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Title: Measuring consistency of interval-valued preference relations: comments and comparison Abstract: The concepts of consistency definition and consistency index are usually used to measure the consistency of a preference relation. When interval numbers are used to express the preference information, the consistency of the derived interval-valued preference relations (IVPRs) is worth being investigated. In this study, a comment is provided for the ideas behind consistency definitions and consistency indexes of interval multiplicative reciprocal matrices (IMRMs) and interval additive reciprocal matrices (IARMs), respectively. A comparison is made by considering the two kinds of consistency definitions of IVPRs. It is found that the method of defining the consistency of IVPRs in terms of the imaginary intervals is equivalent to that of defining the approximate consistency. Numerical examples are reported to illustrate the differences of the two consistency definitions of IVPRs. The observations illustrate that the fundamental inconsistency of IVPRs is compatible with the underlying idea of fuzzy sets. It is revealed that a consistent preference relation is only a particular case with a fixed value of the defined consistency index. In general, the consistency index could be used to quantify the deviation degree from a consistent real-valued preference relation.

Title: Cyber Security Awareness, Knowledge and Behavior: A Comparative Study Abstract: Cyber-attacks represent a potential threat to information security. As rates of data usage and internet consumption continue to increase, cyber awareness turned to be increasingly urgent. This study focuses on the relationships between cyber security awareness, knowledge and behavior with protection tools among individuals in general and across four countries: Israel, Slovenia, Poland and Turkey in particular. Results show that internet users possess adequate cyber threat awareness but apply only minimal protective measures usually relatively common and simple ones. The study findings also show that higher cyber knowledge is connected to the level of cyber awareness, beyond the differences in respondent country or gender. In addition, awareness is also connected to protection tools, but not to information they were willing to disclose. Lastly, findings exhibit differences between the explored countries that affect the interaction between awareness, knowledge, and behaviors. Results, implications, and recommendations for effective based cyber security training programs are presented and discussed.

Title: Solving combined economic emission dispatch model via hybrid differential evaluation and crow search algorithm Abstract: One of the major aspects regarding the operation and planning of a power system was to reduce the emission of pollutions and fuel costs in thermal power plants. This issue was resolved as an optimization crisis, where the reduction of emission of pollutions and fuel cost was done and it is known as the combined economic emission dispatch (CEED) problem. Various techniques were introduced for improving the performance of the power plants with respect to algorithm reliability, solution accuracy, global optimality, and convergence speed for resolving the CEED issues. Therefore, this work establishes a CEED approach for the smart grid system and resolves it by exploiting the hybridized concepts of the crow search algorithm (CSA) and differential evolution (DE). The hybridized model of the two well-known schemes is achieved by updating the solutions of both the schemes and merging them with the random searching model. Thus, the new approach is named as hybrid DE and CSA model. The CEED approach is subjected to reduce its cost and therefore, sufficient trade-off between the emission and economic costs could be sustained. The presented hybrid scheme is simulated on 3 diverse bus systems and its performance is evaluated over other state-of-the-art models in terms of CPU time and generation strategy.

Title: On the influence of software application for visualization in teaching double integrals Abstract: In this paper the authors described the influence of the computer-based environment on students' learning achievement of the multidimensional calculus, in particular double integrals. The research was conducted with the second year students at the University of Kragujevac, Serbia, with two groups of students: the experimental and the control one. During the learning process of the experimental group, the materials made in Wolfram Mathematica were used for visualization. Students from the experimental group used these materials in order to successfully solve their double integral tasks. In the control group, students did not use a computer. The students in both groups got the identical tasks in their learning process and for the exam. During the exam, the students from both groups were not allowed to use computers. The results of the students' exam tasks were analyzed, with the emphasis on influence of visualization using computer environment, in determining the domain and integration bounds within solving double integrals. It was shown that the students from the experimental group had better results in all the exam tasks and that the software application for the visualization of multivariate functions contributed to better students' achievements in determining the domain of integration and the integration bounds in order to solve double integrals.

Title: The minimum weighted covariance determinant estimator revisited Abstract: This paper is devoted to robust estimation of parameters of multivariate data. It investigates the minimum weighted covariance determinant estimator, which is based on implicit weights assigned to individual observations and is highly resistant to the presence of outlying values (outliers). We propose alternative versions of the estimator, which can be computed by means of the same (approximate) algorithm. Based on numerical experiments, we recommend especially a version of the estimator based on minimizing the product of (only) several eigenvalues of the weighted covariance matrix of the data. This version is namely able to overcome the performance of several available estimators including MM-estimators on contaminated data. Another proposal with promising performance is a two-stage adaptive weighting scheme for the estimator.

Title: Gender, Performance, and Self-Efficacy: A Quasi-Experimental Field Study Abstract: With chronic labor shortages in STEM-related industries, much research has focused on how to get more women and minorities interested in STEM careers. The most recent studies seem to indicate that the actual gap in user performance between genders has narrowed, although women tend to have less self-efficacy. However, all these previous studies involved student subjects in an educational context. This research uses a quasi-experimental field study with actual managers to test whether there are differences between genders when performing a variety of tasks of differing complexity on different computing devices and whether there are differences in self-efficacy. Subjects' performance was measured by question accuracy and time taken to complete a task, while self-efficacy was measured by self-assessed confidence. The results support recent studies indicating that the gender gap in performance is minimal in accuracy with no differences in time spent, while the gap in self-efficacy has remained.

Title: Unleashing the hidden powers of low-cost IoT boards: GPU-based edutainment case study Abstract: The Ubiquitous interconnected smart devices enabled by the recent evolution of low-cost, generic, small-size, powerful computing platforms devised the term Internet of Things (IoT), which cross-cuts many areas of our modern day living. IoT applications go way beyond simple sensing and actuation to sophisticated localized processing and decision-making. The recent advances in embedded systems produced a long list of IoT boards equipped with powerful central processing units (CPUs), and graphics processing units (GPUs). Unfortunately, even with the limited energy consumption and high processing power of such GPUs, CPUs are usually the only computational element utilized by the hosted applications, thus hindering the capabilities of the entire board. This is mainly due to the complicated nature of GPUbased programming. In this paper, we are presenting a case study showing the effect of offloading the computationally intensive part of a latency-sensitive educational game to a low-cost Raspberry Pi's GPU, thus enabling the board to seamlessly host the entire game operations. Relying mainly on the boards CPU shows very long interaction latency i.e., 4.82 s. By efficiently leveraging the powerful coprocessor, VideoCore GPU, we are able to significantly improve the interaction latency to a fraction of a second, making the game conveniently playable. (C) 2020 The Authors. Production and hosting by Elsevier B.V. on behalf of King Saud University.

Title: Development of professional competencies for artificial intelligence in finite element analysis Abstract: This study identified the competency requirement for artificial intelligence in finite element analysis. The 10 Delphi group members included 5 field engineers in mechanical fields and 5 scholars from a technology institute. Next, 10 field experts were invited to participate. Using the Delphi technique and analytic hierarchy process, questionnaires were designed to assess competency indicators of artificial intelligence in finite element analysis. The data collected from questionnaires were analyzed using a nonparametric Wilcoxon signed-rank test, the Z value of the Kolmogorov-Smirnovone (KS) test, and relative weight. To fulfill the research objectives, a questionnaire was designed to collect data for 40 general competencies in 10 domains: (1) introduction to the finite element method, (2) pretreatment, (3) coordinate system, (4) model construction skills, (5) boundary conditions and solutions, (6) post processor application, (7) machine learning, (8) neural network, (9) deep learning, and (10) artificial intelligence in finite element analysis. The results of the three rounds of the Delphi technique expert questionnaire revealed essential professional competencies for AI in FEA. These findings can be used to devise a training and development plan and provide valuable references for educators in the field of engineering and technical education.

Title: Optimal inventory control policies for avoiding food waste Abstract: We develop and employ a socially responsible inventory model that determines an optimal order quantity and an optimal time instance of donation, taking into account, expectations on the net stock levels at the end of the order cycles. The optimized results of the policy are compared to those derived from the implementation of two currently applied policies namely the non-donation policy and the naive policy which involves the donation of a fixed amount of the company's produce. A main insight revealed through the implementation of the proposed policies in a numerical experimentation indicates that the employment of the proposed donation policy could potentially lead to significantly higher expected profits compared to the other two policies.

Title: Human face recognition with combination of DWT and machine learning Abstract: To enhance the accuracy of object recognition, various combination of recognition algorithms are used in recent literature. In this paper coherence of Discrete Wavelet Transform (DWT) is combined with four dif-ferent algorithms: error vector of principal component analysis (PCA), eigen vector of PCA, eigen vector of Linear Discriminant Analysis (LDA) and Convolutional Neural Network (CNN) then combination of four results are done using entropy of detection probability and Fuzzy system. From this research the accuracy of recognition is found dependent on image and diversity of database. The combined method of the paper provides recognition rate of 89.56% for the worst case and 93.34% for the best case both can be said better in comparison with the previous works where individual method has been implemented on a specific set of images.CO 2020 The Authors. Production and hosting by Elsevier B.V. on behalf of King Saud University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Title: Combining analytics and simulation methods to assess the impact of shared, autonomous electric vehicles on sustainable urban mobility Abstract: Urban mobility is currently undergoing three fundamental transformations with the sharing economy, electrification, and autonomous vehicles changing how people and goods move across cities. In this paper, we demonstrate the valuable contribution of decision support systems that combine data-driven analytics and simulation techniques in understanding complex systems such as urban transportation. Using the city of Berlin as a case study, we show that shared, autonomous electric vehicles can substantially reduce resource investments while keeping service levels stable. Our findings inform stakeholders on the trade-off between economic and sustainability-related considerations when fostering the transition to sustainable urban mobility.

