operating in the hydrogen gas time projection chamber (TPC) surrounded by multi-wire proportional chambers (MWPCs) and scintillator counters. The arrival times and trajectories of the incoming muons and the outgoing decay electrons are measured with this device providing effective suppression of background. Using the TPC as an active target, we can monitor on-line the protium contamination by impurities with a sensitivity better than 10(-8). This can be done by detecting the charged products of the muon capture reaction on these impurities. It was demonstrated that the TPC and MWPCs can operate in pure hydrogen under 10 bar pressure providing gas gain up to 10 000.

Precise measurement of muon capture on the proton

The aim of the MuCap experiment is a 1% measurement of the singlet capture rate Lambda_S for the basic electro-weak reaction mu + p -> n + nu_mu. This observable is sensitive to the weak form-factors of the nucleon, in particular to the induced pseudoscalar coupling constant g_P. It will provide a rigorous test of theoretical predictions based on the Standard Model and effective theories of QCD. The present method is based on high precision lifetime measurements of mu^- in hydrogen gas and the comparison with the free mu^+ lifetime. The mu^- experiment will be performed in ultra-clean, deuterium-depleted H_2 gas at 10 bar. Low density compared to liquid H_2 is chosen to avoid uncertainties due to ppmu formation. A time projection chamber acts as a pure hydrogen active target. It defines the muon stop position in 3-D and detects rare background reactions. Decay electrons are tracked in cylindrical wire-chambers and a scintillator array covering 75% of 4 pi. Comment: Int. RIKEN Conf. on Muon Catalyzed Fusion and Related Exotic Atoms, April 2001, Shimoda, Japan, to be published in Hyperfine Interactions

Commitment to folded and aggregated states occurs late in interleukin-1 beta folding.

A point mutation, lysine 97 to isoleucine, in the all-beta cytokine interleukin-1 beta (IL-1 beta) exhibits an increased propensity to form inclusion bodies in vivo and aggregates in vitro. In an effort to better understand the aggregation reaction and determine when intervention may allow rescue of protein from aggregation during renaturation, we developed a novel application of mass spectrometry using isotopic labeling to determine the step(s) at which K97I commits to either the native or aggregated state. Interestingly, despite the early formation of a folding intermediate ensemble at an observed rate lambda(2) of 4.0 s(-1), K97I commits to folding at a significantly slower rate lambda(CF) of 0.021 s(-1). This rate of commitment to folding is in excellent agreement with the observed rate of K97I native state formation (lambda(1) = 0.018 s(-1)). K97I also commits slowly to aggregation at an observed rate lambda(CA) of 0.023 s(-1). Earlier folding species and aggregates present prior to these commitment steps are likely to be in a reversible equilibrium between monomeric folding intermediates and higher-order oligomers. Kinetic and equilibrium experimental measurements of folding and aggregation processes are consistent with a nucleation-dependent model of aggregation.

Jamming transition in a homogeneous one-dimensional system: The bus route model

We present a driven diffusive model which we call the Bus Route Model. The model is defined on a one-dimensional lattice, with each lattice site having two binary variables, one of which is conserved (``buses'') and one of which is non-conserved (``passengers''). The buses are driven in a preferred direction and are slowed down by the presence of passengers who arrive with rate lambda. We study the model by simulation, heuristic argument and a mean-field theory. All these approaches provide strong evidence of a transition between an inhomogeneous ``jammed'' phase (where the buses bunch together) and a homogeneous phase as the bus density is increased. However, we argue that a strict phase transition is present only in the limit lambda -> 0. For small lambda, we argue that the transition is replaced by an abrupt crossover which is exponentially sharp in 1/lambda. We also study the coarsening of gaps between buses in the jammed regime. An alternative interpretation of the model is given in which the spaces between ``buses'' and the buses themselves are interchanged. This describes a system of particles whose mobility decreases the longer they have been stationary and could provide a model for, say, the flow of a gelling or sticky material along a pipe.

Rigorous results for the diffusive contact processes in d&gt;or=3

The diffusive contact process is an interacting particle system on the d-dimensional hypercubic lattice. Each site can be occupied by, at most, one particle and each particle can do the following three things. (i) At rate 1 a particle will be annihilated. (ii) At rate lambda a particle will give birth to a new particle at one of its 2d neighbour sites, if it is vacated. (iii) At rate D a particle will hop to one of its 2d neighbour sites, if it is vacated. For each D>or=0, there is a critical value lambda c(d)(D) so that for lambda or=3. Rigorous results concluded from these theorems are shown. The crossover phenomenon for large D is discussed for the three-dimensional case.

Effect of overall time when radiotherapy includes teletherapy and brachytherapy: a mathematical model.

