On Multi-Objective Minimum Spanning Tree Problem under Uncertain Paradigm

Minimum spanning tree problem (MSTP) has allured many researchers and practitioners due to its varied range of applications in real world scenarios. Modelling these applications involves the incorporation of indeterminate phenomena based on their subjective estimations. Such phenomena can be represented rationally using uncertainty theory. Being a more realistic variant of MSTP, in this article, based on the principles of the uncertainty theory, we have studied a multi-objective minimum spanning tree problem (MMSTP) with indeterminate problem parameters. Subsequently, two uncertain programming models of the proposed uncertain multi-objective minimum spanning tree problem (UMMSTP) are developed and their corresponding crisp equivalence models are investigated, and eventually solved using a classical multi-objective solution technique, the epsilon-constraint method. Additionally, two multi-objective evolutionary algorithms (MOEAs), non-dominated sorting genetic algorithm II (NSGAII) and duplicate elimination non-dominated sorting evolutionary algorithm (DENSEA) are also employed as solution methodologies. With the help of the proposed UMMSTP models, the practical problem of optimizing the distribution of petroleum products was solved, consisting in the search for symmetry (balance) between the transportation cost and the transportation time. Thereafter, the performance of the MOEAs is analyzed on five randomly developed instances of the proposed problem.

Patterns in the Population History of Northern Eurasia from the Mesolithic to the Early Bronze Age, Based on Craniometry and Genetics

This study examines the craniometric differentiation of Northern Eurasian groups with reference to genetic and partly linguistic facts. Measurements of 66 series of male crania from that territory, dating to various periods from the Mesolithic to the Early Bronze Age, were subjected to statistical methods especially destined for detecting spatial patterns, specifi cally gradients. Using the nonmetric multidimensional scaling of the matrix of D2 distances corrected for sample size, a two-dimensional projection of group constellation was generated, and a minimum spanning tree, showing the shortest path between group centroids in the multivariate space, was constructed. East-west clines in Northern Eurasia, detected by both genetic and craniometric traits, likely indicate not so much gene fl ow as isolation by distance, resulting from an incomplete evolutionary divergence of various fi lial groups constituting the Boreal meta-population. The western fi lial component, which, in Siberia and Eastern Central Asia, is mostly represented by Afanasyevans, has evidently made little contribution to the genetic makeup of later populations. The eastern fi lial component, which had appeared in the Cis-Baikal region from across Lake Baikal no later than the Neolithic, admixed with the autochthonous Paleosiberian component. The latter’s principal marker—the ANE autosomal component—had been present in Siberia since the Upper Paleolithic. Likewise autochthonous were both Eurasian formations—Northern and Southern; statis tical analysis has made it possible to make these more inclusive, whereby the former has been expanded in the eastern direction to include the Kuznetsk Basin, and the latter westwards, to the Middle Irtysh. Nothing suggests that Eastern European groups had taken part in the origin of either the Northern Eurasian formation or the proto-Uralic groups.

An accurate star identification approach based on spectral graph matching for attitude measurement of spacecraft

Star identification is the foundation of star trackers, which are used to precisely determine the attitude of spacecraft. In this paper, we propose a novel star identification approach based on spectral graph matching. In the proposed approach, we construct a feature called the neighbor graph for each main star, transforming the star identification to the problem of finding the most similar neighbor graph. Then the rough search and graph matching are cooperated to form a dynamic search framework to solve the problem. In the rough search stage, the total edge weight in the minimum spanning tree of the neighbor graph is selected as an indicator, then the k-vector range search is applied for reducing the search scale. Spectral graph matching is utilized to achieve global matching, identifying all stars in the neighbor circle with good noise-tolerance ability. Extensive simulation experiments under the position noise, lost-star noise, and fake-star noise show that our approach achieves higher accuracy (mostly over 99%) and better robustness results compared with other baseline algorithms in most cases.

Smell Detection Agent Optimisation Framework and Systems Biology Approach to Detect Dys-Regulated Subnetwork in Cancer Data

Network biology has become a key tool in unravelling the mechanisms of complex diseases. Detecting dys-regulated subnetworks from molecular networks is a task that needs efficient computational methods. In this work, we constructed an integrated network using gene interaction data as well as protein–protein interaction data of differentially expressed genes derived from the microarray gene expression data. We considered the level of differential expression as well as the topological weight of proteins in interaction network to quantify dys-regulation. Then, a nature-inspired Smell Detection Agent (SDA) optimisation algorithm is designed with multiple agents traversing through various paths in the network. Finally, the algorithm provides a maximum weighted module as the optimum dys-regulated subnetwork. The analysis is performed for samples of triple-negative breast cancer as well as colorectal cancer. Biological significance analysis of module genes is also done to validate the results. The breast cancer subnetwork is found to contain i) valid biomarkers including PIK3CA, PTEN, BRCA1, AR and EGFR; ii) validated drug targets TOP2A, CDK4, HDAC1, IL6, BRCA1, HSP90AA1 and AR; iii) synergistic drug targets EGFR and BIRC5. Moreover, based on the weight values assigned to nodes in the subnetwork, PLK1, CTNNB1, IGF1, AURKA, PCNA, HSPA4 and GAPDH are proposed as drug targets for further studies. For colorectal cancer module, the analysis revealed the occurrence of approved drug targets TYMS, TOP1, BRAF and EGFR. Considering the higher weight values, HSP90AA1, CCNB1, AKT1 and CXCL8 are proposed as drug targets for experimentation. The derived subnetworks possess cancer-related pathways as well. The SDA-derived breast cancer subnetwork is compared with that of tools such as MCODE and Minimum Spanning Tree, and observed a higher enrichment (75%) of significant elements. Thus, the proposed nature-inspired algorithm is a novel approach to derive the optimum dys-regulated subnetwork from huge molecular network.

