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Structures of genetic regulatory networks are not fixed. These structural perturbations can cause changes to the reachability of systems' state spaces. As system structures are related to genotypes and state spaces are related to phenotypes, it is important to study the relationship between structures and state spaces. However, there is still no method can quantitively describe the reachability differences of two state spaces caused by structural perturbations. Therefore, Difference in Reachability between State Spaces (DReSS) is proposed. DReSS index family can quantitively describe differences of reachability, attractor sets between two state spaces and can help find the key structure in a system, which may influence system's state space significantly. First, basic properties of DReSS including non-negativity, symmetry and subadditivity are proved. Then, typical examples are shown to explain the meaning of DReSS and the differences between DReSS and traditional graph distance. Finally, differences of DReSS distribution between real biological regulatory networks and random networks are compared. Results show most structural perturbations in biological networks tend to affect reachability inside and between attractor basins rather than to affect attractor set itself when compared with random networks, which illustrates that most genotype differences tend to influence the proportion of different phenotypes and only a few ones can create new phenotypes. DReSS can provide researchers with a new insight to study the relation between genotypes and phenotypes., (© The Author(s) 2020. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.)

Background: Classification of diseases based on genetic information is of great significance as the basis for precision medicine, increasing the understanding of disease etiology and revolutionizing personalized medicine. Much effort has been directed at understanding disease associations by constructing disease networks, and classifying patient samples according to gene expression data. Integrating human gene networks overcomes limited coverage of genes. Incorporating pathway information into disease classification procedure addresses the challenge of cellular heterogeneity across patients., Results: In this work, we propose a disease classification model LAMP, which concentrates on the layered assessment on modules and pathways. Directed human gene interactions are the foundation of constructing the human gene network, where the significant roles of disease and pathway genes are recognized. The fast unfolding algorithm identifies 11 modules in the largest connected component. Then layered networks are introduced to distinguish positions of genes in propagating information from sources to targets. After gene screening, hierarchical clustering and refined process, 1726 diseases from KEGG are classified into 18 categories. Also, it is expounded that diseases with overlapping genes may not belong to the same category in LAMP. Within each category, entropy is applied to measure the compositional complexity, and to evaluate the prospects for combination diagnosis and gene-targeted therapy for diseases., Conclusion: In this work, by collecting data from BioGRID and KEGG, we develop a disease classification model LAMP, to support people to view diseases from the perspective of commonalities in etiology and pathology. Comprehensive research on existing diseases can help meet the challenges of unknown diseases. The results provide suggestions for combination diagnosis and gene-targeted therapy, which motivates clinicians and researchers to reposition the understanding of diseases and explore diagnosis and therapy strategies.

To solve the combinatorial optimization problems, especially the minimal Vertex-cover problem with high efficiency, is a significant task in theoretical computer science and many other subjects. Aiming at detecting the solution space of Vertex-cover, a new structure named mutual-determination is defined and discovered for Vertex-cover on general graphs, which results in the emergence of strong correlations among the unfrozen nodes. Based on the backbones and mutual-determinations with node ranks by leaf removal, we propose a Mutual-determination and Backbone Evolution Algorithm to achieve the reduced solution graph, which provides a graphical expression of the solution space of Vertex-cover. By this algorithm, the whole solution space and detailed structures such as backbones can be obtained strictly when there is no leaf-removal core on the given graph. Compared with the current algorithms, the Mutual-determination and Backbone Evolution Algorithm performs as well as the replica symmetry one in a certain interval but has a small gap higher than the replica symmetric breaking one and has a relatively small error for the exact results. The algorithm with the mutual-determination provides a new viewpoint to solve Vertex-cover and understand the organizations of the solution spaces, and the reduced solution graph gives an alternative way to catch detailed information of the ground/steady states.

The satisfiability of a class of random Boolean equations named massive algebraic system septated to linear and nonlinear subproblems is studied in this paper. On one hand, the correlation between the magnetization of generators and the clustering of solutions of the linear subproblem is investigated by analyzing the Gaussian elimination process. On the other hand, the characteristics of maximal elements of solutions of the nonlinear subproblem are studied by introducing the partial order among solutions. Based on the algebraic characteristics of these two subproblems, the upper and lower bounds of satisfiability threshold of massive algebraic system are obtained by unit-clause propagation and leaf-removal process, and coincide as the ratio of nonlinear equations q>0.739 in which analytical values of the satisfiability threshold can be derived. Furthermore, a complete algorithm with heuristic decimation is proposed to observe the approximation of the satisfiability threshold, which performs more efficiently than the classical ones.

