General formulation of long-range degree correlations in complex networks.

Correlations between energy levels can help distinguish whether a many-body system is of integrable or chaotic nature. The study of short-range and long-range spectral correlations generally involves quantities which are very different, unless one uses the $k$-th nearest neighbor ($k$NN) level spacing distribution. For nearest-neighbor (NN) spectral spacings, the distribution in random matrices is well captured by the Wigner surmise. This well-known approximation, derived exactly for a 2$\times$2 matrix, is simple and satisfactorily describes the NN spacings of larger matrices. There have been attempts in the literature to generalize Wigner's surmise to further away neighbors. However, as we show, the current proposal in the literature fails to accurately capture numerical data.
Using the known variance of the distributions from random matrix theory, we propose a corrected surmise for the $k$NN spectral distributions. This surmise better characterizes spectral correlations while retaining the simplicity of Wigner's surmise. We test the predictions against numerical results and show that the corrected surmise is systematically more accurate at capturing data from random matrices. Using the XXZ spin chain with random on-site disorder, we illustrate how these results can be used as a refined probe of many-body quantum chaos for both short- and long-range spectral correlations.

We propose a fluctuation analysis to quantify spatial correlations in complex networks. The approach considers the sequences of degrees along shortest paths in the networks and quantifies the fluctuations in analogy to time series. In this work, the Barabasi-Albert (BA) model, the Cayley tree at the percolation transition, a fractal network model, and examples of real-world networks are studied. While the fluctuation functions for the BA model show exponential decay, in the case of the Cayley tree and the fractal network model the fluctuation functions display a power law behavior. The fractal network model comprises long-range anticorrelations. The results suggest that the fluctuation exponent provides complementary information to the fractal dimension.

We have studied some ferroquadrupolar phases of the S = 1 Heisenberg model with bilinear and biquadratic exchange interactions on the square lattice up to the second nearest neighbor, using the SU(3) Schwinger bosons formalism in a mean field approximation. This technique is very convenient to treat nematic order. This technique has the advantage of using the fundamental representation of the SU(N) group instead of SU(2), designed to capture spin-quadrupolar order in addition to the dipolar magnetic order. We also present quadrupole structure factors that can be measured in future experiments. Our calculations can have implications in the study of iron-based superconductors.

The controllability analysis of complex networks is of great importance for modern network science and engineering. Existing research shows that the controllability of a complex network is affected not only by the degree distribution of the network,but also by the degree correlation.Although the effect of degree correlations on the network controllability is well studied for directed networks,it is not yet very clear for the case of undirected networks.To explore the impact of degree correlations on the controllability of undirected networks and their corresponding generalized (bidirectional and directed) networks,in this paper,we use the simulated annealing algorithm to change the network degree correlation coefficients by link rewiring.First,the undirected Erdős-Rényi random network and the modified scale-free network are taken as example models to be investigated.Numerical simulations show that the controllability measure (density of driver nodes) of undirected networks decreases monotonically with the increase of the degree correlation coefficient under a constant degree distribution.Specifically,when the degree correlation coefficient changes from -1 to 0,the controllability measure decreases rapidly;while the decrease in the controllability measure is not obvious when the degree correlation coefficient changes from 0 to 1.Next,the bidirectional networks and some directed networks are considered;in these networks,the in-degree of each node is equal to its out-degree,thus link rewiring results in the simultaneous changes of various degree correlations (i.e.,in-in,in-out,out-in,and out-out degree correlations).Further investigations show that these bidirectional and directed networks also follow the above rule,which is verified by the two real networks.The increase of the degree correlation coefficient in undirected networks also implies the increases of various degree correlation coefficients in the corresponding directed networks.Although the effect of a single degree correlation on the controllability of directed networks is clear,the comprehensive effect of the simultaneous changes in various degree correlations on the network controllability cannot be additively and therefore directly estimated by the relevant results in the corresponding directed networks;namely,the effect of the degree correlation on the controllability in an undirected network has its special rule.Some explanations are given for this phenomenon.Moreover,for a large sparse network without self-loops,no matter how assortative or disassortative it is,its structural controllability and exact controllability are verified to be almost the same.These studies will deepen the understanding of the relationship between the network controllability and the network structure.

