One-parameter Model Research Articles

Monitoring Liquid-Liquid Mixtures Using Fractional Calculus and Image Analysis

A fractional-calculus-based model is used to analyze the data obtained from the image analysis of mixtures of olive and soybean oil, which were quantified with the RGB color system. The model consists in a linear fractional differential equation, containing one fractional derivative of order α and an additional term multiplied by a parameter k. Using a hybrid parameter estimation scheme (genetic algorithm and a simplex-based algorithm), the model parameters were estimated as k = 3.42 ± 0.12 and α = 1.196 ± 0.027, while a correlation coefficient value of 0.997 was obtained. For the sake of comparison, parameter α was set equal to 1 and an integer order model was also studied, resulting in a one-parameter model with k = 3.11 ± 0.28. Joint confidence regions are calculated for the fractional order model, showing that the derivative order is statistically different from 1. Finally, an independent validation sample of color component B equal to 96 obtained from a sample with olive oil mass fraction equal to 0.25 is used for prediction purposes. The fractional model predicted the color B value equal to 93.1 ± 6.6.

Inference in Ising models

The Ising spin glass is a one-parameter exponential family model for binary data with quadratic sufficient statistic. In this paper, we show that given a single realization from this model, the maximum pseudolikelihood estimate (MPLE) of the natural parameter is $\sqrt{a_{N}}$-consistent at a point whenever the log-partition function has order $a_{N}$ in a neighborhood of that point. This gives consistency rates of the MPLE for ferromagnetic Ising models on general weighted graphs in all regimes, extending the results of Chatterjee (Ann. Statist. 35 (2007) 1931–1946) where only $\sqrt{N}$-consistency of the MPLE was shown. It is also shown that consistent testing, and hence estimation, is impossible in the high temperature phase in ferromagnetic Ising models on a converging sequence of simple graphs, which include the Curie–Weiss model. In this regime, the sufficient statistic is distributed as a weighted sum of independent $\chi^{2}_{1}$ random variables, and the asymptotic power of the most powerful test is determined. We also illustrate applications of our results on synthetic and real-world network data.

Multiparameter models in the management of the development of territories, taking into account the influence of hydrometeorological factors

The article considers the geoinformation management of the territory as a way to manage the organizational and technical systems and territories distributed in space. The article describes the main factors for the development and implementation of management decisions, requirements for the territorial management system and the structure of knowledge and data. Mathematical one-parameter and multiparameter models of risk assessment of management decisions applied to the natural and climatic potential of the development of the territory were considered.

МАТЕМАТИЧНЕ МОДЕЛЮВАННЯ ДОЗВУКОВОГО ТУРБУЛЕНТНОГО ОБТІКАННЯ ПРОФІЛЮ NACA 0015, ЩО КОЛИВАЄТЬСЯ

Представлено результати розрахунків профілю NACA 0015, що коливається, для трьох режимів течії: слабкий відрив потоку, що відповідає середньому куту атаки 4°; розвинений відрив – 11° (докритичне обтікання профілю); масивний відрив – 15° (закритичне обтікання профілю). Для чисельного моделювання обтікання профілю, що коливається, застосовуються осереднені за Рейнольдсом нестаціонарні рівняння Нав'є-Стокса нестисливої рідини, замкнуті однопараметричною моделлю турбулентної в'язкості. Розроблений неявний скінчено-об'ємний чисельний алгоритм базується на методі штучної стисливості, що модифікований для розрахунку нестаціонарних задач. Аналізуються отримані поля завихренности, миттєві лінії течії, гістерезисні криві нестаціонарних аеродинамічних навантажень профілю для трьох характерних режимів обтікання. Розроблена методика дозволяє відтворювати структуру нестаціонарного відривного обтікання профілю, що коливається. Відмінності в аеродинамічних характеристиках стаціонарного профілю і профілю, що коливається, при одних і тих же кутах атаки добре узгоджуються з експериментальними даними. Порівняння результатів розрахунків обтікання профілю, що коливається з експериментальними даними і відомими розрахунками інших авторів показало перевагу моделі турбулентності SALSA в порівнянні з іншими моделями, що тестувались особливо при наявності масивного відриву потоку.

