Discrete Mixture Research Articles

Fluctuations of the Magnetization in the p-Spin Curie–Weiss Model

In this paper we study the fluctuations of the magnetization in the p-spin Curie–Weiss model, for $$p \geqslant 3$$ p ⩾ 3 . We provide a complete description of the asymptotic distribution of the magnetization in the p-spin Curie–Weiss model, complementing the well-known results in the 2-spin case. Our results unearth various new phase transitions, such as the existence of a certain ‘critical’ curve in the parameter space, where the limiting distribution of the magnetization is a discrete mixture, with local Gaussian fluctuations around each of the atoms. The number of atoms (mixture components) is either two or three depending on the sign of one of the parameters and the parity of p. Another interesting revelation is the existence of certain ‘special’ points in the parameter space where the magnetization converges to a non-Gaussian limiting distribution at rate $$N^{\frac{1}{4}}$$ N 1 4 .

Conscious perception can be both graded and discrete.

The attentional blink (AB) paradigm has been used to address an enduring debate about the nature of conscious perception: Does the temporary impairment in conscious perception of the second (T2) of two serially presented targets result from a probabilistic all-or-none loss of information, or does T2 transition into consciousness along a continuum of perceptual fidelity? To investigate this question, we presented noisy orientation patterns as targets embedded in a rapid serial sequence of nonoriented noise distractors, and evaluated perception of T2 orientation using a continuous report paradigm. Using discrete mixture models and variable resource models, we evaluated the effects of manipulating both perceptual and central demands on the precision of T2 responses and the estimated frequency of random guessing. When perceptual competition between targets was emphasized by their sharing of a common visual feature (i.e., orientation), the attentional blink was associated with degraded precision of T2 perception. By contrast, when the task required switching between different attended features across two visually distinct targets, T2 awareness was impaired in an all-or-none manner as evidenced by significant increases in guessing responses. Both statistical and model comparison analyses indicated that loss of target information can be graded or discrete, depending on whether perceptual or higher central stages are taxed by processing demands. Our findings provide new insights into the mechanisms underlying the attentional blink and help reconcile conflicting views regarding how information can be lost from awareness. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Heterogeneity in patterns of pain development after nerve injury in rats and the influence of sex

The genesis of neuropathic pain is complex, as sensory abnormalities may differ between patients with different or similar etiologies, suggesting mechanistic heterogeneity, a concept that is largely unexplored. Yet, data are usually grouped for analysis based on the assumption that they share the same underlying pathogenesis. Sex is a factor that may contribute to differences in pain responses. Neuropathic pain is more prevalent in female patients, but pre-clinical studies that can examine pain development in a controlled environment have typically failed to include female subjects. This study explored patterns of development of hyperalgesia-like behavior (HLB) induced by noxious mechanical stimulation in a neuropathic pain model (spared nerve injury, SNI) in both male and female rats, and autonomic dysfunction that is associated with chronic pain. HLB was analyzed across time, using both discrete mixture modeling and rules-based longitudinal clustering. Both methods identified similar groupings of hyperalgesia trajectories after SNI that were not evident when data were combined into groups by sex only. Within the same hyperalgesia development group, mixed models showed that development of HLB in females was delayed relative to males and reached a magnitude similar to or higher than males. The data also indicate that sympathetic tone (as indicated by heart rate variability) drops below pre-SNI level before or at the onset of development of HLB. This study classifies heterogeneity in individual development of HLB and identifies sexual dimorphism in the time course of development of neuropathic pain after nerve injury. Future studies addressing mechanisms underlying these differences could facilitate appropriate pain treatments.