Robustness and Optimization of Complex Networks: Reconstructability, Algorithms and Modeling

Superconductivity in an attractive two-band Hubbard model with second nearest neighbors

Complex networks describe a broad range of systems in nature and society. As a fundamental concept of graph theory, the path connecting nodes and edges plays a crucial role in network science, where the computation of shortest path lengths and numbers has garnered substantial focus. It is well known that powers of the adjacency matrix can calculate the number of walks, specifying their corresponding lengths. However, developing methodologies to quantify both the number and length of shortest paths through the adjacency matrix remains a challenge. Here, we extend powers of the adjacency matrix from walks to shortest paths. We address the all-pairs shortest path count problem and propose a fast algorithm based on powers of the adjacency matrix that counts both the number and the length of all shortest paths. Numerous experiments on synthetic and real-world networks demonstrate that our algorithm is significantly faster than the classical algorithms across various network types and sizes. Moreover, we verified that the time complexity of our proposed algorithm significantly surpasses that of the current state-of-the-art algorithms. The superior property of the algorithm allows for rapid calculation of all shortest paths within large-scale networks, offering significant potential applications in traffic flow optimization and social network analysis.

Treatment of missing data values in a neural network based decision support system for acute abdominal pain

Indoor positioning system has been an essential work to substitute the Global Positioning System (GPS). GPS utilizing Global Navigation Satellite Systems (GNSS) cannot provide an accurate positioning in the indoor due to the multipath effect and shadow fading. Fingerprinting method with Wi-Fi technology is a promising system to solve this issue. However, there are several problems with the fingerprinting method. The fingerprinting database collected has different sample sizes where the previous researcher does not indicate any standard for the sample size to be used. In this paper, the effect of the sample sizes in fingerprinting database for Wi-Fi technology has been discussed deeply. The statistical analyzation for different sample sizes has been analyzed. Furthermore, two methods which are K- Nearest Neighbor (KNN) and Deep Neural Network (DNN) are being used to examine the effect of the sample sizes in term of accuracy and distance error. The discussion in this paper will contribute to the better sample size selection depending on the method taken by the user. The result shows that sample sizes are an important metrics in developing the indoor positioning system as it effects the result of the location estimation.

Protein structure classification is an important issue in understanding the associations between sequence and structure as well as possible functional and evolutionary relationships. Recently structural genomes initiatives and other high-throughput experiments have populated the biological databases at a rapid pace. In this paper, three types of classifiers, k nearest neighbors, class center and nearest neighbor and probabilistic neural networks and their homogenous ensemble for multiclass protein fold recognition problem are evaluated firstly, and then a heterogenous ensemble Voting System is designed for the same problem. The different features and/or their combinations extracted from the protein fold dataset are used in these classification models. The heterogenous classification results are then put into a voting system to get the final result. The experimental results show that the proposed method can improve prediction accuracy by 4%–10% on a benchmark dataset containing 27 SCOP folds.

This paper investigates the accuracy of five state-of-the-art machine learning techniques — decision tree J48, nearest neighbors, k-nearest neighbors (k-NN), backpropagation neural network, and naive Bayes — for image-based snake species identification problem. Conventionally, snake species identification is conducted manually based on the observation of the characteristics such head shape, body pattern, body color, and eyes shape. Images of 22 species of snakes that can be found in Malaysia were collected into a database, namely the Snakes of Perlis Corpus. Then, an intelligent approach is proposed to automatically identify a snake species based on an image which is useful for content retrieval purpose where a snake species can be predicted whenever a snake image is given as input. Our experiment shows that backpropagation neural network and nearest neighbour are highly accurate with greater than 87 % accuracy on CEDD descriptor in this problem.