Title: CYCLIC PARTITIONS OF COMPLETE AND ALMOST COMPLETE UNIFORM HYPERGRAPHS Abstract: We consider cyclic partitions of the complete k-uniform hypergraph on a finite set V, minus a set of s edges, s >= 0. An s-almost t-complementary k-hypergraph is a k-uniform hypergraph with vertex set V and edge set E for which there exists a permutation theta is an element of Sym(V) such that the sets E, E-theta, E-theta 2, . . . ,E (theta t-1) partition the set of all k-subsets of V minus a set of s edges. Such a permutation theta is called an s-almost (t, k)-complementing permutation . The s-almost t-complementary k-hypergraphs are a natural generalization of the almost self-complementary graphs which were previously studied by Clapham, Kamble et al. and Wojda. We prove the existence of an s-almost p(alpha)-complementary k-hypergraph of order n, where p is prime, s=Pi(i >= 0)(n(i) k(i)), and n(i) and k(i) are the entries in the base-p(alpha) representations of n and k, respectively. This existence result yields a combinatorial argument which generalizes Lucas' classic 1878 number theory result to prime powers, which was originally proved by Davis and Webb in 1990 by another method. In addition, we prove an alternative statement of the necessary and sufficient conditions for the existence of a p(alpha)-complementary k-hypergraph, and the equivalence of these two conditions yield an interesting relationship between the base-p representation and the base-p(alpha) representation of a positive integer n. Finally, we determine a set of necessary and sufficient conditions on n for the existence of a t-complementary k-uniform hypergraph on n vertices for composite values of t, extending previous results due to Wojda, Szymanski and Gosselin.

Title: AGCNN: Adaptive Gabor Convolutional Neural Networks with Receptive Fields for Vein Biometric Recognition Abstract: In recent years, finger vein recognition has attracted more attention and research as a secure method of identification. Convolutional neural networks have achieved great success in the field of finger vein recognition, yet they suffer from high computational complexity, large parameters, and other challenges. To solve these problems, we propose a Gabor convolutional neural network with receptive fields. We use Gabor filters with receptive field properties to design Gabor convolutional layers. Then we replace the conventional convolutional layer with the Gabor convolutional layer; analyze the influence of different loss functions, convolution kernel size, and feature size on the network model; and choose the most suitable model parameters and loss function. Finally, we systematically investigate comparative performance using AGCNN and CNNs in different finger vein databases. Experimental results show that the parameter complexity of AGCNN is significantly less than that of CNNs with a slight performance decrease.

Title: Local transform directional pattern and optimization driven DBN for age estimation Abstract: Age estimation is an interesting and challenging research area, gaining significant importance in the recent era and is employed in various applications, such as intelligent surveillance, face recognition, biometrics, and so on. Various techniques are employed in the literature for age estimation from the face images. This paper introduces the age estimation scheme from the face image, and estimation is done by defining a novel feature extraction strategy, named Local Transform Directional Pattern (LTDP). The database containing the input images has many unwanted regions, and thus, the Viola Jones algorithm detects the required face region. After detecting the face regions, active appearance model extracts the active appearance features, and the proposed LTDP extracts the texture features. The proposed LTDP feature extraction model modifies the existing Local Directional Pattern (LDP) with several other texture feature extraction models. After the feature extraction, the Cuckoo search based Deep Belief Network (CDBN) classifier estimates the age of the person from the face image based on the extracted features. The simulation results reveal that the proposed LTDP with the CDBN classifier achieved high performance with the values of 2.3416, 0.9803, and 0.9724 for MAE, AEO, and AEM, respectively.

Title: Sparse-FCM and deep learning for effective classification of land area in multi-spectral satellite images Abstract: Remote sensing plays a major role in crop classification, land use classification, and land cover classification such that the information for the classification is assured with the help of the satellite images. This paper concentrates on the land use classification and proposes an optimization algorithm, called Firefly Harmony Search (FHS) for training the Deep Belief Neural Network (DBN). The FHS algorithm is the integration of the Firefly Algorithm and Harmony Search Algorithm (HSA), which tunes the weights of DBN to perform the multi-class classification. For the effective classification, the multispectral image is subjected to the sparse Fuzzy C-Means to form segments such that the feature extraction is effective, free from dimensionality issues and computational complexities. The features extracted from the segments of the multi-spectral images include vegetation indices and statistical features. Then, these features are fed to the DBN, which is tuned using the FHS algorithm for performing the land use classification. Experimentation using four datasets proves the effectiveness of the proposed multi-class classification approach. The accuracy, sensitivity, and specificity of the method are found to be 0.9317, 0.9568, and 0.0379, respectively, that is effective over the existing land use classification methods.

Title: Ascending Subgraph Decompositions of Oriented Graphs that Factor into Triangles Abstract: In 1987, Alavi, Boals, Chartrand, Erdos, and Oellermann conjectured that all graphs have an ascending subgraph decomposition (ASD). In a previous paper, Wagner showed that all oriented complete balanced tripartite graphs have an ASD. In this paper, we will show that all orientations of an oriented graph that can be factored into triangles with a large portion of the triangles being transitive have an ASD. We will also use the result to obtain an ASD for any orientation of complete multipartite graphs with 3n partite classes each containing 2 vertices (a K(2 : 3n)) or 4 vertices (a K(4 : 3n)).

Title: Randomized selection algorithm for online stochastic unrelated machines scheduling Abstract: We consider an online stochastic unrelated machines scheduling problem. Specifically, a set of jobs arriving online over time must be randomly scheduled on the unrelated machines, which implies that the information of each job, including the release date and the weight, is not known until it is released. Furthermore, the actual processing time of each job is disclosed upon completion of this job. In addition, we focus on unrelated machines, which means that each job has a processing speed on every machine. Our goal is to minimize the expected total weighted completion time of all jobs. In this paper, we present a randomized selection algorithm for this problem and prove that the competitive ratio is a constant. Moreover, we show that it is asymptotic optimal for the online stochastic uniform machines scheduling problem when some parameters are bounded. Moreover, our proof does not require any probabilistic assumption on the job parameters.

Title: Robust model reference control for uncertain second-order system subject to parameter uncertainties Abstract: This paper is devoted to designing a robust model reference controller for uncertain second-order systems subject to parameter uncertainties. The system matrix of the first-order reference model is more general and the parameter uncertainties are assumed to be norm-bounded. The design of robust controller can be devided into two separate problems: problem robust stabilization and problem robust compensation. Based on the solution of generalized Sylvester matrix equations, we obtain some sufficient conditions to guarantee the complete parameterization of the controller. Then, the problem robust compensation of the closed-loop system is estimated by solving a convex optimisation problem with a set of linear matrix equations constraints. Two simulation examples are provided to illustrate the effectiveness of the proposed technique.

Title: Representation theorems of monotonicity generators for BSDEs via L-p (p > 1) solutions in general time intervals Abstract: The objective of this article is to show a representation theorem for generators of backward stochastic differential equations via L-p (p > 1) solutions in general time intervals when the generator satisfies a monotonicity condition and a polynomial growth condition in y and a Lipschitz condition in z both non-uniformly with respect to t. As its application, the corresponding converse comparison theorem for L-p (p > 1) solutions is obtained by this representation theorem.

Title: A study on cross-border e-commerce partner selection in B2B mode Abstract: The emergence of cross-border e-commerce has brought new opportunities to traditional enterprises. This paper discusses the partner selection of cross-border e-commerce companies in the B2B mode. It constructs a theoretical model of partner selection of cross-border e-commerce enterprises based on literature review. Through the mathematical analysis of an asymmetric evolutionary game model, it is considered that the model has an evolutionarily stable strategy. Based on it, a multi-agent model is constructed. The results of the simulation reveal the mediation role of trust between corporate reputation and enterprise cooperation. Simultaneously, it verified the moderation effect of information sharing between the trust and cooperation of cross-border e-commerce companies. It also provides explanations for the inconsistency in the relationship between trust and cooperative behavior. From both mathematical and data perspectives, this paper attempts to test the theoretical model proposed, which enriches the methodology to test the theory.

Title: Finding the Maximum Multi Improvement on neighborhood exploration Abstract: Neighborhood search techniques are often employed to deal with combinatorial optimization problems. Previous works got good results in applying a novel neighborhood search methodology called Multi Improvement (MI). First and best improvement are classical approaches for neighborhood exploration, while the MI has emerged due to the advance of new parallel computing technologies. The MI formalizes the concept of heuristic and exact exploration of independent moves for a given neighborhood structure, however, the advantages of an application of MI face the difficulty to select a great set of independent moves (which can be performed simultaneously). Most of the existing implementations of MI select these moves through heuristic methods, while others have succeeded in implementing exact dynamic programming approaches. In this paper, we propose a formal description for the Maximum Multi Improvement Problem (MMIP), as a theoretical background for the MI. Moreover, we develop three dynamic programming algorithms for solving the MMIP, given a solution tour for a Traveling Salesman Problem and neighborhood operators 2-Opt, 3-Opt, and OrOpt-k. The analysis suggests the rise of a new open topic focused on developing novel efficient neighborhood searches.

Title: Optimal designs of the exponentially weighted moving average (EWMA) median chart for known and estimated parameters based on median run length Abstract: In the literature, the sole dependence on the ARL as the performance measure of a control chart has received much criticism. This is because interpretation based on the ARL alone can be misleading, as the shape and skewness of the run-length distribution vary according to the magnitude of the process mean shift. Therefore, we consider the median run length (MRL) performance measure for optimal EWMA median chart when process parameters are known and estimated. We provide an illustrative example to show the application of the optimal EWMA median chart based on expected median run length (EMRL).