BAO extractor: bias and redshift space effects

We study a new procedure to measure the sound horizon scale via Baryonic Acoustic Oscillations (BAO). Instead of fitting the measured power spectrum (PS) to a theoretical model containing the cosmological informations and all the nonlinear effects, we define a procedure to project out (or to “extract”) the oscillating component from a given nonlinear PS. We show that the BAO scale extracted in this way is extremely robust and, moreover, can be reproduced by simple theoretical models at any redshift. By using N-body simulations, we discuss the effect of the nonlinear evolution of the matter field, of redshift space distortions and of scale-dependent halo bias, showing that all these effects can be reproduced with sub-percent accuracy. We give a one-parameter theoretical model based on a simple (IR) modification of 1-loop perturbation theory, which reproduces the BAO scale from measurements of halo clustering in redshift space at better than 0.1% level and does not need any external UV input, such as coefficients measured from N-body simulations.

Cross-cultural adaptation and construct validity of the Korean version of a physical activity measure for community-dwelling elderly.

[Purpose] This study aimed to cross-cultural adapt and validate the Korean version of an physical activity measure (K-PAM) for community-dwelling elderly. [Subjects and Methods] One hundred and thirty eight community-dwelling elderlies, 32 males and 106 female, participated in the study. All participants were asked to fill out a fifty-one item questionnaire measuring perceived difficulty in the activities of daily living (ADL) for the elderly. One-parameter model of item response theory (Rasch analysis) was applied to determine the construct validity and to inspect item-level psychometric properties of 51 ADL items of the K-PAM. [Results] Person separation reliability (analogous to Cronbach’s alpha) for internal consistency was ranging 0.93 to 0.94. A total of 16 items was misfit to the Rasch model. After misfit item deletion, 35 ADL items of the K-PAM were placed in an empirically meaningful hierarchy from easy to hard. The item-person map analysis delineated that the item difficulty was well matched for the elderlies with moderate and low ability except for high ceilings. [Conclusion] Cross-cultural adapted K-PAM was shown to be sufficient for establishing construct validity and stable psychometric properties confirmed by person separation reliability and fit statistics.

Beauty at a glance: The feeling of beauty and the amplitude of pleasure are independent of stimulus duration.

Over time, how does beauty develop and decay? Common sense suggests that beauty is intensely felt only after prolonged experience of the object. Here, we present one of various stimuli for a variable duration (1–30 s), measure the observers' pleasure over time, and, finally, ask whether they felt beauty. On each trial, participants (N = 21) either see an image that they had chosen as “movingly beautiful,” see an image with prerated valence, or suck a candy. During the stimulus and a further 60 s, participants rate pleasure continuously using a custom touchscreen web app, EmotionTracker.com. After each trial, participants judge whether they felt beauty. Across all stimulus kinds, durations, and beauty responses, the dynamic pleasure rating has a stereotypical time course that is well fit by a one-parameter model with a brief exponential onset (roughly 2.5 s), a sustained plateau during stimulus presentation, and a long exponential decay (roughly 70 s). Across conditions, only the plateau amplitude varies. Beauty and pleasure amplitude are nearly independent of stimulus duration. The final beauty rating is positively correlated with pleasure amplitude (r = 0.60), and nearly independent of duration (r = 0.10). Beauty's independence from duration is unlike Bentham's 18th-century notion of value (utility), which he supposed to depend on the product of pleasure amplitude and duration. Participants report having felt pleasure as strongly after a mere 1 s stimulus as after longer durations, up to 30 s. Thus, we find that amplitude of pleasure is independent of stimulus duration.

Measuring cancer caregiver health literacy: Validation of the Health Literacy of Caregivers Scale-Cancer (HLCS-C) in an Australian population.

Caregivers have been largely neglected in health literacy measurement. We assess the construct validity, and internal consistency of the Health Literacy of Caregivers Scale-Cancer (HLCS-C), and present a revised, psychometrically robust scale. Using data from 297 cancer caregivers (12.4% response rate) recruited from Melbourne, Australia between January-July 2014, confirmatory factor analysis (CFA) was conducted to evaluate the HLCS-C's proposed factor structure. Items were evaluated for: item difficulty, unidimensionality and overall item fit within their domain. Item-threshold-ordering was examined though one-parameter Item Response Theory models. Internal consistency was assessed using Raykov's reliability coefficient. CFA results identified 42 poorly performing/redundant items which were subsequently removed. A 10-factor model was fitted to 46 acceptable items with no correlated residuals or factor cross-loadings accepted. Adequate fit was revealed (χ2WLSMV =1463.807[df=944], p<.001, RMSEA=0.043, CFI=0.980, TLI=0.978, WRMR=1.00). Ten domains were identified: Proactivity and determination to seek information; Adequate information about cancer and cancer management; Supported by healthcare providers (HCP) to understand information; Social support; Cancer-related communication with the care recipient (CR); Understanding CR needs and preferences; Self-care; Understanding the healthcare system; Capacity to process health information; and Active engagement with HCP. Internal consistency was adequate across domains (0.78-0.92). The revised HLCS-C demonstrated good structural, convergent, and discriminant validity, and high internal consistency. The scale may be useful for the development and evaluation of caregiver interventions.

