Linear Combinations Of Parameters Research Articles

Blood Count Scattergrams Are Fingerprints of Blood: Using AI to Inform Health Status

Introduction: Blood count analysers are routinely used to assess health status and for disease monitoring. The major analysers generate more than 300 red cell, leukocyte and platelet parameters. However, in clinical practice, only 10-20 are utilised; a greater number are reviewed by laboratories but some are merely for ensuring instrument stability and quality assurance. Although there are hundreds more measurable parameters available through extended analytical channels, these are not assessed due to the complexity of the numerical analysis and questions as to the clinical utility. However, these extended analytical parameters have potential to be used to generate real-time ‘3-Dimensional (3-D)‘ details of blood cells. Aim: In this study we assessed 312 parameters generated from 5,800 patient samples (of all ages and genders) at a tertiary care hospital (National Institute of Blood Disease, Karachi-Pakistan). These were anonymously outputted and processed by machine learning (ML). Method: The methodology of the present study was based on the waterfall model. The output data from a haematology analyser (Sysmex XN-1000, Kobe Japan) in CSV format, having a total 433 columns, was pre-processed to remove unnecessary features (such as date, analysis details, rack position, receiving time, alerts and others) using Pandas and Numpy libraries, and where required scaling was performed. Data labeling was conducted on conclusions reported on their respective confirmatory tests. The processed data (which included 312 features of the total 433 columns) was labeled (with 67 conclusions on their confirmatory tests). The extracted data was fed to the artificial intelligence Machine Learning models through Python modules and libraries for training, testing, and validation purposes. The web application was developed on modern Python framework (Flask) to automate and provide an option of ‘drag and drop’ the CSV file exported from analyser, we connected pre-processing (data engineering), Machine Learning, and Prediction view by set of different tools (majorly JavaScript libraries). This generated various metrics including accuracy, precision, recall and the mean of precision and recall (F1 score) in relation to the prediction (results) from the CSV file submitted to our system. For each forecast the entire precision report and prediction box were added an optional visualisation on our web panel. Results: Analysis of 1.8 million data points (312 parameters x 5,800 samples) presented promising predictive potential, as, on principal component analysis (PCA) pilot the total variance was remained 41.6% showing that a linear combination of parameters can explain much variability. On a heat map the clustering and visualisation advocated the predictive potential and signatory deviational trends (fingerprints) respectively of these 3-D blood cell features. Examples included separation of myeloid from lymphoid, chronic from acute, bacteria from viral, deficiency of iron from deficiency from vitamin B12 / Folic acid, and differentiation of haemoglobinopathies. The patterns of normal, immature and abnormal blood cells under the title of cell population data was well demonstrated from results of our machine learning models. Of note, we observed an accuracy of 85.6% along with 91.2% precision for one of the ML models used (Random Forest Classifier). Conclusion: The opportunities and challenges of such high dimensional cell population data derived from a complete blood count can provide a novel patient-specific haematological fingerprint. This extended deviational patterning (fingerprint) can provide interpretive diagnostic data with practical disease-specific patterns. This pilot study shows that complete blood count data driven machine learning applications has great potential to uncover disease-associated patterns which could be applied in practice. It also has capacity to provide baseline testing would could assist in sequential health monitoring and potentially the generation of personal reference ranges.

Building clone-consistent ecosystem models.

Many ecological studies employ general models that can feature an arbitrary number of populations. A critical requirement imposed on such models is clone consistency: If the individuals from two populations are indistinguishable, joining these populations into one shall not affect the outcome of the model. Otherwise a model produces different outcomes for the same scenario. Using functional analysis, we comprehensively characterize all clone-consistent models: We prove that they are necessarily composed from basic building blocks, namely linear combinations of parameters and abundances. These strong constraints enable a straightforward validation of model consistency. Although clone consistency can always be achieved with sufficient assumptions, we argue that it is important to explicitly name and consider the assumptions made: They may not be justified or limit the applicability of models and the generality of the results obtained with them. Moreover, our insights facilitate building new clone-consistent models, which we illustrate for a data-driven model of microbial communities. Finally, our insights point to new relevant forms of general models for theoretical ecology. Our framework thus provides a systematic way of comprehending ecological models, which can guide a wide range of studies.

