Max stable set problem to found the initial centroids in clustering problem

In this paper, we propose a new approach to solve the document-clustering using the K-Means algorithm. The latter is sensitive to the random selection of the k cluster centroids in the initialization phase. To evaluate the quality of K-Means clustering we propose to model the text document clustering problem as the max stable set problem (MSSP) and use continuous Hopfield network to solve the MSSP problem to have initial centroids. The idea is inspired by the fact that MSSP and clustering share the same principle, MSSP consists to find the largest set of nodes completely disconnected in a graph, and in clustering, all objects are divided into disjoint clusters. Simulation results demonstrate that the proposed K-Means improved by MSSP (KM_MSSP) is efficient of large data sets, is much optimized in terms of time, and provides better quality of clustering than other methods.

Optimizing over the Closure of Rank Inequalities with a Small Right-Hand Side for the Maximum Stable Set Problem via Bilevel Programming

In the context of the maximum stable set problem, rank inequalities impose that the cardinality of any set of vertices contained in a stable set be, at most, as large as the stability number of the subgraph induced by such a set. Rank inequalities are very general, as they subsume many classical inequalities such as clique, hole, antihole, web, and antiweb inequalities. In spite of their generality, the exact separation of rank inequalities has never been addressed without the introduction of topological restrictions on the induced subgraph and the tightness of their closure has never been investigated systematically. In this work, we propose a methodology for optimizing over the closure of all rank inequalities with a right-hand side no larger than a small constant without imposing any restrictions on the topology of the induced subgraph. Our method relies on the exact separation of a relaxation of rank inequalities, which we call relaxed k-rank inequalities, whose closure is as tight. We investigate the corresponding separation problem, a bilevel programming problem asking for a subgraph of maximum weight with a bound on its stability number, whose study could be of independent interest. We first prove that the problem is [Formula: see text]-hard and provide some insights on its polyhedral structure. We then propose two exact methods for its solution: a branch-and-cut algorithm (which relies on a family of faced-defining inequalities which we introduce in this paper) and a purely combinatorial branch-and-bound algorithm. Our computational results show that the closure of rank inequalities with a right-hand side no larger than a small constant can yield a bound that is stronger, in some cases, than Lovász’s Theta function, and substantially stronger than bounds obtained with standard inequalities that are valid for the stable set problem, including odd-cycle inequalities and wheel inequalities. Summary of Contribution: This paper proposes two original methods for solving a challenging cut-separation problem (of bilevel type) for a large class of inequalities valid for one of the key operations research problems, namely, the max stable set problem. An extensive set of experimental results validates the proposed methods. All the source code and data sets are available online on GitHub.

Phylogenetic Relatedness and Genome Structure of Yersinia ruckeri Revealed by Whole Genome Sequencing and a Comparative Analysis

Yersinia ruckeri is the causative agent of enteric redmouth disease (ERM), a serious infection that affects global aquaculture with high economic impact. The present study used whole genome sequences to perform a comparative analysis on 10 Y. ruckeri strains and to explore their genetic relatedness to other members of the genus. Y. ruckeri, Yersinia entomophaga, and Yersinia nurmii formed a species complex that constitutes the most basal lineage of the genus. The results showed that the taxonomy of Y. ruckeri strains is better defined by using a core genome alignment and phylogenetic analysis. The distribution of accessory genes in all Yersinia species revealed the presence of 303 distinctive genes in Y. ruckeri. Of these, 169 genes were distributed in 17 genomic islands potentially involved in the pathogenesis of ERM via (1) encoding virulence factors such as Afp18, Yrp1, phage proteins and (2) improving the metabolic capabilities by enhancing utilization and metabolism of iron, amino acids (specifically, arginine and histidine), and carbohydrates. The genome of Y. ruckeri is highly conserved regarding gene structure, gene layout and functional categorization of genes. It contains various components of mobile genetic elements but lacks the CRISPR-Cas system and possesses a stable set of virulence genes possibly playing a critical role in pathogenicity. Distinct virulence plasmids were exclusively restricted to a specific clonal group of Y. ruckeri (CG4), possibly indicating a selective advantage. Phylogenetic analysis of Y. ruckeri genomes revealed the co-presence of multiple genetically distant lineages of Y. ruckeri strains circulating in Germany. Our results also suggest a possible dissemination of a specific group of strains in the United States, Peru, Germany, and Denmark. In conclusion, this study provides new insights into the taxonomy and evolution of Y. ruckeri and contributes to a better understanding of the pathogenicity of ERM in aquaculture. The genomic analysis presented here offers a framework for the development of more efficient control strategies for this pathogen.