Convex environmental contours

Environmental contours are widely used as a basis for e.g., ship design, especially in early design phases. The traditional approach to such contours is based on the well-known Rosenblatt transformation. Here we focus on convex contours estimated using Monte Carlo methods and establish a rigorous mathematical foundation for such contours. In the present paper we also present an improved simulation procedure based on importance sampling. In particular, we show how this procedure can be extended to cases with omission factors and where the joint distribution of the environmental variables is a discrete mixture. It is well-known that contours constructed using Monte Carlo simulation typically have certain irregularities. In particular, the sets bounded by the estimated contours appear to be convex. However, when the curves are investigated more closely, they include a large number of small loops. In the present paper we provide a precise condition for convexity, and propose a smoothing method which can be used to eliminate the loops. The methods are illustrated by a numerical example.

Dynamic Bayesian Network-based Surface Roughness Accuracy Grade Prediction in Turning

A hybrid DBN model - Discrete and gaussian mixture hidden markov model with the weighted evidence fusion strategy (DGMWEFS), based on Discrete hidden Markov model (DHMM), Mixture of Gaussians hidden Markov model (MoGHMM), and DS evidence theory, is developed for surface roughness accuracy grade prediction. By analyzing the influence of tool vibration on the surface topography, the singular spectrum with wavelet analysis is proposed to extract the fusion feature (Ec). The ρ comparison is developed to overcome defect of the traditional probability comparison. For the multiple outputs of DHMM and MoGHMM, the weighted evidence fusion strategy based on the DS evidence theory is proposed for final decisions. Experiment of turning the workpiece with multi-material and hardness scale shows that, compared with the DHMM (prediction accuracy 85%) and MoGHMM(prediction accuracy 78%), the DGMWEFS proposed estimates the surface roughness with higher accuracy (prediction accuracy 93%).Therefore, the monitoring strategy proposed can be better used for supervising accuracy grade, which can be readily integrated into a computer integrated manufacturing environment.

Trust in Hospital Physicians Among Patients With Substance Use Disorder Referred to an Addiction Consult Service: A Mixed-methods Study.

Trust is essential in patient-physician relationships. Hospitalized patients with substance use disorders (SUDs) often experience stigma and trauma in the hospital, which can impede trust. Little research has explored the role of hospital-based addictions care in creating trusting relationships with patients with SUDs. This study describes how trust in physicians changed among hospitalized people with SUDs who were seen by an interprofessional addiction medicine service. We analyzed data from hospitalized patients with SUD seen by an addiction consult service from 2015 to 2018. Participants completed surveys at baseline and 30 to 90 days after hospital discharge. Follow-up assessments included open-ended questions exploring participant experiences with hospitalization and the addiction consult service. We measured provider trust using the Wake Forest Trust scale. We modeled trust trajectories using discrete mixture modeling, and sampled qualitative interviews from those trust trajectories. Of 328 participants with SUD who had prior hospitalizations but had not previously been seen by an addiction consult service, 196 (59.8%) had both baseline and follow-up trust scores. We identified 3 groups of patients: Persistent-Low Trust, Increasing Trust, and Persistent-High Trust and 4 qualitative themes around in-hospital trust: humanizing care, demonstrating addiction expertise, reliability, and granting agency. Most participants retained or increased to high trust levels after hospitalization with an addiction consult service. Addiction consult services can create environments where healthcare providers build trust with, and humanize care for, hospitalized patients with SUD, and can also mitigate power struggles that hospitalized patients with SUD frequently experience.

Swiss family physicians and home visits: a 10-year retrospective analysis and typology based on billing data

In the context of an aging population, homecare visits by family physicians may contribute to maintaining older patients at home; however, home visits by family physicians have decreased in number in the last decade with the emergence of homecare-oriented healthcare services. We aimed to describe the diversity of activities and evolution over time of home visits by Swiss family physicians. This was a retrospective observational descriptive study. We used billing data collected by the cantonal trust centre for home visits made by family physicians of the canton of Vaud, Switzerland from 2006 to 2015. We separated billed items into specific categories, including the Tarmed catalogue (Swiss pricing system for medical services), laboratory catalogue, medications, medical material and vaccines. We compared billing patterns between emergency and routine visits. We used discrete mixture models to identify cluster classes of visits, and compare their characteristics. From 2006 to 2015, Vaud family physicians made 451,634 home visits for which they billed a median of 5 items per visit (range 2–95). Most home visits (65%, 293,713) were routine visits consisting of consultation time without additional investigation. We identified four cluster classes of visits comprising routine visits, routine visits with laboratory tests, emergency visits during the day and emergency visits during the night. Routine visits were the main cluster class while emergency home visits were rare. Family physician home visits are mainly routine visits without additional investigation. Thus, we wonder if a part of this activity could be delegated to other healthcare professionals.

