Rank Structure Research Articles

Tensor Q-rank: new data dependent definition of tensor rank

Recently, the \({ Tensor}~{ Nuclear}~{ Norm}~{ (TNN)}\) regularization based on t-SVD has been widely used in various low tubal-rank tensor recovery tasks. However, these models usually require smooth change of data along the third dimension to ensure their low rank structures. In this paper, we propose a new definition of data dependent tensor rank named tensor Q-rank by a learnable orthogonal matrix \(\mathbf {Q}\), and further introduce a unified data dependent low rank tensor recovery model. According to the low rank hypothesis, we introduce two explainable selection methods of \(\mathbf {Q}\), under which the data tensor may have a more significant low tensor Q-rank structure than that of low tubal-rank structure. Specifically, maximizing the variance of singular value distribution leads to Variance Maximization Tensor Q-Nuclear norm (VMTQN), while minimizing the value of nuclear norm through manifold optimization leads to Manifold Optimization Tensor Q-Nuclear norm (MOTQN). Moreover, we apply these two models to the low rank tensor completion problem, and then give an effective algorithm and briefly analyze why our method works better than TNN based methods in the case of complex data with low sampling rate. Finally, experimental results on real-world datasets demonstrate the superiority of our proposed models in the tensor completion problem with respect to other tensor rank regularization models.

Market ranking and network structure: pathway to dominance

PurposeThe relationship between interlocking directorates and firm performance has been increasingly debated, with a focus on whether firm's centrality in interlock networks is associated with performance. The purpose of this study is to examine not only how a firm's position in this network is associated with performance but also how the performance of network partners can impact a firm's performance. This study examines how firms effectively utilise the interlock network to achieve the goal of higher market capitalisation – termed market capitalisation rank (MCR).Design/methodology/approachThe premise of the study is the UK FTSE 350 firms from 2014 to 2018. The paper makes use of a temporal network autocorrelation model to examine how firm characteristics, the structural position in the interlock network and the performance of network partners affect MCR over time.FindingsThe analysis indicates that firms with ties (via the interlock network) to firms with high market capitalisation are more likely to enhance their own MCR, highlighting network partners have the opportunity to play a critical role in a firm's dominance strategy to optimise firm value.Originality/valueThe value of this research is that it does not only look at the impact of a firm's position in the network on performance, but the impact of the performance of network partners on a firm's market performance as well.

The COVID-19 Vaccine Preference for Youngsters Using PROMETHEE-II in the IFSS Environment

Extensive decision-making during the vaccine preparation period is unpredictable. An account of the severity of the disease, the younger people with COVID-19 comorbidities and other chronic diseases are also at a higher risk of the COVID-19 pandemic. In this research article, the preference ranking structure for the COVID-19 vaccine is recommended for young people who have been exposed to the effects of certain chronic diseases. Multiple Criteria Decision-Making (MCDM) approach effectively handles this vague information. Furthermore, with the support of the Intuitionistic Fuzzy Soft Set (IFSS), the entries under the new extension of the Preference Ranking Organization Method for Enrichment Evaluation-II (PROMETHEE-II) is suggested for Preference Ranking Structure. The concept of intuitionistic fuzzy soft sets is parametric in nature. IFSS suggests how to exploit an intuitionistic ambiguous input from a decision-maker to make up for any shortcomings in the information provided by the decider. The weight of the inputs is calculated under the Intuitionistic Fuzzy Weighted Average (IFWA) operator, the Simply Weighted Intuitionistic Fuzzy Average (SWIFA) operator, and the Simply Intuitionistic Fuzzy Average (SIFA) operator. An Extended PROMETHEE-based ranking, outranking approach is used, and the resultant are recommended under the lexicographic order. Its sustainability and feasibility are explored for three distinct priority structures and the possibilities of the approach. To demonstrate the all-encompassing intuitionistic fuzzy PROMETHEE approach, a practical application regarding COVID-19 severity in patients is given, and then it is compared to other existing approaches to further explain its feasibility, and the sensitivity of the preference structure is examined according to the criteria.