Title: Examining the spillover effect of sustainable consumption on microloan repayment: A big data-based research Abstract: Social value-oriented consumers perform more sustainable consumption than conventional consumers do because consumers’ choices reflect their latent social values on environmental protection. However, whether sustainable consumption prompts more social value-oriented behaviors outside the consumption domain remains uncertain. The increased availability of consumer-level big data presents an opportunity to investigate consumers’ cross-domain behavior subsequent to sustainable consumption, which broadens the comprehension of sustainable consumption by going beyond the boundary of consumption behavior. Supported by a joint dataset comprising information on both consumers’ consumption behavior and their microloan repayment behavior, this study examines the effects of sustainable consumption on consumers’ subsequent debt default behavior to empirically test the cross-domain spillover effects of sustainable consumption behavior. The results suggest that the default probability of green consumers overall was 4.34 % lower than that of nongreen consumers, even though this positive effect on repayment disappears when sustainable consumption is for health reasons. The findings contribute to research on sustainable consumption by providing empirical evidence indicating that sustainable consumption has positive spillover effects in other domains. The results also provide an alternative perspective for identifying high-quality borrowers for microloan platforms.

Title: Multidimensional outlier detection and robust estimation using S-n covariance Abstract: This article presents a robust method for detecting multiple outliers from multidimensional data using robust Mahalanobis distance. Initial scatter matrix for robust Mahalanobis distance is constructed using a robust estimator of covariance () established from a robust scale estimator S-n and casewise median are chosen to be the location vector. The performance of the proposed method is evaluated using the results of simulated samples. This outlier detection method is compared with some well-known methods available in the current literature. The application of the proposed method in real-life data is also executed in this article.

Title: Multiscale deep network based multistep prediction of high-dimensional time series from power transmission systems Abstract: Internet of energy makes the future power and energy network a more complicated and intelligent system. With the development of energy industry, the sample data of such system is high dimensional, dynamic, correlative, and complex. In order to meet people's needs and reduce the power redundancy, predicting the future energy demand and production is an essential approach. It is necessary for us to predict the later hours' or days' data, which means multistep prediction. However, the common one-step prediction model cannot forecast the power demand or production to make adequate preparation and the data have thousands of dimensions, which makes the problem challenging. In addition, the changeable pattern makes the common prediction algorithm do not perform good enough. In this article, we propose a sequence to sequence model to make multistep prediction with a baseline mean squared error (MSE) of 1.49x10(-5). In addition, we improve the model to be a multiscale deep network and decrease the MSE to 1.23x10(-5) through adding extra information to match different patterns. Furthermore, the multitask learning trick makes the MSE decrease to 1.18x10(-5).

Title: An approximation algorithm for the uniform capacitated k-means problem Abstract: In this paper, we consider the uniform capacitated k-means problem (UC-k-means), an extension of the classical k-means problem (k-means) in machine learning. In the UC-k-means, we are given a set $$\mathcal {D}$$ of n points in d-dimensional space and an integer k. Every point in the d-dimensional space has an uniform capacity which is an upper bound on the number of points in $$\mathcal {D}$$ that can be connected to this point. Every two-point pair in the space has an associated connecting cost, which is equal to the square of the distance between these two points. We want to find at most k points in the space as centers and connect every point in $$\mathcal {D}$$ to some center without violating the capacity constraint, such that the total connecting costs is minimized. Based on the technique of local search, we present a bi-criteria approximation algorithm, which has a constant approximation guarantee and violates the cardinality constraint within a constant factor, for the UC-k-means.

Title: Goodness of fit tests of the two-parameter gamma distribution against the three-parameter generalized gamma distribution Abstract: The generalized Gamma distribution is widely used in survival analysis, engineering and economics, and it includes the Gamma distribution as a special case. In real life applications, the Generalized Gamma distribution may be an unnecessarily complicated distribution to fit when one of the simpler models may be sufficient to analyze the data. The aim of this paper is to develop tests of goodness of fit of the two parameter gamma distribution against its three parameter counterpart. Specifically, we develop Wald, , score, likelihood ratio, and gradient tests. These tests are then compared in terms of empirical size and power using a simulation study.

Title: Tensor mutual information and its applications Abstract: Correlation analysis has long been a question of great interest in measuring the relationship among different variables and has been applied in many fields, such as dimension reduction, classification, and so on. However, current methods of correlation analysis take into account the linear relationship between multiple variables and only few works on nonlinear interaction of two variables have been considered. In this article, we first present a nonlinear analysis method of multiple (two or more) variables based on mutual information for tensor analysis (MITA). In addition, we extend the mutual-information matrix analysis directly to MITA and show the multivariable mutual information formula based on Venn diagram. Experiments on multiview dimension reduction, including attacking internet traffic prediction, advertisement classification, and biometric structure prediction illustrate the effectiveness of the proposed method, especially in the case of low-dimensional subspace.

Title: A novel improved symbiotic organisms search algorithm Abstract: For last two decades, nature-inspired metaheuristic algorithms together with their modified, improved, and hybrid versions have been gaining huge popularity in the field of optimization in solving continuous and complex real-life optimization problems. In this work, a novel improved symbiosis organism search (SOS) algorithm, called self-adaptive beneficial factor-based improved SOS (SaISOS, in short) is suggested. The self-adaptive benefit factors and a modified mutualism phase (called "Three-way mutualism phase") have been introduced here to upgrade the performance of SOS algorithm. A random weighted reflection coefficient and a new control operator have also been introduced. To validate the proposed algorithm and to compare its performance with other state-of-the-art algorithms, 15 IEEE-CEC 2015 functions have been employed and the experimental results confirm that SaISOS provides competitive results on most occasions. Also, the proposed algorithm is used to solve five real-world optimization problems. Considering the average output, it is observed that the proposed method performs significantly better in solving the real-world problems compared to the alternative state-of-the art techniques considered in this work.

Title: Enhanced clustering models with wiki-based k-nearest neighbors-based representation for web search result clustering Abstract: Information retrieval is a difficult process due to the overabundance of information on the web. Nowadays, search result responds to user queries with too many results although only a few are relevant. Therefore, the existing clustering methods that fail in clustering snippets (short texts) of web documents due to the low frequencies of document terms should be deeply investigated. One of the approaches that can be used to solve this problem is the expansion of document terms with semantically similar terms. Hence, a list of terms with their closest and accurate semantically similar words (word representation) must be built. This study aims to design and develop a new framework to enhance the performance of web search result clustering (WSRC). The research also presents a new unsupervised distributed word representation scheme where each word is represented by a vector of its semantically related words; such as scheme expands snippets and user queries. The proposed framework consists of several activities, such as (1) various standard datasets (Open Directory Project [ODP]-239 and MORESQUE) that are used for evaluating search result clustering algorithms for most cited dataset works, (2) text pre-processing, (3) document representation based on a new wiki-based k-nearest neighbors (KNN) representation method, (4) effect of the proposed model on the performance of traditional clustering methods (k-means, k-medoids, single-linkage, and complete-linkage) for WSRC, and (5) evaluation stage of the proposed method. Results indicate that enhanced clustering methods, according to the new wiki-KNN based representation method in comparison with the baseline methods, show a significant improvement in WSRC. Furthermore, the new data representation scheme has enhanced the overall performance of clustering methods. (C) 2020 The Authors. Production and hosting by Elsevier B.V. on behalf of King Saud University.

Title: Improving accuracy models using elastic net regression approach based on empirical mode decomposition Abstract: In this study, an elastic net (EN) regression model based on the empirical mode decomposition (EMD) algorithm is used in two applications, namely, numerical experiment and actual time series data. EMD is used to analyze a nonstationary and nonlinear signal dataset, which includes a set of orthogonal intrinsic mode functions (IMFs) and residual components. EN regression is used to select the most significant predictor variables influencing response variables and can address the multicollinearity problem between predictor variables. The main objective of this study is to apply the proposed method, EMD-EN, by using two variables for selecting important orthogonal IMFs and the residual components of predictor variables with significant effects on response variables. Moreover, this study uses the EMD-EN method in two different applications involving nonstationary and nonlinear problems. Results show that the proposed method outperforms other competitive methods in the numerical experiment and applications.

Title: System reliability for a multi-state distribution network with multiple terminals under stocks Abstract: To achieve the most efficiency in supply chain management, the capability of distribution networks is a key point for the entire supply chain. Stocks are critical for enhancing the efficiency of satisfying the demand of retailers in the distribution network. A configuration of a distribution network is consisted of routes and nodes. Each route connects a pair of nodes and each node is denoted as a supplier, a distribution center, or a retailer. For each route, it has a carrier whose available capacity for demand transmission is multi state. Hence, a distribution network is also regarded as a multi state network and such a network is named as a multi state distribution network (MDN) in here. The propose of this paper is to evaluate the system reliability which is defined as the probability that the MDN can meet all retailers’ demand under stocks. In practical, all retailers’ demand should be satisfied by stocks in the distribution centers (DCs) firstly. Therefore flow assignment in MDN model is mainly clarified by the relationship between the demand of retailers, stocks on DCs, and suppliers. The concept of minimal capacity vectors (MCVs) is then proposed and an algorithm is developed to obtaining MCVs for evaluating system reliability.

Title: On inequalities with bounded coefficients and pitch for the min knapsack polytope Abstract: The min knapsack problem appears as a major component in the structure of capacitated covering problems. Its polyhedral relaxations have been extensively studied, leading to strong relaxations for networking, scheduling and facility location problems.

Title: Correction to: Solving a home energy management problem by Simulated Annealing Abstract: Solving a home energy management problem by Simulated Annealing.

Title: On the fractional moments of a truncated centered multivariate normal distribution Abstract: In this paper, we study the fractional moments of a truncated centered multivariate normal distribution, with a focus on their computation. We develop computational methods, including ones based on the holonomic gradient method, the second-order Laplace approximation, and the Monte Carlo method. These methods enable us to compute higher order fractional moments without evaluating multiple integrals. Via numerical experiments, we investigate their performances. Some applications, including robust graphical modeling based on the alternative multivariate t-distribution, are also presented.