Turbulent heat transfer and flow analysis of hybrid Al2O3-CuO/water nanofluid: An experiment and CFD simulation study

The utilization of nanofluid is found to considerably enhance the heat transfer performance. The present study fabricated a hybrid Al2O3-CuO/water nanofluid and investigated its turbulent thermal and flow performance in a circular tube. Experimentally, the heat transfer coefficient and pressure drop of hybrid nanofluids with mass concentrations ranging from 0.5% to 3% were measured under different Reynolds number. The effect of selection of thermophysical property models on performance was also concerned. Numerically, Computational Fluid Dynamics (CFD) simulations based on Discrete Phase Model (DPM), mixture and Eulerian multiphase model were conducted and compared. Results reveal a relative enhancement of 2–35% in heat transfer performance of hybrid nanofluid under various flow rates. In addition, the enhancement tends to increase with the increment of nanofluid concentration and decrement of flow rate. The pressure drop also shows different degrees of enlargement up to 12%. Different thermophysical property models lead to different Nusselt and Reynolds numbers, which results to various levels of deviations among different models. Generally, the thermal and flow characteristics adopting different models have similar trend but different magnitudes. By selecting certain models, the thermal performance factor has a value in the range of 1.01–1.29 and shows an increment with the increase of concentration and decrease of Reynolds number. The developed CFD models show desirable prediction accuracies for experimental heat transfer coefficient but seriously underestimate the pressure drop. Specifically, the Eulerian model exhibits the smallest deviation of 8.1% with the experimental heat transfer coefficient followed by the mixture model and DPM with the derivations of 10.2% and 12.5% respectively. The present study can help to understand the heat and flow behaviour of hybrid nanofluid in heat transfer devices.

Discrete mixture representations of parametric distribution families: Geometry and statistics

We investigate existence and properties of discrete mixture representations $P_{\theta }=\sum _{i\in E}w_{\theta }(i)\,Q_{i}$ for a given family $P_{\theta }$, $\theta \in \Theta $, of probability measures. The noncentral chi-squared distributions provide a classical example. We obtain existence results and results about geometric and statistical aspects of the problem, the latter including loss of Fisher information, Rao-Blackwellization, asymptotic efficiency and nonparametric maximum likelihood estimation of the mixing probabilities.

Dynamic Discrete Mixtures for High-Frequency Prices

The tick structure of the financial markets entails discreteness of stock price changes. Based on this empirical evidence, we develop a multivariate model for discrete price changes featuring a mechanism to account for the large share of zero returns at high frequency. We assume that the observed price changes are independent conditional on the realization of two hidden Markov chains determining the dynamics and the distribution of the multivariate time series at hand. We study the properties of the model, which is a dynamic mixture of zero-inflated Skellam distributions. We develop an expectation-maximization algorithm with closed-form M-step that allows us to estimate the model by maximum likelihood. In the empirical application, we study the joint distribution of the price changes of a number of assets traded on NYSE. Particular focus is dedicated to the assessment of the quality of univariate and multivariate density forecasts, and of the precision of the predictions of moments like volatility and correlations. Finally, we look at the predictability of price staleness and its determinants in relation to the trading activity on the financial markets.

Concomitant back and leg pain as predictors for trajectories of poor outcome after single level lumbar micro-decompression alone and with micro-discectomy: a study of 3,308 patients.