Manifold Optimization-Assisted Gaussian Variational Approximation

Gaussian variational approximation is a popular methodology to approximate posterior distributions in Bayesian inference, especially in high-dimensional and large data settings. To control the computational cost, while being able to capture the correlations among the variables, the low rank plus diagonal structure was introduced in the previous literature for the Gaussian covariance matrix. For a specific Bayesian learning task, the uniqueness of the solution is usually ensured by imposing stringent constraints on the parameterized covariance matrix, which could break down during the optimization process. In this article, we consider two special covariance structures by applying the Stiefel manifold and Grassmann manifold constraints, to address the optimization difficulty in such factorization architectures. To speed up the updating process with minimum hyperparameter-tuning efforts, we design two new schemes of Riemannian stochastic gradient descent methods and compare them with other existing methods of optimizing on manifolds. In addition to fixing the identification issue, results from both simulation and empirical experiments prove the ability of the proposed methods of obtaining competitive accuracy and comparable converge speed in both high-dimensional and large-scale learning tasks. Supplementary materials for this article are available online.

SCOTT COMPLEXITY OF COUNTABLE STRUCTURES

AbstractWe define the Scott complexity of a countable structure to be the least complexity of a Scott sentence for that structure. This is a finer notion of complexity than Scott rank: it distinguishes between whether the simplest Scott sentence is $\Sigma _{\alpha }$ , $\Pi _{\alpha }$ , or $\mathrm {d-}\Sigma _{\alpha }$ . We give a complete classification of the possible Scott complexities, including an example of a structure whose simplest Scott sentence is $\Sigma _{\lambda + 1}$ for $\lambda $ a limit ordinal. This answers a question left open by A. Miller.We also construct examples of computable structures of high Scott rank with Scott complexities $\Sigma _{\omega _1^{CK}+1}$ and $\mathrm {d-}\Sigma _{\omega _1^{CK}+1}$ . There are three other possible Scott complexities for a computable structure of high Scott rank: $\Pi _{\omega _1^{CK}}$ , $\Pi _{\omega _1^{CK}+1}$ , $\Sigma _{\omega _1^{CK}+1}$ . Examples of these were already known. Our examples are computable structures of Scott rank $\omega _1^{CK}+1$ which, after naming finitely many constants, have Scott rank $\omega _1^{CK}$ . The existence of such structures was an open question.

Endogeneity in the mutual fund flow-performance relationship: An Instrumental Variable Solution

We use an instrumental variables (IV) approach to examine the effects of dynamic endogeneity when estimating the relationship between mutual fund flows and performance. Unlike the one-stage estimation approach commonly used in prior research, the IV approach allows us to address reverse causality between flow and performance. Through rigorous exclusion tests, we conclude that fund media coverage, risk ranking, and management structure win in a horse race as exogenous instruments for fund flow, while the fund turnover ratio and institutional share perform best as instruments for fund performance. We then demonstrate that endogeneity bias leads to inaccurate inferences in one-stage estimates, as evidenced by the reversals of the signs of flow and performance coefficient estimates when we switch to the IV approach. We find that careful attention to model specification allows us to resolve several widespread inconsistencies in the literature that were likely driven by model misspecification.

Multi-objective discrete water wave optimization algorithm for solving the energy-saving job shop scheduling problem with variable processing speeds

For the job shop with variable processing speeds, the aim of energy saving and consumption reduction is implemented from the perspective of production scheduling. By analyzing the characteristics of the workshop, a multi-objective mathematical model is established with the objective of reducing the total energy consumption and shortening the makespan. A multi-objective discrete water wave optimization (MODWWO) algorithm is proposed for solving the problem. Firstly, a two-vector encoding method is adopted to divide the scheduling solution into two parts, which represent speed selection and operation permutation in the scheduling solution, respectively. Secondly, some dispatching rules are used to initialize the population and obtain the initial scheduling solutions. Then, three operators of the basic water wave optimization algorithm are redesigned to make the algorithm adaptive for the multi-objective discrete scheduling problem under study. A new propagation operator is presented with the ability of balancing global exploration and local exploitation based on individual rank and neighborhood structures. A novel refraction operator is designed based on crossover operation, by which each individual can learn from the current best individual to absorb better information. And a breaking operator is modified based on the local search strategy to enhance the exploitation ability. Finally, extensive simulation experiments demonstrate that the proposed MODWWO algorithm is effective for solving the considered energy-saving scheduling problem.