Title: Graphs with Unique Maximum Packing of Closed Neighborhoods Abstract: A packing of a graph G is a subset P of the vertex set of G such that the closed neighborhoods of any two distinct vertices of P do not intersect. We study graphs with a unique packing of the maximum cardinality. We present several general properties for such graphs. These properties are used to characterize the trees with a unique maximum packing. Two characterizations are presented where one of them is inductive based on five operations.

Title: A consistent test of independence and goodness-of-fit in linear regression models Abstract: We propose a new approach to simultaneously test the assumptions of independence and goodness-of-fit for a multiple linear regression model say H-0, vs. H-1: H-0 is false. Our approach is based on the difference between the empirical distribution function of and a consistent estimator of where satisfies H-0 (even if doesn't) and iff H-0 holds. The p-value of the test is based on the resampling distribution from The new test is consistent, i.e., its power tends to 1 as the sample size increases, even when On the contrary, the consistency of existing tests is proven under special cases of H-1, but not all cases under H-1. Moreover, our simulation study suggests that existing tests e.g., the test in Sen and Sen (2014) and the quantile regression test can have powers for large sample sizes.

Title: The impact of place-of-origin on price premium for agricultural products: empirical evidence from Taobao.com Abstract: The impact of place-of-origin on price premium for agricultural products in the online marketplace has received limited attention in the existing literature. This study draws from the elaboration likelihood model and investigates whether place-of-origin affects price premium. Moreover, this study explores how other cues [seller’s reputation, positive word-of-mouth (WOM) volume, and WOM valence] moderate the relationship between place-of-origin and price premium for agricultural products in the online marketplace. The result of the empirical study reveals that place-of-origin indeed has a significant and positive impact on price premium. Furthermore, the study finds a negative interactive effect between place-of-origin and other cues (seller’s reputation, positive WOM volume, and WOM valence) on the price premium for agricultural products in an e-commerce setting. The results highlight the importance of place-of-origin in the competitive online market and have implications both for academic research and for online retailing practice.

Title: Semantic-Gap-Oriented Feature Selection and Classifier Construction in Multilabel Learning Abstract: Multilabel learning focuses on assigning instances with different labels. In essence, the multilabel learning aims at learning a predictive function from feature space to a label space. The predictive function learning procedure can be regarded as a feature selection procedure and as a classifier construction procedure. For feature selection, we extract features for each label based on the learned...

Title: A Unifying Framework for Human–Agent Collaborative Systems—Part I: Element and Relation Analysis Abstract: The human–agent collaboration (HAC) is a prospective research topic whose great applications and future scenarios have attracted vast attention. In a broad sense, the HAC system (HACS) can be broken down into six elements: “Man,” “Agents,” “Goal,” “Network,” “Environment,” and “Tasks.” By merging these elements and building a relation graph, this article proposes a systematic analysis framework fo...

Title: Bit-Rate Conditions for the Consensus of Quantized Multiagent Systems Based on Event Triggering Abstract: This article investigates the asymptotic consensus problem for multiple discrete-time agents with general dynamics under event-triggered sampling. In such multiagent systems (MASs), the information exchanged between neighboring agents is quantized and transmitted through a digital communication network. Due to the limited bandwidth, it is impossible for agents to capture the precise states of neig...

Title: Sampled-Data Consensus of Linear Time-Varying Multiagent Networks With Time-Varying Topologies Abstract: The main purpose of this article is to investigate the consensus of linear multiagent networks with time-varying characteristics under sampled-data communications, where the time-varying characteristics include both time-varying topologies and the node’s linear time-varying dynamics. By using the decoupling method, we prove that the sampled-data consensus problem of multiagent networks is equal to...

Title: Random Shapley Forests: Cooperative Game-Based Random Forests With Consistency Abstract: The original random forests (RFs) algorithm has been widely used and has achieved excellent performance for the classification and regression tasks. However, the research on the theory of RFs lags far behind its applications. In this article, to narrow the gap between the applications and the theory of RFs, we propose a new RFs algorithm, called random Shapley forests (RSFs), based on the Shapley ...

Title: A Robust Image-Sequence-Based Framework for Visual Place Recognition in Changing Environments Abstract: This article proposes a robust image-sequence-based framework to deal with two challenges of visual place recognition in changing environments: 1) viewpoint variations and 2) environmental condition variations. Our framework includes two main parts. The first part is to calculate the distance between two images from a reference image sequence and a query image sequence. In this part, we remove the...

Title: Quasisynchronization of Heterogeneous Dynamical Networks via Event-Triggered Impulsive Controls Abstract: The time-triggered impulsive control of complex homogeneous dynamical networks has received wide attention due to its occasional occupation of the communication channels. This article is devoted to quasisynchronization of heterogeneous dynamical networks via event-triggered impulsive controls with less channel occupation. Two kinds of triggered mechanisms, that is, the centralized event-triggered ...

Title: Adaptive Distance-Based Band Hierarchy (ADBH) for Effective Hyperspectral Band Selection Abstract: Band selection has become a significant issue for the efficiency of the hyperspectral image (HSI) processing. Although many unsupervised band selection (UBS) approaches have been developed in the last decades, a flexible and robust method is still lacking. The lack of proper understanding of the HSI data structure has resulted in the inconsistency in the outcome of UBS. Besides, most of the UBS me...

Title: Optimal Stealth Attack Strategy Design for Linear Cyber-Physical Systems Abstract: This article studies the problem of the optimal stealth attack strategy design for linear cyber-physical systems (CPSs). Virtual systems that reflect the attacker’s target are constructed, and a linear attack model with varying gains is designed based on the virtual models. Unlike the existing optimal stealth attack strategies that are designed based on sufficient conditions, necessary and suffici...

Title: Hallucinating Color Face Image by Learning Graph Representation in Quaternion Space Abstract: Recently, learning-based representation techniques have been well exploited for grayscale face image hallucination. For color images, the previous methods only handle the luminance component or each color channel individually, without considering the abundant correlations among different channels as well as the inherent geometrical structure of data manifold. In this article, we propose a learning...

Title: Self-Learning Robust Control Synthesis and Trajectory Tracking of Uncertain Dynamics Abstract: In this article, we investigate the self-learning robust control synthesis and tracking design of general uncertain dynamical systems. Based on the adaptive critic learning, the robust stabilization method is developed with the help of conducting problem transformation. In addition, by considering the optimal control solution with a discounted cost function, the established method is extended to a...

Title: Attentive Relational State Representation in Decentralized Multiagent Reinforcement Learning Abstract: In multiagent reinforcement learning (MARL), it is crucial for each agent to model the relation with its neighbors. Existing approaches usually resort to concatenate the features of multiple neighbors, fixing the size and the identity of the inputs. But these settings are inflexible and unscalable. In this article, we propose an attentive relational encoder (ARE), which is a novel scalable feedfor...

Title: AN ACCELERATED METHOD FOR DERIVATIVE-FREE SMOOTH STOCHASTIC CONVEX OPTIMIZATION Abstract: We consider an unconstrained problem of minimizing a smooth convex function which is only available through noisy observations of its values, the noise consisting of two parts. Similar to stochastic optimization problems, the first part is of stochastic nature. The second part is additive noise of unknown nature but bounded in absolute value. In the two-point feedback setting, i.e., when pairs of function values are available, we propose an accelerated derivative-free algorithm together with its complexity analysis. The complexity bound of our derivative-free algorithm is only by a factor of root n larger than the bound for accelerated gradient-based algorithms, where n is the dimension of the decision variable. We also propose a nonaccelerated derivative-free algorithm with a complexity bound similar to the stochastic gradient-based algorithm; that is, our bound does not have any dimension-dependent factor except logarithmic. Notably, if the difference between the starting point and the solution is a sparse vector, for both our algorithms, we obtain a better complexity bound if the algorithm uses an 1-norm proximal setup rather than the Euclidean proximal setup, which is a standard choice for unconstrained problems.

Title: Extending some results on the second neighborhood conjecture Abstract: If in a directed graph, v is an out-neighbor of u and w is an out-neighbor of v but not of u, then w is said to be a second out-neighbor of u. A vertex in a directed graph is said to have a large second neighborhood if it has at least as many second out-neighbors as out neighbors. The Second Neighborhood Conjecture, first stated by Seymour, asserts that there is a vertex having a large second neighborhood in every oriented graph (a directed graph without loops or digons). It is straightforward to see that the conjecture is true for any oriented graph whose underlying undirected graph is bipartite. We extend this to show that the conjecture holds for oriented graphs whose vertex set can be partitioned into an independent set and a 2-degenerate graph. Fisher proved the conjecture for tournaments and later Havet and Thomass & eacute; provided a different proof for the same using median orders of tournaments. Havet and Thomass & eacute; in fact showed the stronger statement that if a tournament contains no sink, then it contains at least two vertices with large second neighborhoods. Using their techniques, Fidler and Yuster showed that the conjecture remains true for tournaments from which either a matching or a star has been removed. We extend this result to show that the conjecture holds even for tournaments from which both a matching and a star have been removed. This implies that a tournament from which a matching has been removed contains either a sink or two vertices with large second neighborhoods. (c) 2022 Elsevier B.V. All rights reserved. <comment>Superscript/Subscript Available</comment

Title: Tight Bounds on the Convergence Rate of Generalized Ratio Consensus Algorithms Abstract: The problems discussed in this article are motivated by general ratio consensus algorithms, introduced by Kempe et al. in 2003 in a simple form as the push-sum algorithm, later extended by Bénézit et al. in 2010 under the name weighted gossip algorithm. We consider a communication protocol described by a strictly stationary, ergodic, sequentially primitive sequence of nonnegative mat...

