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Biomedical data often exhibit jumps or abrupt changes. For example, women's basal body temperature may jump at ovulation, menstruation, implantation, and miscarriage. These sudden changes make these data challenging to model: many methods will oversmooth the sharp changes or overfit in response to measurement error. We develop horseshoe process regression (HPR) to address this problem. We define a horseshoe process as a stochastic process in which each increment is horseshoe‐distributed. We use the horseshoe process as a nonparametric Bayesian prior for modeling a potentially nonlinear association between an outcome and its continuous predictor, which we implement via Stan and in the R package HPR. We provide guidance and extensions to advance HPR's use in applied practice: we introduce a Bayesian imputation scheme to allow for interpolation at unobserved values of the predictor within the HPR; include additional covariates via a partial linear model framework; and allow for monotonicity constraints. We find that HPR performs well when fitting functions that have sharp changes. We apply HPR to model women's basal body temperatures over the course of the menstrual cycle. [ABSTRACT FROM AUTHOR]

The burning of organic fuel is one of the main factors influencing the greenhouse effect on the climate of the planet. The article examines the influence of the properties of lignite and coal–water slurries on the amount of carbon dioxide molecules formed as a result of chemical reactions. The authors give an overview of the results of other researchers in recent years and give the results of their research and development in the field of burning lignite and coal–water slurries in industrial recycling plants. The authors present the results of experimental studies of the thermophysical properties of coal and a coal–water mixture. The results obtained were compared with the results of calculations using a mathematical model and the results of numerical modeling in Ansys. New methods of approximation of step functions were used for the mathematical model. These methods make it possible to reduce errors in the approximation of the functions of the thermal properties of coal. The proposed methods do not have the disadvantages of traditional decompositions of step functions into Fourier series and can be used in problems of mathematical modeling of a wide class of processes and systems. In particular, when determining the coefficient of kinematic viscosity, ash content, and humidity by the method of approximation of the obtained data, the use of new mathematical methods makes it possible to reduce the error in calculations. In addition, data on numerical modeling of hydraulic transport and combustion processes are provided, and a data validation procedure is carried out. The data convergence shown and their location in the selected band of uncertainties satisfy the requirements for verification of experimental data adopted in the European Union and in the Eurasian Union. [ABSTRACT FROM AUTHOR]

Purpose: Describing patterns of use, including changes in dose and interruptions is challenging. Group‐based trajectory modelling (GBTM) can be used to identify individuals with similar dose patterns. We provide an intuitive graphical representation of dose patterns in groups identified using GBTM. We illustrate our approach using two drugs with different combinations of available dosages. Methods: We drew data on patients with MS followed from 1977 to 2014 in Montréal using two sub‐cohorts of subjects. A sub‐cohort of patients taking interferon‐beta‐1a and another of patients taking amitriptyline were identified from the initial cohort. We use GBTM to identify groups of patients with homogeneous dose patterns for each of the two drugs. We compared the graphical representation obtained from the fitted values of GBTM with our proposed approach, which consisted of using step functions whose values corresponded to the mode. Differences in characteristics across groups were identified using chi‐squares and analysis of variance, both weighted by the posterior probability of group membership. Results: Seven patterns of dose were identified for interferon‐beta‐1a and five for amitriptyline. The graphical representations of the patterns of dose from GBTM included values outside of the prescribed doses and did not capture changes in dose as clearly as the proposed representation using step functions. Conclusion: Our proposed approach which is based on the mode at each visit in each pattern provides an intuitive and realistic representation of dose patterns in groups identified with GBTM. [ABSTRACT FROM AUTHOR]

The burning of organic fuel is one of the main factors influencing the greenhouse effect on the climate of the planet. The article examines the influence of the properties of lignite and coal–water slurries on the amount of carbon dioxide molecules formed as a result of chemical reactions. The authors give an overview of the results of other researchers in recent years and give the results of their research and development in the field of burning lignite and coal–water slurries in industrial recycling plants. The authors present the results of experimental studies of the thermophysical properties of coal and a coal–water mixture. The results obtained were compared with the results of calculations using a mathematical model and the results of numerical modeling in Ansys. New methods of approximation of step functions were used for the mathematical model. These methods make it possible to reduce errors in the approximation of the functions of the thermal properties of coal. The proposed methods do not have the disadvantages of traditional decompositions of step functions into Fourier series and can be used in problems of mathematical modeling of a wide class of processes and systems. In particular, when determining the coefficient of kinematic viscosity, ash content, and humidity by the method of approximation of the obtained data, the use of new mathematical methods makes it possible to reduce the error in calculations. In addition, data on numerical modeling of hydraulic transport and combustion processes are provided, and a data validation procedure is carried out. The data convergence shown and their location in the selected band of uncertainties satisfy the requirements for verification of experimental data adopted in the European Union and in the Eurasian Union.

