Hypothesis Of Independence Research Articles

Deep Multi-Instance Conv-Transformer Frameworks for Landmark-Based Brain MRI Classification

For brain diseases, e.g., autism spectrum disorder (ASD), with unclear biological characteristics, the detection of imaging-based biomarkers is a critical task for diagnosis. Several landmark-based categorization approaches have been developed for the computer-aided diagnosis of brain diseases, such as Alzheimer’s disease (AD), utilizing structural magnetic resonance imaging (sMRI). With the automatic detection of the landmarks of brain disease, more detailed brain features were identified for clinical diagnosis. Multi-instance learning is an effective technique for classifying brain diseases based on landmarks. The multiple-instance learning approach relies on the assumption of independent distribution hypotheses and is mostly focused on local information, thus the correlation among different brain regions may be ignored. However, according to previous research on ASD and AD, the abnormal development of different brain regions is highly correlated. Vision Transformers, with self-attention modules to capture the relationship between embedded patches from a whole image, have recently demonstrated superior performances in many computer vision tasks. Nevertheless, the utilization of 3D brain MRIs imposes a substantial computational load, especially while training with Vision Transformer. To address the challenges mentioned above, in this research, we proposed a landmark-based multi-instance Conv-Transformer (LD-MILCT) framework as a solution to the aforementioned issues in brain disease diagnosis. In this network, a two-stage multi-instance learning strategy was proposed to explore both spatial and morphological information between different brain regions; the Vision Transformer utilizes a multi-instance learning head (MIL head) to fully utilize the features that are not involved in the ultimate classification. We assessed our proposed framework using T1-weighted MRI images from both AD and ASD databases. Our method outperformed existing deep learning and landmark-based methods in terms of brain MRI classification tasks.

RANK-BASED INDICES FOR TESTING INDEPENDENCE BETWEEN TWO HIGH-DIMENSIONAL VECTORS.

To test independence between two high-dimensional random vectors, we propose three tests based on the rank-based indices derived from Hoeffding's , Blum-Kiefer-Rosenblatt's and Bergsma-Dassios-Yanagimoto's . Under the null hypothesis of independence, we show that the distributions of the proposed test statistics converge to normal ones if the dimensions diverge arbitrarily with the sample size. We further derive an explicit rate of convergence. Thanks to the monotone transformation-invariant property, these distribution-free tests can be readily used to generally distributed random vectors including heavily tailed ones. We further study the local power of the proposed tests and compare their relative efficiencies with two classic distance covariance/correlation based tests in high dimensional settings. We establish explicit relationships between and Pearson's correlation for bivariate normal random variables. The relationships serve as a basis for power comparison. Our theoretical results show that under a Gaussian equicorrelation alternative, (i) the proposed tests are superior to the two classic distance covariance/correlation based tests if the components of random vectors have very different scales; (ii) the asymptotic efficiency of the proposed tests based on and are sorted in a descending order.

Pengaruh Media Pembelajaran Animasi Terhadap Hasil Belajar Siswa Pada Mata Pelajaran IPA Kelas IV SD N 1 Poncowati Kecamatan Terbanggi Besar Kabupaten Lampung Tengah

Learning media is an information medium for teaching and learning activities so that it can provide effectiveness and interactivity in learning. The research objective in writing this is to determine the effect of animated media on student learning outcomes in science subjects for fourth grade students at SDN 1 Poncowati, Terbanggi Besar District, Central Lampung Regency. This study uses a type of quantitative research. With a quasi-experimental approach. The population in this study were all students of class IV B and class IV C of SDN 1 Poncowati, Terbanggi Besar District, Central Lampung Regency. The instruments used are test and non-test. using independent simple t-test hypothesis testing. This data collection technique uses observation, test and documentation methods. The results of this study indicate that the value of learning outcomes obtained after applying animation media to the experimental class has increased compared to the class that was not given treatment, namely animation media. This can be seen from the mean or average value of the experimental class, namely 79.93 with 96.6% completeness. And there is a significant influence between Animation Media on student learning outcomes. In this study researchers. This assessment results in a sig (2-tailed) value of 0.014 <0.05, which means 0.014 is smaller than 0.05. So it can be concluded that the hypothesis is accepted, namely that there is an influence of animation media on the learning outcomes of fourth grade students at SD N 1 Poncowati, Terbanggi Besar District, Central Lampung Regency.

An independence test for functional variables based on kernel normalized cross-covariance operator

We propose an independence test for random variables valued into metric spaces by using a test statistic obtained from appropriately centering and rescaling the squared Hilbert–Schmidt norm of the usual empirical estimator of normalized cross-covariance operator. We then get asymptotic normality of this statistic under independence hypothesis, so leading to a new test for independence of functional random variables. A simulation study that allows to compare the proposed test to existing ones is provided.