Title: A matrix-less method to approximate the spectrum and the spectral function of Toeplitz matrices with real eigenvalues Abstract: It is known that the generating function f of a sequence of Toeplitz matrices {Tn(f)}n may not describe the asymptotic distribution of the eigenvalues of Tn(f) if f is not real. In this paper, we assume as a working hypothesis that, if the eigenvalues of Tn(f) are real for all n, then they admit an asymptotic expansion of the same type as considered in previous works, where the first function, called the eigenvalue symbol $\mathfrak {f}$ , appearing in this expansion is real and describes the asymptotic distribution of the eigenvalues of Tn(f). This eigenvalue symbol $\mathfrak {f}$ is in general not known in closed form. After validating this working hypothesis through a number of numerical experiments, we propose a matrix-less algorithm in order to approximate the eigenvalue distribution function $\mathfrak {f}$ . The proposed algorithm, which opposed to previous versions, does not need any information about neither f nor $\mathfrak {f}$ is tested on a wide range of numerical examples; in some cases, we are even able to find the analytical expression of $\mathfrak {f}$ . Future research directions are outlined at the end of the paper.

Title: Accelerated parallel non-conjugate sampling for Bayesian non-parametric models Abstract: Inference of latent feature models in the Bayesian nonparametric setting is generally difficult, especially in high dimensional settings, because it usually requires proposing features from some prior distribution. In special cases, where the integration is tractable, we can sample new feature assignments according to a predictive likelihood. We present a novel method to accelerate the mixing of latent variable model inference by proposing feature locations based on the data, as opposed to the prior. First, we introduce an accelerated feature proposal mechanism that we show is a valid MCMC algorithm for posterior inference. Next, we propose an approximate inference strategy to perform accelerated inference in parallel. A two-stage algorithm that combines the two approaches provides a computationally attractive method that can quickly reach local convergence to the posterior distribution of our model, while allowing us to exploit parallelization.

Title: On decidability of amenability in computable groups Abstract: The main result of the paper states that there is a finitely presented group G with decidable word problem where detection of finite subsets of G which generate amenable subgroups is not decidable.

Title: Understanding Neural Networks and Individual Neuron Importance via Information-Ordered Cumulative Ablation Abstract: In this work, we investigate the use of three information-theoretic quantities—entropy, mutual information with the class variable, and a class selectivity measure based on Kullback–Leibler (KL) divergence—to understand and study the behavior of already trained fully connected feedforward neural networks (NNs). We analyze the connection between these information-theoretic quantities and classification performance on the test set by cumulatively ablating neurons in networks trained on MNIST, FashionMNIST, and CIFAR-10. Our results parallel those recently published by Morcos et al., indicating that class selectivity is not a good indicator for classification performance. However, looking at individual layers separately, both mutual information and class selectivity are positively correlated with classification performance, at least for networks with ReLU activation functions. We provide explanations for this phenomenon and conclude that it is ill-advised to compare the proposed information-theoretic quantities across layers. Furthermore, we show that cumulative ablation of neurons with ascending or descending information-theoretic quantities can be used to formulate hypotheses regarding the joint behavior of multiple neurons, such as redundancy and synergy, with comparably low computational cost. We also draw connections to the information bottleneck theory for NNs.

Title: Optimal Cyber-Insurance Contract Design for Dynamic Risk Management and Mitigation Abstract: With the recent growing number of cyberattacks and the constant lack of effective defense methods, cyber risks have become ubiquitous in enterprise networks, manufacturing plants, and government computer systems. Cyber insurance provides a valuable approach to transfer the cyber risks to insurance companies and further improve the security status of the insured. The designation of effective cyber-insurance contracts requires considerations from both the insurance market and the dynamic properties of the cyber risks. To capture the interactions between the users and the insurers, we present a dynamic moral-hazard type of principal–agent model incorporated with Markov decision processes, which are used to capture the dynamics and correlations of the cyber risks as well as the user’s decisions on the protections. We study and fully analyze a case with a two-state two-action user under linear coverage insurance and further show the risk compensation, Peltzman effect, linear insurance contract principle, and zero-operating profit principle in this case. Numerical experiments are provided to verify our conclusions and further extend to cases of a four-state three-action user under linear coverage insurance and threshold coverage insurance.

Title: Predicting Brazilian Court Decisions Abstract: Predicting case outcomes is useful for legal professionals to understand case law, file a lawsuit, raise a defense, or lodge appeals, for instance. However, it is very hard to predict legal decisions since this requires extracting valuable information from myriads of cases and other documents. Moreover, legal system complexity along with a huge volume of litigation make this problem even harder. This paper introduces an approach to predicting Brazilian court decisions, including whether they will be unanimous. Our methodology uses various machine learning algorithms, including classifiers and state-of-the-art Deep Learning models. We developed a working prototype whose F1-score performance is similar to 80.2% by using 4,043 cases from a Brazilian court. To our knowledge, this is the first study to present methods for predicting Brazilian court decision outcomes.

Title: Scalar Multivariate Risk Measures with a Single Eligible Asset Abstract: In this paper we present results on scalar risk measures in markets with transaction costs. Such risk measures are defined as the minimal capital requirements in the cash asset. First, some results are provided on the dual representation of such risk measures, with particular emphasis given on the space of dual variables as (equivalent) martingale measures and prices consistent with the market model. Then, these dual representations are used to obtain the main results of this paper on time consistency for scalar risk measures in markets with frictions. It is well known from the superhedging risk measure in markets with transaction costs, as in Jouini and Kallal (1995), Roux and Zastawniak (2016), and Loehne and Rudloff (2014), that the usual scalar concept of time consistency is too strong and not satisfied. We will show that a weaker notion of time consistency can be defined, which corresponds to the usual scalar time consistency but under any fixed consistent pricing process. We will prove the equivalence of this weaker notion of time consistency and a certain type of backward recursion with respect to the underlying risk measure with a fixed consistent pricing process. Several examples are given, with special emphasis on the superhedging risk measure.

Title: Consensus of a class of nonlinear fractional-order multi-agent systems via dynamic output feedback controller Abstract: This paper addresses the consensus of a class of nonlinear fractional-order multi-agent systems (FOMASs) with positive real uncertainty. First, a fractional non-fragile dynamic output feedback controller is put forward via the output measurements of neighboring agents, then appropriate state transformation reduced the consensus problem to a stability one. A sufficient condition based on direct Lyapunov approach, for the robust asymptotic stability of the transformed system and subsequently for the consensus of the main system is presented. In addition, utilizing S-procedure and Schur complement, the systematic stabilization design algorithm is proposed for fractional-order system with and without nonlinear terms. The results are formulated as an optimization problem with linear matrix inequality constraints. Simulation results are given to verify the effectiveness of the theoretical results.

Title: The density and minimal gap of visible points in some planar quasicrystals Abstract: It has previously been observed that the limiting gap distribution of the directions to visible points of planar quasicrystals may vanish near zero, that is, there exist planar quasicrystals with a positive limiting minimal normalised gap between the angles of visible points. The exact values of these limiting minimal normalised gaps have not been determined. In this paper we give explicit formulas for the densities of visible points for planar quasicrystals from several families, which include the Ammann-Beenker point set and the vertex sets of some rhombic Penrose tilings. Combining these results with a known characterisation of the limiting minimal gap in terms of a probability measure on an associated homogeneous space of quasicrystals, we give explicit values of the limiting minimal normalised gap between the angles of visible points for several families of planar quasicrystals, in particular, for the Ammann-Beenker point set and for the vertex sets of some rhombic Penrose tilings. We also compare our results with numerical observations.

Title: Turan Number of Disjoint Triangles in 4-Partite Graphs Abstract: Let k >= 2 and n(1) >= n(2) >= n(3) >= n(4) be integers such that n(4) is sufficiently larger than k. We determine the maximum number of edges of a 4-partite graph with parts of sizes n(1), ..., n(4) that does not contain k vertex-disjoint triangles. For any r > t >= 3, we give a conjecture on the maximum number of edges of an r-partite graph that does not contain k vertex-disjoint cliques K-t.

Title: Subdivision of Maps of Digital Images Abstract: A digital image is a finite set of integer lattice points in an ambient Euclidean space together with a suitable adjacency relation between points. Subdivision, which is a process of enlarging a digital image in the photographic sense, provides a basic tool for operating with digital images. But given a map of digital images, there is as yet no general way to define a map of their subdivisions that might reasonably be called a subdivision of the map. In this paper, we construct such maps of subdivisions when the map of digital images has a 1- or 2-dimensional domain. From our constructions we deduce path covering and homotopy covering results that play a role in our development of the digital fundamental group.

Title: An active-set algorithm for norm constrained quadratic problems Abstract: We present an algorithm for the minimization of a nonconvex quadratic function subject to linear inequality constraints and a two-sided bound on the 2-norm of its solution. The algorithm minimizes the objective using an active-set method by solving a series of trust-region subproblems (TRS). Underpinning the efficiency of this approach is that the global solution of the TRS has been widely studied in the literature, resulting in remarkably efficient algorithms and software. We extend these results by proving that nonglobal minimizers of the TRS, or a certificate of their absence, can also be calculated efficiently by computing the two rightmost eigenpairs of an eigenproblem. We demonstrate the usefulness and scalability of the algorithm in a series of experiments that often outperform state-of-the-art approaches; these include calculation of high-quality search directions arising in Sequential Quadratic Programming on problems of the CUTEst collection, and Sparse Principal Component Analysis on a large text corpus problem (70 million nonzeros) that can help organize documents in a user interpretable way.