ОЦЕНКА МЕР СОЦИАЛЬНОЙ ПОДДЕРЖКИ МЕДИЦИНСКИХ РАБОТНИКОВ ИРКУТСКОЙ ОБЛАСТИ, ЗАЯВЛЕННЫХ В ОФИЦИАЛЬНЫХ ПРЕДЛОЖЕНИЯХ ОБ ИХ ТРУДОУСТРОЙСТВЕ

Significance. Social support measures for healthcare workers are one of the key mechanisms for retaining specialists. Meanwhile, according to the Ministry of Health of the Russian Federation, the current indicators of their implementation remain unsatisfactory. The purpose of the study was to assess frequency and structure of social support measures for medical workers based on the data of the official employment proposals posted by state medical organizations on the website of the Ministry of Health of the Irkutsk Region. Material and methods. Statistical charts have been developed, they included information from the employment proposals posted on the official website of the Ministry of Health of the Irkutsk Region, the total number of proposals added up to 429. Statistical methods to process the material included calculation of the extensive and intensive indexes without determining confidence intervals because the general aggregate was used in all cases. Results. The most wanted out of all doctors are district therapists (7.0% in the structure of doctors’ vacancies), followed by obstetricians-gynecologists (6.7%) and infectious disease specialists (6.1%). As for nursing staff, the highest number of employment proposals were looking for feldshers (22.4%), ward nurses (12.9%) and district nurses (11.2%). Of the total number of job proposals, social support measures were stated in 76.2 proposals out of 100, while the frequency of these measures added up to 77.4 out of 100 for doctors and 63.8 for nurses. The stated social support measures for doctors in the ascending order include as follows: issues related to housing (79.2 per 100 employment proposals); direct financial support (72.2 per 100); provision of a place in a preschool facility without waiting (35.1); additional vacation and travel expense reimbursement (27.2); reimbursement of expenses related to relocation and travel to the place of employment (14.4); payment for postgraduate and additional professional education (9.3). The rank structure of social support measures for nursing staff differs in the order, starting from the third. Conclusion. In both absolute and relative terms, the measures of social support stated by the employment proposals for doctors prevail. While primary health care workers are in highest demand, the need for such specialists is not directly reflected by the corresponding frequency of the stated social support measures. The results obtained are relevant to the development and implementation of the evidence-based personnel policy in healthcare at the level of an individual region of the Russian Federation.

Bayesian Low Rank Tensor Ring for Image Recovery.

Low rank tensor ring based data recovery can recover missing image entries in signal acquisition and transformation. The recently proposed tensor ring (TR) based completion algorithms generally solve the low rank optimization problem by alternating least squares method with predefined ranks, which may easily lead to overfitting when the unknown ranks are set too large and only a few measurements are available. In this article, we present a Bayesian low rank tensor ring completion method for image recovery by automatically learning the low-rank structure of data. A multiplicative interaction model is developed for low rank tensor ring approximation, where sparsity-inducing hierarchical prior is placed over horizontal and frontal slices of core factors. Compared with most of the existing methods, the proposed one is free of parameter-tuning, and the TR ranks can be obtained by Bayesian inference. Numerical experiments, including synthetic data, real-world color images and YaleFace dataset, show that the proposed method outperforms state-of-the-art ones, especially in terms of recovery accuracy.

Features of the Image of the Father in Tuvan Teenagers from Single-Parent Families in the Republic of Tyva

Introduction. Family relations are currently undergoing transformation. Often the man is not the head of the family. In the Republic of Tuva, the image of the father as the head of the family who financially supports the family has changed significantly. The purpose of the article is to identify the differences in the image of the father in complete and incomplete families of different types in the Republic of Tyva. Materials and Methods. The results of an empirical study of the features of the reflection of the father’s image in the minds of adolescents from single-parent families in the Tyva Republic are presented. It was attended by 166 people between the ages of 13 and 14, of which 62 are boys. The study of the father’s image was carried out using the SOCH(I) method of V. L. Sitnikov. In this methodology, the rank structure of different images of the father of boys and girls from different types of families is distinguished on the basis of a quantitative comparison of the use of characteristics of different modalities. Results. There are two factors in the formation of the image of a father among adolescents: the traditional image of a father, the way he should be, is mainly traced among adolescents from single-parent families; and the modern father, who shares the headship of the family with the mother of the child, an egalitarian family. The peculiarities of the father’s image in adolescent boys and girls, characteristic of complete orphaned and divorced families, were revealed in significant differences. Discussion and Conclusion. The analysis of the father’s image in adolescents was carried out taking into account gender. In Tuvan adolescents, two types of father images prevail, depending on the type of family. For adolescents from orphaned and divorced families, a stereotypical image of a father is characteristic, formed on the basis of traditional ideas, of Tuvan culture. The image of the father of adolescents from complete families, as a rule, is distinguished by individuality, since it reflects not a collective image generalized by culture, but specific ideas about a real person.

