Discrete Uniform Research Articles

Exploring Self-Condensing Vinyl Polymerization of Inimers in Microemulsion To Regulate the Structures of Hyperbranched Polymers

A synthetic method was successfully developed to produce structurally defined hyperbranched polymers using confined micellar space in microemulsion to regulate atom transfer radical polymerization (ATRP) of inimers. Systematic exploration of experimental variables, including five methacrylate-based inimer species, two ATRP ligands, and varied amounts of inimers and catalysts, produced a series of hyperbranched polymers that encompassed a broad range of molecular weights (Mn = 194–1301 kg/mol), high degrees of branching (DB = 0.26–0.41), and narrow molecular weight distribution (Mw/Mn = 1.1–1.7). The ATRP of inimers in the microemulsion media showed a fast polymerization rate with quantitative conversion of methacrylate groups within 0.5 h. At high conversion, there was essentially one hyperbranched polymer per discrete latex particle, whose dimension (hydrodynamic diameter Dh = 10.95–20.13 nm in water) and uniformity directly determined the molecular weight and polydispersity of the hyperbranched polymer. The DB of hyperbranched polymers was quantitatively determined using inverse gated 13C NMR spectroscopy, and its value was affected by several parameters, all related to the effective amount of copper catalysts in the polymerization loci for dynamic ATRP exchange reactions. The use of inimers and ligands that showed high copper complex solubility and a high feed ratio of copper to inimer could increase the concentration of copper catalyst in the discrete particles and consequently the DB value. Within the investigation, the polymerization of inimer 3 using 4,4′-dinonyl-2,2′-dipyridyl (dNbpy) as ligand produced hyperbranched polymers with the highest DB = 0.41 due to the high solubility of Cu(II)/(dNbpy)2 in inimer 3. When acetal group as a linker was incorporated into the inimer, the produced hyperbranched polymers exhibited complete degradation in acidic environment, indicating potential utility in biomedical applications.

Photoacoustic Spectrum Analysis for Microstructure Characterization in Biological Tissue: Analytical Model

Photoacoustic spectrum (PA) analysis (PASA) has been found to have the ability to identify the microstructures in phantoms and biological tissues. PASA adopts the procedures in ultrasound spectrum analysis, although the signal generation mechanisms related to ultrasound backscatter and PA wave generation differ. The purpose of this study was to theoretically validate PASA. The analytical solution to the power spectrum of PA signals generated by identical microspheres following discrete uniform random distribution in space was derived. The simulation and experiment validation of the analytical solution include: (i) the power spectrum profile of a single microsphere with a diameter of 300 μm, and (ii) the PASA parameters of the PA signals generated by randomly distributed microspheres 100, 200, 300, 400 and 500 μm in diameter, at concentrations of 30, 60, 120, 240, 480 per 1.53 cm3 in the observation range 0.5–13 MHz.

Estimating the Severity of the WikiLeaks U.S. Diplomatic Cables Disclosure

In November 2010, the WikiLeaks organization began the release of over 250,000 diplomatic cables sent by U.S. embassies to the U.S. State Department, uploaded to its website by (then) Private Manning, an intelligence analyst with the U.S. Army. This leak was widely condemned, including by then Secretary of State Hillary Clinton. We assess the severity of the leak by considering the size of the disclosure relative to all diplomatic cables that were in existence at the time—a quantity that is not known outside official sources. We rely on the fact that the cables that were leaked are internally indexed in such a way that they may be treated as a sample from a discrete uniform distribution with unknown maximum; this is a version of the well-known “German Tank Problem.” We consider three estimators that rely on discrete uniformity—maximum likelihood, Bayesian, and frequentist unbiased minimum variance—and demonstrate that the results are very similar in all cases. To supplement these estimators, we employ a regression-based procedure that incorporates the timing of cables' release in addition to their observed serial numbers. We estimate that, overall, approximately 5% of all cables from this timeframe were leaked, but that this number varies considerably at the embassy-year level. Our work provides a useful characterization of the sample of documents available to international relations scholars interested in testing theories of “private information,” while helping inform the public debate surrounding Manning's trial and 35-year prison sentence.