Cluster Analysis of Cell Nuclei in H&E-Stained Histological Sections of Prostate Cancer and Classification Based on Traditional and Modern Artificial Intelligence Techniques

Biomarker identification is very important to differentiate the grade groups in the histopathological sections of prostate cancer (PCa). Assessing the cluster of cell nuclei is essential for pathological investigation. In this study, we present a computer-based method for cluster analyses of cell nuclei and performed traditional (i.e., unsupervised method) and modern (i.e., supervised method) artificial intelligence (AI) techniques for distinguishing the grade groups of PCa. Two datasets on PCa were collected to carry out this research. Histopathology samples were obtained from whole slides stained with hematoxylin and eosin (H&E). In this research, state-of-the-art approaches were proposed for color normalization, cell nuclei segmentation, feature selection, and classification. A traditional minimum spanning tree (MST) algorithm was employed to identify the clusters and better capture the proliferation and community structure of cell nuclei. K-medoids clustering and stacked ensemble machine learning (ML) approaches were used to perform traditional and modern AI-based classification. The binary and multiclass classification was derived to compare the model quality and results between the grades of PCa. Furthermore, a comparative analysis was carried out between traditional and modern AI techniques using different performance metrics (i.e., statistical parameters). Cluster features of the cell nuclei can be useful information for cancer grading. However, further validation of cluster analysis is required to accomplish astounding classification results.

Reassortment Network of Influenza A Virus

Influenza A virus (IAV) genomes are composed of eight single-stranded RNA segments. Genetic exchange through reassortment of the segmented genomes often endows IAVs with new genetic characteristics, which may affect transmissibility and pathogenicity of the viruses. However, a comprehensive understanding of the reassortment history of IAVs remains lacking. To this end, we assembled 40,296 whole-genome sequences of IAVs for analysis. Using a new clustering method based on Mean Pairwise Distances in the phylogenetic trees, we classified each segment of IAVs into clades. Correspondingly, reassortment events among IAVs were detected by checking the segment clade compositions of related genomes under specific environment factors and time period. We systematically identified 1,927 possible reassortment events of IAVs and constructed their reassortment network. Interestingly, minimum spanning tree of the reassortment network reproved that swine act as an intermediate host in the reassortment history of IAVs between avian species and humans. Moreover, reassortment patterns among related subtypes constructed in this study are consistent with previous studies. Taken together, our genome-wide reassortment analysis of all the IAVs offers an overview of the leaping evolution of the virus and a comprehensive network representing the relationships of IAVs.

Recognition of Electroencephalography-Related Features of Neuronal Network Organization in Patients With Schizophrenia Using the Generalized Choquet Integrals

In this study, we focused on the verification of suitable aggregation operators enabling accurate differentiation of selected neurophysiological features extracted from resting-state electroencephalographic recordings of patients who were diagnosed with schizophrenia (SZ) or healthy controls (HC). We built the Choquet integral-based operators using traditional classification results as an input to the procedure of establishing the fuzzy measure densities. The dataset applied in the study was a collection of variables characterizing the organization of the neural networks computed using the minimum spanning tree (MST) algorithms obtained from signal-spaced functional connectivity indicators and calculated separately for predefined frequency bands using classical linear Granger causality (GC) measure. In the series of numerical experiments, we reported the results of classification obtained using numerous generalizations of the Choquet integral and other aggregation functions, which were tested to find the most appropriate ones. The obtained results demonstrate that the classification accuracy can be increased by 1.81% using the extended versions of the Choquet integral called in the literature, namely, generalized Choquet integral or pre-aggregation operators.

The Impact of COVID-19 on the Dynamic Topology and Network Flow of World Stock Markets

Studies examining the impact of COVID-19 using network dynamics are scant and tend to evaluate a specific local stock market. We present a thorough investigation of 58 world stock market networks using a complex network approach spanning across the uncertain times that have resulted from the coronavirus outbreak. First, we use the daily closing prices of the world stock market indices to construct dynamic complex networks and sixteen minimum spanning tree (MST) maps for the period from December 2019 to March 2021. Second, we present the topological evolution properties of time-varying MSTs by applying normalized tree length, diameter, average path length, and centrality measures. Moreover, the empirical results suggest that (1) the highest correlation among the world stock markets is observed during the first wave of the COVID-19 pandemic in the months of February–March 2020; (2) most of the MSTs appear lower in hierarchy, and many chain-like structures are formed due to the sheer impact of pandemic-related crises; (3) Germany remained a hub node in many of the MSTs; and (4) the tree severely contracted during the first wave of the COVID-19 outbreak (during the months of February and March 2020) and expanded slightly afterwards. Moreover, the results obtained from this study can be used for the development of financial stability policies and stock market regulations worldwide.

An approximation of balanced score in neutrosophic graphs with weak edge weights

Neutrosophic concept is known undirected graph theory to involve with complex logistic networks, not clearly given and unpredictable real life situations, where fuzzy logic malfunctions to model. The transportation objective is to ship all logistic nodes in the network. The logistic network mostly experiences in stable condition, but for some edges found to be volatile. The weight of these erratic edges may vary at random (bridge-lifting/bascule, ad hoc accident on road, traffic condition) In this article, we propose an approximation algorithm for solving minimum spanning tree (MST) of an undirected neutrosophic graphs (UNG), in which the edge weights represent neutrosophic values. The approximation upon the balanced score calculation is introduced for all known configurations in alternative MST. As the result, we further compute decisive threshold value for the weak weights amid minimum cost pre-computation. If the threshold triggers then the proper MST can direct the decision and avoid post-computation. The proposed algorithm is also related to other existing approaches and a numerical analysis is presented.