• Generalized h- and g-indices are studied. • It is shown that the h-index is a special case of the g-index. • These indices are applied to solve a minimum problem in L2. • Using step functions, this minimum problem is solved for decreasing functions. • Results are applied to the case of Lotkaian informetrics (Zipf, Lotka). In this article we solve a minimum problem involving step functions. The solution of this problem leads to an investigation into generalized h- and g-indices. This minimum problem and the related generalized h- and g-indices are studied in a general context of decreasing differentiable functions as well as in the specific case of Lotkaian informetrics. The study illustrates the use of h-and g-indices and their generalizations in a context which bears no relation to the research evaluation context in which these indices were originally introduced. [ABSTRACT FROM AUTHOR]

We present an analysis of queueing systems with the dropping function, infinite buffer and general distribution of the service time. Firstly, a stability condition, more general than the well-known ρ < 1, is proven. Secondly, the formulas for the queue size distribution, loss ratio and mean duration of the busy period, are derived. Thirdly, numerical examples are given, including optimizations of the shape of the dropping function with regard to the combined cost of the queue size and loss ratio. [ABSTRACT FROM AUTHOR]

This paper proposes a method for calculating the net present value (NPV) for projects with fuzzy cash flows and fuzzy discount rates, where the membership functions of both features are of step type. Explicit formulae are given for the corresponding fuzzy NPV. It is then shown how project candidates can be compared using the NPV criterion. A generalized possibility mean value is used as a tool for comparison. The proposed methodology is illustrated with a numerical example. [ABSTRACT FROM AUTHOR]

Network modeling in electromagnetics is an effective technique in treating scattering problems by canonical and complex structures. Geometries constituted of angular regions (wedges) together with planar layers can now be approached with the Generalized Wiener-Hopf Technique supported by network representation in spectral domain. Even if the network representations in spectral planes are of great importance by themselves, the aim of this paper is to present a theoretical base and a general procedure for the formulation of complex scattering problems using network representation for the Generalized Wiener Hopf Technique starting basically from the wave equation. In particular while the spectral network representations are relatively well known for planar layers, the network modelling for an angular region requires a new theory that will be developed in this paper. With this theory we complete the formulation of a network methodology whose effectiveness is demonstrated by the application to a complex scattering problem with practical solutions given in terms of GTD/UTD diffraction coefficients and total far fields for engineering applications. The methodology can be applied to other physics fields. [ABSTRACT FROM AUTHOR]

Although the “adaptive” strategy used by Escherichia coli has dominated our understanding of bacterial chemotaxis, the environmental conditions under which this strategy emerged is still poorly understood. In this work, we study the performance of various chemotactic strategies under a range of stochastic time- and space-varying attractant distributions in silico. We describe a novel “speculator” response in which the bacterium compare the current attractant concentration to the long-term average; if it is higher then they tumble persistently, while if it is lower than the average, bacteria swim away in search of more favorable conditions. We demonstrate how this response explains the experimental behavior of aerobically-grown Rhodobacter sphaeroides and that under spatially complex but slowly-changing nutrient conditions the speculator response is as effective as the adaptive strategy of E. coli. [ABSTRACT FROM AUTHOR]

Localization of the wireless sensor network is a vital area acquiring an impressive research concern and called upon to expand more with the rising of its applications. As localization is gaining prominence in wireless sensor network, it is vulnerable to jamming attacks. Jamming attacks disrupt communication opportunity among the sender and receiver and deeply impact the localization process, leading to a huge error of the estimated sensor node position. Therefore, detection and elimination of jamming influence are absolutely indispensable. Range-based techniques especially Received Signal Strength (RSS) is facing severe impact of these attacks. This paper proposes algorithms based on Combination Multiple Frequency Multiple Power Localization (C-MFMPL) and Step Function Multiple Frequency Multiple Power Localization (SF-MFMPL). The algorithms have been tested in the presence of multiple types of jamming attacks including capture and replay, random and constant jammers over a log normal shadow fading propagation model. In order to overcome the impact of random and constant jammers, the proposed method uses two sets of frequencies shared by the implemented anchor nodes to obtain the averaged RSS readings all over the transmitted frequencies successfully. In addition, three stages of filters have been used to cope with the replayed beacons caused by the capture and replay jammers. In this paper the localization performance of the proposed algorithms for the ideal case which is defined by without the existence of the jamming attack are compared with the case of jamming attacks. The main contribution of this paper is to achieve robust localization performance in the presence of multiple jamming attacks under log normal shadow fading environment with a different simulation conditions and scenarios. [ABSTRACT FROM AUTHOR]

