Sums Of Variables Research Articles

Definition of conditionally permanent part of current liabilities of a bank

The article deals with the questions of the definition of the conditionally permanent part of current liabilities of a bank. The purpose of this article is to develop a scientific and methodological approach to determine the conditionally permanent part of the current liabilities of a bank under the conditions of the complexity of data acquisition and processing of the data on factors that influence on demand deposits. The main hypothesis is the assumption of the heterogeneity of the variance of the daily cumulative sum of demand deposits. The analysis of scientific and methodological approaches that allow determining a stable part of current liabilities proves the need for further improvement of scientific instruments. In particular, a coefficient analysis that is proposed by some of the scholars, mainly, considers the average values of turnover on accounts, which in turn, can vary considerably throughout the calendar year. The use of the probability distributions to determine the expected value of the constant sum of deposits is possible only in the case of «ideal» financial conditions, when the impact of factors on the aggregate sum of deposits is not taken into account. The developed statistical models leave out the possible heterogeneity of the dispersion of this balance. In the article, it is proposed to apply econometric methods, namely, the methods of time series analysis to test the hypothesis of the variance heterogeneity of the cumulative sum of demand deposits, using daily data. In particular, the formalization and evaluation of EGARCH-model parameters are conducted. The EGARCH-model allows to take into account the non-linear, asymmetric effects of fluctuations in the financial series. The determination of the conditionally permanent part of demand deposits is proposed on the basis of the revealed regularities. The results of the research prove the hypothesis of the non-stationary character of the variance in daily balance of demand deposits. It may result from the economic shocks influence. The proposed scientific and methodological approach may be applied in the bank liabilities management both at the micro level and at the regional level of banking network.

Eutherian morphological disparity across the end-Cretaceous mass extinction

© 2015 The Linnean Society of London. In the aftermaths of mass extinction events, during radiations of clades, and in several other evolutionary scenarios, there is often a decoupling of taxonomic diversity and morphological disparity. The placental mammal radiation after the end-Cretaceous mass extinction is one of the archetypal adaptive radiations, but the change in morphological disparity of the entire skeleton has never been quantified across this important boundary. We reconstruct ancestral morphologies of 680 discrete morphological characters onto dated phylogenies of 177 mostly Cretaceous and Palaeogene eutherians (placental mammals and their stem relatives). Using a new approach to incorporate morphologies representing ghost lineages, we assess three measures of morphological disparity (sum of ranges, sum of variances and mean pairwise dissimilarity) across stage-level time bins within the Cretaceous and Palaeogene. We find that the range-based metric suggests that eutherian disparity increased immediately after the end-Cretaceous mass extinction, while both variance-based metrics declined from the Campanian to the Maastrichtian, but showed no change in disparity from the Maastrichtian to the Puercan - the first North American Land Mammal Age of the Paleocene. Increases in variance-based metrics lag behind the range-based metric and per-lineage accumulation rate, suggesting that the response of mammals to the Cretaceous-Palaeogene event was characterized by an early radiation that increased overall morphospace occupation, followed later by specialization that resulted in increased dissimilarity.

Texture metric that predicts target detection performance

Two texture metrics based on gray level co‐occurrence error (GLCE) are used to predict probability of detection and mean search time. The two texture metrics are local clutter metrics and are based on the statistics of GLCE probability distributions. The degree of correlation between various clutter metrics and the target detection performance of the nine military vehicles in complex natural scenes found in the Search_2 dataset are presented. Comparison is also made between four other common clutter metrics found in the literature: root sum of squares, Doyle, statistical variance, and target structure similarity. The experimental results show that the GLCE energy metric is a better predictor of target detection performance when searching for targets in natural scenes than the other clutter metrics studied.