Testing independence of functional variables by an Hilbert–Schmidt independence criterion estimator

We propose a method for testing independence of functional variables by using an estimator of the Hilbert–Schmidt Independence Criterion obtained from an appropriate modification of the usual estimator. We get asymptotic normality of this estimator both under independence hypothesis and under the alternative hypothesis. A simulation study that allows to compare the proposed test to an existing one is provided.

Using spatial ordinal patterns for non-parametric testing of spatial dependence

We analyze data occurring in a regular two-dimensional grid for spatial dependence based on spatial ordinal patterns (SOPs). After having derived the asymptotic distribution of the SOP frequencies under the null hypothesis of spatial independence, we use the concept of the type of SOPs to define the statistics to test for spatial dependence. The proposed tests are not only implemented for real-valued random variables, but a solution for discrete-valued spatial processes in the plane is provided as well. The performances of the spatial-dependence tests are comprehensively analyzed by simulations, considering various data-generating processes. The results show that SOP-based dependence tests have good size properties and constitute an important and valuable complement to the spatial autocorrelation function. To be more specific, SOP-based tests can detect spatial dependence in non-linear processes, and they are robust with respect to outliers and zero inflation. To illustrate their application in practice, two real-world data examples from agricultural sciences are analyzed.

An Empirical Bayes Approach to Controlling the False Discovery Exceedance

In large-scale multiple hypothesis testing problems, the false discovery exceedance (FDX) provides a desirable alternative to the widely used false discovery rate (FDR) when the false discovery proportion (FDP) is highly variable. We develop an empirical Bayes approach to control the FDX. We show that, for independent hypotheses from a two-group model and dependent hypotheses from a Gaussian model fulfilling the exchangeability condition, an oracle decision rule based on ranking and thresholding the local false discovery rate (lfdr) is optimal in the sense that the power is maximized subject to the FDX constraint. We propose a data-driven FDX procedure that uses carefully designed computational shortcuts to emulate the oracle rule. We investigate the empirical performance of the proposed method using both simulated and real data and study the merits of FDX control through an application for identifying abnormal stock trading strategies.

Using statistical techniques to validate the hypothesis of independence in control charts

The aim of this study was to identify and present the occurrence of autocorrelation in statistical data. To achieve this objective, a theoretical discussion was held on the subject and two exercises were also carried out using the R Statistical Software to show whether or not autocorrelation exists in statistical data. As a contribution of this research, a statistical technique using this software to show autocorrelation in data is pointed out.

Copy thy neighbor: Spatial interdependences in the democracy-repression nexus

How does spatial interdependence between countries affect domestic levels of repression? The current literature on state repression focuses on unit-level/common shocks explanations and treats countries’ interdependence as a statistical nuisance. This article relaxes the null hypothesis of policy independence in state repression and examines the theoretical and empirical implications of spatial interdependence in the democracy–repression nexus. Combining spatial-econometric analysis with latent measures of democracy and repression in 138 countries between 1947 and 2007, the article shows that (1) there is a robust diffusion effect of repression at a regional level, (2) previous literature has overestimated the suppressing effect of democracy (when spatial interdependence is not accounted for), and (3) trade relations and security alliances are the main drivers of regional diffusion of repression.

Social groups and polarization of aesthetic values from symmetry and complexity

When deciding what images we prefer, our brain must weigh many aesthetic variables, such as symmetry and complexity. To date, aesthetic research has mainly focused on investigating one variable at a time. In this article, we use symmetry and complexity to study the problem of multi aesthetic-variable interactions. For symmetry and complexity, there are two simple interaction hypotheses. The independence hypothesis proposes that the evaluation of aesthetic variables is mutually independent. Meanwhile, Birkhoff’s aesthetic-measure hypothesis predicts that people prefer images high in symmetry and low in complexity, and dislike the opposite. To test these hypotheses, we generated images that systematically varied in levels of symmetry and complexity. We then compared the subjects’ preference maps to identify regions of likes and dislikes. Unlike the predictions from these hypotheses, we found that most, but not all subjects, formed two distinct natural clusters, termed “islands,” in terms of likes and dislikes. We also found that people with more art exposure were less likely to belong to an island. If someone did belong to an island, their gender influenced which cluster they belonged to. We discuss alternate hypotheses, possible mechanisms for the occurrence of islands, and their possible social implications.

Tests of independence and randomness for arbitrary data using copula-based covariances

In this article, we study tests of independence for data with arbitrary distributions in the non-serial case, i.e., for independent and identically distributed random vectors, as well as in the serial case, i.e., for time series. These tests are derived from copula-based covariances and their multivariate extensions using Möbius transforms. We find the asymptotic distributions of these statistics under the null hypothesis of independence or randomness, as well as under contiguous alternatives. This enables us to find out locally most powerful test statistics for some alternatives, whatever the margins. Numerical experiments are performed for Wald’s type combinations of these statistics to assess the finite sample performance.

