New Robust PCA for Outliers and Heavy Sparse Noises’ Detection via Affine Transformation, the L ∗ , w and L 2,1 Norms, and Spatial Weight Matrix in High-Dimensional Images: From the Perspective of Signal Processing

In this paper, we propose a novel robust algorithm for image recovery via affine transformations, the weighted nuclear, L ∗ , w , and the L 2,1 norms. The new method considers the spatial weight matrix to account the correlated samples in the data, the L 2,1 norm to tackle the dilemma of extreme values in the high-dimensional images, and the L ∗ , w norm newly added to alleviate the potential effects of outliers and heavy sparse noises, enabling the new approach to be more resilient to outliers and large variations in the high-dimensional images in signal processing. The determination of the parameters is involved, and the affine transformations are cast as a convex optimization problem. To mitigate the computational complexity, alternating iteratively reweighted direction method of multipliers (ADMM) method is utilized to derive a new set of recursive equations to update the optimization variables and the affine transformations iteratively in a round-robin manner. The new algorithm is superior to the state-of-the-art works in terms of accuracy on various public databases.

Costless delay in negotiations

We study bargaining models in discrete time with a finite number of players, stochastic selection of the proposing player, endogenously determined sets and orders of responders, and a finite set of feasible alternatives. The standard optimality conditions and system of recursive equations may not be sufficient for the existence of a subgame perfect equilibrium in stationary strategies (SSPE) in case of costless delay. We present a characterization of SSPE that is valid for both costly and costless delay. We address the relationship between an SSPE under costless delay and the limit of SSPEs under vanishing costly delay. An SSPE always exists when delay is costly, but not necessarily so under costless delay, even when mixed strategies are allowed for. This is surprising as a quasi SSPE, a solution to the optimality conditions and the system of recursive equations, always exists. The problem is caused by the potential singularity of the system of recursive equations, which is intimately related to the possibility of perpetual disagreement in the bargaining process.

System analysis of the impact of reputation capital upon activation of economic activity in the region

The search for the factors that launch the mechanisms of economic dynamics remain polemical and generate contradictions between various economic schools and directions. This is caused by the differences in fundamental approaches, as well as by conjunctural transformations that initiate new forms and instruments for activation of economic growth in modern reality. The debates and works dedicated to the contribution of nonmaterial factors to the dynamics of the key macroeconomic indicators of regional systems are particularly acute. In this regard, it is an essential methodological aspect in studying the regional development is the application of approaches that are based on the principles of reputation economics, which covers the reproduction processes through the prism of reputation capital. Considering the relevance of this problem, the author carries out comprehensive analysis of the impact of the reputation capital of the region (classified as intangible assets) upon the growth of business activity of the economic agents. Leaning on the methods of building the system of recursive equations, the key patterns of the impact of reputation upon activation of economic activity in the region are determined. Substantiation is given to the main vectors of implementation of government regional policy through the prism of the theory of reputation economy. The article offers an interpretation, which discloses the priorities and peculiarities of regional development in the era of the Fourth Industrial Revolution, as well as the specific features of strategic territorial management.

Analyzing Dynamic Code

Dynamic languages, such as JavaScript, employ string-to-code primitives to turn dynamically generated text into executable code at run-time. These features make standard static analysis extremely hard if not impossible, because its essential data structures, i.e., the control-flow graph and the system of recursive equations associated with the program to analyze, are themselves dynamically mutating objects. Nevertheless, assembling code at run-time by manipulating strings, such as by eval in JavaScript, has been always strongly discouraged, since it is often recognized that “ eval is evil ,” leading static analyzers to not consider such statements or ignoring their effects. Unfortunately, the lack of formal approaches to analyze string-to-code statements pose a perfect habitat for malicious code, that is surely evil and do not respect good practice rules, allowing them to hide malicious intents as strings to be converted to code and making static analyses blind to the real malicious aim of the code. Hence, the need to handle string-to-code statements approximating what they can execute, and therefore allowing the analysis to continue (even in the presence of dynamically generated program statements) with an acceptable degree of precision, should be clear. To reach this goal, we propose a static analysis allowing us to collect string values and to soundly over-approximate and analyze the code potentially executed by a string-to-code statement.

Displaying the Structure of the Solutions for Some Fifth-Order Systems of Recursive Equations

This paper presents the solutions to the following nonlinear systems of rational difference equations: x n + 1 = x n − 3 y n − 4 / y n 1 + x n − 1 y n − 2 x n − 3 y n − 4 , y n + 1 = y n − 3 x n − 4 / x n ± 1 ± y n − 1 x n − 2 y n − 3 x n − 4 where initial conditions x − δ , y − δ δ = 4,3 , … , 0 are nonnegative real numbers. Finally some numerical simulations are presented to verify obtained theoretical results.

Form Factors and Correlation Functions

At the heart of a quantum field theory are the correlation functions of the various fields. In the case of integrable models, the correlators can be expressed in terms of the spectral series based on the matrix elements on the asymptotic states. These matrix elements, also known as form factors, satisfy a set of functional and recursive equations that can exactly solved in many cases of physical interest. Chapter 19 covers general properties of form factors, Faddeev–Zamolodchikov algebra, symmetric polynomials, kinematical and bound state poles, the operator space and kernel functions, the stress-energy tensor and vacuum expectation values and the Ising model in a magnetic field.

Systematic behaviours of different quantities related to sequential prompt emission in fission

The deterministic modelling of sequential prompt emission in fission based on recursive equations of residual temperature was applied to numerous fission cases. This fact emphasized systematics and correlations between different quantities characterizing the residual fragments and the sequential emission. General forms of residual temperature distributions for each emission sequence are determined on the basis of these systematics, having as application the inclusion of sequential emission into the Los Alamos model. Also the systematics can serve to obtain indicative values of different average quantities in the absence of any prompt emission model.

CONSENSUS PROBLEMS IN WEIGHTED HIERARCHICAL GRAPHS

We present the hierarchical graph for the growth of weighted networks in which the structural growth is coupled with the edges’ weight dynamical evolution. We investigate consensus problems of the graph from weighted Laplacian spectra perspective, focusing on three important quantities of consensus problems, convergence speed, delay robustness, and first-order coherence, which are determined by the second smallest eigenvalue, largest eigenvalue, and sum of reciprocals of each nonzero eigenvalue of weighted Laplacian matrix, respectively. Unlike previous enquiries, we want to emphasize the importance of weight factor in the study of coherence problems. In what follows, we attempt to study that the weighted Laplacian eigenvalues of the weighted hierarchical graphs, which are determined through analytic recursive equations. We find in our study that the value of convergence speed and delay robustness in weighted hierarchical graphs increases as weight factor increases and the value of first-order coherence decreases as weight factor increases. Moreover, as is expected, weight factor affects the performance of consensus behavior and can be regarded as a leverage in the problem of consensus problems. This paper puts forward the proposal and the countermeasure for stability optimization of networks from the perspective of weight factor for future researchers.