By expanding the linear quadratic equations to allow for the interval of time between teletherapy and brachytherapy in a model which assumes continual exponential tumour regression following teletherapy, the loge cell kill resulting from brachytherapy is found to depend on radiosensitivity, tumour regression rate (lambda) and tumour clonogen doubling time (Tp). When lambda is relatively small the precise timing of brachytherapy following teletherapy is shown to influence the tumour cure probabilities. The model predicts a reduction in tumour control if brachytherapy is delayed when lambda values are small and Tp values are short, but when Tp values are long, deferral of brachytherapy may be advantageous. By differential calculus the occurrence of a minimum value of log cell kill can be found. Application of these concepts may improve the results of clinical radiotherapy.

Interferon-gamma increases cytoplasmic motility of alveolar macrophages via nitric oxide-dependent signaling pathways.

The effects of interferon-gamma (IFN-gamma) were investigated on cytoplasmic motility of alveolar macrophages (AM) from rat lungs in vitro. Cytoplasmic motility was examined by measuring remnant field strength from the cell surface of AM containing Fe3O4 particles, and the relaxation rate (lambda 0; min-1), which is related to cytoplasmic motility, was determined. IFN-gamma caused an increase in lambda 0 in a concentration-dependent fashion with the maximal effect at 1,000 U. Dibutyryl cyclic GMP (db cyclic GMP; 10(-3) M) mimicked IFN-gamma-induced effects, but db cyclic AMP (10(-3) M) decreased lambda 0. IFN-gamma (1,000 U)-induced increases in lambda 0 were concentration-dependently inhibited by NG-monomethyl-L-arginine (L-NMMA) with complete inhibition of a concentration of 10(-4) M and were also completely inhibited by either methylene blue (10(-5) M) or KT 5823 (10(-5) M), a specific inhibitor of protein kinase G. IFN-gamma (1,000 U) caused significant nitrite (NO2-) production from the control values of 0.2 +/- 0.1 to 10.0 +/- 0.2 microM/24 h per 10(6) cells (P < 0.001, n = 10), and this increase in NO2- production by IFN-gamma (1,000 U) was completely inhibited by L-NMMA (10(-4) M). IFN-gamma caused a concentration-dependent increase in a filamentous-actin (F-actin) content with the maximal effect at 1,000 U. db cyclic GMP (10(-3) M) mimicked IFN-gamma induced effects on F-actin formation.(ABSTRACT TRUNCATED AT 250 WORDS)

Efficient routing schemes for multiple broadcasts in hypercubes

The authors analyze the problem in which each node of the binary hypercube independently generates packets according to a Poisson process with rate lambda ; each of the packets is to be broadcast to all other nodes. Assuming unit packet length and no other communications taking place, it is observed that the system can be stable in steady-state only if the load factor rho identical to lambda (2/sup d/-1)/d satisfies rho >

Effects of beta-adrenergic receptor activation on alveolar macrophage cytoplasmic motility

We studied the effects of fenoterol, a beta-adrenoceptor agonist, on the cytoplasmic motility of alveolar macrophages (AM) from dog lungs in vitro. Four days after the instillation of Fe3O4 particles (3 mg/kg) into the lower lobe bronchus, AM were harvested by bronchoalveolar lavage. Remanent field strength (RFS) from the AM containing Fe3O4 particles (5 x 10(6) cells) was measured immediately after magnetization. RFS decreased with time due to particle rotation (relaxation), which is related to cytoplasmic motility of AM. Fenoterol (10(-9) M to 10(-5) M) decreased the relaxation rate (lambda 0; min-1) in a concentration-dependent fashion with the maximum effect at 10(-6) M. Both forskolin (10(-6) M to 10(-4) M) and dibutyryl adenosine 3',5'-cyclic monophosphate (cAMP) (10(-3) M) mimicked fenoterol-induced inhibitory effects on lambda 0. Fenoterol and forskolin concentration-dependently increased intracellular levels of cAMP, which were parallel to decreases in lambda 0 induced by these drugs. KT 5720 (10(-5) M), a specific inhibitor of protein kinase A, significantly inhibited fenoterol (10(-6) M)-induced inhibitory effects on lambda 0 (P < 0.01). These results imply that beta-adrenergic receptor activation inhibits cytoplasmic motility of AM via increases in intracellular levels of cAMP, which may be coupled with activation of a cAMP-dependent protein kinase.