Specific Features of the Structure of Various Coal Ranks at the Nano Level

Structural factors and functions of radial distribution of atoms of different coal ranks have been calculated by X-ray diffraction analysis. This made it possible to establish that the main structural component is the clusters with graphite-like packing of atoms. The predominant size of these clusters (calculated from the peaks of small-angle X-ray scattering at 5° in CoKα-radiation) for coals with a carbon content of 83--95 % is within 2--3 nm. Fossil coal is an amorphous carbonaceous substance consisting of polymorphic modifications in the sp2- and sp3-states. According to the results obtained using Raman scattering spectroscopy, the physical properties of amorphous natural coals are strongly dependent on the ratio of sp2- and sp3-hybridization of atomic orbitals. Moreover, studies have shown that the carbon atoms of the coal matrix in the sp2-state are represented by both aromatic and aliphatic conjugated chain fragments. It was found that the degree of ordering in rank LF coals is higher than in coals of a higher stage of metamorphism. This is possible if the hydrocarbon matrix in rank LF coals can be represented as a polymer consisting of conjugated chains with periodicity. With an increase in the stage of coal metamorphism, starting with coal rank G, the transformation of the coal structure occurs with a violation of the periodicity of the conjugated fragments of the polymer matrix connecting graphite-like clusters, a decrease in their length, and an increase in randomness in their arrangement

Crystal structure classification in ABO3 perovskites via machine learning

Crystal structure classification of perovskites (ABO3) is done using the Light Gradient Boosting Machine (Light GBM) algorithm. In this work, we have identified features such as electronegativity, ionic radius, valence, and bond lengths of A-O and B-O pairs that enable a priori crystal structure prediction. We have taken 5329 ABO3 perovskites and applied the proposed model to 675 compounds. It successfully categorized the compounds into cubic, tetragonal, orthorhombic, and rhombohedral structures with 80.3% best accuracy using 5-fold cross-validation. Therefore, the model can be used as a preliminary, fast, and inexpensive method to classify perovskites into their respective crystal systems. Feature importance graph and SHapley Additive exPlanations (SHAP) are used in feature ranking and crystal structure prediction. These composition-structure predictions will find applications in ceramic engineering and solid-state chemistry.

Resilience support to enhance positive health outcomes for police officers in five Anglosphere nations: a scoping review protocol

IntroductionLaw enforcement involves exposure to threatening situations and traumatic events that place police officers at risk for negative physical and mental health outcomes. Resilience support, among other elements of training,...

Mini-Workshop: Rank One Groups and Exceptional Algebraic Groups

Rank one groups are a class of doubly transitive groups that are natural generalizations of the groups SL2(k). The most interesting examples arise from exceptional algebraic groups of relative rank one. This class of groups is, in turn, intimately related to structurable algebras. The goal of the mini-workshop was to bring together experts on these topics in order to make progress towards a better understanding of the structure of rank one groups.

Commutative algebraic monoid structures on affine surfaces

Abstract We classify commutative algebraic monoid structures on normal affine surfaces over an algebraically closed field of characteristic zero. The answer is given in two languages: comultiplications and Cox coordinates. The result follows from a more general classification of commutative monoid structures of rank 0, n - 1 n-1 or 𝑛 on a normal affine variety of dimension 𝑛.

Variations of hodge structures of rank three k-Higgs bundles and moduli spaces of holomorphic triples

There is an isomorphism between the moduli spaces of \(\sigma \)-stable holomorphic triples and some of the critical submanifolds of the moduli space of k-Higgs bundles of rank three, whose elements \((E,\varphi ^k)\) correspond to variations of Hodge structure, VHS. There are special embeddings on the moduli spaces of k-Higgs bundles of rank three. The main objective here is to study the cohomology of the critical submanifolds of such moduli spaces, extending those embeddings to moduli spaces of holomorphic triples.

Low-Rank Covariance Function Estimation for Multidimensional Functional Data

Multidimensional function data arise from many fields nowadays. The covariance function plays an important role in the analysis of such increasingly common data. In this article, we propose a novel nonparametric covariance function estimation approach under the framework of reproducing kernel Hilbert spaces (RKHS) that can handle both sparse and dense functional data. We extend multilinear rank structures for (finite-dimensional) tensors to functions, which allow for flexible modeling of both covariance operators and marginal structures. The proposed framework can guarantee that the resulting estimator is automatically semipositive definite, and can incorporate various spectral regularizations. The trace-norm regularization in particular can promote low ranks for both covariance operator and marginal structures. Despite the lack of a closed form, under mild assumptions, the proposed estimator can achieve unified theoretical results that hold for any relative magnitudes between the sample size and the number of observations per sample field, and the rate of convergence reveals the phase-transition phenomenon from sparse to dense functional data. Based on a new representer theorem, an ADMM algorithm is developed for the trace-norm regularization. The appealing numerical performance of the proposed estimator is demonstrated by a simulation study and the analysis of a dataset from the Argo project. Supplementary materials for this article are available online.

