Mixture Models (Mathematics)

The objective of this work is to automatically recognize faces from video sequences in a realistic, unconstrained setup in which illumination conditions are extreme and greatly changing, viewpoint and user motion pattern have a wide variability, and video input is of low quality. At the centre of focus are face appearance manifolds: this thesis presents a significant advance of their understanding and application in the sphere of face recognition. The two main contributions are the Generic Shape-Illumination Manifold recognition algorithm and the Anisotropic Manifold Space clustering.

The Generic Shape-Illumination Manifold algorithm shows how video sequences of unconstrained head motion can be reliably compared in the presence of greatly changing imaging conditions. Our approach consists of combining a priori domain-specific knowledge in the form of a photometric model of image formation, with a statistical model of generic face appearance variation. One of the key ideas is the reillumination algorithm which takes two sequences of faces and produces a third, synthetic one, that contains the same poses as the first in the illumination of the second.

The Anisotropic Manifold Space clustering algorithm is proposed to automatically determine the cast of a feature-length film, without any dataset-specific training information. The method is based on modelling coherence of dissimilarities between appearance manifolds: it is shown how inter- and intra-personal similarities can be exploited by mapping each manifold into a single point in the manifold space. This concept allows for a useful interpretation of classical clustering approaches, which highlights their limitations. A superior method is proposed that uses a mixture-based generative model to hierarchically grow class boundaries corresponding to different individuals.

The Generic Shape-Illumination Manifold is evaluated on a large data corpus acquired in real-world conditions and its performance is shown to greatly exceed that of state-of-the-art methods in the literature and the best performing commercial software. Empirical evaluation of the Anisotropic Manifold Space clustering on a popular situation comedy is also described with excellent preliminary results.

Crowding refers to the inability to recognize objects in clutter, setting a fundamental limit on various perceptual tasks such as reading and facial recognition. While prevailing models suggest that crowding is a unitary phenomenon occurring at an early level of processing, recent studies have shown that crowding might also occur at higher levels of representation. Here we investigated whether local and global crowding interference co-occurs within the same display. To do so, we tested the distinctive contribution of local flanker features and global configurations of the flankers on the pattern of crowding errors. Observers (n = 27) estimated the orientation of a target when presented alone or surrounded by flankers. Flankers were grouped into a global configuration, forming
an illusory rectangle when aligned or a rectangular configuration when misaligned. We analyzed the error distributions by fitting probabilistic mixture models. Results showed that participants often misreported the orientation of a flanker instead of that of the target. Interestingly, in some
trials the orientation of the global configuration was misreported. These results suggest that crowding occurs simultaneously across multiple levels of visual processing and crucially depends on the spatial
configuration of the stimulus. Our results pose a challenge to models of crowding with an early single pooling stage and might be better explained by models which incorporate the possibility of multilevel crowding and account for complex target-flanker interactions.

"Ceramic Artifacts" presents an analysis of 15 incipient plain ware sherds recovered from late Cienega phase (ca. 400 B.C. - A.D. 50) deposits at the Santa Cruz Bend and Coffee Camp sites and 1,306 sherds (83 rim sherds and reconstructible vessels) from Agua Caliente phase (ca. A.D. 50 - 500) deposits at the Square Hearth and Stone Pipe sites. The analyses utilize a behavioral approach emphasizing material provenance, manufacture, use, re-use, and discard attributes. Economic issues related to vessel function, especially that of the Agua Caliente phase seed jars, or tecomates, are reviewed, and an argument that Agua Caliente phase potters practiced an expedient manufacturing technology is developed.

"A Petrographic Approach to Sand-Tempered Pottery Provenance Studies: Examples from Two Hohokam Local Systems" summarizes methods developed by the authors to model sand temper resource compositions in Arizona's Tucson and Tonto basins and major findings regarding the concentration of production and spatial distribution of sand-tempered Hohokam pottery in those basins. The petrofacies approach to provenance determination and ethnographic/ethnoarchaeological data used to evaluate annual prehistoric ceramic ceramic production rates should prove useful in reconstructing pottery manufacturing and distributions systems elsewhere.