NIMG-14IDENTIFICATION OF TRUE FUNCTIONAL ACTIVITY USING RADIOMIC TEXTURE ANALYSIS OF FUNCTIONAL MRI ECHO PLANNAR IMAGING

BACKGROUND: FMRI maps commonly show multiple areas of false positive activity. We aimed to identify areas of true fMRI activation by using complex MRI texture analysis (TA) of raw EPI data, thus enhancing the identification of true activity. METHODS: 12 right handed healthy volunteers were recruited (IRB approved). All scans were performed on a 3.0T GE MR scanner. FMRI consisted of a high resolution 3D T1 weighted structural scan and a gradient echo EPI functional scan. FMRI data analysis was performed using SPM8 software for a sentence completion block design task. T map for each individual was displayed using xjview toolbox and thresholded individually to optimize visualization of language area. Each activity cluster was selected and saved. Board-certified neuroradiologists and neuroscientists classified different clusters into two separate groups Expected (E) and Non Expected (NE) based on their anatomical locations. TA was performed using the mean EPI volume for each individual, and 20 invariant texture features were obtained. Efficacy of TA in fMRI was assessed by decision tree and validated using a 4 fold cross validation. RESULTS: fMRI areas of activity in individual scans were identified based on their texture features with 95.3% accuracy, sensitivity 95.3% and specificity 95.3%. Sum of Variance, Cluster shade, sum of average and information measure of correlation were the most important texture features. These features had higher texture values in the NE ROIs indicating more homogeneous areas. Texture features were able to significantly differentiate areas of true versus false activity. CONCLUSIONS: Extracted features indicated that true activity has more heterogeneous texture compared to non-expected activity Quantitative TA of functional MRI using texture feature can enhance the accuracy and sensitivity of the test to true activity and help eliminate false activation

Robust estimation and filtering in uncertain linear systems under unknown covariations

In the problems of estimation and filtering under uncertainty in the regressors, parameters, and covariances of random noise and perturbations, the best possible upper boundary of the proportionality coefficient between the root-mean-square error of estimate or filter and the sum of variances of all random factors was determined. This boundary which was named the level of suppression of random perturbations is characterized in terms of the linear matrix inequalities. The minimax estimate and minimax filter optimizing this index were established. The optimal robust estimate and filter were obtained using additional information about the membership of the covariance matrix in the given convex polyhedron.

Information Gathering in Bayesian Networks Applied to Petroleum Prospecting

The optimal design of data acquisition is not obvious in Bayesian network models. The dependency structure may vary dramatically, which makes learning and information evaluation complicated and sometimes non-intuitive. The motivation for working on this topic is petroleum exploration, and the application of this paper is prospect selection in the North Sea. Here, the data gathering is often carried out during seasonal campaigns, and it is useful to plan the experimentation and to understand which data are likely to be most informative. Information measures are used to compare possible future observation sets. Four information measures are studied: Shannon Entropy, sum of variances, Node-wise Entropy and overall prediction error. The Shannon Entropy is commonly considered the standard measure of information, and the Node-wise Entropy measure can be interpreted as an approximation to the former. The variance measure links uncertainty and variance. The prediction error measure is tied to decision-making rules. The results lead to new insight about prospect selection. For example, the Node-wise Entropy and the variance measure behave similarly, and the optimal observation set of Shannon Entropy does not correspond to what one intuitively would consider as minimizing unknown information in this case.

Sum uncertainty relations for arbitrary N incompatible observables.

We formulate uncertainty relations for arbitrary N observables. Two uncertainty inequalities are presented in terms of the sum of variances and standard deviations, respectively. The lower bounds of the corresponding sum uncertainty relations are explicitly derived. These bounds are shown to be tighter than the ones such as derived from the uncertainty inequality for two observables [Phys. Rev. Lett. 113, 260401 (2014)]. Detailed examples are presented to compare among our results with some existing ones.

