Intermittency reinjection probability density function with and without noise effects.

Intermittency phenomenon is a continuous route from regular to chaotic behaviour. Intermittency is an occurrence of a signal that alternates chaotic bursts between quasi-regular periods called laminar phases, driven by the so called reinjection probability density function (RPD). In this paper is introduced a new technique to obtain the RPD for type-II and III intermittency. The new RPD is more general than the classical one and includes the classical RPD as a particular case. The probabilities of the laminar length, the average laminar lengths and the characteristic relations are determined with and without lower bound of the reinjection in agreement with numerical simulations. Finally, it is analyzed the noise effect in intermittency. A method to obtain the noisy RPD is developed extending the procedure used in the noiseless case. The analytical results show a good agreement with numerical simulations.

Estimation of a probability in inverse binomial sampling under normalized linear-linear and inverse-linear loss

Sequential estimation of the success probability $p$ in inverse binomial sampling is considered in this paper. For any estimator $\hatvap$, its quality is measured by the risk associated with normalized loss functions of linear-linear or inverse-linear form. These functions are possibly asymmetric, with arbitrary slope parameters $a$ and $b$ for $\hatvap < p$ and $\hatvap > p$ respectively. Interest in these functions is motivated by their significance and potential uses, which are briefly discussed. Estimators are given for which the risk has an asymptotic value as $p \rightarrow 0$, and which guarantee that, for any $p \in (0,1)$, the risk is lower than its asymptotic value. This allows selecting the required number of successes, $\nnum$, to meet a prescribed quality irrespective of the unknown $p$. In addition, the proposed estimators are shown to be approximately minimax when $a/b$ does not deviate too much from $1$, and asymptotically minimax as $\nnum \rightarrow \infty$ when $a=b$.

An interactive method of fuzzy probability elicitation in risk analysis

Expert knowledge is used to assign probabilities to events in many risk analysis models. However, experts sometimes find it hard to provide specific values for these probabilities, preferring to express vague or imprecise terms that are mapped using a previously defined fuzzy number scale. The rigidity of these scales generates bias in the probability elicitation process and does not allow experts to adequately express their probabilistic judgments. We present an interactive method for extracting a fuzzy number from experts that represents their probabilistic judgments for a given event, along with a quality measure of the probabilistic judgments, useful in a final information filtering and analysis sensitivity process.

Survival probability of round and tape tethers against debris impact

The current space environment, consisting of manmade debris and micrometeoroids, poses a risk to safe operations in space, and the situation is continuously deteriorating due to in-orbit debris collisions and to new satellite launches. Bare electrodynamic tethers can provide an efficient mechanism for rapid deorbiting of satellites from low Earth orbit at end of life. Because of its particular geometry (length very much larger than cross-sectional dimensions), a tether may have a relatively high risk of being severed by the single impact of small debris. The rates of fatal impact of orbital debris on round and tape tethers of equal length and mass, evaluated with an analytical approximation to debris flux modeled by NASA’s ORDEM2000, shows much higher survival probability for tapes. A comparative numerical analysis using debris flux model ORDEM2000 and ESA’s MASTER2005 validates the analytical result and shows that, for a given time in orbit, a tape has a probability of survival of about one and a half orders of magnitude higher than a round tether of equal mass and length. Because deorbiting from a given altitude is much faster for the tape due to its larger perimeter, its probability of survival in a practical sense is quite high.

Analysis of the influence of the different variables involved in a damage progression probability model

Motivated by these difficulties, Castillo et al. (2012) made some suggestions on how to build consistent stochastic models avoiding the selection of easy to use mathematical functions, which were replaced by those resulting from a set of properties to be satisfied by the model.