Modelling of air flow supply in a room at variable regime by using both K - E and spalart – allmaras turbulent model

Abstract The abstract is to The article is devoted to the decision of actual task of air distribution efficiency increasing with the help of swirl and spread air jets to provide normative parameters of air in the production apartments. The mathematical model of air supply with swirl and spread air jets in that type of apartments is improved. It is shown that for reachin of air distribution maximal efficiency it is necessary to supply air by air jets, that intensively extinct before entering into a working area. Simulation of air flow performed with the help of CFD FLUENT (Ansys FLUENT). Сalculations of the equation by using one-parameter model of turbulence Spalart-Allmaras are presented. The graphical and the analytical dependences on the basis of the conducted experimental researches, which can be used in subsequent engineering calculations, are shown out. Dynamic parameters of air flow that is created due to swirl and spread air jets at their leakage at variable regime and creation of dynamic microclimate in a room has been determined. Results of experimental investigations of air supply into the room by air distribution device which creates swirl air jets for creation more intensive turbulization air flow in the room are presented. Obtained results of these investigations give possibility to realize engineer calculations of air distribution with swirl air jets. The results of theoretical researches of favourable influence of dynamic microclimate to the man are presented. When using dynamic microclimate, it’s possible to decrease conditioning and ventilation system expenses. Human organism reacts favourably on short lasting deviations from the rationed parameters of air environment.

Conditional fiducial models

The fiducial is not unique in general, but we prove that in a restricted class of models it is uniquely determined by the sampling distribution of the data. It depends in particular not on the choice of a data generating model. The arguments lead to a generalization of the classical formula found by Fisher (1930). The restricted class includes cases with discrete distributions, the case of the shape parameter in the Gamma distribution, and also the case of the correlation coefficient in a bivariate Gaussian model. One of the examples can also be used in a pedagogical context to demonstrate possible difficulties with likelihood-, Bayesian-, and bootstrap-inference. Examples that demonstrate non-uniqueness are also presented. It is explained that they can be seen as cases with restrictions on the parameter space. Motivated by this the concept of a conditional fiducial model is introduced. This class of models includes the common case of iid samples from a one-parameter model investigated by Hannig (2013), the structural group models investigated by Fraser (1968), and also certain models discussed by Fisher (1973) in his final writing on the subject.

Method for Describing Fatigue Processes in Structural Materials

The article studies one of the methods for phenomenological description of fatigue processes in structurally-inhomogeneous structural materials. The initial statement about the interrelationship between the static and cyclic material properties is investigated using the complete stress-strain curves or diagrams method (CSSD). Based on the analysis of the mathematic modeling results, the interrelationship is predicted to exist between the highly-localized fatigue process in a structurally-inhomogeneous material and the degradation of a static CSSD for a macroscopic specimen. It is noted that the conditions under which the specimen fails in a testing machine are similar to the ones for the material in a construction. Then the results are given for the direct experimental testing of the model predictions, illustrated with the examples of cyclic degradation of several structural materials. The tests on multiple-cycle fatigued specimens reveal degradation of several mechanical properties. The justification for the selection of the available plasticity of a material as a parameter representative of the fatigue process is given. The authors describe a few examples of building one-parameter cyclic degradation models for steels and some prospects of using the complete strain-stress diagrams for various purposes.

Bayes Factor Covariance Testing in Item Response Models.

Two marginal one-parameter item response theory models are introduced, by integrating out the latent variable or random item parameter. It is shown that both marginal response models are multivariate (probit) models with a compound symmetry covariance structure. Several common hypotheses concerning the underlying covariance structure are evaluated using (fractional) Bayes factor tests. The support for a unidimensional factor (i.e., assumption of local independence) and differential item functioning are evaluated by testing the covariance components. The posterior distribution of common covariance components is obtained in closed form by transforming latent responses with an orthogonal (Helmert) matrix. This posterior distribution is defined as a shifted-inverse-gamma, thereby introducing a default prior and a balanced prior distribution. Based on that, an MCMC algorithm is described to estimate all model parameters and to compute (fractional) Bayes factor tests. Simulation studies are used to show that the (fractional) Bayes factor tests have good properties for testing the underlying covariance structure of binary response data. The method is illustrated with two real data studies.