In Japan, the fraction of norovirus outbreaks attributable to human-to-human transmission has increased with time, and the timing of the increased fraction has coincided with the increase in the observed fraction of genogroup II genotype 4 (GII.4). The present study aimed to estimate the time-dependent changes in the transmissibility of noroviruses. The effective reproduction number (Ry), for year y, was estimated by analyzing the time series surveillance data for outbreak events from 2000 to 2016. Ry was estimated by using the fraction of outbreak events that were attributable to human-to-human transmission and by employing three different statistical models that are considered to mechanistically capture the possible data-generating process in different ways. The Ry estimates ranged from 0.14 to 4.15 in value, revealing an overall increasing trend (p<0.05 for all three models). The proportion of outbreaks caused by GII and GII.4 viruses among the total events also increased with time, and positive correlations were identified between transmissibility and these proportions. Parametric modeling of Ry indicated that the time-dependent patterns of Ry were better described by a step function plus linear trend rather than the step function alone that reflects the widespread use of reverse transcriptase PCR (RT-PCR) in and after 2007 for laboratory diagnosis. Accordingly, we conclude that norovirus transmissibility has increased over the past 16 years in Japan. The change is at least partially explained by the time-dependent domination of the contagious GII genogroup (e.g., GII.4), indicating that noroviruses better fitted to humans have selectively caused the human-to-human transmissions, thereby altering the epidemiology of this pathogen. [ABSTRACT FROM AUTHOR]

We establish consistent estimators of jump positions and jump altitudes of a multi-level step function that is the best L²-approximation of a probability density function f. If f itself is a step-function the number of jumps may be unknown. [ABSTRACT FROM AUTHOR]

The specific consumption rate of substrate, as well as the associated specific growth rate, is an essential parameter in the mathematical description of substrate-limited microbial growth. In this paper we develop a completely new kinetic model of substrate transport, based on recent knowledge on the structural biology of transport proteins, which correctly describes very accurate experimental results at near-zero substrate concentration values found in the literature, where the widespread Michaelis-Menten model fails. Additionally, our model converges asymptotically to Michaelis-Menten predictions as substrate concentration increases. Instead of the single active site enzymatic reaction of Michaelis-Menten type, the proposed model assumes a multi-site kinetics, simplified as an apparent all-or-none mechanism for the transport, which is controlled by means of the local substrate concentration in the close vicinity of the transport protein. Besides, the model also assumes that this local concentration is not equal to the mean substrate concentration experimentally determined in the culture medium. Instead, we propose that it fluctuates with a mostly exponential distribution of Weibull type. [ABSTRACT FROM AUTHOR]

The K-harmonic means clustering algorithm (KHM) is a new clustering method used to group data such that the sum of the harmonic averages of the distances between each entity and all cluster centroids is minimized. Because it is less sensitive to initialization than K-means (KM), many researchers have recently been attracted to studying KHM. In this study, the proposed iSSO-KHM is based on an improved simplified swarm optimization (iSSO) and integrates a variable neighborhood search (VNS) for KHM clustering. As evidence of the utility of the proposed iSSO-KHM, we present extensive computational results on eight benchmark problems. From the computational results, the comparison appears to support the superiority of the proposed iSSO-KHM over previously developed algorithms for all experiments in the literature. [ABSTRACT FROM AUTHOR]

This paper considers a network of energy harvesting wireless nodes transmitting simultaneously in a Gaussian interference channel and investigates a distributed power allocation algorithm that maximizes the sum-rate. The power consumption model is based on a series of step functions that allow to model, among others, radio frequency circuits being on/off and the startup power consumption of the transmitter. After showing that the sum-rate maximization problem is nonsmooth, nonconvex, and NP-hard, the Iterative Smooth and Convex approximation Algorithm (ISCA) is proposed, which successively approximates the step functions by proper smooth functions to obtain a sequence of smooth nonconvex problems that can be solved by means of the successive convex approximation method. It is demonstrated that the ISCA distributedly converges to a stationary solution of the sum-rate maximization problem. For the particular case of point to point communications, the numerical results show that the ISCA is able to avoid bad stationary solutions, performing close to the globally optimal solution. The performance of the ISCA is also evaluated in the interference channel and with real solar energy harvesting data. [ABSTRACT FROM PUBLISHER]