Fast Diameter Computation within Split Graphs

When can we compute the diameter of a graph in quasi linear time? We address this question for the class of {\em split graphs}, that we observe to be the hardest instances for deciding whether the diameter is at most two. We stress that although the diameter of a non-complete split graph can only be either $2$ or $3$, under the Strong Exponential-Time Hypothesis (SETH) we cannot compute the diameter of an $n$-vertex $m$-edge split graph in less than quadratic time -- in the size $n+m$ of the input. Therefore it is worth to study the complexity of diameter computation on {\em subclasses} of split graphs, in order to better understand the complexity border. Specifically, we consider the split graphs with bounded {\em clique-interval number} and their complements, with the former being a natural variation of the concept of interval number for split graphs that we introduce in this paper. We first discuss the relations between the clique-interval number and other graph invariants such as the classic interval number of graphs, the treewidth, the {\em VC-dimension} and the {\em stabbing number} of a related hypergraph. Then, in part based on these above relations, we almost completely settle the complexity of diameter computation on these subclasses of split graphs: - For the $k$-clique-interval split graphs, we can compute their diameter in truly subquadratic time if $k={\cal O}(1)$, and even in quasi linear time if $k=o(\log{n})$ and in addition a corresponding ordering of the vertices in the clique is given. However, under SETH this cannot be done in truly subquadratic time for any $k = \omega(\log{n})$. - For the {\em complements} of $k$-clique-interval split graphs, we can compute their diameter in truly subquadratic time if $k={\cal O}(1)$, and even in time ${\cal O}(km)$ if a corresponding ordering of the vertices in the stable set is given. Again this latter result is optimal under SETH up to polylogarithmic factors. Our findings raise the question whether a $k$-clique interval ordering can always be computed in quasi linear time. We prove that it is the case for $k=1$ and for some subclasses such as bounded-treewidth split graphs, threshold graphs and comparability split graphs. Finally, we prove that some important subclasses of split graphs -- including the ones mentioned above -- have a bounded clique-interval number.

Multi-Run Concrete Autoencoder to Identify Prognostic lncRNAs for 12 Cancers

Background: Long non-coding RNA plays a vital role in changing the expression profiles of various target genes that lead to cancer development. Thus, identifying prognostic lncRNAs related to different cancers might help in developing cancer therapy. Method: To discover the critical lncRNAs that can identify the origin of different cancers, we propose the use of the state-of-the-art deep learning algorithm concrete autoencoder (CAE) in an unsupervised setting, which efficiently identifies a subset of the most informative features. However, CAE does not identify reproducible features in different runs due to its stochastic nature. We thus propose a multi-run CAE (mrCAE) to identify a stable set of features to address this issue. The assumption is that a feature appearing in multiple runs carries more meaningful information about the data under consideration. The genome-wide lncRNA expression profiles of 12 different types of cancers, with a total of 4768 samples available in The Cancer Genome Atlas (TCGA), were analyzed to discover the key lncRNAs. The lncRNAs identified by multiple runs of CAE were added to a final list of key lncRNAs that are capable of identifying 12 different cancers. Results: Our results showed that mrCAE performs better in feature selection than single-run CAE, standard autoencoder (AE), and other state-of-the-art feature selection techniques. This study revealed a set of top-ranking 128 lncRNAs that could identify the origin of 12 different cancers with an accuracy of 95%. Survival analysis showed that 76 of 128 lncRNAs have the prognostic capability to differentiate high- and low-risk groups of patients with different cancers. Conclusion: The proposed mrCAE, which selects actual features, outperformed the AE even though it selects the latent or pseudo-features. By selecting actual features instead of pseudo-features, mrCAE can be valuable for precision medicine. The identified prognostic lncRNAs can be further studied to develop therapies for different cancers.

The essential oil composition of Artemisia jacutica Drob. from the flora of Buryatia, Russia

This paper represents the results of the GC-MS analysis of the essential oil’s composition of Artemisia jacutica Drob. collected within the Republic of Buryatia in 2015-2020. A. jacutica is an East Siberian endemic plant which has been widely used in folk medicine of Yakutia for the treatment of gastrointestinal diseases. 59 compounds were identified in total, which were represented by mono- and sesquiterpenoids. Neryl-2-methylbutanoate, neryl-hexanoate, γ-eudesmol, and chamazulene were constant components of the oil, whereas γ-eudesmol and chamazulene predominated (the content reaches over 40%). Essential oils of A. jacutica collected in different years were characterized by a stable set of dominant constituents, while the content of sesquiterpenoids was over 92%. The samples of the 2018-2020 years of collection had a greater variety of constituents (31-36 compounds): derivatives of nerol, geraniol, 1,8-cineole, seline-4-diene, compared to the 2015-2017 samples.