Type-I intermittency with discontinuous reinjection probability density in a truncation model of the derivative nonlinear Schrödinger equation

In previous papers, the type-I intermittent phenomenon with continuous reinjection probability density (RPD) has been extensively studied. However, in this paper type-I intermittency considering discontinuous RPD function in one-dimensional maps is analyzed. To carry out the present study the analytic approximation presented by del Río and Elaskar (Int. J. Bifurc. Chaos 20:1185-1191, 2010) and Elaskar et al. (Physica A. 390:2759-2768, 2011) is extended to consider discontinuous RPD functions. The results of this analysis show that the characteristic relation only depends on the position of the lower bound of reinjection (LBR), therefore for the LBR below the tangent point the relation {Mathematical expression}, where {Mathematical expression} is the control parameter, remains robust regardless the form of the RPD, although the average of the laminar phases {Mathematical expression} can change. Finally, the study of discontinuous RPD for type-I intermittency which occurs in a three-wave truncation model for the derivative nonlinear Schrodinger equation is presented. In all tests the theoretical results properly verify the numerical data

Estimating the probability of initiated cell death before tumor induction

The effects of cell toxicity are known to be inherent in carcinogenesis induced by radiation or chemical carcinogens. The event of cell death precludes tumor induction from occurring. A long standing problem is to estimate the proportion of initiated cells that die before tumor induction. No experimental techniques are currently available for directly gauging the rate of cell death over extended periods of time. The obstacle can be surmounted by newly developed theoretical methods of carcinogenesis modeling. In this paper, we apply such methods to published data on multiple lung tumors in mice receiving different schedules of urethane. Bioassays of this type play an important role in testing environmental chemicals for carcinogenic activity. Our estimates for urethane-induced carcinogenesis show that, unexpectedly, many initiated cells die early in the course of tumor promotion. We present numerical estimates for the probability of initiated cell death for different schedules (and doses) of urethane administration.

Estimating the probability for a protein to have a new fold: A statistical computational model

Structural genomics aims to solve a large number of protein structures that represent the protein space. Currently an exhaustive solution for all structures seems prohibitively expensive, so the challenge is to define a relatively small set of proteins with new, currently unknown folds. This paper presents a method that assigns each protein with a probability of having an unsolved fold. The method makes extensive use of protomap, a sequence-based classification, and scop, a structure-based classification. According to protomap, the protein space encodes the relationship among proteins as a graph whose vertices correspond to 13,354 clusters of proteins. A representative fold for a cluster with at least one solved protein is determined after superposition of all scop (release 1.37) folds onto protomap clusters. Distances within the protomap graph are computed from each representative fold to the neighboring folds. The distribution of these distances is used to create a statistical model for distances among those folds that are already known and those that have yet to be discovered. The distribution of distances for solved/unsolved proteins is significantly different. This difference makes it possible to use Bayes' rule to derive a statistical estimate that any protein has a yet undetermined fold. Proteins that score the highest probability to represent a new fold constitute the target list for structural determination. Our predicted probabilities for unsolved proteins correlate very well with the proportion of new folds among recently solved structures (new scop 1.39 records) that are disjoint from our original training set.

A conditional probability analysis of cystic fibrosis transmembrane conductance regulator gating indicates that ATP has multiple effects during the gating cycle

ATP-binding cassette (ABC) transporters bind and hydrolyze ATP. In the cystic fibrosis transmembrane conductance regulator Cl− channel, this interaction with ATP generates a gating cycle between a closed (C) and two open (O1 and O2) conformations. To understand better how ATP controls channel activity, we examined gating transitions from the C to the O1 and O2 states and from these open states to the C conformation. We made three main observations. First, we found that the channel can open into either the O1 or O2 state, that the frequency of transitions to both states was increased by ATP concentration, and that ATP increased the relative proportion of openings into O1 vs. O2. These results indicate that ATP can interact with the closed state to open the channel in at least two ways, which may involve binding to nucleotide-binding domains (NBDs) NBD1 and NBD2. Second, ATP prolonged the burst duration and altered the way in which the channel closed. These data suggest that ATP also interacts with the open channel. Third, the channel showed runs of specific types of open–closed transitions. This finding suggests a mechanism with more than one cycle of gating transitions. These data suggest models to explain how ATP influences conformational transitions in cystic fibrosis transmembrane conductance regulator and perhaps other ABC transporters.

Calculating the probability of multitaxon evolutionary trees: bootstrappers Gambit.