We expand the literature of volatility and Value-at-Risk forecasting of oil price returns by comparing the recently proposed Mixture Memory GARCH (MMGARCH) model to other discrete volatility models (GARCH, RiskMetrics, EGARCH, APARCH, FIGARCH, HYGARCH, and FIAPARCH). We incorporate an Expectation-Maximization algorithm for parameter estimation of the MMGARCH and find different structures in volatility level as well as shock persistence. MMGARCH is also able to cover asymmetric and long memory effects. Furthermore, a dissimilar memory structure in variance of WTI and Brent crude oil prices is observed which is supported by additional tests. Parameter estimation and comparison of the models reveal significant long memory and asymmetry in oil price returns. In regard of variance forecasting and Value-at-Risk prediction, it is shown that MMGARCH outperforms the aforementioned models due to its dynamic approach in varying the volatility level and memory of the process. We find MMGARCH superior for application in risk management as a result of its flexibility in adjusting to variance shifts and shocks.

In this thesis, we address several problems related to modelling complex systems. The difficulty of modelling complex systems lies partly in their topology and how they form rather complex networks. From this perspective, our interest in networks (graphs) is part of a broader current of research on complex systems.
Graphical models provide powerful tools to model and make the statistical inference regarding complex relationships among variables. In this context, Gaussian graphical models are commonly used, since inference in such models is often tractable. In Chapter 2, we introduce a novel Bayesian framework for Gaussian graphical model determination.
We carry out the posterior inference by using an efficient sampling scheme which is a trans-dimensional MCMC approach based on birth-death process. In particular, we construct an efficient search algorithm which explores the graph space to detect the underlying graph with high accuracy. We cover the theory and computational details of the proposed method. We then apply the method to large-scale real applications from mammary gene expression studies to show its empirical usefulness.

In many automatic face recognition applications, a set of a person's face images is available rather than a single image. In this paper, we describe a novel method for face recognition using image sets. We propose a flexible, semi-parametric model for learning probability densities confined to highly non-linear but intrinsically low-dimensional manifolds. The model leads to a statistical formulation of the recognition problem in terms of minimizing the divergence between densities estimated on these manifolds. The proposed method is evaluated on a large data set, acquired in realistic imaging conditions with severe illumination variation. Our algorithm is shown to match the best and outperform other state-of-the-art algorithms in the literature, achieving 94% recognition rate on average.

In recent years, Next-generation sequencing (NGS) experiments have become the most established method to measure gene expression. The resulting read count data matrix can be modelled using the Poisson or the negative binomial distributions, for which the equi-dispersion constraint does not hold. However, the low number of replicates for each gene makes direct estimate of parameters unreliable. To address this issue, many strategies have been developed with the leading objective of testing for differentially expressed genes between different biological conditions. An innovative approach consists of fitting a mixtures of negative binomial to overcome the trade-off between a common or a gene-specific dispersion. Estimates of the parameters can be obtained through the EM algorithm and test statistics are consistently derived. In our work we extended this method by introducing a novel likelihood ratio test (LRT) statistics. Therefore, via a wide simulation study we evaluated its performances with a particular focus on the distribution of empirical type-1 and type-2 errors. Results show that LRT is a very powerful test, whilst the nominal value of type-1 error is not always reached. Under several scenarios, the most commonly used test statistics are compared with LRT also in terms of empirical cumulative distribution function (ECDF) of the null genes, receiver operating characteristic curve (ROC) and area under the curve (AUC).

Background: The gamma-Gompertz multiplicative frailty model is the most common parametric model applied to human mortality data at adult and old ages. The resulting life expectancy has been calculated so far only numerically. Objective: Properties of the gamma-Gompertz distribution have not been thoroughly studied. The focus of the paper is to shed light onto its first moment or, demographically speaking, characterize life expectancy resulting from a gamma-Gompertz force of mortality. The paper provides an exact formula for gamma-Gompertz life expectancy at birth and a simpler high-accuracy approximation that can be used in practice for computational convenience. In addition, the article compares actual (life-table) to model-based (gamma-Gompertz) life expectancy to assess on aggregate how many years of life expectancy are not captured (or overestimated) by the gamma-Gompertz mortality mechanism. Comments: A closed-form expression for gamma-Gomeprtz life expectancy at birth contains a special (the hypergeometric) function. It aids assessing the impact of gamma-Gompertz parameters on life expectancy values. The paper shows that a high-accuracy approximation can be constructed by assuming an integer value for the shape parameter of the gamma distribution. A historical comparison between model-based and actual life expectancy for Swedish females reveals a gap that is decreasing to around 2 years from 1950 onwards. Looking at remaining life expectancies at ages 30 and 50, we see this gap almost disappearing.

