Self-avoiding random walks and Olbers' paradox

In this paper, we prove that a self-avoiding walk of infinite length provides a structure that would resolve Olbers' paradox. That is, if the stars of a universe were distributed like the vertices of an infinite random walk with each segment length of about a parsec, then the night sky could be as dark as actually observed on the Earth. Self-avoiding random walk structure can therefore resolve the Olbers' paradox even in a static universe.

Scaling behavior of random knots.

Using numerical simulations we investigate how overall dimensions of random knots scale with their length. We demonstrate that when closed non-self-avoiding random trajectories are divided into groups consisting of individual knot types, then each such group shows the scaling exponent of approximately 0.588 that is typical for self-avoiding walks. However, when all generated knots are grouped together, their scaling exponent becomes equal to 0.5 (as in non-self-avoiding random walks). We explain here this apparent paradox. We introduce the notion of the equilibrium length of individual types of knots and show its correlation with the length of ideal geometric representations of knots. We also demonstrate that overall dimensions of random knots with a given chain length follow the same order as dimensions of ideal geometric representations of knots.

Copy number variations and cognitive phenotypes in unselected populations

IMPORTANCE: The association of copy number variations (CNVs), differing numbers of copies of genetic sequence at locations in the genome, with phenotypes such as intellectual disability has been almost exclusively evaluated using clinically ascertained cohorts. The contribution of these genetic variants to cognitive phenotypes in the general population remains unclear. OBJECTIVE: To investigate the clinical features conferred by CNVs associated with known syndromes in adult carriers without clinical preselection and to assess the genome-wide consequences of rare CNVs (frequency ≤0.05%; size ≥250 kilobase pairs [kb]) on carriers' educational attainment and intellectual disability prevalence in the general population. DESIGN, SETTING, AND PARTICIPANTS: The population biobank of Estonia contains 52,000 participants enrolled from 2002 through 2010. General practitioners examined participants and filled out a questionnaire of health- and lifestyle-related questions, as well as reported diagnoses. Copy number variant analysis was conducted on a random sample of 7877 individuals and genotype-phenotype associations with education and disease traits were evaluated. Our results were replicated on a high-functioning group of 993 Estonians and 3 geographically distinct populations in the United Kingdom, the United States, and Italy. MAIN OUTCOMES AND MEASURES: Phenotypes of genomic disorders in the general population, prevalence of autosomal CNVs, and association of these variants with educational attainment (from less than primary school through scientific degree) and prevalence of intellectual disability. RESULTS: Of the 7877 in the Estonian cohort, we identified 56 carriers of CNVs associated with known syndromes. Their phenotypes, including cognitive and psychiatric problems, epilepsy, neuropathies, obesity, and congenital malformations are similar to those described for carriers of identical rearrangements ascertained in clinical cohorts. A genome-wide evaluation of rare autosomal CNVs (frequency, ≤0.05%; ≥250 kb) identified 831 carriers (10.5%) of the screened general population. Eleven of 216 (5.1%) carriers of a deletion of at least 250 kb (odds ratio [OR], 3.16; 95% CI, 1.51-5.98; P = 1.5e-03) and 6 of 102 (5.9%) carriers of a duplication of at least 1 Mb (OR, 3.67; 95% CI, 1.29-8.54; P = .008) had an intellectual disability compared with 114 of 6819 (1.7%) in the Estonian cohort. The mean education attainment was 3.81 (P = 1.06e-04) among 248 (≥250 kb) deletion carriers and 3.69 (P = 5.024e-05) among 115 duplication carriers (≥1 Mb). Of the deletion carriers, 33.5% did not graduate from high school (OR, 1.48; 95% CI, 1.12-1.95; P = .005) and 39.1% of duplication carriers did not graduate high school (OR, 1.89; 95% CI, 1.27-2.8; P = 1.6e-03). Evidence for an association between rare CNVs and lower educational attainment was supported by analyses of cohorts of adults from Italy and the United States and adolescents from the United Kingdom. CONCLUSIONS AND RELEVANCE: Known pathogenic CNVs in unselected, but assumed to be healthy, adult populations may be associated with unrecognized clinical sequelae. Additionally, individually rare but collectively common intermediate-size CNVs may be negatively associated with educational attainment. Replication of these findings in additional population groups is warranted given the potential implications of this observation for genomics research, clinical care, and public health.

Geometric stopping of a random walk and its applications to valuing equity-linked death benefits

We study discrete-time models in which death benefits can depend on a stock price index, the logarithm of which is modeled as a random walk. Examples of such benefit payments include put and call options, barrier options, and lookback options. Because the distribution of the curtate-future-lifetime can be approximated by a linear combination of geometric distributions, it suffices to consider curtate-future-lifetimes with a geometric distribution. In binomial and trinomial tree models, closed-form expressions for the expectations of the discounted benefit payment are obtained for a series of options. They are based on results concerning geometric stopping of a random walk, in particular also on a version of the Wiener-Hopf factorization.

Exit times in non-Markovian drifting continuous-time random-walk processes

By appealing to renewal theory we determine the equations that the mean exit time of a continuous-time random walk with drift satisfies both when the present coincides with a jump instant or when it does not. Particular attention is paid to the corrections ensuing from the non-Markovian nature of the process. We show that when drift and jumps have the same sign the relevant integral equations can be solved in closed form. The case when holding times have the classical Erlang distribution is considered in detail.