Title: On the computational complexity of the bipartizing matching problem Abstract: Given a graph $$G=(V,E)$$ , an edge bipartization set of G is a subset $$E'\subseteq E(G)$$ such that  $$G'=(V,E{\setminus } E')$$ is bipartite. An edge bipartization set that is also a matching of G is called a bipartizing matching of G. Let  $${\mathscr {BM}}$$ be the family of all graphs admitting a bipartizing matching. Although every graph has an edge bipartization set, the problem of recognizing graphs G having bipartizing matchings ( $$G\in \mathscr {BM}$$ ) is challenging. A (k, d)-coloring of a graph G is a k-coloring of V(G) such that each vertex of G has at most d neighbors with the same color as itself. Clearly a (k, 0)-coloring is a proper vertex k-coloring of G and, for any  $$d>0$$ , the k-coloring is non-proper, also known as defective. A graph belongs to  $$\mathscr {BM}$$ if and only if it admits a (2, 1)-coloring. Lovász (1966) proved that for any integer  $$k>0$$ , any graph of maximum degree  $$\varDelta $$ admits a  $$\left( k,\lfloor \varDelta /k \rfloor \right) $$ -coloring. In this paper, we show that it is NP-complete to determine whether a 3-colorable planar graph of maximum degree 4 belongs to $$\mathscr {BM}$$ , i.e., (2, 1)-colorable. Besides, we show that it is NP-complete to determine whether planar graphs of maximum degree 6 or 8 admit a (2, 2) or (2, 3)-coloring, respectively. Due to Lovász (1966), our results are tight in the sense that on graphs with maximum degree three, five, and seven, there always exists a (2, 1), (2, 2), and (2, 3)-coloring, respectively. Finally, we present polynomial-time algorithms for particular graph classes, besides some remarks on the parameterized complexity of the problem of recognizing graphs in  $${\mathscr {BM}}$$ .

Title: Equitable factorizations of edge-connected graphs Abstract: In this paper, we show that every (3k - 3)-edge-connected graph G, under a certain degree condition, can be edge-decomposed into k factors G(1), ..., G(k) such that for each vertex v is an element of V(G(i)), vertical bar dG(i)(v)- d(G)(v)/k vertical bar < 1, where 1 <= i <= k. As an application, we deduce that every 6-edge-connected graph G can be edge-decomposed into three factors G(1), G(2), and G(3) such that for each vertex v is an element of V(G(i))(3) with 1 <= i <= 3, vertical bar dG(i)(v) - d(G)(v)/3 vertical bar < 1, unless 3 G has exactly one vertex z with d(G)(z) (sic) 0. Next, we show that every odd-(3k - 2)-edge connected graph G can be edge-decomposed into k factors G(1), ..., G(k) such that for each vertex v is an element of V(G(i)), d(Gi)(v) and d(G) (v) have the same parity and vertical bar d(Gi)(v) - dG(v)/k vertical bar < 2, where k is an odd positive integer and 1 <= i <= k. Finally, we give a sufficient edge-connectivity condition for a graph G to have a parity factor F with specified odd-degree vertices such that for each vertex v, vertical bar d(F)(v) - epsilon d(G)(v)vertical bar < 2, where s is a real number with 0 < s < 1. (C) 2022 Elsevier B.V. All rights reserved.

Title: Monte Carlo and Quasi-Monte Carlo Density Estimation via Conditioning Abstract: Estimating the unknown density from which a given independent sample originates is more difficult than estimating the mean, in the sense that for the best popular density estimators, the mean integrated square error converges slower than at the canonical rate of $\mathcal{O}(1/n)$. When the sample is generated from a simulation model and we have control over how this is done, we can do better. We study an approach in which conditional Monte Carlo permits one to obtain a smooth estimator of the cumulative distribution function, whose sample derivative is an unbiased estimator of the density at any point, and therefore converges at a faster rate than the usual density estimators, under mild conditions. By combining this with randomized quasi-Monte Carlo to generate the sample, we can achieve an even faster rate.

Title: A FIRST-ORDER FRAMEWORK FOR INQUISITIVE MODAL LOGIC Abstract: We present a natural standard translation of inquisitive modal logic InqML into first-order logic over the natural two-sorted relational representations of the intended models, which captures the built-in higher-order features of InqML. This translation is based on a graded notion of flatness that ties the inherent second-order, team-semantic features of InqML over information states to subsets or tuples of bounded size. A natural notion of pseudo-models, which relaxes the non-elementary constraints on the intended models, gives rise to an elementary, purely model-theoretic proof of the compactness property for InqML. Moreover, we prove a Hennessy-Milner theorem for InqML, which crucially uses omega-saturated pseudo-models and the new standard translation. As corollaries we also obtain van Benthem style characterisation theorems.

Title: Structure-Adaptive Manifold Estimation Abstract: We consider a problem of manifold estimation from noisy observations. Many manifold learning procedures locally approximate a manifold by a weighted average over a small neighborhood. However, in the presence of large noise, the assigned weights become so corrupted that the averaged estimate shows very poor performance. We suggest a structure-adaptive procedure, which simultaneously reconstructs a smooth manifold and estimates projections of the point cloud onto this manifold. The proposed approach iteratively refines the weights on each step, using the structural information obtained at previous steps. After several iterations, we obtain nearly "oracle" weights, so that the final estimates are nearly efficient even in the presence of relatively large noise. In our theoretical study, we establish tight lower and upper bounds proving asymptotic optimality of the method for manifold estimation under the Hausdorlf loss, provided that the noise degrades to zero fast enough.

Title: LAEO-Net++: Revisiting People Looking at Each Other in Videos Abstract: Capturing the ‘mutual gaze’ of people is essential for understanding and interpreting the social interactions between them. To this end, this paper addresses the problem of detecting people Looking At Each Other (LAEO) in video sequences. For this purpose, we propose LAEO-Net++, a new deep CNN for determining LAEO in videos. In contrast to previous works, LAEO-Net++ takes spatio-temporal tr...

Title: Folding Bilateral Backstepping Output-Feedback Control Design for an Unstable Parabolic PDE Abstract: We present a novel methodology for designing output-feedback backstepping bilateral boundary controllers for an unstable 1D diffusion-reaction partial differential equation (PDE) with spatially varying reaction. Using folding transforms the parabolic PDE into a $2 \times 2$ coupled PDE system with coupling through compatibility...

Title: Fractional Cocoloring of Graphs Abstract: The cochromatic number Z(G) of a graph G is the fewest number of colors needed to color the vertices of G so that each color class is a clique or an independent set. In a fractional cocoloring of G a non-negative weight is assigned to each clique and independent set so that for each vertex v, the sum of the weights of all cliques and independent sets containing v is at least one. The smallest total weight of such a fractional cocoloring of G is the fractional cochromatic number $$Z_f(G)$$ . In this paper we prove results for the fractional cochromatic number $$Z_f(G)$$ that parallel results for Z(G) and the well studied fractional chromatic number $$\chi _f{(G)}$$ . For example $$Z_f(G)=\chi _f(G)$$ when G is triangle-free, except when the only nontrivial component of G is a star. More generally, if G contains no k-clique, then $$Z_f(G)\le \chi _f(G)\le Z_f(G)+R(k,k)$$ , where R(k, k) is the minimum integer n such that every n-vertex graph has a k-clique or an independent set of size k. Moreover, every graph G with $$\chi _f(G)=m$$ contains a subgraph H with $$Z_f(H)\ge (\frac{1}{4} - o(1))\frac{m}{\log _2 m}$$ . We also prove that the maximum value of $$Z_f(G)$$ over all graphs G of order n is $$\varTheta (n/\log n)$$ , and the maximum over all graphs embedded on an orientable surface of genus g is $$\varTheta (\sqrt{g} / \log g)$$ .

Title: The complexity of the vertex-minor problem Abstract: A graph H is a vertex-minor of a graph G if it can be reached from G by the successive application of local complementations and vertex deletions. Vertex-minors have been the subject of intense study in graph theory over the last decades and have found applications in other fields such as quantum information theory. Therefore it is natural to consider the computational complexity of deciding whether a given graph G has a vertex-minor isomorphic to another graph H. Here we prove that this decision problem is NP-complete, even when restricting H and G to be circle graphs, a class of graphs that has a natural relation to vertex-minors.

Title: Multivariate polynomials for generalized permutohedra. Abstract: Using the notion of Mahonian statistic on acyclic posets, we introduce a $q$-analogue of the $h$-polynomial of a simple generalized permutohedron. We focus primarily on the case of nestohedra and on explicit computations for many interesting examples, such as $S_n$-invariant nestohedra, graph associahedra, and Stanley--Pitman polytopes. For the usual (Stasheff) associahedron, our generalization yields an alternative $q$-analogue to the well-studied Narayana numbers.

Title: lpdensity: Local Polynomial Density Estimation and Inference Abstract: Density estimation and inference methods are widely used in empirical work. When the underlying distribution has compact support, conventional kernel-based density estimators are no longer consistent near or at the boundary because of their well-known boundary bias. Alternative smoothing methods are available to handle boundary points in density estimation, but they all require additional tuning parameter choices or other typically ad hoc modifications depending on the evaluation point and/or approach considered. This article discusses the R and Stata package lpdensity implementing a novel local polynomial density estimator proposed and studied in Cattaneo, Jansson, and Ma (2020, 2022), which is boundary adaptive and involves only one tuning parameter. The methods implemented also cover local polynomial estimation of the cumulative distribution function and density derivatives. In addition to point estimation and graphical procedures, the package offers consistent variance estimators, mean squared error optimal bandwidth selection, robust bias-corrected inference, and confidence bands construction, among other features. A comparison with other density estimation packages available in R using a Monte Carlo experiment is provided.

Title: Strong Embeddings for Transitory Queueing Models Abstract: In this paper we establish strong embedding theorems, in the sense of the Komlos-Major-Tusnady framework, for the performance metrics of a general class of transitory queueing models of nonstationary queueing systems. The nonstationary and non-Markovian nature of these models makes the computation of performance metrics hard. The strong embeddings yield error bounds on sample path approximations by diffusion processes, in the form of functional strong approximation theorems.