Identification of essential plasma protein using manifold regularized sparse group-lasso for prediction of Alzheimer’s disease

Accurate diagnose of Alzheimer’s disease (AD), especially in its early stage, is very important for the possible delay and early treatment of the disease. Many researches indicate that the change of the expression level of plasma proteins will lead to the emergence of AD, which creates a new focus on finding essential proteins that affects AD. Nearly all the existing models were constructed on the independent hypothesis, where each candidate protein is treated independently. However, proteomics studies suggest that the essential proteins in cells do not act independently under illness conditions. Instead, they perform biological functions in groups, where each group is composed of proteins with similar functions. Accordingly, we propose a manifold regularized sparse group-lasso (i.e., MSGL) method to identify essential proteins that will incur AD. Specifically, we firstly propose a novel method to calculate the similarity between pairs of proteins with the aid of Gene Ontology, and then use the spectral clustering algorithm to divide the proteins into groups. Next, we adopt a sparse group-lasso model to select proteins according to both intra-group sparsity and inter-group sparsity, which ensures only a small number of proteins in a few of groups will be selected. In addition, we also introduce a manifold-based Laplacian regularizer to preserve the data distribution information. Finally, support vector machine (SVM) is used to classify AD patients. The experimental results show that our method can achieve a classification accuracy of 97.5%, a sensitivity of 97.6%, and specificity of 97.4%, demonstrating great potential in classification of AD patients.

Application of a nonparametric technique for testing the hypothesis of independence of random variables in conditions of a large volume of statistical data

The problem of testing the hypothesis about the independence of random variables in conditions of large volumes of statistical data is considered. The results of solving the problem are necessary when estimating probability densities of random variables and synthesizing information processing algorithms. A nonparametric technique is proposed for testing the hypothesis about the independence of random variables in a sample containing a large amount of statistical data. The technique is based on compression of the initial statistical information by decomposition of the range of values of random variables. The generated data array consists of the centers of sampling intervals and the corresponding frequencies of observations from the original sample. The information obtained is used in the construction of a nonparametric pattern recognition algorithm corresponding to the maximum likelihood criterion. The evaluation of the distribution laws in classes is carried out under the assumption of independence and dependence of the compared random variables. When restoring the laws of distribution of random variables in classes, regression estimates of probability densities are used. Under these conditions, estimates of the probabilities of pattern recognition errors in classes are calculated. According to their minimum value, a decision is made on the independence or dependence of random variables. The technique was applied in the analysis of remote sensing data of forest areas, linear and nonlinear dependencies between pairs of spectral characteristics of the objects of study were determined.Keywords:

Testing semiparametric model-equivalence hypotheses based on the characteristic function

We propose three test criteria each of which is appropriate for testing, respectively, the equivalence hypotheses of symmetry, homogeneity, and independence, with multivariate data. All quantities have the common feature of involving weighted-type distances between characteristic functions and are convenient from the computational point of view if the weight function is properly chosen. The asymptotic behaviour of the tests under the null and alternative hypotheses is investigated. Numerical studies and a real-data application are conducted in order to examine the performance of the criteria in finite samples.

Investigating the influence of input angular momentum on independence hypothesis in heavy-ion induced fusion reactions

The experimental verification of compound nucleus theory has successfully been performed for light ion induced reactions using proton and α-particle beams on different targets. However, such studies using the heavy ion beams are scarce due to the complex nature of heavy ion interaction process. The present work is an attempt to validate the Bohr's independent hypothesis using heavy ion beam of 18O beam on 159Tb targets and 12C on 165Ho targets, forming the same compound nucleus 177Ta. A channel wise analysis of cross section data for evaporation residues produced in 18O+159Tb and 12C+165Ho systems has been performed within the framework of statistical model code PACE4 and found to reasonably agree with the experimental data. Further, a comparison of reaction cross section data for the same evaporation residues produced in the two different systems has been found to follow Bohr's compound nucleus hypothesis at relatively higher excitation energies. However, at relatively lower excitation energies, a significant deviation in the measured cross section data of the same residues in the above mentioned systems have been observed and is attributed to the discrepancies in angular momentum values. Such discrepancies are well explained on the basis of input angular momentum involved in the reactions.

Developing and assessing the use of demonstration videos in the preclinical simulation laboratory.