Publication bias leads consumers of research to observe a selected sample of statistical estimates calculated by producers of research. We calculate critical values for statistical significance that could help to adjust after the fact for the distortions created by this selection effect, assuming that the only source of publication bias is file drawer bias. These adjusted critical values are easy to calculate and differ from unadjusted critical values by approximately 50%—rather than rejecting a null hypothesis when the t-ratio exceeds 2, the analysis suggests rejecting a null hypothesis when the t-ratio exceeds 3. Samples of published social science research indicate that on average, across research fields, approximately 30% of published t-statistics fall between the standard and adjusted cutoffs. [ABSTRACT FROM AUTHOR]

Objective: The study investigates the effect on cooperation in multiplayer games, when the population from which all individuals are drawn is structured—i.e. when a given individual is only competing with a small subset of the entire population. Method: To optimize the focus on multiplayer effects, a class of games were chosen for which the payoff depends nonlinearly on the number of cooperators—this ensures that the game cannot be represented as a sum of pair-wise interactions, and increases the likelihood of observing behaviour different from that seen in two-player games. The chosen class of games are named “threshold games”, and are defined by a threshold, M > 0, which describes the minimal number of cooperators in a given match required for all the participants to receive a benefit. The model was studied primarily through numerical simulations of large populations of individuals, each with interaction neighbourhoods described by various classes of networks. Results: When comparing the level of cooperation in a structured population to the mean-field model, we find that most types of structure lead to a decrease in cooperation. This is both interesting and novel, simply due to the generality and breadth of relevance of the model—it is likely that any model with similar payoff structure exhibits related behaviour. More importantly, we find that the details of the behaviour depends to a large extent on the size of the immediate neighbourhoods of the individuals, as dictated by the network structure. In effect, the players behave as if they are part of a much smaller, fully mixed, population, which we suggest an expression for. [ABSTRACT FROM AUTHOR]

Various statistical models involve a certain function, say f , like the mean regression as a function of a covariate, the hazard rate as a function of time, the spectral density of a time series as a function of frequency, or an intensity as a function of geographical position, etc. Such functions are often modelled parametrically, whether for frequentist or Bayesian uses, and under weak conditions there are so-called Bernshteĭn–von Mises theorems implying that these two approaches are large-sample equivalent. Results of this nature do not necessarily hold up in nonparametric and high-dimensional setups, however. The aim of the present paper is to exhibit a unified framework and methodology for both frequentist and Bayesian nonparametric analysis, involving priors that set f constant over windows, and where the number m of such windows grows with sample size n . Applications include nonparametric regression, maximum likelihood with nonparametrically varying parameter functions, hazard rates being functions of covariates, and nonparametric analysis of stationary time series. We work out conditions on the number and sizes of the windows under which Bernshteĭn–von Mises type theorems can be established, with the prior changing with sample size via the growing number of windows. These conditions entail e.g. that if m ∝ n α , then α ∈ ( 1 4 , 1 2 ) is required. Illustrations of the general methodology are given, including setups with nonparametric regression, hazard rate estimation, and inference about frequency spectra for stationary time series. [ABSTRACT FROM AUTHOR]

The stability of several density profiles constructed from a linear combination of step functions in a vertically orientated two-dimensional porous medium are considered. A quasi-steady-state approximation is made so that the initial stability of the system can be approximated. Using a similar approach to that of Tan and Homsy (Phys Fluids 29:3549-3556, ) a dispersion equation for each density profile is obtained analytically at time zero. Neutral stability curves are then obtained to allow the regions of the parameter space to be divided into stable and unstable regions. [ABSTRACT FROM AUTHOR]

New methods of approximation of step functions with an estimation of the error of the approximation are suggested. The suggested methods do not have any of the disadvantages of traditional approximations of step functions by means of Fourier series and can be used in problems of mathematical modeling of a wide range of processes and systems. [ABSTRACT FROM AUTHOR]

We establish sufficient conditions under which the harmonic measure distribution functions hn of a sequence of domains Dn converge pointwise to the distribution function h of the limiting domain D, at all points of continuity of h. In the case of a model example, we establish this convergence of the distribution functions. Here, the value of the function h(r) gives the harmonic measure of the part of the boundary of the domain that lies within distance r of a fixed basepoint in the domain, thus relating the geometry of the domain to the behaviour of Brownian motion in the domain. [ABSTRACT FROM AUTHOR]

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Copyright of Pflüger's Archiv Für Die Gesamte Physiologie Des Menschen Und Der Tiere is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)