Being part of a delinquent group has been shown to facilitate the expression of an individual's own delinquent propensities. However, this facilitation effect has not been investigated from a developmental perspective within a population heterogeneity model. Using a semiparametric mixture model with data from the Montreal Longitudinal Experimental Study, this article addresses important issues in the developmental trends of membership to delinquent groups. We explore how the rate of violent behaviors follows delinquent peer group trajectories and investigate a differential facilitation effect of delinquent peers on violence across multiple developmental pathways. Results suggest that 25% of males followed a childhood or an adolescence delinquent group affiliation trajectory. These two groups account far most of the violent acts assessed during adolescence. In addition, the rate of violent behaviors follows these developmental trajectories. Controlling for these delinquent group trajectories, we also found that being involved in a delinquent group at any specific time during adolescence is associated with an increased rate of violent behaviors, and that leaving these groups results in a decrease in violent behaviors. This facilitation effect appears homogeneous over time and across developmental trajectories. Results are discussed from a social interactional perspective.

ABSTRACT Laminar and turbulent mixed convection heat transfer of water-Cu nanofluids in a rectangular shallow cavity was studied utilizing a two-phase mixture model. The upper movable lid of the cavity was at a lower temperature compared to the bottom wall. Simulations were performed for Grashof numbers of 105 (laminar flow) and 1010 (turbulent flow) for Richardson numbers from 0.03 to 30, and nanoparticle volume fractions of 0.00 to 0.04. The two-dimensional governing equations were discretized using a finite volume method. The effects of nanoparticle concentration, shear and buoyancy forces, and turbulence on hydraulics and thermal behavior of nanofluid flow were studied. The model predictions for very low solid volume fraction ( ) were found to be in good agreement with earlier numerical studies for a base fluid. It is shown that for a specific Grashof (Gr) and Richardson (Ri) numbers, increasing the volume fraction of nanoparticles enhances the convective heat transfer coefficient and consequently the Nusselt number (Nu) while an increase in the solid volume fraction had a negligible effect on the wall shear stress and the corresponding skin friction factor.

Word segmentation refers to the process of defining the word regions of a text line. It is a critical stage towards word and character recognition as well as word spotting and mainly concerns three basic stages, namely preprocessing, distance computation and gap classification. In this paper, we propose a novel word segmentation method which uses the Student’s-t distribution for the gap classification stage. The main advantage of the Student’s-t distribution concerns its robustness to the existence of outliers. In order to test the efficiency of the proposed method we used the four benchmarking datasets of the ICDAR/ICFHR Handwriting Segmentation Contests as well as a historical typewritten dataset of Greek polytonic text. It is observed that the use of mixtures of Student’s-t distributions for word segmentation outperforms other gap classification methods in terms of Recognition Accuracy and F-Measure. Also, in terms of all examined benchmarks, the Student's-t is shown to produce a perfect segmentation result in significantly more cases than the state-of-the-art Gaussian mixture model.

Geographic profiling (GP) was originally developed as an analytical tool in criminology, where it uses the spatial locations of linked crimes (for example murder, rape or arson) to identify areas that are most likely to include the offender's residence. The technique has been extremely successful in this field and is now widely used by police forces and investigative agencies around the world. More recently, the same method has been applied to biological data, notably in spatial epidemiology, where it uses the locations of disease cases to identify infection sources: the identification of these sources is critical to control efforts of diseases such as malaria, since targeted intervention is more efficient and cost-effective than untargeted intervention.
Here, we solve the problem of identifying multiple sources, even when the number of sources is unknown – a requirement for many biological studies. We present a new, rigorous mathematical and computational method and show why previous Bayesian methods were often outperformed by the empirically developed criminal geographic targeting (CGT) algorithm used in criminology.
We use simulations and real-world examples to compare our model to both the CGT algorithm and to an existing Bayesian model. We demonstrate that our method combines the advantages of both previous methods, particularly in cases featuring large data sets and multiple sources.
Our approach provides an increase in search efficiency over other methods and is likely to lead to improved targeting of interventions and more efficient use of resources. We suggest that the Dirichlet process mixture (DPM) model provides a useful and practical tool for conservation biologists and epidemiologists that can be used to inform management decisions and public health policy.