Purpose: Adaptive slicing is a key step in three-dimensional (3D) printing as it is closely related to the building time and the surface quality. This study aims to develop a novel adaptive slicing method based on ameliorative area ratio and accurate cusp height for 3D printing using stereolithography (STL) models. Design/methodology/approach: The proposed method consists of two stages. In the first stage, the STL model is sliced with constant layer thickness, where an improved algorithm for generating active triangular patches, the list is developed to preprocess the model faster. In the second stage, the model is first divided into several blocks according to the number of contours, then an axis-aligned bounding box-based contour matching algorithm and a polygons intersection algorithm are given to compare the geometric information between several successive layers, which will determine whether these layers can be merged to one. Findings: Several benchmarks are applied to verify this new method. Developed method has also been compared with the uniform slicing method and two existing adaptive slicing methods to demonstrate its effectiveness in slicing. Originality/value: Compared with other methods, the method leads to fewer layers whilst keeping the geometric error within a given threshold. It demonstrates that the proposed slicing method can reach a trade-off between the building time and the surface quality. [ABSTRACT FROM AUTHOR]

Algorithms using 4-pixel Feistel structure and chaotic systems have been shown to resolve security problems caused by large data capacity and high correlation among pixels for color image encryption. In this paper, a fast color image encryption algorithm based on the modified 4-pixel Feistel structure and multiple chaotic maps is proposed to improve the efficiency of this type of algorithm. Two methods are used. First, a simple round function based on a piecewise linear function and tent map are used to reduce computational cost during each iteration. Second, the 4-pixel Feistel structure reduces round number by changing twist direction securely to help the algorithm proceed efficiently. While a large number of simulation experiments prove its security performance, additional special analysis and a corresponding speed simulation show that these two methods increase the speed of the proposed algorithm (0.15s for a 256*256 color image) to twice that of an algorithm with a similar structure (0.37s for the same size image). Additionally, the method is also faster than other recently proposed algorithms. [ABSTRACT FROM AUTHOR]

With the security requirements of networks, biometrics authenticated schemes which are applied in the multi-server environment come to be more crucial and widely deployed. In this paper, we propose a novel biometric-based multi-server authentication and key agreement scheme which is based on the cryptanalysis of Mishra et al.’s scheme. The informal and formal security analysis of our scheme are given, which demonstrate that our scheme satisfies the desirable security requirements. The presented scheme provides a variety of significant functionalities, in which some features are not considered in the most of existing authentication schemes, such as, user revocation or re-registration and biometric information protection. Compared with several related schemes, our scheme has more secure properties and lower computation cost. It is obviously more appropriate for practical applications in the remote distributed networks. [ABSTRACT FROM AUTHOR]

Abstract: This paper proves that the winning strategy for Hauser’s version of Hironaka’s polyhedra game is almost arbitrary. The winning strategy and its associated invariants are based on an algorithm of matrix triangulations and matrix diagonalizations. It is proved that if a set sequence constitutes a winning strategy for the game, then so does every set sequence containing it. The same holds for Hironaka’s version of the game if every move is permissible. [Copyright &y& Elsevier]

Abstract: In this paper, we present a new algorithm for computing local extrema by modifying and combining algorithms in symbolic and numerical computation. This new algorithm improves the classical steepest descent method that may not terminate, by combining a Sturm’s theorem based separation method and a sufficient condition on infeasibility. In addition, we incorporate a grid subdivision method into our algorithm to approximate all local extrema. The complexity of our algorithm is polynomial in a newly defined condition number, and singly exponential in the number of variables. [Copyright &y& Elsevier]

Abstract: By modifying and combining algorithms in symbolic and numerical computation, we propose a real-root-counting based method for deciding the feasibility of systems of polynomial equations. Along with this method, we also use a modified Newton operator to efficiently approximate the real solutions when the systems are feasible. The complexity of our method can be measured by a number of arithmetic operations which is singly exponential in the number of variables. [ABSTRACT FROM AUTHOR]

We introduce a new method to interpolate scattered 3D data points with a single B-spline surface patch which is globally smooth. Given a set of scattered 3D data points and their corresponding parametrization, our method first constructs a set α of B-spline bases using a weighted strategy, and inserts knots to the knot vectors based on α. Then, the knot insertion procedure is iterated until a set β of B-spline bases exists, which indicates the existence of the interpolation surface. Finally, by applying the fairing energy minimizing with interpolation constraints, a globally smooth B-spline surface which interpolates the data points can be produced. Experimental results demonstrate that the generated B-spline surfaces often have fewer control points than those of traditional methods, while keeping the scattered data points interpolated accurately. The implementation of our algorithm and the scripts to reproduce all the results are available at https://github.com/wangbolun300/sparse_data. • An iterative knot insertion algorithm is introduced to guarantee the existence of B-spline interpolation surfaces when fitting scattered 3D data points. • The generated B-spline surfaces often use fewer control points than those of tranditional interpolation methods. • A novel parameter δ is introduced to improve the stability of control point solving. • The control points can be solved by a global fairing energy minimization procedure with strict interpolation constraints. Thus, the generated B-spline surface is globally smooth. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we propose a well targeted algorithm (GAS algorithm) for detecting communities in high clustered networks by presenting group action technology on community division. During the processing of this algorithm, the underlying community structure of a clustered network emerges simultaneously as the corresponding partition of orbits by the permutation groups acting on the node set are achieved. As the derivation of the orbit partition, an algebraic structure -cycle can be considered as the origin of the community. To be a priori estimation for the community structure of the algorithm, the community separability is introduced to indicate whether a network has distinct community structure. By executing the algorithm on several typical networks and the LFR benchmark, it shows that this GAS algorithm can detect communities accurately and effectively in high clustered networks. Furthermore, we compare the GAS algorithm and the clique percolation algorithm on the LFR benchmark. It is shown that the GAS algorithm is more accurate at detecting non-overlapping communities in clustered networks. It is suggested that algebraic techniques can uncover fresh light on detecting communities in complex networks. [ABSTRACT FROM AUTHOR]