This study aims to report the development of a preclinical simulation laboratory Demonstration Video Series (DVS) for the 2021-2022 academic year, measure its usage and usefulness, and compare these findings to the usage and usefulness of the existing didactic lecture videos. The DVS videos were intended to be viewed before each preclinical simulation laboratory session along with the pre-existing didactic lectures (DL) by University of California San Francisco (UCSF) learners. Usage measurements included the percentage of the class that viewed each video, the number of views that each video received, and the average duration of each video that was watched. Usefulness of the videos was measured by a survey that assessed learner perspective on knowledge and ability to apply that knowledge during the simulation lab exercises. Both usage and usefulness of the DVS were then compared to the usage and usefulness of the DL. Both descriptive statistics and independent sample hypothesis tests were performed to compare the differences in proportion between DVS and DL mediums. Statistically significant differences were found in terms of both usage and usefulness of the DVS compared to the DL, with DVS being utilized more overall. With an 81% response rate, survey analysis revealed statistically significant differences among the learners' perspectives on the usefulness of the DVS compared to the DL, with a clear preference for the DVS over the DL and an overwhelmingly positive perception of the DVS. The DVS was found to be a valuable addition to the preclinical laboratory sessions for first-year learners.

Smooth integers and de Bruijn's approximation Ʌ

This paper is concerned with the relationship of $y$ -smooth integers and de Bruijn's approximation $\Lambda (x,\,y)$ . Under the Riemann hypothesis, Saias proved that the count of $y$ -smooth integers up to $x$ , $\Psi (x,\,y)$ , is asymptotic to $\Lambda (x,\,y)$ when $y \ge (\log x)^{2+\varepsilon }$ . We extend the range to $y \ge (\log x)^{3/2+\varepsilon }$ by introducing a correction factor that takes into account the contributions of zeta zeros and prime powers. We use this correction term to uncover a lower order term in the asymptotics of $\Psi (x,\,y)/\Lambda (x,\,y)$ . The term relates to the error term in the prime number theorem, and implies that large positive (resp. negative) values of $\sum _{n \le y} \Lambda (n)-y$ lead to large positive (resp. negative) values of $\Psi (x,\,y)-\Lambda (x,\,y)$ , and vice versa. Under the Linear Independence hypothesis, we show a Chebyshev's bias in $\Psi (x,\,y)-\Lambda (x,\,y)$ .

ВЕРОЯТНОСТНЫЙ АНАЛИЗ НАДЕЖНОСТИ ФЕРМ СТАТИСТИЧЕСКИМ ГЕНЕРИРОВАНИЕМ ДАННЫХ

Probabilistic analysis of structural reliability allows to get a quantitative assessment of the safety level of buildings and structures, as well as to compare various technical options of structural elements by the safety criterion or by the risk criterion. The article discusses approaches to evaluation the reliability of systems on the example of steel trusses. A new approach to the reliability analysis of trusses is presented based on the method of statistical data sampling. This approach allows to get the information of the reliability level of a system in a simple and accessible form, and modern computing techniques makes the calculation process operational even in the case of multi-element systems. In assessing the reliability of systems, it should carefully consider the modeling of the system operation, since the use of the hypothesis of complete independence of the system elements can lead to a significant underestimation of the probability of non-failure of a series system. The permissible value of the probability of non-failure for the truss must be set based on the value of the permissible risk, reflecting the socio-economic consequences of system failure.

Comparison of Methods for Testing the Hypothesis of Independence of Random Variables Based on a Nonparametric Classifier and Pearson’s Chi-Squared Test

Comparison of Methods for Testing the Hypothesis of Independence of Random Variables Based on a Nonparametric Classifier and Pearson’s Chi-Squared Test

MAIN FEATURES OF CONCRETE DEFORMATION UNDER THE ACTION OF DYNAMIC LOADS

This article is devoted to the features of the general model of compressed concrete deformation in concrete and reinforced concrete elements and structures under the dynamic loads action. The proposed model is a further in-depth development of the previously developed generalized deformation and force model of concrete and reinforced concrete resistance to force effects. It is based on the hypothesis of invariability and independence from the loading mode of the specific potential energy of concrete ultimate deformation (destruction) in a standard sample. A critical analysis of the research results by other authors published today on the above-mentioned subject has been performed. The main attention is paid to the well-known dynamic increase factor (DIF). The main advantages and disadvantages of the currently existing methods and ways of its determination have been classified and analyzed. An analytically justified function of its maximum possible values under the dynamic loads action was obtained. The various factors influence on the DIFu limit values for compressed concrete is taken into account using an integrated parameter – the well-known coefficient of elastic-plastic concrete properties k. The dependence of intermediate DIF values on the compressed concrete deformation rate under the different intensity dynamic loads action is proposed. The effectiveness of the developed method of determining the DIF coefficient for compressed concrete according to the proposed dependence was evaluated by comparing the theoretical calculations results with individual researchers experimental data. Similar comparisons were also made with the calculations results performed according to well-known European methods of the CEB FIB.