Calls to list polar bears as a threatened species under the United States Endangered Species Act are based on forecasts of substantial long-term declines in their population. Nine government reports were written to help US Fish and Wildlife Service managers decide whether or not to list polar bears as a threatened species. We assessed these reports based on evidence-based (scientific) forecasting principles. None of the reports referred to sources of scientific forecasting methodology. Of the nine, Amstrup et al. [Amstrup, S. C., B. G. Marcot, D. C. Douglas. 2007. Forecasting the rangewide status of polar bears at selected times in the 21st century. Administrative Report, USGS Alaska Science Center, Anchorage, AK.] and Hunter et al. [Hunter, C. M., H. Caswell, M. C. Runge, S. C. Amstrup, E. V. Regehr, I. Stirling. 2007. Polar bears in the Southern Beaufort Sea II: Demography and population growth in relation to sea ice conditions. Administrative Report, USGS Alaska Science Center,
Anchorage, AK.] were the most relevant to the listing decision, and we devoted our attention to them. Their forecasting procedures depended on a complex set of assumptions, including the erroneous assumption that general circulation models provide valid forecasts of summer sea ice in the regions that polar bears inhabit. Nevertheless, we audited their conditional forecasts of what would happen to the polar bear population assuming, as the authors did, that the extent of summer sea ice would decrease substantially during the coming decades. We found that Amstrup et al. properly applied 15 percent of relevant forecasting principles and Hunter et al. 10 percent. Averaging across the two papers, 46 percent of the principles were clearly contravened and 23 percent were apparently contravened. Consequently, their forecasts are unscientific and inconsequential to decision makers. We recommend that researchers apply all relevant principles properly when important public-policy decisions depend on their forecasts.

In formal, logico-semantic terms, the concept of an object, individual or thing is widely thought to be exhaustive. Whatever we may say or think – it is supposed – our thought or talk is always thought or talk of objects. Here, I briefly sketch out and defend a rival view: like that of a property, the concept of an object is best understood in terms of that which it excludes. Object-concepts correspond to count nouns; but count nouns are just one of two great categories of nouns, the other being that of non-count nouns. Both count nouns, and the concept of an object, are inseparable from reference and identity – but non-count nouns are not; and they are not a vehicle for thought or talk of objects in the first place.

New insights into phase separation in colloidal suspensions are provided via a new dynamical theory based on the Polydisperse Lattice-Gas model. The model gives a simplified description of polydisperse colloids, incorporating a hard-core repulsion combined with polydispersity in the strength of the attraction between neighbouring particles. Our mean-field equations describe the local concentration evolution for each of an arbitrary number of species, and for an arbitrary overall composition of the system. We focus on the predictions for the dynamics of colloidal gas-liquid phase separation after a quench into the coexistence region. The critical point and the relevant spinodal curves are determined analytically, with the latter depending only on three moments of the overall composition. The results for the early-time spinodal dynamics show qualitative changes as one crosses a 'quenched' spinodal that excludes fractionation and so allows only density fluctuations at fixed composition. This effect occurs for dense systems, in agreement with a conjecture by Warren that, at high density, fractionation should be generically slow because it requires inter-diffusion of particles. We verify this conclusion by showing that the observed qualitative changes disappear when direct particle-particle swaps are allowed in the dynamics. Finally, the rich behaviour beyond the spinodal regime is examined, where we find that the evaporation of gas bubbles with strongly fractionated interfaces causes long-lived composition heterogeneities in the liquid phase; we introduce a two-dimensional density histogram method that allows such effects to be easily visualized for an arbitrary number of particle species.