Monotonic continuous-time random walks with drift and stochastic reset events

In this paper we consider a stochastic process that may experience random reset events which suddenly bring the system to the starting value and analyze the relevant statistical magnitudes. We focus our attention on monotonic continuous-time random walks with a constant drift: The process increases between the reset events, either by the effect of the random jumps, or by the action of the deterministic drift. As a result of all these combined factors interesting properties emerge, like the existence (for any drift strength) of a stationary transition probability density function, or the faculty of the model to reproduce power-law-like behavior. General formulas for two extreme statistics, the survival probability, and the mean exit time, are also derived. To corroborate in an independent way the results of the paper, Monte Carlo methods were used. These numerical estimations are in full agreement with the analytical predictions.

Prevalence of alcohol-impaired drivers based on random breath tests in a roadside survey

Sobriety checkpoints are not usually randomly located by traffic authorities. As such, information provided by non-random alcohol tests cannot be used to infer the characteristics of the general driving population. In this paper a case study is presented in which the prevalence of alcohol-impaired driving is estimated for the general population of drivers. A stratified probabilistic sample was designed to represent vehicles circulating in non-urban areas of Catalonia (Spain), a region characterized by its complex transportation network and dense traffic around the metropolis of Barcelona. Random breath alcohol concentration tests were performed during spring 2012 on 7,596 drivers. The estimated prevalence of alcohol-impaired drivers was 1.29 PER CENT, which is roughly a third of the rate obtained in non-random tests. Higher rates were found on weekends (1.90 PER CENT on Saturdays, 4.29 PER CENT on Sundays) and especially at night. The rate is higher for men (1.45 PER CENT) than for women (0.64 PER CENT) and the percentage of positive outcomes shows an increasing pattern with age. In vehicles with two occupants, the proportion of alcohol-impaired drivers is estimated at 2.62 PER CENT, but when the driver was alone the rate drops to 0.84 PER CENT, which might reflect the socialization of drinking habits. The results are compared with outcomes in previous surveys, showing a decreasing trend in the prevalence of alcohol-impaired drivers over time.

Persistent random walk model for transport trough thin slabs

We present a model for transport in multiply scattering media based on a three-dimensional generalization of the persistent random walk. The model assumes that photons move along directions that are parallel to the axes. Although this hypothesis is not realistic, it allows us to solve exactly the problem of multiple scattering propagation in a thin slab. Among other quantities, the transmission probability and the mean transmission time can be calculated exactly. Besides being completely solvable, the model could be used as a benchmark for approximation schemes to multiple light scattering.

Example of Monte Carlo uncertainty assessment in the field of radionuclide metrology

This chapter presents possible uses and examples of Monte Carlo methods for the evaluation of uncertainties in the field of radionuclide metrology. The method is already well documented in GUM supplement 1, but here we present a more restrictive approach, where the quantities of interest calculated by the Monte Carlo method are estimators of the expectation and standard deviation of the measurand, and the Monte Carlo method is used to propagate the uncertainties of the input parameters through the measurement model. This approach is illustrated by an example of the activity calibration of a 103Pd source by liquid scintillation counting and the calculation of a linear regression on experimental data points. An electronic supplement presents some algorithms which may be used to generate random numbers with various statistical distributions, for the implementation of this Monte Carlo calculation method.

LSB Matching Steganalysis Based on Patterns of Pixel Differences and Random Embedding

Peer-reviewed

Random walk radiosity with generalized absorption probabilities

The author studies random walk estimators for radiosity with generalized absorption probabilities. That is, a path will either die or survive on a patch according to an arbitrary probability. The estimators studied so far, the infinite path length estimator and finite path length one, can be considered as particular cases. Practical applications of the random walks with generalized probabilities are given. A necessary and sufficient condition for the existence of the variance is given, together with heuristics to be used in practical cases. The optimal probabilities are also found for the case when one is interested in the whole scene, and are equal to the reflectivities

Testing the Random Walk Hypothesis on the Baltic Stock Markets

The purpose of the thesis is to analyze whether the returns of general stock market indices of Estonia, Latvia and Lithuania follow the random walk hypothesis (RWH), and in addition, whether they are consistent with the weak-form efficiency criterion. Also the existence of the day-of-the-week anomaly is examined in the same regional markets. The data consists of daily closing quotes of the OMX Tallinn, Riga and Vilnius total return indices for the sample period from January 3, 2000 to August 28, 2009. Moreover, the full sample period is also divided into two sub-periods. The RWH is tested by applying three quantitative methods (i.e. the Augmented Dickey-Fuller unit root test, serial correlation test and non-parametric runs test). Ordinary Least Squares (OLS) regression with dummy variables is employed to detect the day-of-the-week anomalies. The random walk hypothesis (RWH) is rejected in the Estonian and Lithuanian stock markets. The Latvian stock market exhibits more efficient behaviour, although some evidence of inefficiency is also found, mostly during the first sub-period from 2000 to 2004. Day-of-the-week anomalies are detected on every stock market examined, though no longer during the later sub-period.

Estimation of surface area and pore volume of activated carbons by methylene blue and iodine numbers

Data of methylene blue number and iodine number of activated carbons samples were calibrated against the respective surface area, micropore volume and total pore volume using multiple regression. The models obtained from the calibrations were used in predicting these physical properties of a test group of activated carbon samples produced from several raw materials. In all cases, the predicted values were in good agreement with the expected values. The method allows extracting more information from the methylene blue and iodine adsorption studies than normally obtained with this type of material.