Modelling the evolution of transcription factor binding preferences in complex eukaryotes

Transcription factors (TFs) exert their regulatory action by binding to DNA with specific sequence preferences. However, different TFs can partially share their binding sequences due to their common evolutionary origin. This “redundancy” of binding defines a way of organizing TFs in “motif families” by grouping TFs with similar binding preferences. Since these ultimately define the TF target genes, the motif family organization entails information about the structure of transcriptional regulation as it has been shaped by evolution. Focusing on the human TF repertoire, we show that a one-parameter evolutionary model of the Birth-Death-Innovation type can explain the TF empirical repartition in motif families, and allows to highlight the relevant evolutionary forces at the origin of this organization. Moreover, the model allows to pinpoint few deviations from the neutral scenario it assumes: three over-expanded families (including HOX and FOX genes), a set of “singleton” TFs for which duplication seems to be selected against, and a higher-than-average rate of diversification of the binding preferences of TFs with a Zinc Finger DNA binding domain. Finally, a comparison of the TF motif family organization in different eukaryotic species suggests an increase of redundancy of binding with organism complexity.

Contests with group size uncertainty: Experimental evidence

In many contest situations, the number of participants is not observable at the time of investment. We design a laboratory experiment to study individual behavior in Tullock (lottery) contests with group size uncertainty. There is a fixed pool of n potential players, each with independent probability q∈(0,1] of participating. We independently manipulate each of the parameters and test the implied comparative statics predictions. Our results provide considerable support for the theory, both in terms of comparative statics and point predictions. Most surprisingly, we find no evidence of overbidding in treatments where there is a nontrivial probability that group size is one. This stands in stark contrast to the robust overbidding observed in experimental contests with deterministic group size. We propose a one-parameter model that incorporates nonlinear probability weighting and a modified version of joy of winning, which we call Constant Winning Aspirations (CWA), and show that it neatly organizes all of our results.

Identification of impacts of climate change and direct human activities on streamflow in Weihe River Basin in Northwest China

Climate change and human activities make major influences on hydrology, which are known to have important impacts on streamflow variation. Therefore, it is critically important to identify how climate change and human activities will impact streamflow variation. Thus, the goal of this study is to identify the impacts of climate change and direct human activities on annual streamflow at four hydrologic stations in the Weihe River basin of China, with the estimation of evaporation based on the Budyko hypothesis. The Mann-Kendall test was employed to detect the break points of the four stations. According to the occurrence time of break points, the data series were divided into two periods: pre-change period (1960-1984) and post-change (1985-2010) period. The parameter of one-parameter Budyko-type model was calibrated with observed data during the pre-change period, with the R2 values ranged from 0.95 to 0.97 and the NSE values ranged from 0.80 to 0.94, and the high R2 and Nash-Sutcliffe Efficiency coefficient shows the model has good performance. The contribution ratios of climate change impacts on decreasing streamflow were 37%, 23%, 57% and 43%, and those of the impacts of direct human activities were 63%, 77%, 43% and 57% for the Linjiacun, Xianyang, Lintong and Huaxian station, respectively. Both the climate change and direct human activities have positive impacts on streamflow decrease at all of the four stations, and the direct human activities are the main factor causing the decrease of annual streamflow. Keywords: streamflow, climate change; human activities; evaporation, hydrological cycle, watershed, Budyko hypothesis, Weihe River basin DOI: 10.25165/j.ijabe.20171004.2313 Citation: Fan J J, Huang Q, Liu D F. Identification of impacts of climate change and direct human activities on streamflow in Weihe River Basin in Northwest China. Int J Agric & Biol Eng, 2017; 10(4): 119–129.

Physical and cognitive effort discounting across different reward magnitudes: Tests of discounting models.

The effort required to obtain a rewarding outcome is an important factor in decision-making. Describing the reward devaluation by increasing effort intensity is substantial to understanding human preferences, because every action and choice that we make is in itself effortful. To investigate how reward valuation is affected by physical and cognitive effort, we compared mathematical discounting functions derived from research on discounting. Seven discounting models were tested across three different reward magnitudes. To test the models, data were collected from a total of 114 participants recruited from the general population. For one-parameter models (hyperbolic, exponential, and parabolic), the data were explained best by the exponential model as given by a percentage of explained variance. However, after introducing an additional parameter, data obtained in the cognitive and physical effort conditions were best described by the power function model. Further analysis, using the second order Akaike and Bayesian Information Criteria, which account for model complexity, allowed us to identify the best model among all tested. We found that the power function best described the data, which corresponds to conventional analyses based on the R2 measure. This supports the conclusion that the function best describing reward devaluation by physical and cognitive effort is a concave one and is different from those that describe delay or probability discounting. In addition, consistent magnitude effects were observed that correspond to those in delay discounting research.