In small area estimation, generalized linear mixed models represent a useful tool for deriving best prediction of counts or proportions. For non-Gaussian responses, computing the Empirical Best Prediction and the corresponding analytic approximation to its Mean Squared Error requires the solution of (possibly) multiple integrals that, in general, do not admit closed form. Monte Carlo methods and parametric bootstrap are common choices, even though their computational burden represents a non trivial issue. We propose to estimate model parameters within a NonParametric Maximum Likelihood framework. In this context, the distribution of the area-specific random parameters is left unspecified and is approximated by a (discrete) nonparametric distribution. Given the discrete nature of the mixing distribution, we can avoid integral approximations and considerably reduce the computational effort in the case of non-Gaussian responses. Within this framework, we derive the Empirical Best Prediction for a (possibly non-linear) mixed effect and the analytic approximation of the corresponding MSE. The proposed approach is presented for a general response that belongs to the Exponential Family. Then, we focus on the relevant case of binary data. The method is tested via a large scale simulation study and applied to unit-level data from the 2012 Italian Labor Force Survey.

THERE ARE TWO GOALS IN THIS PROJECT. First, I looked at books of glazes with pictures of a series of test tiles showing a gradual change in colour as the quantity of iron or other metal oxide increases or decreases. I thought that it would be possible to develop a predictive model for estimating the entire range in colour with far fewer test tiles. I would like to offer my results to other potters. Second, it is difficult to devise projects that require integrating several sciences. This project uses skills that should be familiar to people with a high school level algebra and chemistry class. On the other hand, the entire project could also be expanded to explore issues in statistics and chemistry at the college level. This is the first step, made possible with the help of Sam Sheller and his students in the 2003 ceramics class at Smithville High School in Ohio, USA.
Science is about observing, experimenting,

A longitudinal study with a nested preventive intervention was used to test five hypotheses generated from developmental theories of antisocial behavior. The longitudinal study followed 909 boys from their kindergarten year up to 17 years of age. The randomized multimodal preventive intervention targeted a subsample of boys who were rated disruptive by their kindergarten teacher. Semiparametric analyses of developmental trajectories for self-reported physical aggression, vandalism, and theft identified more types of trajectories than expected from recent theoretical models. Also, these trajectories did not confirm theoretical models, which suggest a general increase of antisocial behavior during adolescence. The majority of boys were on either a low-level antisocial behavior trajectory or a declining trajectory. Less than 6% appeared to follow a trajectory of chronic antisocial behavior. Comparisons between disruptive and nondisruptive kindergarten boys confirmed the hypothesis that disruptive preschool children are at higher risk of following trajectories of frequent antisocial behavior. Comparisons between treated and untreated disruptive boys confirmed that an intensive preventive intervention between 7 and 9 years of age, which included parent training and social skills training, could change the long-term developmental trajectories of physical aggression, vandalism, and theft for disruptive kindergarten boys in low socioeconomic areas. The results suggest that trajectories of violent behavior can be deflected by interventions that do not specifically target the physiological deficits that are often hypothesized to be a causal factor. The value of longitudinal-experimental studies from early childhood onward is discussed.

Lumbar intervertebral disc (IVD) degeneration is the leading cause of lower back pain. While lumbar IVDs have low cellularity and limited capacity of regeneration, they bear high mechanical loads. Accelerated disc degeneration may happen because of undue cell stimulation, and cell nutrition also seems to be particularly infl uent in the disc. Cell nutrition depends on exchange of oxygen, glucose, and lactate between the periphery and the various regions of the IVD, which in turn depends on mechanical deformations. The mechanical regulation of disc cell nutrition, known as indirect mechanotransduction, is diffi cult to study in vivo or in vitro . This review reports on an important alternative in the form of numerical methods, which are based on the ability of poromechanical models to be coupled to solute transport-reaction models. Models need to address intricate nonlinear and time-dependent phenomena, but have allowed for important mechanisms to be proposed, complementing current knowledge gained from in vivo or in vitro observations.