Atypical Sound Perception in ASD Explained by Inter-Trial (In)consistency in EEG.

A relative indifference to the human voice is a characteristic of Autism Spectrum Disorder (ASD). Yet, studies of voice perception in ASD provided contradictory results: one study described an absence of preferential response to voices in ASD while another reported a larger activation to vocal sounds than environmental sounds, as seen in typically developed (TD) adults. In children with ASD, an absence of preferential response to vocal sounds was attributed to an atypical response to environmental sounds. To have a better understanding of these contradictions, we re-analyzed the data from sixteen children with ASD and sixteen age-matched TD children to evaluate both inter- and intra-subject variability. Intra-subject variability was estimated with a single-trial analysis of electroencephalographic data, through a measure of inter-trial consistency, which is the proportion of trials showing a positive activity in response to vocal and non-vocal sounds. Results demonstrate a larger inter-subject variability in response to non-vocal sounds, driven by a subset of children with ASD (7/16) who do not show the expected negative Tb peak in response to non-vocal sounds around 200 ms after the start of the stimulation due to a reduced inter-trial consistency. A logistic regression model with age and clinical parameters allowed demonstrating that not a single parameter discriminated the subgroups of ASD participants. Yet, the electrophysiologically-based groups differed on a linear combination of parameters. Children with ASD showing a reduced inter-trial consistency were younger and characterized by lower verbal developmental quotient and less attempt to communicate by voice. This data suggests that a lack of specialization for processing social signal may stem from an atypical processing of environmental sounds, linked to the development of general communication abilities. Discrepancy reported in the literature may arise from that heterogeneity and it may be inadequate to divide children with ASD based only on intellectual quotient or language abilities. This analysis could be a useful tool in providing complementary information for the functional diagnostic of ASD and evaluating verbal communication impairment.

Spline smoothing for experimental data under zero median of the noise

We propose an algorithm for computing parameter estimates for a smoothing cubic spline that minimize the estimated expectation of losses. Instead of the usual assumption that the noise is centered we use an assumption which is more realistic for many practical smoothing problems, namely that it is zero median. The problem setting is augmented by prior deterministic information in the form of constraints on linear combinations of parameters of spline functions. We obtain explicit representations of such estimates and give their qualitative interpretation. Based on the results of a numerical experiment, we establish a high degree of robustness of the solutions to the presence of outliers in the measurements, including same sign outliers, and the possibility to fairly reliably determine the actual accuracy of the resulting estimates of spline parameters by the attained minimum risk value.

Effective data collection and refinement of pertubated structures

Approaches to determining the influence of individual measurements on the precision of crystallographic least squares parameters have been known for a long while.[1] Situations in which the precision of a single parameter (or linear combination of parameters) is critical can include: determination of novel bond lengths; refinement of site occupancies in mixed metal or mixed oxidation state systems; determination of the fraction of excited state molecules in a time-resolved pump-probe experiment. Such calculations are easily applicable to point-detector instruments, where individual influential reflections could be remeasured one-by-one. However, on a modern area detector instrument many reflections are measured on one frame and therefore some consideration of the appropriate strategy of reciprocal space scans is permitted to allow a more efficient use of the instrument. The highly influential partial data collection is then feed into an appropriate refinement model. Occupancies in mixed-metal or mixed-oxidation state systems and fractions and positions of excited state molecules during a time-resolved pump-probe experiment can be determined using direct refinement of the perturbation of the structure from the ground state. Re-factoring to modern Fortran of the Crystals software is in progress to allow the implementation of new algorithms such as a difference refinement.[2] We present an analysis of diffractometer strategy selection to prioritize scans which give the best improvement in specific least-squares parameters and a novel algorithm for the refinement of the partial data using crystals.

Structural susceptibility and separation of time scales in the van der Pol oscillator

We use an extension of the van der Pol oscillator as an example of a system with multiple time scales to study the susceptibility of its trajectory to polynomial perturbations in the dynamics. A striking feature of many nonlinear, multiparameter models is an apparently inherent insensitivity to large-magnitude variations in certain linear combinations of parameters. This phenomenon of "sloppiness" is quantified by calculating the eigenvalues of the Hessian matrix of the least-squares cost function. These typically span many orders of magnitude. The van der Pol system is no exception: Perturbations in its dynamics show that most directions in parameter space weakly affect the limit cycle, whereas only a few directions are stiff. With this study, we show that separating the time scales in the van der Pol system leads to a further separation of eigenvalues. Parameter combinations which perturb the slow manifold are stiffer and those which solely affect the jumps in the dynamics are sloppier.