Lumbar decompression is the commonest spinal intervention. One in four patients have suboptimal outcome postoperatively, however no large studies identified clear poor outcome predictors. The aim of this study was to study low back pain (LBP) as a predictor of poor outcome following lumbar micro-decompression. Prospectively collected spinal registry data was analysed for patients who underwent primary, single-level, decompression with or without discectomy at single spinal centre (2011-2017). Based on the response to the Likert global outcome question, we had two outcome groups (good & poor). Percentage of achievement of minimum clinically relevant change (MCRC) for Core Outcome Measures Index (COMI) score, LBP and leg pain (LP) was examined. A two-step approach was adopted. First, COMI score, LBP and LP visual analogue scales (VAS) trajectories were modelled using a discrete mixture model. Second, multinomial logistic regression was used to determine the association between variables and trajectories. We included 3,308 patients with mean follow up (1.4 y). MCRC was achieved in COMI score in 63% of cases, 42% in LBP and 62% in LP. A three-group trajectory model was identified: large-improvement (LI) (n=980), moderate-improvement (MI) (n=1,364) and no-improvement (NI) (n=966) with 99.5%, 84.5% and 31.5% of patients presenting good outcome, respectively. Higher pre-operative LBP and COMI score and smoking were strongly associated with MI and NI. In addition, higher LP, post-operative surgical complications, previous surgery at same level, conservative treatment >6 months and anxiety/depression were associated with NI. This is the first large-scale study reporting preoperative LBP severity, spinal stenosis and smoking as predictors for poor functional outcomes post lumbar decompression with or without discectomy. This is very useful while counselling patients for surgery to meet realistic expectations.

Bedtime, body mass index and obesity risk in preschool-aged children.

Although sleep duration is a risk factor for obesity in young children, less is known about other aspects of sleep health, including bedtime, on obesity risk. To determine whether bedtime is associated with body mass index (BMI) z-score or obesity risk in children ages 2 to 5 years, and to determine if associations are independent of sleep duration. Cohort analyses were undertaken using three early life obesity prevention trials (POI, INSIGHT, Healthy Beginnings) and a longitudinal cohort study (HOME). Bedtime was assessed by questionnaire and BMI through clinical measurement between 2 and 5 years in 1642 children. Adjusted regression models examined whether BMI z-score and obesity (BMI z-score ≥ 2) were associated with bedtime, nocturnal sleep time and 24-hour sleep time. A discrete mixture model categorized children into bedtime trajectory groups across time points. Bedtime was inconsistently associated with BMI z-score. Although each hour later of bedtime was associated with greater odds of obesity at ages 3 (OR; 95% CI: 1.05; 1.003, 1.10) and 5 (1.35; 1.08, 1.69) years, odds were attenuated after adjustment for nocturnal or 24-hour sleep time. Longer nocturnal sleep duration at 2 years was associated with lower odds of obesity (OR 0.90; 0.86, 0.94), as was longer 24-hour sleep duration at 3 years in girls (0.70; 0.62, 0.78). BMI z-score and odds of obesity were not significantly different between 'early to bed' and 'late to bed' trajectory groups. Timing of bedtime appears inconsistently related to obesity in young children, possibly via influencing overall sleep duration.

On the nonparametric maximum likelihood estimator for Gaussian location mixture densities with application to Gaussian denoising

We study the nonparametric maximum likelihood estimator (NPMLE) for estimating Gaussian location mixture densities in $d$-dimensions from independent observations. Unlike usual likelihood-based methods for fitting mixtures, NPMLEs are based on convex optimization. We prove finite sample results on the Hellinger accuracy of every NPMLE. Our results imply, in particular, that every NPMLE achieves near parametric risk (up to logarithmic multiplicative factors) when the true density is a discrete Gaussian mixture without any prior information on the number of mixture components. NPMLEs can naturally be used to yield empirical Bayes estimates of the oracle Bayes estimator in the Gaussian denoising problem. We prove bounds for the accuracy of the empirical Bayes estimate as an approximation to the oracle Bayes estimator. Here our results imply that the empirical Bayes estimator performs at nearly the optimal level (up to logarithmic factors) for denoising in clustering situations without any prior knowledge of the number of clusters.