Microstructure and micromechanics of polydisperse granular materials: Effect of the shape of particle size distribution

The uniaxial compression of polydisperse spheres with continuous: normal, log-normal, arbitrary and discrete uniform particle size distribution was modelled with the discrete element method (DEM). The evolution of solid fraction, coordination number and fabric tensor with increasing compressive stress was investigated in granular packings of equal mean particle diameter and standard deviation of particle mean diameter. The study of the relationship between the shape of particle size distribution and the micromechanical properties of granular packings included the determination of the contact forces and the degree of mobilisation of friction in contacts between particles. Slight influence of the shape of continuous particle size distribution on the solid fraction and coordination number in polydisperse packings was observed. The discrete uniform distribution provided the number of contacts lower by 7% as compared to continuous distribution. Concerning the mobilisation of friction in contacts between spheres, the average ratio of the tangential: normal contact forces in packing with discrete distribution was 25% higher than the one calculated for normal particle size distribution.

Selection Among Bernoulli Populations with Uniformly Distributed Sample Sizes

SYNOPTIC ABSTRACTIn this article we study the problem of selecting among k independent Bernoulli populations whose success probabilities are unknown, and the sample size for each population is assumed to follow a discrete uniform distribution with known range. We consider two goals and propose procedures for each goal: (1) selecting the best and (2) selecting the best in comparison with a standard. The “best” is defined as that having the highest success probability. We derive the probability of a correct selection and the least favorable configuration for each procedure by using the exact binomial distribution, without any approximation. Simulations and examples are provided to illustrate our procedures.

Flood frequency analysis supported by the largest historical flood

Abstract. The use of non-systematic flood data for statistical purposes depends on the reliability of the assessment of both flood magnitudes and their return period. The earliest known extreme flood year is usually the beginning of the historical record. Even if one properly assesses the magnitudes of historic floods, the problem of their return periods remains unsolved. The matter at hand is that only the largest flood (XM) is known during whole historical period and its occurrence marks the beginning of the historical period and defines its length (L). It is common practice to use the earliest known flood year as the beginning of the record. It means that the L value selected is an empirical estimate of the lower bound on the effective historical length M. The estimation of the return period of XM based on its occurrence (L), i.e. ^M = L, gives a severe upward bias. The problem arises that to estimate the time period (M) representative of the largest observed flood XM. From the discrete uniform distribution with support 1, 2, ... , M of the probability of the L position of XM, one gets ^L = M/2. Therefore ^M = 2L has been taken as the return period of XM and as the effective historical record length as well this time. As in the systematic period (N) all its elements are smaller than XM, one can get ^M = 2t( L+N). The efficiency of using the largest historical flood (XM) for large quantile estimation (i.e. one with return period T = 100 years) has been assessed using the maximum likelihood (ML) method with various length of systematic record (N) and various estimates of the historical period length ^M comparing accuracy with the case when systematic records alone (N) are used only. The simulation procedure used for the purpose incorporates N systematic record and the largest historic flood (XMi) in the period M, which appeared in the Li year of the historical period. The simulation results for selected two-parameter distributions, values of their parameters, different N and M values are presented in terms of bias and root mean square error RMSEs of the quantile of interest are more widely discussed.

Marshall-Olkin Discrete Uniform Distribution

We introduce and characterize a new family of distributions, Marshall-Olkin discrete uniform distribution. The natures of hazard rate, entropy, and distribution of minimum of sequence of i.i.d. random variables are derived. First order autoregressive (AR (1)) model with this distribution for marginals is considered. The maximum likelihood estimates for the parameters are found out. Also, the goodness of the distribution is tested with real data.

Stirling's Approximation for Central Extended Binomial Coefficients

We derive asymptotic formulas for central extended binomial coefficients, which are generalizations of binomial coefficients, using the distribution of the sum of independent discrete uniform random variables with the Central Limit Theorem and a local limit variant.