Multi-objective optimal experimental designs for event-related fMRI studies

In this article, we propose an efficient approach to find optimal experimental designs for event-related functional magnetic resonance imaging (ER-fMRI). We consider multiple objectives, including estimating the hemodynamic response function (HRF), detecting activation, circumventing psychological confounds and fulfilling customized requirements. Taking into account these goals, we formulate a family of multi-objective design criteria and develop a genetic-algorithm-based technique to search for optimal designs. Our proposed technique incorporates existing knowledge about the performance of fMRI designs, and its usefulness is shown through simulations. Although our approach also works for other linear combinations of parameters, we primarily focus on the case when the interest lies either in the individual stimulus effects or in pairwise contrasts between stimulus types. Under either of these popular cases, our algorithm outperforms the previous approaches. We also find designs yielding higher estimation efficiencies than m-sequences. When the underlying model is with white noise and a constant nuisance parameter, the stimulus frequencies of the designs we obtained are in good agreement with the optimal stimulus frequencies derived by Liu and Frank, 2004, NeuroImage 21: 387-400. In addition, our approach is built upon a rigorous model formulation.

Principal component analysis of weak lensing surveys

Aims. We study degeneracies between cosmological parameters and measurement errors from cosmic shear surveys. We simulate realistic survey topologies with non-uniform sky coverage, and quantify the effect of survey geometry, depth and noise from intrinsic galaxy ellipticities on the parameter errors. This analysis allows us to optimise the survey geometry. Methods. We carry out a principal component analysis of the Fisher information matrix to assess the accuracy with which linear combinations of parameters can be determined. Using the shear two-point correlation functions and the aperture mass dispersion, which can directly be measured from the shear maps, we study various degeneracy directions in a multi-dimensional parameter space spanned by $\Omega_{\rm m}$, $\Omega_\Lambda$, $\sigma_8$, the shape parameter Γ , the spectral index n s , along with parameters that specify the distribution of source galaxies. Results. A principal component analysis is an effective tool to probe the extent and dimensionality of the error ellipsoid. If only three parameters are to be obtained from weak lensing data, a single principal component is dominant and contains all information about the main parameter degeneracies and their errors. For four or more free parameters, the first two principal components dominate the parameter errors. The degeneracy directions are insensitive against variations in the noise or survey geometry. The variance of the dominant principal component of the Fisher matrix, however, scales with the noise. Further, it shows a minimum for survey strategies which have small cosmic variance and measure the shear correlation up to several degrees. This minimum is less pronounced if external priors are added, rendering the optimisation less effective. The minimisation of the Fisher error ellipsoid can lead to slightly different results than the principal component analysis.

Numerical simulations of Class I and Class II uniaxial compression curves using an elasto-plastic cellular automaton and a linear combination of stress and strain as the control method

Class I and Class II behavior of the rock failure process under uniaxial compression has been numerically simulated using an elasto-plastic cellular automaton (EPCA). A linear combination of stress and strain was used as the feedback signal to control the loading process in the numerical model. Uniaxial compressive simulations of heterogeneous rock failure were made using this control method and by considering different homogeneity indices and different linear combinations of parameters, as well as different yield criteria. The results indicate that Class II behavior can be numerically simulated in a complementary way to the laboratory testing method utilized in a servo-controlled testing machine. Whether the rock behaves in a Class I or Class II manner depends on the homogeneity of the rock sample, the linear combination parameters and the yield criterion selected.