The mapping of land cover and land use is a key application of remotely sensed data. Studies have suggested the outputs of statistical models that estimate the posterior probability of class membership can be interpreted as subpixel area proportions. This paper examines the correlation between posterior probability of class membership, estimated using neural network and nearest neighbour models, and area proportion. In addition, the paper describes several models, again based on neural networks and nearest neighbour algorithms, that have been developed to estimate the land cover area proportions explicitly. Both types of model were applied to a Landsat TM data set. The results demonstrated that better estimates of the true land cover area were obtained using models that predicted the area proportion directly than were obtained using models that predicted the posterior probability of class membership. Further, it was found that a linear model (single-layer neural network) and a nearest neighbour smoothing model produced higher correlation and lower errors than the other models investigated.

Traffic flow prediction provides support for travel management, vehicle scheduling, and intelligent transportation system construction. In this work, a graph space–time network (GSTNCNI), incorporating complex network feature information, is proposed to predict future highway traffic flow time series. Firstly, a traffic complex network model using traffic big data is established, the topological features of traffic road networks are then analyzed using complex network theory, and finally, the topological features are combined with graph neural networks to explore the roles played by the topological features of 97 traffic network nodes. Consequently, six complex network properties are discussed, namely, degree centrality, clustering coefficient, closeness centrality, betweenness centrality, point intensity, and shortest average path length. This study improves the graph convolutional neural network based on the above six complex network properties and proposes a graph spatial–temporal network consisting of a combination of several complex network properties. By comparison with existing baselines containing graph convolutional neural networks, it is verified that GSTNCNI possesses high traffic flow prediction accuracy and robustness. In addition, ablation experiments are conducted for six different complex network features to verify the effect of different complex network features on the model’s prediction accuracy. Experimental analysis indicates that the model with combined multiple complex network features has a higher prediction accuracy, and its performance is improved by 31.46% on average, compared with the model containing only one complex network feature.

Recently, the spatial network databases (SNDB) have been studied for emerging applications such as location-based services including mobile search and car navigation. In practice, objects, like cars and people with mobile phones, can usually move on an underlying network (road, railway, sidewalk, river, etc.), where the network distance is determined by the length of the practical shortest path connecting two objects. In this paper, we propose materialization-based query processing algorithms for typical spatial queries in SNDB, such as range search and k nearest neighbors (k-NN) search. By using a materialization-based technique with the shortest network distances of all the nodes on the network, the proposed query processing algorithms can reduce the computation time of the network distance as well as the number of disk I/Os required for accessing nodes. Thus, the proposed query processing algorithms improve the existing efficient k-NN (INE) and range search (RNE) algorithms proposed by Papadias et al. [1], respectively. It is shown that our range query processing algorithm achieves about up to one of magnitude better performance than RNE and our k-NN query processing algorithm achieves about up to 150% performance improvements over INE.

For most clustering methods, not only the number of clusters must be set in advance, but also various hyperparameters such as initial centroids, number of nearest neighbours, the minimum number of points, neighbourhood radius, and cutoff distance all require pre-specification. As one of the most promising unsupervised learning methods in machine intelligence, existing clustering methods cannot simultaneously handle datasets with arbitrary shapes, different densities, distinct sizes, and overlapping. Background outliers and high dimensionality make clustering problems more challenging. In this paper, we propose a novel universal clustering methodology, called G2-SCANN, which yields the best clustering performance for all 30 synthetic and real datasets without any hyperparameter tuning if the exact number of clusters is known. Firstly, the shortest path length (SPL) in complex network or graph-based geodesic distance is used to give a locally backbone-structured description of graph vertex similarity. Accordingly, SPL-weighted local degree (SLD) is defined as vertex attributes of a SPL-weighted graph expressed by G2-SPL adjacency matrix with ε-natural neighbourhood. Secondly, the process of calculating SLD for every data point in a bottom-up way directly leads to division from a complete graph constituted by all data points to a group of SLD trees. This brings the interpretability and the elimination of lone trees. Thirdly, contrastive learning of largest SLD values for finding root vertices of each divisive tree is conducted and top-down category message is then transmitted from the root vertices to all the leaf ones of a SLD tree. It eventually produces tree-like clusters. Totally, the proposed G2-SCANN method leverages both local neighbouring similarity of data points and global information about data distribution and makes it perform better than other methods.