English

Despite the widespread of democracy, the term has no unified meaning; and thus a lack of clarity which renders communication ineffective. Democracy is a political term which allows individuals the freedom of choice when electing government officials. It gives individuals the most involvement in government oversight, elections and changes, as opposed to other forms of governance. However, this study focuses on the freedom of choice within a classroom setting. A recent definition of democracy enables individuals to have more freedom and ability in society along with their identities. Thus it ultimately leads to a more peaceful and prolific lives as individuals are integrated with their society. During this study, the survey model was used to determine the democratic values of the prospective teachers in the fourth year students from faculty of different departments in a Turkish state university. The study carried out with survey models aims to describe the specifications of the mass and the present situation. The research group is a total 402 prospective teachers studying in the Department of Preschool Teaching (n = 41), Guidance and Counseling (n = 41), Social Studies Teaching (n = 75), Science Teaching (n = 60), Primary School Teaching (n = 108), Turkish Teaching (n = 77) in the faculty of education. As an instrument, ‘Democratic Values Scale’ by Selvi is used to collect the data. The likert-type scale consists of 24 items, including three sub-dimensions with its factor load values ranging from .41 to .72. The sum variance explained by sub-dimensions is 44.81 %. These have shown that the validity of this scale is high. From the findings, we could say this study is so important to demonstrate in different way and approach that there is a democratically well-equipped and planned doctrine and philosophy of education in Turkey. In turn, this reflects on teachers, class, and practically prospective students. In conclusion, the study found that there is in place a democratically well-equipped and planned doctrine and philosophy of education in Turkey. This was found at the student and teacher level, as well as within the prospective student population. Key words: Teacher education, value, and democratic value.

Autonomous rock classification using Bayesian image analysis for Rover-based planetary exploration

A robust classification system is proposed to support autonomous geological mapping of rocky outcrops using grayscale digital images acquired by a planetary exploration rover. The classifier uses 13 Haralick textural parameters to describe the surface of rock samples, automatically catalogues this information into a 5-bin data structure, computes Bayesian probabilities, and outputs an identification.The system has been demonstrated using a library of 30 digital images of igneous, sedimentary and metamorphic rocks. The images are 3.5×3.5cm2 in size and composed of 256×256 pixels with 256 grayscale levels. They are first converted to gray level co-occurrence matrices which quantify the number of times adjacent pixels of similar intensity are present. The Haralick parameters are computed from these matrices. When all 13 parameters are used, classification accuracy, defined using an empirical scoring system, is 65% due to a large number of false positives. When the number of parameters and the choice of parameter is optimized, classification accuracy increases to 80%. The best results were achieved with 3 parameters that can be interpreted visually (angular second moment, contrast, correlation) together with two statistical parameters (sum of squares variance and difference variance) and a parameter derived from information theory (information measure of correlation II).The system has been kept simple not to draw excessive computational power from the rover. It could, however, be easily extended to handle additional parameters such as images acquired at different wavelengths.

Implications and applications of the variance-based uncertainty equalities

In quantum mechanics, the variance-based Heisenberg-type uncertainty relations are a series of mathematical inequalities posing the fundamental limits on the achievable accuracy of the state preparations. In contrast, we construct and formulate two quantum uncertainty equalities, which hold for all pairs of incompatible observables and indicate the new uncertainty relations recently introduced by L. Maccone and A. K. Pati [Phys. Rev. Lett. 113, 260401 (2014)]. In fact, we obtain a series of inequalities with hierarchical structure, including the Maccone-Pati's inequalities as a special (weakest) case. Furthermore, we present an explicit interpretation lying behind the derivations and relate these relations to the so-called intelligent states. As an illustration, we investigate the properties of these uncertainty inequalities in the qubit system and a state-independent bound is obtained for the sum of variances. Finally, we apply these inequalities to the spin squeezing scenario and its implication in interferometric sensitivity is also discussed.

Optimum Time-Censored Modified Ramp-Stress ALT for the Burr Type XII Distribution with Warranty: A Goal Programming Approach

Accelerated life tests (ALTs) are used to make timely assessments of the life time distribution of highly reliable materials and components. Much of the previous work on ALTs has focused on constant-stress, step-stress, ramp-stress schemes and their various combinations. In the literature ramp-stress ALTs that have been formulated can be conducted when more than one test chambers are available; installation of which may prove to be costly. Even when one test chamber is used the stress rate remains constant throughout the duration of the experiment. It is not only necessary but imperative to examine if the test specimen is able to withstand differing stress conditions with the passage of time. This paper therefore, presents an optimal design of multi-objective modified ramp-stress ALT model with weighted goal programming approach. The modified ramp-stress uses one test chamber in place of the various chambers used in simple ramp-stress ALT thus saving experimental cost. With the market being increasingly competitive the emphasis today is on goal attainment with minimum deviations. Goal programming is a method to solve multi-objective problems that has applications in varied fields of engineering and operational research. The optimal plan consists in finding out relevant experimental variables, namely, stress rate, stress rate change point and warranty period, by using goal programming on weighted sum of variance of reliability function and expected warranty cost with pre-specified mission time under normal operating conditions. The Burr type XII life distribution and time-censored data have been used for the purpose. Burr type XII life distribution has been found appropriate for accelerated life testing experiments. The method developed has been explained using a numerical example and sensitivity analysis carried out. Comparative study has also been done to highlight the merits of the proposed model.