SU-FF-T-377: Theory of Parameter Correlation in a Population Tumor Control Model Assuming High Heterogeneity in the Radiosensitivity

Purpose: In this work we present a theoretical investigation of the parameter correlation in a population tumor control model assuming high population heterogeneity in the radiosensitivity. Method and Materials: A number of authors have shown that ambiguity exists when radiobiological parameters are obtained by fitting population dose response data with a heterogeneous (population) tumor control model. The difficulty is that many different sets of parameter values can be used to construct TCP curves that are identical. These sets of parameters may be described as linear combinations of parameters. We use the Roberts and Hendry (1998 IJROBP 41 689–699) closed formula to investigate this ambiguity. Results: The Roberts and Hendry closed formula can be reduced to depend on two generalized parameters. For our analysis we introduce the following notation: TCP = Φ(δ), δ = (γ − κ)/σ, where κ = (α + βd − λ/d)D − ln(k), σ = σαD, and γ = 0.577 (Euler gamma constant). When the model is plotted in the κ−σ space, the iso-TCP lines are linear, and intersect at the point κ = γ, σ = 0. Parameter correlation occurs when combinations of α′ = (α + βd − λ/d), σα and ln(k) produce the same value of TCP for any value of the dose, D. This correlation can be proven by two methods: analytic or geometric. The specific form of the parameter correlation is: α′D50 − ln(k) = γ, (D50 is the dose D where TCP(D)= 50%) and σα /α′ = constant. Conclusion: When fitting a high heterogeneity TCP population model to clinical data, parameter correlation between the quantities (α + βd − λ/d) and ln(k) exist. A linear relation characterized by a slope of 1/D50 represents this correlation.

On reparameterization of random effects in linear mixed models

The Empirical Best Linear Unbiased Predictor of random effects in linear mixed models may be non-unique. For fixed effects two approaches are used to derive unique solutions – one is based on using estimable linear combinations of parameters and the other one uses reparametrization constraints. It is shown that both approaches can be applied in a similar manner to derive unique prediction results for random effects.

New limit on signals of Lorentz violation in electrodynamics.

We describe the results of an experiment to test for spacetime anisotropy terms that might exist from Lorentz violations. The apparatus consists of a pair of cylindrical superconducting cavity-stabilized oscillators operating in the TM010 mode with one axis east-west and the other vertical. Spatial anisotropy is detected by monitoring the beat frequency at the sidereal rate and its first harmonic. We see no anisotropy to a part in 10(13). This puts a comparable bound on four linear combinations of parameters in the general standard model extension, and a weaker bound of < 4 x 10(-9) on three others.

Further Comments on Models of Pathogen Evolution in Cultivar Mixtures and the Definition of Pathogen Fitness

Further Comments on Models of Pathogen Evolution in Cultivar Mixtures and the Definition of Pathogen Fitness

Prerelease Stratification in Tag-Recovery Models with Time Dependence

A statistical model is developed for estimating time-dependent survival and recovery rates of tagged populations that are stratified into groups at release. For populations of fish, the groups might include different sexes or stocks, or they might be distinguished by the location or method of capture. In the model developed here, survival and recovery rates are formulated as linear combinations of parameters that include the effects of time, group, and time–group interactions. Methods of testing the statistical significance of these potential sources of variation are described and illustrated with the recoveries of different stocks of anadromous striped bass (Morone saxatilis). For the striped bass data, elimination of time- and stock-specific sources of variation substantially improved the precision of survival estimates without introducing important bias. During 1988–89 the average survival of both stocks was 0.78 (SE = 0.04). Calculations of statistical power indicate that stock-specific differences in survival of ± 0.2 could have been detected about 50% of the time, given the low rates of recovery and numbers of fish released.

Effective interactions for the 0p1s0d nuclear shell-model space.

Shell-model interactions are constructed in the cross-shell model space connecting the 0p and 1s0d shells with due regard for the perturbative effects of the neighboring 0s and 0f1p shells. The interactions have three distinctive 0p-shell, cross-shell, and 1s0d-shell parts. The latter is taken to be the previously determined W interaction. The 0p-shell interaction is represented by two-body matrix elements and the cross-shell by either a potential or by two-body matrix elements. The interactions are determined by least-squares fits to 51 0p-shell and 165 cross-shell binding energies. It is found that the addition of monopole terms to a potential that is otherwise similar to that of the Millener-Kurath interaction results in a great improvement in the fit. In the fit to two-body matrix elements, 45 of 97 possible linear combinations of parameters are varied and the root-mean-square deviation for the 165 cross-shell energies is 330 keV. Examples of the application of the interactions are given for the prediction of neutron-rich binding energies, Gamow-Teller decays, and 0\ensuremath{\Elzxh}\ensuremath{\omega}, 1\ensuremath{\Elzxh}\ensuremath{\omega}, and 2\ensuremath{\Elzxh}\ensuremath{\omega} energy spectra.