Accuracy of Demographic Inferences from the Site Frequency Spectrum: The Case of the Yoruba Population

Some methods for demographic inference based on the observed genetic diversity of current populations rely on the use of summary statistics such as the Site Frequency Spectrum (SFS). Demographic models can be either model-constrained with numerous parameters, such as growth rates, timing of demographic events, and migration rates, or model-flexible, with an unbounded collection of piecewise constant sizes. It is still debated whether demographic histories can be accurately inferred based on the SFS. Here, we illustrate this theoretical issue on an example of demographic inference for an African population. The SFS of the Yoruba population (data from the 1000 Genomes Project) is fit to a simple model of population growth described with a single parameter (e.g., founding time). We infer a time to the most recent common ancestor of 1.7million years (MY) for this population. However, we show that the Yoruba SFS is not informative enough to discriminate between several different models of growth. We also show that for such simple demographies, the fit of one-parameter models outperforms the stairway plot, a recently developed model-flexible method. The use of this method on simulated data suggests that it is biased by the noise intrinsically present in the data.

Modeling feedback control of unstable separatrix location in beam-driven field-reversed configurations

We present a linear, one-parameter model for rigid displacement of a toroidally symmetric plasma. When the feedback control is feasible, plasma inertia can be neglected, and the instability growth rate is proportional to wall resistivity. We benchmark the linear model against non-linear, hybrid simulations of an axially unstable, beam-driven field-reversed configuration to fix the free parameter of the model. The resulting parameter-free model is validated using linear and non-linear closed-loop simulations with active feedback control by voltage-controlled coils. In closed loop simulations, the predictions of the parameter-free linear model agree satisfactory with the non-linear results. Implications for the feedback control of the positional instability in experiments are discussed. The presented model has been used to guide the design of the feedback control hardware in the C-2W experiment.

Exact and Approximate Statistical Inference for Nonlinear Regression and the Estimating Equation Approach.

The exact density distribution of the nonlinear least squares estimator in the one-parameter regression model is derived in closed form and expressed through the cumulative distribution function of the standard normal variable. Several proposals to generalize this result are discussed. The exact density is extended to the estimating equation (EE) approach and the nonlinear regression with an arbitrary number of linear parameters and one intrinsically nonlinear parameter. For a very special nonlinear regression model, the derived density coincides with the distribution of the ratio of two normally distributed random variables previously obtained by Fieller (1932), unlike other approximations previously suggested by other authors. Approximations to the density of the EE estimators are discussed in the multivariate case. Numerical complications associated with the nonlinear least squares are illustrated, such as nonexistence and/or multiple solutions, as major factors contributing to poor density approximation. The nonlinear Markov-Gauss theorem is formulated based on the near exact EE density approximation.

Assuming measurement invariance of background indicators in international comparative educational achievement studies: a challenge for the interpretation of achievement differences

BackgroundLarge-scale cross-national studies designed to measure student achievement use different social, cultural, economic and other background variables to explain observed differences in that achievement. Prior to their inclusion into a prediction model, these variables are commonly scaled into latent background indices. To allow cross-national comparisons of the latent indices, measurement invariance is assumed. However, it is unclear whether the assumption of measurement invariance has some influence on the results of the prediction model, thus challenging the reliability and validity of cross-national comparisons of predicted results.MethodsTo establish the effect size attributed to different degrees of measurement invariance, we rescaled the ‘home resource for learning index’ (HRL) for the 37 countries (n=166,709 students) that participated in the IEA’s combined ‘Progress in International Reading Literacy Study’ (PIRLS) and ‘Trends in International Mathematics and Science Study’ (TIMSS) assessments of 2011. We used (a) two different measurement models [one-parameter model (1PL) and two-parameter model (2PL)] with (b) two different degrees of measurement invariance, resulting in four different models. We introduced the different HRL indices as predictors in a generalized linear mixed model (GLMM) with mathematics achievement as the dependent variable. We then compared three outcomes across countries and by scaling model: (1) the differing fit-values of the measurement models, (2) the estimated discrimination parameters, and (3) the estimated regression coefficients.ResultsThe least restrictive measurement model fitted the data best, and the degree of assumed measurement invariance of the HRL indices influenced the random effects of the GLMM in all but one country. For one-third of the countries, the fixed effects of the GLMM also related to the degree of assumed measurement invariance.ConclusionThe results support the use of country-specific measurement models for scaling the HRL index. In general, equating procedures could be used for cross-national comparisons of the latent indices when country-specific measurement models are fitted. Cross-national comparisons of the coefficients of the GLMM should take into account the applied measurement model for scaling the HRL indices. This process could be achieved by, for example, adjusting the standard errors of the coefficients.