Longitudinal Stability and Change in Time-Frequency Measures from an Oddball Task During Adolescence and Early Adulthood

Time-frequency representations of electroencephalographic signals lend themselves to granular analysis of cognitive and psychological processes. Characterizing developmental trajectories of time-frequency measures can thus inform us about the development of the processes involved. We decomposed EEG activity in a large sample of individuals (N = 1692; 917 females) assessed at approximately three-year intervals from the age of 11 to their mid-20s. Participants completed an oddball task that elicits a robust P3 response. Principal component analysis served to identify meaningful dimensions of time-frequency energy. Component loadings were virtually identical across assessment waves. A common and stable set of time-frequency dynamics thus characterized EEG activity throughout this age range. Trajectories of change in component scores suggest that aspects of brain development reflected in these components comprise two distinct phases, with marked decreases in component amplitude throughout much of adolescence followed by smaller yet significant rates of decreases into early adulthood. Although the structure of time-frequency activity was stable throughout adolescence and early adulthood, we observed subtle change in component loadings as well. Our findings suggest that striking developmental change in event-related potentials emerges through gradual change in the magnitude and timing of a stable set of dimensions of time-frequency activity, illustrating the usefulness of time-frequency representations of EEG signals and longitudinal designs for understanding brain development. In addition, two components were associated with childhood externalizing psychopathology, independent of sex, which extends the existing literature and provides proof of concept of the notion that developmental trajectories might serve as candidate endophenotypes for psychiatric disorders.

ECONOMIC SPACE IN MODERN SCIENTIFIC DISCOURSE

The article is devoted to the study of the definition of economic space in modern scientific discourse. The urgency of the article is substantiated by the necessity to improve the methodology and practice of regional governance due to the global markets’ trends. Also the actuality of the work is determined by the specific of Ukraine regional management and necessity to modernize its methodological bases due to needs for the development of the economic space of Ukraine in terms of global competition. The aim of the study is to generalize, critically analyze and develop theoretical bases for defining the concept of "economic space". The study has used dialectical, monographic and analytical methods, and also the method of comparative analysis, system and process approaches. The comparative and critical analysis of existing theories of productive forces development has been made. Various definitions of economic space have been systematized and analyzed. It is substantiated that the system approach is the most suitable for use in the process of defining the concept of economic space. Economic space is a territory in which economic agents operate and interact within the available resource, institutional, social, infrastructural and other constraints. The concept of economic space reflects the functioning of the system, in which the object of management for a certain period keeps the structure and properties unchanged. The region is defined as a stable set of elements interconnected by socio-economic conditions, common interests, strategic goals and a single value system. The development of this system is provided by available resource potential, cross-sectoral and interregional cooperation, and active participation of public institutions in regional socio-economic processes. The relative independence of the region as a system is determined by its socio-economic unity with the national economy (quasi-state). At the same time region is a system with competitive advantages and the ability to self-development (quasi-corporation). It isn’t only a territorial unit; also it is a social basic unit of economic space due to the fact that the population, differentiated by demographic and socio-economic characteristics, is the central element of the territorial system and a single territorial community.

Monetary attitudes of young people in conditions of socioeconomic instability

In modern society, the younger generation is one of the most creative and active parts of its functioning. The constantly changing monetary attitudes of young people act as a driving force that affects the level of competitiveness and dynamic development of the socio-economic sphere. The attitudes of young people towards money and its management determine the vector in the formation of both an economically strong, politically stable state and an entire society. A stable set of attitudes is determined by the attitude to money, preferences in its management, goals, and strategies in the formation of various types of financial behavior, ways to achieve material well-being, orientation to economic values, and other important components. In this article, the author presents partial results of a large-scale study on the behavior of young people in the financial market, which reflect the monetary attitudes of young Muscovites that determine behavior in various areas of financial life: the desire to improve well-being, goals, and methods of achieving financial well-being, attitude to money and ways of managing it, attitude to savings and savings instruments, the investment potential of young people, as well as plans for the use of investment instruments. As a result of the conducted research, the following was revealed: the majority of respondents are characterized by a critical attitude to monetary transactions and financial institutions, lack of inclination to excessive spending, and risky investment. The desire of young people to accumulate and find ways to increase capital indicates far-sightedness, and preferences in financial instruments with the lowest share of risk, indicates caution in matters of capital management. This is an active, not afraid of the new, generation of Muscovites, showing a desire and interest in new forms of financial relationships, young people who form trends, young people whose attitudes, needs, and behavior need to be constantly studied by all participants of the financial eco-system.