Sampling Performance of Some Joint One-Sided Preliminary Test Estimators under Squared Error Loss

IN MANY AREAS OF SCIENCE, when drawing conclusions concerning a set of phenomena, individual or linear combinations of parameters are assumed to be nonnegative, nonpositive, or to lie between upper and lower bounds. Likewise, many functions are assumed to be monotonic, convex, or quasiconvex. Consequently, questions naturally arise as to the correctness of the assumptions and, within the context of statistical inference, how to evaluate the evidence against these assumptions and to use the data at hand to seek the appropriate statistical model and the corresponding method of estimation. Within the context of the general linear statistical model, multivariate analogues of one-sided (inequality hypotheses) tests have been explored by Bartholomew (1959), Kudo (1963), Osterhoff (1969), Barlow, et al. (1972), Yancey, Judge, and Bock (1981), Yancey, Bohrer, and Judge (1982), Gourieroux, Holly, and Montfort (GHM) (1982), Judge and Yancey (1986), Wolak (1987) and Shapiro (1988). In general, the likelihood ratio framework has been used in developing a test statistic and determining acceptance and rejection regions. In order to facilitate the interpretation of these test results in econometric practice, in this paper we evaluate, under a squared error loss (SEL) measure, the risk characteristics of the preliminary test (PT) estimators that evolve when, based on the data at hand, an estimation decision is taken as a result of the outcomes of two one-sided multivariate hypothesis tests.

Orthogonalization–Triangularization Methods in Statistical Computations

Abstract Procedures are presented for reducing a data matrix to triangular form by using orthogonal transformations. It is shown how an analysis of variance can be constructed from the triangular reduction of the data matrix. Procedures for calculating sums of squares, degrees of freedom, and expected mean squares are presented. It is demonstrated that all statistics needed for inference on linear combinations of parameters of a linear model may be calculated from the triangular reduction of the data matrix.

Optimal Bayesian Experimental Design for Linear Models

Optimal Bayesian experimental designs for estimation and prediction in linear models are discussed. The designs are optimal for estimating a linear combination of the regression parameters $\mathbf{c}^T\theta$ or prediction at a point where the expected response is $\mathbf{c}^T\mathbf{\theta}$ under squared error loss. A distribution on $\mathbf{c}$ is introduced to represent the interest in particular linear combinations of the parameters. In the usual notation for linear models minimizing the preposterior expected loss leads to minimizing the quantity $\mathrm{tr}\psi(R + XX^T)^{-1}$. The matrix $\psi$ is defined to be $E(\mathbf{cc}^T)$ and the matrix $R$ is the prior precision matrix of $\theta$. A geometric interpretation of the optimal designs is given which leads to a parallel of Elfving's theorem for $\mathbf{c}$-optimality. A bound is given for the minimum number of points at which it is necessary to take observations. Some examples of optimal Bayesian designs are given and optimal designs for prediction in polynomial regression are derived. The optimality of rounding non-integer designs to integer designs is discussed.

ON THE INTERPRETATION OF RESISTIVITY SOUNDINGS BY THE LEAST‐SQUARES METHOD*

AbstractAn interactive least‐squares method for the interpretation of VES curves was proposed by Johansen (1977). The method permits one to select some parameters (thicknesses and/or resistivities of individual layers) and to change the rest in such a way that the interpreted model approaches the measured data. This note suggests a modification of Johansen's method, in which not only the individual parameters can be selected but also linear combinations of parameters—in particular, the sum of thicknesses of several layers.

Anomalous Hydrocarbon-Gas Effects in Surface Strata over Buried Oil Pools (Kotovo Field, Volgograd Area)

Data from gas surveys provide two linear combinations of parameters for the hydrocarbon-gas components that incorporate features of the distribution above buried oil pools. This enables one to identify areas of interest for survey drilling.