TIP curves are cumulative poverty gap curves used for representing the three different aspects of poverty: incidence, intensity and inequality. The paper provides Bayesian inference for TIP curves, linking their expression to a parametric representation of the income distribution using a mixture of lognormal densities. We treat specifically the question of zero-inflated income data and survey weights, which are two important issues in survey analysis. The advantage of the Bayesian approach is that it takes into account all the information contained in the sample and that it provides small sample confidence intervals and tests for TIP dominance. We apply our methodology to evaluate the evolution of child poverty in Germany after 2002, providing thus an update the portrait of child poverty in Germany given in Corak et al. (2008).

The article aims at describing in a unified framework all plateau-generating random effects models in terms of i) plausible distributions for the hazard (baseline mortality) and the random effect (unobserved heterogeneity, frailty), as well as ii) impact of frailty on the baseline hazard. Mortality plateaus result from multiplicative (proportional) and additive hazards, but not from accelerated failure time models. Frailty can have any distribution with regularly-varying-at- 0 density and the distribution of frailty among survivors to each subsequent age converges to a gamma. In a multiplicative setting the baseline cumulative hazard can be represented as the inverse of the negative logarithm of any completely monotone function. If the plateau is reached, the only meaningful solution at the plateau is provided by the gamma-Gompertz model.

Aims/Objectives: Effective and efficient heart disease prediction via nonparametric mixture regression models. Data Source: Data used in this paper is from the UCI database of the Cleveland Clinic Foundation for heart disease. The original data source contains 76 raw attributes with 303 observations each. For the purpose of this paper only 14 attributes were used as explained in section 4. Methodology: Cluster analysis was applied via mixture models in the form of Nonparametric Density-based models. The clusters were identified using a graph theory based technique. Voronoi diagrams were used and and their distributions were estimated nonparametrically through a mixture model with Gaussian kernels. The optimal number of clusters and components of the identified clusters were determined, analysed and diagnosed using a density based silhouette information criteria. All the data analysis and model diagnosis were performed in R using the PdfCluster package. Results: Different number of components resulted in different number of clusters when nonparametric mixture are used on heart disease. However, the optimal number of clusters under heart disease risks were found to be represented by two clusters with two components using density based silhouette information criteria. These were both well separated and classified as indicated by lack of spurious clusters and high positive density based silhouette values (See Figs. 2 and 4). Their properties are given in Table 2. The result is irregardless of the flexible conditions which are assumptions free on: shape of the distribution, number of components and number of clusters. Conclusion: When nonparametric mixture models are used, individuals under risks of heart diseases can be diagnosed either under high or low risk depending on the dominant characteristics on a given individual. Those under high risk have attributes that makes them progress to heart diseases faster compared to those under low risk. Therefore by classifying individuals into these categories, medical personnel can quickly diagonise heart disease and efficiently identify characteristics associated with each category.

Self‐compacting concrete (SCC) was developed in 1988 and introduced by Professor H. Okamura to achieve durability of structures with low skilled laborers. The three properties of SCC that differentiates it from traditional concrete are passing ability, filling ability and segregation resistance. The present study highlights the developments concerning SCC in the period from 1995 to 2017. This information is important for researchers and professionals working in this area. SCC can be optimized to a larger extent to find the best alternative either by use of additives or tailor‐made mix design. Based on different principles and parameters, design methods can be categorized into six classes namely empirical design method, statistical factorial design method, strength‐based design method, rheology of paste method, particle packing method and Eco‐SCC mixture design method. To develop SCC with high quality a suitable method can be chosen depending upon the situation and application.

Recently, observed departures from the classical Gaussian mixture model in real datasets motivated the introduction of mixtures of skew t, and remarkably widened the application of model based clustering and classification to great many real datasets. Unfortunately, when data contamination occurs, classical inference for these models could be severely affected. In this paper we introduce robust estimation of mixtures of skew normal, to resist sparse outliers and even pointwise contamination that may arise in data collection. Hence, in each component, the skewed nature of the data is explicitly modeled, while any departure from it is dealt by the robust approach. Some applications on real data show the effectiveness of the proposal. Sommario Recentemente, a fronte di dataset reali multimodali con asimmetria e code pesanti, ` e stato introdotto il modello mistura di t asimmetriche, ampliando consi-derevolmente il campo di applicazione delle classiche misture di distribuzioni Gaussiane. La stima di questi modelli nonè però robusta rispetto a contaminazioni puntuali. In questo lavoro si introduce uno stimatore robusto per le misture di nor-mali asimmetriche, in grado di resistere a valori anomali e a contaminazione pun-tuale nella raccolta dei dati. La natura asimmetrica dei datì e esplicitamente model-lata in ciascuna componente, mentre la stima robusta consente di gestire ogni al