Title: On cyclic quiver parabolic Kostka-Shoji polynomials Abstract: We obtain an explicit combinatorial formula for certain parabolic Kostka-Shoji polynomials associated with the cyclic quiver, generalizing results of Shoji and of Liu and Shoji.

Title: 2D PET Image Reconstruction Using Robust L1 Estimation of the Gaussian Mixture Model. Abstract: An image or volume of interest in positron emission tomography (PET) is reconstructed from pairs of gamma rays emitted from a radioactive substance. Many image reconstruction methods are based on estimation of pixels or voxels on some predefined grid. Such an approach is usually associated with limited resolution of the reconstruction, high computational complexity due to slow convergence and noisy results. This paper explores reconstruction of PET images using the underlying assumption that the originals of interest can be modeled using Gaussian mixture models. A robust segmentation method based on statistical properties of the model is presented, with an iterative algorithm resembling the expectation-maximization algorithm. Use of parametric models for image description instead of pixels circumvent some of the mentioned limitations.

Title: Parallel random block-coordinate forward–backward algorithm: a unified convergence analysis Abstract: We study the block-coordinate forward–backward algorithm in which the blocks are updated in a random and possibly parallel manner, according to arbitrary probabilities. The algorithm allows different stepsizes along the block-coordinates to fully exploit the smoothness properties of the objective function. In the convex case and in an infinite dimensional setting, we establish almost sure weak convergence of the iterates and the asymptotic rate o(1/n) for the mean of the function values. We derive linear rates under strong convexity and error bound conditions. Our analysis is based on an abstract convergence principle for stochastic descent algorithms which allows to extend and simplify existing results.

Title: Optimal Reinsurance and Investment Strategies Under Mean-Variance Criteria: Partial and Full Information Abstract: This paper is concerned with an optimal reinsurance and investment problem for an insurance firm under the criterion of mean-variance. The driving Brownian motion and the rate in return of the risky asset price dynamic equation cannot be directly observed. And the short-selling of stocks is prohibited. The problem is formulated as a stochastic linear-quadratic control problem where the control variables are constrained. Based on the separation principle and stochastic filtering theory, the partial information problem is solved. Efficient strategies and efficient frontier are presented in closed forms via solutions to two extended stochastic Riccati equations. As a comparison, the efficient strategies and efficient frontier are given by the viscosity solution to the HJB equation in the full information case. Some numerical illustrations are also provided.

Title: On variation of eigenvalues of birth and death matrices and random walk matrices Abstract: The purpose of this note is twofold: firstly to improve the known results on variation of extreme eigenvalues of birth and death matrices and random walk matrices; and secondly to progress towards the solution of a thirty years old open problem concerning the variation of eigenvalues of these matrices.(c) 2022 Elsevier Inc. All rights reserved.

Title: Infinite lexicographic products Abstract: We generalize the lexicographic product of first-order structures by presenting a framework for constructions which, in a sense, mimic iterating the lexicographic product infinitely and not necessarily countably many times. We then define dense substructures in infinite products and show that any countable product of countable transitive homogeneous structures has a unique countable dense substructure, up to isomorphism. Furthermore, this dense substructure is transitive, homogeneous and elementarily embeds into the product. This result is then utilized to construct a rigid elementarily indivisible structure.

Title: Anti-van der Waerden Numbers on Graphs Abstract: In this paper arithmetic progressions on the integers and the integers modulo n are extended to graphs. A k-term arithmetic progression of a graph G (k-AP) is a list of k distinct vertices such that the distance between consecutive pairs is constant. A rainbow k-AP is a k-AP where each vertex is colored distinctly. This allows for the definition of the anti-van der Waerden number of a graph G, which is the least positive integer r such that every exact r-coloring of G contains a rainbow k-AP. Much of the focus of this paper is on 3-term arithmetic progressions for which general bounds are obtained based on the radius and diameter of a graph. The general bounds are improved for trees and Cartesian products and exact values are determined for some classes of graphs. Longer k-term arithmetic progressions are considered and a connection between the Ramsey number of paths and the anti-van der Waerden number of graphs is established.Please confirm if the inserted city and country name for all affiliations is correct. Amend if necessary.The cities and affiliations are correct.

Title: Estimation and Selection for High-Order Markov Chains with Bayesian Mixture Transition Distribution Models Abstract: We develop a mixture model and diagnostic for Bayesian estimation and selection in high-order, discrete-state Markov chains. Both extend the mixture transition distribution, which constructs a transition probability tensor by aggregating probabilities from a set of single-lag transition matrices, through inclusion of mixture components dependent on multiple lags. We demonstrate two uses for the proposed model: identification of relevant lags through over-specification and shrinkage via priors for sparse probability vectors, and parsimonious approximation of multi-lag dynamics by mixing low-order transition models. The diagnostic yields a general and interpretable mixture decomposition for transition probability tensors estimated by any means. We demonstrate the utility of the model and diagnostic with simulation studies, and further apply the methodology to a data analysis from the high-order Markov chain literature, and to a time series of pink salmon abundance in Alaska, United States. Supplemental files for this article are available online.

Title: Sparsity-Assisted Signal Denoising and Pattern Recognition in Time-Series Data Abstract: We address the problem of signal denoising and pattern recognition in processing batch-mode time-series data by combining linear time-invariant filters, orthogonal multiresolution representations, and sparsity-based methods. We propose a novel approach to designing higher-order zero-phase low-pass, high-pass, and band-pass infinite impulse response filters as matrices, using spectral transformation of the state-space representation of digital filters. We also propose a proximal gradient-based technique to factorize a special class of zero-phase high-pass and band-pass digital filters so that the factorization product preserves the zero-phase property of the filter and incorporates a sparse-derivative component of the input in the signal model. To demonstrate applications of our novel filter designs, we validate and propose new signal models to simultaneously denoise and identify patterns of interest. To denoise or detect a pattern of interest in the signal, our proposed signal models simultaneously combine linear time-invariant (LTI) filters and sparsity-based methods with orthogonal multiresolution representations, such as wavelets and short-time Fourier transform. We illustrate the capabilities of our proposed signal models using sleep-electroencephalography (EEG) data to detect K-complexes and sleep spindles. Reproducible research is available at https://github.com/prateekgv/sasdpr.

Title: Quantum Pin Codes Abstract: We introduce quantum pin codes: a class of quantum CSS codes. Quantum pin codes are a generalization of quantum color codes and Reed-Muller codes and share a lot of their structure and properties. Pin codes have gauge operators, an unfolding procedure and their stabilizers form so-called <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell $ </tex-math></inline-formula> -orthogonal spaces meaning that the joint overlap between any <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell $ </tex-math></inline-formula> stabilizer elements is always even. This last feature makes them interesting for devising magic-state distillation protocols, for instance by using puncturing techniques. We study examples of these codes and their properties.

Title: Consistent Estimation of the Max-Flow Problem: Towards Unsupervised Image Segmentation Abstract: Advances in the image-based diagnostics of complex biological and manufacturing processes have brought unsupervised image segmentation to the forefront of enabling automated, on the fly decision making. However, most existing unsupervised segmentation approaches are either computationally complex or require manual parameter selection (e.g., flow capacities in max-flow/min-cut segmentation). In thi...

Title: Learning Markov Models Via Low-Rank Optimization. Abstract: Modeling unknown systems from data is a precursor of system optimization and sequential decision making. In this paper, we focus on learning a Markov model from a single trajectory of states. Suppose that the transition model has a small rank despite of a large state space, meaning that the system admits a low-dimensional latent structure. We show that one can estimate the full transition model accurately using a trajectory of length that is proportional to the total number of states. We propose two maximum likelihood estimation methods: a convex approach with nuclear-norm regularization and a nonconvex approach with rank constraint. We show that both estimators enjoy optimal statistical rates in terms of the Kullback-Leiber divergence and the $\ell_2$ error. For computing the nonconvex estimator, we develop a novel DC (difference of convex function) programming algorithm that starts with the convex M-estimator and then successively refines the solution till convergence. Empirical experiments demonstrate consistent superiority of the nonconvex estimator over the convex one.

Title: A Dynamic Game Framework for Rational and Persistent Robot Deception With an Application to Deceptive Pursuit-Evasion Abstract: This article studies rational and persistent deception among intelligent robots to enhance security and operational efficiency. We present an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> -player <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> -stage game with an asymmetric information structure where each robot’s private information is modeled as a random variable or its type. The deception is persistent as each robot’s private type remains unknown to other robots for all stages. The deception is rational as robots aim to achieve their deception goals at minimum cost. Each robot forms a dynamic belief of others’ types based on intrinsic or extrinsic information. Perfect Bayesian Nash equilibrium (PBNE) is a natural solution concept for dynamic games of incomplete information. Due to its requirements of sequential rationality and belief consistency, PBNE provides a reliable prediction of players’ actions, beliefs, and expected cumulative costs over the entire <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> stages. The contribution of this work is fourfold. First, we identify the PBNE computation as a nonlinear stochastic control problem and characterize the structures of players’ actions and costs under PBNE. We further derive a set of extended Riccati equations with cognitive coupling under the linear-quadratic (LQ) setting and extrinsic belief dynamics. Second, we develop a receding-horizon algorithm with low temporal and spatial complexity to compute PBNE under intrinsic belief dynamics. Third, we investigate a deceptive pursuit-evasion game as a case study and use numerical experiments to corroborate the results. Finally, we propose metrics, such as deceivability, reachability, and the price of deception (PoD), to evaluate the strategy design and the system performance under deception. Note to Practitioners—Recent advances in automation and adaptive control in multi-agent systems enable robots to use deception to accomplish their objectives. Deception involves intentional information hiding to compromise the security and operational efficiency of the robotic systems. This work proposes a dynamic game framework to quantify the impact of deception, understand the robots’ behaviors and intentions, and design cost-efficient strategies under the deception that persists over stages. Existing research studies on robot deception have relied on experiments while this work aims to lay a theoretical foundation of deception with quantitative metrics, such as deceivability and the PoD. The proposed model has wide applications, including cooperative robots, pursuit and evasion, and human–robot teaming. The pursuit-evasion games are used as case studies to show how the deceiver can amplify the deception by belief manipulation and how the deceived robots can reduce the negative impact of deception by enhanced maneuverability and Bayesian learning. The future work would focus on designing cooperative deception among swarm robotics and robotic systems that are robust to or further benefit from the deception.