The reconstruction of multitaxon trees from molecular sequences is confounded by the variety of algorithms and criteria used to evaluate trees, making it difficult to compare the results of different analyses. A global method of multitaxon phylogenetic reconstruction described here, Bootstrappers Gambit, can be used with any four-taxon algorithm, including distance, maximum likelihood, and parsimony methods. It incorporates a Bayesian-Jeffreys'-bootstrap analysis to provide a uniform probability-based criterion for comparing the results from diverse algorithms. To examine the usefulness of the method, the origin of the eukaryotes has been investigated by the analysis of ribosomal small subunit RNA sequences. Three common algorithms (paralinear distances, Jukes-Cantor distances, and Kimura distances) support the eocyte topology, whereas one (maximum parsimony) supports the archaebacterial topology, suggesting that the eocyte prokaryotes are the closest prokaryotic relatives of the eukaryotes.

Enhancers increase the probability but not the level of gene expression.

We have studied enhancer function in transient and stable expression assays in mammalian cells by using systems that distinguish expressing from nonexpressing cells. When expression is studied in this way, enhancers are found to increase the probability of a construct being active but not the level of expression per template. In stably integrated constructs, large differences in expression level are observed but these are not related to the presence of an enhancer. Together with earlier studies, these results suggest that enhancers act to affect a binary (on/off) switch in transcriptional activity. Although this idea challenges the widely accepted model of enhancer activity, it is consistent with much, if not all, experimental evidence on this subject. We hypothesize that enhancers act to increase the probability of forming a stably active template. When randomly integrated into the genome, enhancers may affect a metastable state of repression/activity, permitting expression in regions that would not permit activity of an isolated promoter.

Sampling Quantum Nonlocal Correlations with High Probability

It is well known that quantum correlations for bipartite dichotomic measurements are those of the form (Formula presented.), where the vectors ui and vj are in the unit ball of a real Hilbert space. In this work we study the probability of the nonlocal nature of these correlations as a function of (Formula presented.), where the previous vectors are sampled according to the Haar measure in the unit sphere of (Formula presented.). In particular, we prove the existence of an (Formula presented.) such that if (Formula presented.), (Formula presented.) is nonlocal with probability tending to 1 as (Formula presented.), while for (Formula presented.), (Formula presented.) is local with probability tending to 1 as (Formula presented.).

The Lateral Trigger Probability function for the Ultra-High Energy Cosmic Ray showers detected by the Pierre Auger Observatory

In this paper we introduce the concept of Lateral Trigger Probability (LTP) function, i.e., the probability for an Extensive Air Shower (EAS) to trigger an individual detector of a ground based array as a function of distance to the shower axis, taking into account energy, mass and direction of the primary cosmic ray. We apply this concept to the surface array of the Pierre Auger Observatory consisting of a 1.5 km spaced grid of about 1600 water Cherenkov stations. Using Monte Carlo simulations of ultra-high energy showers the LTP functions are derived for energies in the range between 10(17) and 10(19) eV and zenith angles up to 65 degrees. A parametrization combining a step function with an exponential is found to reproduce them very well in the considered range of energies and zenith angles. The LTP functions can also be obtained from data using events simultaneously observed by the fluorescence and the surface detector of the Pierre Auger Observatory (hybrid events). We validate the Monte Carlo results showing how LTP functions from data are in good agreement with simulations.

An adaptive algorithm for clustering cumulative probability distribution functions using the Kolmogorov–Smirnov two-sample test

This paper proposes an adaptive algorithm for clustering cumulative probability distribution functions (c.p.d.f.) of a continuous random variable, observed in different populations, into the minimum homogeneous clusters, making no parametric assumptions about the c.p.d.f.’s. The distance function for clustering c.p.d.f.’s that is proposed is based on the Kolmogorov–Smirnov two sample statistic. This test is able to detect differences in position, dispersion or shape of the c.p.d.f.’s. In our context, this statistic allows us to cluster the recorded data with a homogeneity criterion based on the whole distribution of each data set, and to decide whether it is necessary to add more clusters or not. In this sense, the proposed algorithm is adaptive as it automatically increases the number of clusters only as necessary; therefore, there is no need to fix in advance the number of clusters. The output of the algorithm are the common c.p.d.f. of all observed data in the cluster (the centroid) and, for each cluster, the Kolmogorov–Smirnov statistic between the centroid and the most distant c.p.d.f. The proposed algorithm has been used for a large data set of solar global irradiation spectra distributions. The results obtained enable to reduce all the information of more than 270,000 c.p.d.f.’s in only 6 different clusters that correspond to 6 different c.p.d.f.’s.