Unsupervised Bayesian Subpixel Mapping of Hyperspectral Imagery Based on Band-Weighted Discrete Spectral Mixture Model and Markov Random Field

Although accurate training and initialization information is difficult to acquire, unsupervised hyperspectral subpixel mapping (SPM) without relying on this predefined information is an insufficiently addressed research issue. This letter presents a novel Bayesian approach for unsupervised SPM of hyperspectral imagery (HSI) based on the Markov random field (MRF) and a band-weighted discrete spectral mixture model (BDSMM), with the following key characteristics. First, this is an unsupervised approach that allows adjustment of abundance and endmember information adaptively for less relying on algorithm initialization. Second, this approach consists of the BDSMM for accommodating the noise heterogeneity and the hidden label field of subpixels in HSI. The BDSMM also integrates SPM into the spectral mixture analysis and allows enhanced SPM by fully exploring the endmember-abundance patterns in HSI. Third, the MRF and BDSMM are integrated into a Bayesian framework to use both the spatial and spectral information efficiently, and an expectation-maximization (EM) approach is designed to solve the model by iteratively estimating the endmembers and the label field. Experiments on both simulated and real HSI demonstrate that the proposed algorithm can yield better performance than traditional methods.

Effect of particle size distribution on the packing of powder beds: A critical discussion relevant to additive manufacturing

Several additive manufacturing (AM) methods use powder feed materials. Selective laser sintering is an example of a versatile AM method, using feed material in powder form, capable of producing polymer and metallic parts. In the variations of this technique, a laser spot or an electron beam is used to locally sinter or melt a packed powder bed. After the completion of sintering on each layer, further powder is added on top of the existing bed so that the next layer may be joined. A major challenge in this method is controlling the porosity of the powder bed so that the final part has uniform and maximum density. Uniformity in the packing of bed from one layer to the other is important for optimizing the processing parameters. This review is focused on considering the packing characteristics of polydisperse hard particle beds and the determination of the expected density achievable for a given particle size and shape distribution. Models are presented for discrete mixtures as well as continuous distributions. The effect of the initial configuration of a particle bed on its ability to form a highly dense packing is also discussed. Blending of different particle sizes and shapes can be used to substantially increase the packing density, but can also lead to separation or segregation of the bed. Through appropriate control of the particle shape and use of wide distributions, packing densities close to 100 % can theoretically be achieved, but practicality and various effects that appear at small size scales prevent from achieving such high packing densities. Recent advancements have reduced the dependence of AM part quality on the density of the packed particle bed but the packing is still important for considerations such as thermal conductivity of the bed and absorption of laser power in the bed. Improved knowledge of packed bed characteristics can be helpful in developing AM methods for novel material systems.

A family of weighted distributions based on the mean inactivity time and cumulative past entropies

In this paper, a family of mean past weighted ($$\hbox {MPW}_{\alpha }$$) distributions of order $$\alpha $$ is introduced. For the construction of this family, the concepts of the mean inactivity time and cumulative $$\alpha $$-class past entropy are used. Distributional properties and stochastic comparisons with other known weighted distributions are given. Furthermore, an upper bound for the k-order moment of the random variables associated with the new family and a characterization result are obtained. Generalized discrete mixtures that involve $$\hbox {MPW}_{\alpha }$$ distributions and other weighted distributions are also explored.

Local Region Proposing for Frame-Based Vehicle Detection in Satellite Videos

Current new developments in remote sensing imagery enable satellites to capture videos from space. These satellite videos record the motion of vehicles over a vast territory, offering significant advantages in traffic monitoring systems over ground-based systems. However, detecting vehicles in satellite videos are challenged by the low spatial resolution and the low contrast in each video frame. The vehicles in these videos are small, and most of them are blurred into their background regions. While region proposals are often generated for efficient target detection, they have limited performance on satellite videos. To meet this challenge, we propose a Local Region Proposing approach (LRP) with three steps in this study. A video frame is segmented into semantic regions first and possible targets are then detected in these coarse scale regions. A discrete Histogram Mixture Model (HistMM) is proposed in the third step to narrow down the region proposals by quantifying their likelihoods towards the target category, where the training is conducted on positive samples only. Experiment results demonstrate that LRP generates region proposals with improved target recall rates. When a slim Fast-RCNN detector is applied, LRP achieves better detection performance over the state-of-the-art approaches tested.