In this article, it is explored that the issue about applicability of the Mixture Model
analyses technique which can be used in the searches of education sciences. Therefore
in this search, for the semester of 2005-2006, the 643 individuals participated in
the Private Skill Examination of Physical and Sport Education Department, Education
Faculty of Yüzüncü Y›l University (YYU). During interview, information was taken
with regard to AOOBP, gender, occupation of father and mother, settlement and
high school branch from which they graduated. The search data has been gathered
by the structured - interview technique. During the interview, the questions about
the personal features of the participants were asked and the answers were recorded.
The effect level of the variables have indicated the personal features of the registered
participants who had the grade of OSS (Student Selection Examination) examination.
These effect levels have been solved by Mixture Model which belongs to
Latent Class family. This model is a new statistical method for education sciences
in Turkey. At the end of this search, 5 sub-classes have been identified and the variables
have influenced each identified class from different aspects and levels. Besides,
it was observed that the interaction of the variables has been an affective matter
in regard of different sides and level.

. I sent my manuscript  " Unitary symmetry of mixtures of hormones and the solution of the problem of terrorism" in  ACS Central Science,  (Manuscript ID oc-2018-00023c, Editor-in-Chief: Carolyn R. Bertozzi,  E-mail: bertozzi@centralscience.acs.org )

The answer so far I have not received.

The identification of a potential terrorist can be carried out in three ways.
The first method is aimed at the creation of explosive detectors and the corresponding sophisticated hardware, technical and personal support. Its main drawback is demonstrativeness. It remains only to hang a sign: "Terrorists with explosives are held here."
The second way is to analyze the communicative activity of a potential terrorist. The main drawback of this method is easily overcome - the methods of information encryption have already been invented. These methods do not allow you to open and decrypt information. And anyway, an early transition to new types of information transfer will make communicative activity sterile.
The main drawback of the first two methods is that the explosives ceased to be necessary for the commission of the terrorist act. A characteristic example of the last time is the driving of a car on pedestrians.
The third way is to identify the physical parameters of certain physiological substances of a potential terrorist and to create such non-invasive methods for scanning the values of these physical parameters, which in a very short period of time would reliably signal the preaggressive state of a person.
This method can be realized by analyzing the composition of human hormones in four physiological environments in NORM and in PREPOTOLOGY.
His description is devoted to my research of recent years [1,2,3,4,5] and the article presented.
Keyword:  terrorism, hormone mixtures, hormonal passport, hormone bank, combinatorics, homology, unitary symmetry, conservation laws, chipping

Systematic approaches for the design of mixtures, based on a computer-aided mixture/blend design (CAMbD) framework, have the potential to deliver better products and processes. In most existing methodologies the number of mixture ingredients is fixed (usually a binary mixture) and the identity of at least one compound is chosen from a given set of candidate molecules. A novel CAM b D methodology is presented for formulating the general mixture design problem where the number , identity and composition of mixture constituents are optimized simultaneously. To this end, generalized disjunctive programming is integrated into the CAM b D framework to formulate the discrete choices. This generic methodology is applied to a case study to find an optimal solvent mixture that maximizes the solubility of ibuprofen. The best performance in this case study is obtained with a solvent mixture, showing the benefit of using mixtures instead of pure solvents to attain enhanced behavior.

Mixtures of factor analyzers are becoming more and more popular in the area of model based clustering of high-dimensional data. According to the likelihood approach in data modeling, it is well known that the unconstrained log-likelihood function may present spurious maxima and singularities and this is due to specific patterns of the estimated covariance structure, when their determinant approaches 0. To reduce such drawbacks, in this paper we introduce a procedure for the parameter estimation of mixtures of factor analyzers, which maximizes the likelihood function in a constrained parameter space. We then analyze and measure its performance, compared to the usual non-constrained approach, via some simulations and applications to real data sets.