Effects of dietary protein levels on the long-term growth response and fitting growth models of gibel carp (Carassius auratus gibelio).

A 41-wk growth trial was conducted to evaluate the effects of dietary protein levels on the long-term growth response and fitting growth models of gibel carp (Carassius auratus gibelio) with an initial body weight of 1.85 ± 0.17 g. The dietary protein levels were designed at 320 (P32), 360 (P36), 400 (P40), and 440 g/kg (P44), respectively. The growth curves of the gibel carp for each group were fitted and analyzed with four nonlinear regression models (Gompertz, logistic, von Bertalanffy and Richards). The final body weights (mean ± SD) of the fish were 226 ± 6, 231 ± 7, 242 ± 2, and 236 ± 2 g for P32, P36, P40, and P44, respectively. Feed conversion ratio of P40 and P44 groups was significantly lower than that of P32 and P36 groups (P < 0.05). Productive protein value of P44 group was significantly lower than that of P32 and P36 groups, but not different from that of P40 group (P ≥ 0.05). The growth response of the gibel carp for each group was the best fitted by Richards model with the lowest Chi2, residual sum of squares and residual variance, then Gompertz and von Bertalanffy growth models, but the logistic model did not fit the data well justified by Chi2 values. The optimal protein level (400 g/kg) prolonged the stage of fast growth and predicted the highest asymptotic weight, which was close to the harvest size in practice.

An exact algorithm for the mean–standard deviation shortest path problem

This paper studies the reliable path problem in the form of minimizing the sum of mean and standard deviation of path travel time. For the case of independent link travel times, we show that the problem can be solved exactly by repeatedly solving a subproblem minimizing the sum of mean and variance of path travel time. The latter is an additive shortest path problem, and can be solved using a standard labeling algorithm. While these subproblems are similar in form to those obtained from Lagrangian relaxation, this formulation admits proof of finite convergence to the optimal solution. An iterative labeling algorithm is developed that solves the non-additive reliable path problem from a single origin to all destinations. Moreover, a labeling technique is employed to further reduce the computational time of the proposed algorithm by partially updating the network in each iteration. As an alternative, a bisection-type search algorithm is developed that solves the problem for the single-origin and single-destination case. Numerical tests are presented, indicating that the proposed algorithm outperform others recently proposed in the literature: unlike Lagrangian relaxation, two of the proposed algorithms find solutions exactly, and the computation time is an order of magnitude faster than outer approximation methods.

Möbius function in short intervals for function fields

Let μ(A) be the Möbius function defined in a polynomial ring Fq[T] with coefficients in the finite field Fq of q elements (q is odd). In this paper, we present a function field version of partial progress toward a conjecture of Good and Churchhouse. We calculate the mean and the large q limit of the variance of partial sums of the Möbius function on short intervals. Our calculation closely follows the framework of a recent work of Keating and Rudnick, where they consider the distribution of the von Mangoldt function in function fields.

Asymptotic variance of stationary reversible and normal Markov processes

We obtain necessary and sufficient conditions for the regularvariation of the variance of partial sums of functionals of discrete and continuous-time stationary Markov processes with normal transition operators. We also construct a class of Metropolis-Hastings algorithms which satisfy a central limit theorem and invariance principle when the variance is not linear in n.

Limit Theorems for Two Classes of Random Matrices with Dependent Entries

In this paper we study random symmetric matrices with dependent entries. Suppose that all entries have zero mean and finite variances, which can be different. Assuming that the average of normalized sums of variances in each row converges to one and the Lindeberg condition holds true, we prove that the empirical spectral distribution of eigenvalues converges to Wigner's semicircle law. The result can be generalized to the class of covariance matrices with dependent entries. In this case expected empirical spectral distribution function converges to the Marchenko--Pastur law.