Influences of victimization and comorbid conditions on substance use disorder outcomes in justice-involved youth: A discrete time survival mixture analysis.

To understand how exposure to victimization during adolescence and the presence of comorbid psychological conditions influence substance use treatment entry and substance use disorder diagnosis from 14 to 25 years old among serious juvenile offenders, this study included 1,354 serious juvenile offenders who were prospectively followed over 7 years. Growth mixture modeling was used to assess profiles of early victimization during adolescence (14-17 years). Discrete time survival mixture analysis was used to assess time to treatment entry and substance use disorder diagnosis. Posttraumatic stress disorder (PTSD) and major depressive disorder (MDD) were used as predictors of survival time. Mixture models revealed three profiles of victimization: sustained poly-victimization, moderate/decreasing victimization, and low victimization. Youth in the sustained poly-victimization class were more likely to enter treatment earlier and have a substance use diagnosis earlier than other classes. PTSD was a significant predictor of treatment entry for youth in the sustained poly-victimization class, and MDD was a significant predictor of substance use disorder diagnosis for youth in the moderate/decreasing victimization class. Therefore, substance use prevention programming targeted at youth experiencing poly-victimization in early adolescence-especially those who have PTSD or MDD-is needed.

Alternative modelling and inference methods for claim size distributions

AbstractThe upper tail of a claim size distribution of a property line of business is frequently modelled by Pareto distribution. However, the upper tail does not need to be Pareto distributed, extraordinary shapes are possible. Here, the opportunities for the modelling of loss distributions are extended. The basic idea is the adjustment of a base distribution for their tails. The (generalised) Pareto distribution is used as base distribution for different reasons. The upper tail is in the focus and can be modelled well for special cases by a discrete mixture of the base distribution with a combination of the base distribution with an adapting distribution via the product of their survival functions. A kind of smoothed step is realised in this way in the original line function between logarithmic loss and logarithmic exceedance probability. The lower tail can also be adjusted. The new approaches offer the opportunity for stochastic interpretation and are applied to observed losses. For parameter estimation, a modification of the minimum Anderson Darling distance method is used. A new test is suggested to exclude that the observed upper tail is better modelled by a simple Pareto distribution. Q-Q plots are applied, and secondary results are also discussed.

Development of an HPLC Method for Formic Acid Analysis through Peak Exclusion Approach

High Performance Liquid Chromatography (HPLC) is a chemical analysis technique that gives both the quantitative and qualitative analysis of liquid samples. A certain set of parameters, called HPLC method, are defined for analysis of every discrete mixture. Often literature is not available or specifically reported expensive HPLC apparatus is not available for every set of mixtures. Present study concentrated on analysis of formic acid from a mixture of methanol, formaldehyde and water. Formic acid is a basic carboxylic acid that has growing industrial and commercial uses, especially as a refrigerant. A C-18 column was utilized for the analysis by optimizing the parameters like dimensions of the stationary column, nature of mobile phase, flow rate of mobile phase and wavelength of the ultraviolet detector. Comprehendible and reproducible results for the analysis of formic acid were obtained on 25 cm long C-18 stationary column, by tuning the combined effect of water as mobile phase at a flow rate of 1 mL/min and by excluding the unnecessary peaks at 250 nm wavelength of ultraviolet detector, called peak exclusion approach. The calibration curve was found to be linear over the range of 1.25 % v/v formic acid solution in methanol up to 100 % pure formic acid. Limit of detection (LOD) and limit of quantitation (LOQ) were found to be 2.25 % and 6.83 %, respectively.