Semantic ranking structure preserving for cross-modal retrieval

Cross-modal retrieval not only needs to eliminate the heterogeneity of modalities, but also needs to constrain the return order of retrieval results. Accordingly, we propose a novel common representation space learning method, called Semantic Ranking Structure Preserving (SRSP) for Cross-modal Retrieval in this paper. First, the dependency relationship between labels is used to minimize the discriminative loss of multi-modal data and mine potential relationships between samples to get richer semantic information in the common space. Second, we constrain the correlation ranking of representations in common space, so as to break the modal gap and promote the multi-modal correlation learning. The comprehensive experimental comparison results show that our algorithm substantially enhances the performance and consistently outperforms very recent algorithms in terms of widely used cross-modal benchmark datasets.

On factor models with random missing: EM estimation, inference, and cross validation

We consider the estimation and inference in approximate factor models with random missing values. We show that with the low rank structure of the common component, we can estimate the factors and factor loadings consistently with the missing values replaced by zeros. We establish the asymptotic distributions of the resulting estimators and those based on the EM algorithm. We also propose a cross-validation-based method to determine the number of factors in factor models with or without missing values and justify its consistency. Simulations demonstrate that our cross validation method is robust to fat tails in the error distribution and significantly outperforms some existing popular methods in terms of correct percentage in determining the number of factors. An application to the factor-augmented regression models shows that a proper treatment of the missing values can improve the out-of-sample forecast of some macroeconomic variables.

Abstract 3217: An integrated web server for multi-omics data deconvolution

Abstract Tissue data deconvolution has been broadly utilized to characterize the variation of cell components and their relative abundance in cancer tumor microenvironment. Numerous deconvolution methods have been developed with different mathematical and biological considerations. Our previous studies have derived a rigorous mathematical condition for a less biased deconvolution. We have demonstrated a cell type can be reliably inferred from an omics data only of the cell type is with distinct signature genes, i.e., the cell type specific expression signature of the selected marker genes of all cell types are orthogonal or at least non-positively associated with each other, which is named as strong or weak “identifiable” conditions. Our analysis suggests the identifiability of a certain cell type is mostly determined by the significance of its gene markers, which is data set and tissue microenvironment dependent. However, such data set specificity has been commonly ignored in existing methods. In this study, we developed a comprehensive web server, namely ISMD (an Integrated web Server for Multi-omics data Deconvolution), to recommend a best deconvolution method and optimize the gene markers and cell types in analyzing a specific data set. The server solved to two fundamental challenges in the practical application of deconvolution methods, namely (1) method selection and (2) parameter optimization. Specifically, ISMD utilized a semi-supervised approach for method recommendation and parameter optimization, which first evaluate the species, sample size, and tissue type of a given data set and test the low rank structure of commonly used cell type specific markers for cell type and signature gene selection. ISMD can handle the blood, normal, inflammatory, and cancer tissue, and central nervous and hematopoietic systems of human and mouse. The semi-supervised knowledge transfer encoded in ISMD enables its application to multi-omics data including general transcriptomics, ATAC-seq and DNA-methylation data. The method has been validated by using a large collection of tissue samples. A user friend web-server has been released through https://github.com/xiaoyulu95/ISMD. We anticipate ISMD can help to increase the specificity and rigorousness in the application of tissue deconvolution methods, to bring more insights of the role of different cell types and their interactions and stimulate the discovery of new therapeutic targets in a tumor micro-environment. Citation Format: Xiaoyu Lu, Pengtao Dang, Szu-Wei Tu, Wennan Chang, Changlin Wan, Chi Zhang, Sha Cao. An integrated web server for multi-omics data deconvolution [abstract]. In: Proceedings of the Annual Meeting of the American Association for Cancer Research 2020; 2020 Apr 27-28 and Jun 22-24. Philadelphia (PA): AACR; Cancer Res 2020;80(16 Suppl):Abstract nr 3217.