A Novel Segmentation and Contouring Scheme to Assist Accurate Brain Lesion Classification

Segmentation of highly infiltrating glioblastoma multiforme (GBM) in BrainMR Images has been highly challenging as the grey levels of tumor and peritumoral vasogenic edema are quite homogenous and hence identifying a suitable scheme for isolating GBM from the background has been troublesome. This paper proposes a novel segmentation and contouring scheme, using shape sensitive derivative strategy for segmentation and energy minimizing contours for enhancing the edges of the GBM, under investigation. The efficiency of the algorithm has been tested with the aid of extracted tumor features, the Shape Features -circularity, irregularity, Area, Perimeter, Shape Index, Intensity features – Mean, Variance, Standard Variance, Median Intensity, Skewness, and Kurtosis, Texture features –Contrast, Correlation, Entropy, Energy, Homogeneity, cluster shade, sum of square variance. It is obvious, though this algorithm consumes more computational time, it segments the edges effectively and preserve the shape facilitating accurate extraction or estimation of the features further and provides stable and reproducible results. All the classification Schemes, with combined DA and SVM with Higher Rank Features and LDA techniques exhibited appreciable improvement in terms of sensitivity, specificity, positive Predictive value and negative Predictive value, because of the accuracy of shape sensitive derivative segmentation algorithm and energy minimizing contour algorithm.

Stronger uncertainty relations for all incompatible observables.

The Heisenberg-Robertson uncertainty relation expresses a limitation in the possible preparations of the system by giving a lower bound to the product of the variances of two observables in terms of their commutator. Notably, it does not capture the concept of incompatible observables because it can be trivial; i.e., the lower bound can be null even for two noncompatible observables. Here we give two stronger uncertainty relations, relating to the sum of variances, whose lower bound is guaranteed to be nontrivial whenever the two observables are incompatible on the state of the system.

Limit Theorems for Two Classes of Random Matrices with Gaussian Entries

In this note, we consider ensembles of random symmetric matrices with Gaussian elements. Assume that $$ \mathbb{E} $$ X ij = 0 and $$ \mathbb{E}{X}_{ij}^2={\sigma}_{ij}^2 $$ We do not assume that all the σ ij are equal. Assuming that the average of the normalized sums of variances in each row converges to one and the Lindeberg condition holds, we prove that the empirical spectral distribution of eigenvalues converges to Wigner’s semicircle law. We also provide an analogue of this result for sample covariance matrices and prove the convergence to the Marchenko–Pastur law. Bibliography: 5 titles.

Pre-joining process planning model for a batch of skin–stringer panels based on statistical clearances

The residual clearances after pre-joining the panels directly affect the subsequent processes with the automatic drilling and riveting machine, so that these clearances could be used a criterion of pre-joining processes. Moreover, the pre-joining process model for single panel based on clearances criterion is not applicable to determine the processes for batches of panels, which leads to the non-identical pre-joining parameters for every panel, the inconvenient operations for workers, the huge measurement workload of clearances, and the low assembly efficiency. To solve the aforementioned problems, this paper proposes a pre-joining process planning model for a batch of panels based on statistical clearances. The proposed model takes both the stiffness matrices of key points of panels and the measured distribution parameters of sample of initial clearances as an input, regards the weighted sum of mean and variance of residual clearances after pre-joining as an evaluation criterion, thinks the pre-joining parameters adapted to all panels including the number, location, and sequence as an objective, employs the random Bezier curves to fit the clearance distributions of key points of panels and applies the method of Latin hypercube sampling to simulate processes rapidly. Hence, this model may be used to exponentially reduce both the number of degrees of freedom of nodes and the number of statistical simulation, widely adapt the differences of clearance distributions of panels, quickly determine the standardized parameters of pre-joining process and dramatically improve the assembly efficiency. Lastly, the model has been verified with an example consisting of 30 pairs of skin–stringers with the same configuration.