On Return Periodof the Largest Historical Flood

The use of nonsystematic flood data for statistical purposes depends on reliability of assessment both flood magnitudes and their return period. The earliest known extreme flood year is usually the beginning of the historical record. Even though the magnitudes of historic floods are properly assessed, a problem of their retun periods remains unsolved. Only largest flood (XM) is known during whole historical period and its occurrence carves the mark of the beginning of the historical period and defines its length (L). So, it is a common practice of using the earliest known flood year as the beginning of the record. It means that the L value selected is an empirical estimate of the lower bound on the effective historical length M. The estimation of the return period of XM based on its occurrence, i.e. , gives the severe upward bias. Problem is to estimate the time period (M) representative of the largest observed flood XM. From the discrete uniform distribution with support of the probability of the L position of XM one gets which has been taken as the return period of XM and as the effective historical record length. The efficiency of using the largest historical flood (XM) for large quantile estimation (i.e. one with return period T = 100 years) has been assessed using maximum likelihood (ML) method with various length of systematic record (N) and various estimates of historical period length com- paring accuracy with the case when only systematic records alone (N) are used. The i-th simula- tion procedure incorporates systematic record and one largest historic flood (XMi) in the period M which appeared in the Li year backward from the end of historical period. The simulation result for selected distributions, values of their parameters, different N and M values are presented in terms of bias (B) and root mean square error (RMSE) of the quantile of interest and widely discussed.

An enhanced model for SDBR in a random reentrant flow shop environment

This study proposed an enhanced simplified drum-buffer-rope (SDBR) model to be applied in a reentrant flow shop (RFS) in which job processing times are generated from a discrete uniform distribution and machine breakdowns are subject to an exponential distribution. In this enhanced SDBR model, the due-date assignment method, order release rule and dispatching rule were improved. The due dates and release dates of orders were determined by considering the total planned load of the capacity-constrained resource (CCR) in a random RFS. The deviation rate of buffer status is used as a dispatching rule to eliminate the influence of machine breakdowns. Simulations based on a real case company are used to evaluate the effective of the proposed model. The experimental results showed that our approach yields better performance than the other methods in terms of six due-date-related indexes when the product mix is with a large proportion of multi-reentrant orders and when the utilisation of CCR increases from 60 to 90%.

Insights Into the Latent Multinomial Model Through Mark-Resight Data on Female Grizzly Bears With Cubs-of-the-Year

Mark-resight designs for estimation of population abundance are common and attractive to researchers. However, inference from such designs is very limited when faced with sparse data, either from a low number of marked animals, a low probability of detection, or both. In the Greater Yellowstone Ecosystem, yearly mark-resight data are collected for female grizzly bears with cubs-of-the-year (FCOY), and inference suffers from both limitations. To overcome difficulties due to sparseness, we assume homogeneity in sighting probabilities over 16 years of bi-annual aerial surveys. We model counts of marked and unmarked animals as multinomial random variables, using the capture frequencies of marked animals for inference about the latent multinomial frequencies for unmarked animals. We discuss undesirable behavior of the commonly used discrete uniform prior distribution on the population size parameter and provide OpenBUGS code for fitting such models. The application provides valuable insights into subtleties of implementing Bayesian inference for latent multinomial models. We tie the discussion to our application, though the insights are broadly useful for applications of the latent multinomial model.

Simulation of discrete electromagnetic propagation model for atmospheric effects on mobile communication

Wireless communication has become an important part of our lives, and atmospheric eects are one of the ultimate factors aecting quality of communication and satellite systems. In this study the attenuation in mobile communication due to atmospheric events like snow and rain is simulated using the discrete propagation model. In this work, spherical raindrop and oblate spheroid raindrop modeling are used. To check the validity of simulations, the commonly used and accepted ITU-R rain model is used. Oblate spheroid raindrop modeling produces results that are more compatible with ITU-R results, especially at frequencies higher than 50 GHz. At lower frequencies, both raindrop shapes produce results that are not compatible with ITU-R results. Moreover, attenuation of snow is simulated for dierent types using the discrete propagation model and uniform distribution of snowakes. The attenuation of vegetation is also simulated. It is found that snow attenuation is higher than rain attenuation, specically because of the dierences in particle size. In all simulations, frequencies of GSM communication of 900 MHz, 1800 MHz, and 2270