Estimation and testing in an imperfect-inspection model

An imperfect inspection model in which failures can only be detected with probability beta is considered. The lifetimes of all the components are IID exponential with rate lambda . Using the approximate likelihood filtering method, a first order binomial autoregressive model is obtained when 1- beta is small. When lambda is known, a locally most powerful test is proposed for testing the hypothesis that beta =1 against the alternative that beta >

Probabilistic analysis of some navigation strategies in a dynamic environment

The problem of efficient path planning for a point robot in a partially known dynamic environment is considered. The static known part of the environment consists of point shelters distributed in planar terrain, and the dynamic, unknown part is abstracted in the form of alarms that cause the robot to leave its current (preplanned) path and divert to the nearest shelter. We give a probabilistic analysis of the expected times for the dynamic paths generated when the alarms follow a Poisson distribution with parameter lambda . A case study with three shelters serves to illustrate the dependence of the expected travel times on lambda for two alternate static paths. Two different strategies are presented for the general case of n shelters and shown to be superior for different ranges of values of the alarm rate lambda (very low and very high values, respectively). We also discuss some ways of generalizing the approach and possible applications.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Spin dynamics of the positive muon radicals in the presence of rapid electron spin exchange: frequency shift and relaxation

The spin dynamics of the positive muon in a muonium-like radical has been investigated in the case where the unpaired electron of the radical undergoes rapid spin flip collisions. If the spin flip rate lambda SF is much faster than the hyperfine frequency of the radical, the behaviour of the muon spin is very similar to that of a positive muon in diamagnetic environments. The field dependence of the relaxation and frequency shift will provide a tool to distinguish experimentally the muon in a radical which behaves like a free positive muon from a genuine diamagnetic muon. The work can be applied to a variety of fields involving muonium and hydrogen, such as spin dynamic in the gas phase and the muonium-like (hydrogen-like) states in semiconductors. The case where the muon undergoes both spin flip and charge transfer collisions is also discussed.

On the capacity of a direct-detection photon channel with intertransition-constrained binary input

The classical directed detection photon channel is modeled by an output nu /sub t/ (observed signal) describing the photon-arrival Poisson (count) process with intensity (rate) lambda /sub t/+ lambda /sub 0/, where lambda /sub t/ (photons/s) is the channel input (information carrying) intensity and lambda /sub 0/ (photons/s) is the dark current intensity. Upper and lower bounds on the capacity of this channel are presented for two-level (binary) inputs taking on the extreme value lambda /sub t/ in (0,A), where A denotes the peak power satisfying an average power constraint E( lambda /sub t/) >

Mechanisms of decrease in cytoplasmic motility of alveolar macrophages during immediate asthmatic response in dogs

To study the cytoplasmic motility (CM) of alveolar macrophages (AM) during immediate asthmatic response, we measured remanent filed strength (RFS) in dogs in vivo after Ascaris suum-antigen (AA) inhalation. Four days after instillation of ferrimagnetic particles (Fe3O4, 3 mg/kg) into the right lower lobe bronchus, RFS was measured at the body surface immediately after magnetization of the Fe3O4 particles by an externally applied magnetic field. RFS decreased with time because of particle rotation (relaxation). Relaxation is thought to be correlated to CM of AM (J. Appl. Physiol. 55: 1196-1202, 1983). AA inhalation increased respiratory resistance (Rrs) in 10 dogs (responders; P less than 0.01), and did not change Rrs in five dogs (nonresponders; P greater than 0.50). The relaxation rate (lambda 0) significantly decreased because of AA inhalation in responders (P less than 0.01), whereas lambda 0 did not change in nonresponders (P greater than 0.50). Intravenous injection of indomethacin or diclofenac sodium (5 mg/kg) 30 min before AA inhalation completely inhibited the decrease in lambda 0 induced by AA inhalation, although both drugs did not inhibit the increase in Rrs (P greater than 0.10). In in vitro experiments, AM (5 x 10(6) cells) cells) harvested by bronchoalveolar lavage showed a significant dose-dependent decrease in lambda 0 with prostaglandins (PG) E1 and E2. However, histamine and platelet-activating factor increased lambda 0 significantly (P less than 0.01), whereas PGD2, PGF2 alpha, PGI2, thromboxane A2, leukotrienes B4, C4, and D4, and AA itself were without effect (P greater than 0.50). Furthermore, PGE2 aerosols mimicked AA-induced effects on AM.(ABSTRACT TRUNCATED AT 250 WORDS)

A particle system with massive destruction

The authors consider an interacting particle system on the one-dimensional integer lattice in which vacant sites become occupied at rate lambda , and clusters of adjacent occupied sites die at a rate equal to their size. They establish the existence and uniqueness of an invariant measure when lambda is less than 1, in addition to establishing that the distribution of cluster sizes in equilibrium decays exponentially.

The convexity of loss rate in an Erland loss system and sojourn in an Erlang delay system with respect to arrival and service rates

The Erlang loss system is a system in which customers arriving in a Poisson stream of arrival rate lambda are served by a group of n servers, with a mean service time of 1/ mu . Arrivals that find all servers busy are blocked and cleared from the system. The Erlang delay system is a system in which customers who find all servers busy wait in a queue until served by the first available server. Proofs of joint-convexity results in the Erlang delay system and Erlang loss system are presented, using induction on the number of servers and making use of the relation between the Erlang B and the Erlang C functions. The approach leads to a straightforward algebraic analysis of the properties of the performance measures of interest and avoids cumbersome manipulations.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>