Title: Space-Efficient Vertex Separators for Treewidth Abstract: For n-vertex graphs with treewidth $$k = O(n^{1/2-\epsilon })$$ and an arbitrary $$\epsilon >0$$ , we present a word-RAM algorithm to compute vertex separators using only O(n) bits of working memory. As an application of our algorithm, we give an O(1)-approximation algorithm for tree decomposition. Our algorithm computes a tree decomposition in $$c^k n (\log \log n) \log ^* n$$ time using O(n) bits for some constant $$c > 0$$ . Together with the result of Banerjee et al. (Proceedings of 21st international conference on computing and combinatorics (COCOON 2015). LNCS, vol 9198, Springer, pp 349–360, 2015. https://doi.org/10.1007/978-3-319-21398-9_28 ) we are able to compute a solution for all monadic-second-order problems (MSO) with $$O(n + \tau (k) \cdot p (\log _{p} n) \log n)$$ bits in $$O(\tau (k) \cdot n^{2 + (2/\log p)})$$ time where k is the treewidth of the given graph, p is some arbitrary parameter with $$2 \le p \le n$$ and $$\tau $$ is some function depending on the MSO formula. We finally use the tree decomposition obtained by our algorithm to solve Vertex Cover, Independent Set, Dominating Set, MaxCut and q-Coloring by using polynomial time and O(n) bits as long as the treewidth of the graph is smaller than $$c' \log n$$ for some problem dependent constant $$0< c' < 1$$ .

Title: Neural logic rule layers Abstract: Deep neural networks (DNN) are mainly black boxes, generally suffering from bad interpretability of their behavior and the results obtained. Hence, a human can not easily derive the relations modeled by the network. A reasonable way to provide interpretability for humans are logical rules. In this paper we propose neural logic rule layers (NLRL), which are able to represent arbitrary logic rules in terms of their conjunctive and disjunctive normal forms. Stacking various layers, we are theoretically able to represent arbitrary complex rules by the resulting neural network architecture. The NLRL are end-to-end trainable allowing to learn logic rules directly on the given data without needing any background information about the origin. We show in experiments, that NLRL-enhanced neural networks can model arithmetic and logical operations over the input values. Furthermore, we apply NLRL to image classification tasks and show that interpretability is provided without sacrificing classification performance by exchanging the fully-connected head of the network. We also apply NLRL to a real world industrial control problem where the task is to model the discrete control behaviour of a programmable logic controller (PLC), following a basic step sequence.

Title: Optimization on flag manifolds Abstract: A flag is a sequence of nested subspaces. Flags are ubiquitous in numerical analysis, arising in finite elements, multigrid, spectral, and pseudospectral methods for numerical pde; they arise in the form of Krylov subspaces in matrix computations, and as multiresolution analysis in wavelets constructions. They are common in statistics too—principal component, canonical correlation, and correspondence analyses may all be viewed as methods for extracting flags from a data set. The main goal of this article is to develop the tools needed for optimizing over a set of flags, which is a smooth manifold called the flag manifold, and it contains the Grassmannian as the simplest special case. We will derive closed-form analytic expressions for various differential geometric objects required for Riemannian optimization algorithms on the flag manifold; introducing various systems of extrinsic coordinates that allow us to parameterize points, metrics, tangent spaces, geodesics, distances, parallel transports, gradients, Hessians in terms of matrices and matrix operations; and thereby permitting us to formulate steepest descent, conjugate gradient, and Newton algorithms on the flag manifold using only standard numerical linear algebra.

Title: Smart network based portfolios Abstract: In this article we deal with the problem of portfolio allocation by enhancing network theory tools. We propose the use of the correlation network dependence structure in constructing some well-known risk-based models in which the estimation of the correlation matrix is a building block in the portfolio optimization. We formulate and solve all these portfolio allocation problems using both the standard approach and the network-based approach. Moreover, in constructing the network-based portfolios we propose the use of three different estimators for the covariance matrix: the sample, the shrinkage toward constant correlation and the depth-based estimators . All the strategies under analysis are implemented on three high-dimensional portfolios having different characteristics. We find that the network-based portfolio consistently performs better and has lower risk compared to the corresponding standard portfolio in an out-of-sample perspective.

Title: Clique immersions and independence number Abstract: The analogue of Hadwiger's conjecture for the immersion order states that every graph G contains K-chi(G) as an immersion. If true, this would imply that every graph with n vertices and independence number alpha contains K inverted right perpendiculexpressionr n/alpha right ceiling as an immersion. The best currently known bound for this conjecture is due graph G contains an immersion of a clique on inverted right perpendiculexpressionr chi(G)-4/3.54 right ceiling to vertices. Their result implies that every n-vertex graph with independence number alpha contains an immersion of a clique on inverted right perpendiculexpressionr n/3.54 alpha - 1.13 right ceiling vertices. We improve on this result for all alpha > 3, by showing that every n-vertex graph with independence number alpha > 3 contains an immersion of a clique on left floor n/2.25 alpha-f(alpha) right floor - 1 vertices, where f is a nonnegative function. (C) 2022 Published by Elsevier Ltd.

Title: Generalized Proportional Allocation Policies for Robust Control of Dynamical Flow Networks Abstract: We study a robust control problem for dynamical flow networks. In the considered framework, traffic flows along the links of a transportation network—modeled as a capacited multigraph—and queues up at the nodes, whereby control policies determine which incoming queues are to be allocated service simultaneously, within some predetermined scheduling constraints. We first prove fundamental performanc...

Title: The number of rooted forests in circulant graphs. Abstract: In this paper, we develop a new method to produce explicit formulas for the number $f_{G}(n)$ of rooted spanning forests in the circulant graphs $ G=C_{n}(s_1,s_2,\ldots,s_k)$ and $ G=C_{2n}(s_1,s_2,\ldots,s_k,n).$ These formulas are expressed through Chebyshev polynomials. We prove that in both cases the number of rooted spanning forests can be represented in the form $f_{G}(n)=p\,a(n)^2,$ where $a(n)$ is an integer sequence and $p$ is a prescribed natural number depending on the parity of $n$. Finally, we find an asymptotic formula for $f_{G}(n)$ through the Mahler measure of the associated Laurent polynomial $P(z)=2k+1-\sum\limits_{i=1}^k(z^{s_i}+z^{-s_i}).$

Title: HTP-COMPLETE RINGS OF RATIONAL NUMBERS Abstract: For a ring R, Hilbert's Tenth Problem HTP(R) is the set of polynomial equations over R, in several variables, with solutions in R. We view HTP as an enumeration operator, mapping each set W of prime numbers to HTP(Z[W-1]), which is naturally viewed as a set of polynomials in Z[X-1, X-2, ...]. It is known that for almost all W, the jump W' does not 1-reduce to HTP(R-W). In contrast, we show that every Turing degree contains a set W for which such a 1-reduction does hold: these W are said to be HTP-complete. Continuing, we derive additional results regarding the impossibility that a decision procedure for W' from HTP(Z[W-1]) can succeed uniformly on a set of measure 1, and regarding the consequences for the boundary sets of the HTP operator in case Z has an existential definition in Q.

Title: A Randomly Weighted Minimum Arborescence with a Random Cost Constraint Abstract: We study the minimum spanning arborescence problem on the complete digraph $\vec{K}_n$ where an edge $e$ has a weight $W_e$ and a cost $C_e$, each of which is an independent uniform random variable $U^\alpha$ where $\alpha\leq 1$ and $U$ is uniform $[0,1]$. There is also a constraint that the spanning arborescence $T$ must satisfy $C(T)\leq c_0$. We establish, for a range of values for $c_0,\alpha$, the asymptotic value of the optimum weight via the consideration of a dual problem.

Title: Quantum geometric information flows and relativistic generalizations of G. Perelman thermodynamics for nonholonomic Einstein systems with black holes and stationary solitonic hierarchies Abstract: We investigate classical and quantum geometric information flow theories (GIFs and QGIFs) when the geometric flow evolution and field equations for nonholonomic Einstein systems, NES, are derived from Perelman-Lyapunov-type entropic-type functionals. The term NES encodes models when the fundamental physical equations are subjected to nonholonomic (equivalently, nonintegrable, anholonomic) constraints. There are used canonical geometric variables that allow a general decoupling and integration of systems of nonlinear partial differential equations describing GIFs and QGIFs and Ricci soliton-type configurations. Our approach is different from the constructions elaborated for special classes of solutions characterized by area-hypersurface entropy, related holographic, and dual gauge-gravity models involving generalizations of the Bekenstein-Hawking entropy. We formulate the theory of QGIFs which in certain quasi-classical limits encodes GIFs and models with flow evolution of NES. There are computed, respectively, the von Neumann, relative and conditional entropy; mutual information, entanglement, and Renyi entropy. We construct explicit examples of generic off-diagonal exact and parametric solutions describing stationary solitonic gravitational hierarchies and deformations of black hole configurations. Finally, we show how Perelman's thermodynamic values and extensions to QGIF models can be computed for various new classes of exact solutions which cannot be described following the Bekenstein-Hawking approach.