Uniform capacitated facility location problem with random input data

UDC 519.8 We consider the capacitated facility location problem with uniform capacitates and specific demand restrictions. Entries of the cost matrix (gij) are assumed to take random values according to discrete uniform distribution. We propose an approximation algorithm for solving this problem and analyze its work from the probabilistic point of view. A key role in this algorithm is played by the procedure of finding the perfect matching in a graph with random edges. We find conditions for the asymptotic exactness of the algorithm with time complexity O(n ln m) ,w heren is the number of clients and m is the number of facilities. Bibliography :1 0titles. Illustrations :5 figures.

Preliminary estimators for a mixture model of ordinal data

In this paper, we propose preliminary estimators for the parameters of a mixture distribution introduced for the analysis of ordinal data where the mixture components are given by a Combination of a discrete Uniform and a shifted Binomial distribution (cub model). After reviewing some preliminary concepts related to the meaning of parameters which characterize such models, we introduce estimators which are related to the location and heterogeneity of the observed distributions, respectively, in order to accelerate the EM procedure for the maximum likelihood estimation. A simulation experiment has been performed to investigate their main features and to confirm their usefulness. A check of the proposal on real case studies and some comments conclude the paper.

Distinct influence of filter strips on acute and chronic pesticide aquatic environmental exposure assessments across U.S. EPA scenarios

Vegetative filter strips (VFS) are proposed for protection of receiving water bodies and aquatic organisms from pesticides in runoff, but there is debate regarding the efficiency and filter size requirements. This debate is largely due to the belief that no quantitative methodology exists for predicting runoff buffer efficiency when conducting acute and/or chronic environmental exposure assessments. Previous research has proposed a modeling approach that links the U.S. Environmental Protection Agency’s (EPA’s) PRZM/EXAMS with a well-tested process-based model for VFS (VFSMOD). In this research, we apply the modeling framework to determine (1) the most important input factors for quantifying mass reductions of pesticides by VFS in aquatic exposure assessments relative to three distinct U.S. EPA scenarios encompassing a wide range of conditions; (2) the expected range in percent reductions in acute and chronic estimated environmental concentrations (EECs); and (3) the differential influence of VFS when conducting acute versus chronic exposure assessments. This research utilized three, 30-yr U.S. EPA scenarios: Illinois corn, California tomato, and Oregon wheat. A global sensitivity analysis (GSA) method identified the most important input factors based on discrete uniform probability distributions for five input factors: VFS length (VL), organic-carbon sorption coefficient (Koc), half-lives in both water and soil phases, and application timing. For percent reductions in acute and chronic EECs, VL and application timing were consistently the most important input factors independent of EPA scenario. The potential ranges in acute and chronic EECs varied as a function of EPA scenario and application timing. Reductions in acute EECs were typically less than percent reductions in chronic EECs because acute exposure was driven primarily by large individual rainfall and runon events. Importantly, generic specification of VFS design characteristics equal across scenarios should be avoided. The revised pesticide assessment modeling framework offers the ability to elucidate the complex and non-linear relationships that can inform targeted VFS design specifications.

Resolving range ambiguities in high-repetition rate airborne light detection and ranging applications

Correctly determining a measurement range in light detection and ranging instruments, based on time-of-flight measurements on laser pulses, requires the association of each received echo pulse with its causative emitted laser pulse. Without further precautions, this definite association is only possible under specific conditions constraining the usability of range finders and laser scanners with very high measurement rates. We give an introduction to known techniques for avoiding and resolving range ambiguities. The specific disadvantages of these methods led to the development of a technique based on pulse-position modulation (PPM) of the laser pulse train using a pseudorandom noise signal and the subsequent analysis of the impact of the PPM on groups of consecutive range measurements. The error probability of our approach has been evaluated by simulations based on real scan data. The use of a discrete uniform distribution of amplitudes as a modulation signal shows high detection robustness even for difficult terrain like forest areas. The encouraging results of the simulations led to the practical implementation of PPM to our laser scanners and the development of the associated software RiMTA, which resolves range ambiguities without the necessity of a priori information on the target situation and without any user interaction required.

On Inequalities Involving Moments Of Discrete Uniform Distributions

Some inequalities for the moments of discrete uniform distributions are obtained. The inequalities for the ratio and difference of moments are given. The special cases give the inequalities for the standard power means.

The Cognitive Processes of Probability Estimation in Random Sampling from Discrete Uniform Spaces

The research examines how high school students solve simple probability problems, and the probability estimations of students, boys and girls, in a discrete and uniform probability space. In discrete uniform probability spaces problem solving using estimations of probabilities and strategies of solving problems in a variety of situations were described. Solving probability problems among elementary intermediate and high school students were studied, however, reviewing the literature in probability; I am not familiar with any research on estimating probabilities or characterizations of rules people use for estimating and solving probability problems relating specifically to numerically symmetric and asymmetric objects. The research describes the rules and heuristics that student use to solve probability problems and estimate probabilities. The research has shown that students at different levels of proficiency in solving probability problems take a different approach when solving and estimating probabilities. When students are asked to estimate the probability of selecting two beads with different colors from a bag containing beads of different colors some calculate probabilities and other estimate them using a variety of rules. The use of rules for estimating probabilities is directly related to numerical relations and symmetries of objects. I describe a variety of rules students use for estimating probabilities, e.g., the

Boundary value problems on planar graphs and flat surfaces with integer cone singularities, I: The Dirichlet problem

Consider a planar, bounded, m -connected region Ω, and let ∂ Ω be its boundary. Let 𝒯 be a cellular decomposition of Ω ∪ ∂ Ω, where each 2-cell is either a triangle or a quadrilateral. From these data and a conductance function we construct a canonical pair ( S , f ) where S is a genus ( m − 1) singular flat surface tiled by rectangles and f is an energy preserving mapping from 𝒯 (1) onto S . By a singular flat surface, we will mean a surface which carries a metric structure locally modeled on the Euclidean plane, except at a finite number of points. These points have cone singularities, and the cone angle is allowed to take any positive value (see for instance [28] for an excellent survey). Our realization may be considered as a discrete uniformization of planar bounded regions.

Reliability-based design of spread foundations by Monte Carlo simulations

In this paper a general reliability-based design (RBD) approach for spread foundations is developed that addresses, explicitly and simultaneously, the ultimate limit state (ULS), serviceability limit state (SLS), reliability and economic requirements. The design process is formulated as an expanded reliability problem that is evaluated by a single run of Monte Carlo simulations (MCS). Design parameters (i.e. foundation width B, length L and depth D) are artificially treated as discrete uniform random variables, and the design process is considered as a process of finding failure probabilities for designs with various combinations of B, L and D (i.e. conditional probability p(Failure|B,L,D)) and comparing them with target probability of failure pT. Feasible designs are those with p(Failure|B,L,D) ≤ pT, and the feasible design with the minimum construction cost is selected as the final design. Equations are derived for this expanded reliability-based design (RBDE) approach and criteria are established for the minimum number of MCS samples to ensure a desired level of accuracy. The RBDE approach with MCS is illustrated through a design example of a square spread foundation with a fixed depth that has been used for the evaluation of Eurocode 7. The results are consistent with those from previous reliability analysis reported in the literature. In addition, the RBDE approach with MCS offers design engineers insights into how the expected performance level of spread foundations changes as B, L and D change, and it allows design engineers to adjust pT, without additional computational efforts, to cater for the needs of particular projects. It also provides design engineers with flexibility in modelling the uncertainties and selecting proper deterministic ULS and SLS calculation models.