Circular‐Arc Bigraphs and Its Subclasses

In this article, we obtain two new characterizations of circular‐arc bigraphs. One of them is the representation of a circular‐arc bigraph in terms of two two‐clique circular‐arc graphs while another one represents the same as a union of an interval bigraph and a Ferrers bigraph. Finally, we introduce the notions of proper and unit circular‐arc bigraphs, characterize them and show that, as in the case of circular‐arc graphs, unit circular‐arc bigraphs form a proper subclass of the class of proper circular‐arc bigraphs.     

Using thresholding difference-based estimators for variable selection in partial linear models

A commonly used semiparametric model is considered. We adopt two difference based estimators of the linear component of the model and propose corresponding thresholding estimators that can be used for variable selection. For each thresholding estimator, variable selection in the linear component is developed and consistency of the variable selection procedure is shown. We evaluate our method in a simulation study and implement it on a real data set.     

Factor models in high-dimensional time series—A time-domain approach

High-dimensional time series may well be the most common type of dataset in the so-called “big data” revolution, and have entered current practice in many areas, including meteorology, genomics, chemometrics, connectomics, complex physics simulations, biological and environmental research, finance and econometrics. The analysis of such datasets poses significant challenges, both from a statistical as well as from a numerical point of view. The most successful procedures so far have been based on dimension reduction techniques and, more particularly, on high-dimensional factor models. Those models have been developed, essentially, within time series econometrics, and deserve being better known in other areas. In this paper, we provide an original time-domain presentation of the methodological foundations of those models (dynamic factor models usually are described via a spectral approach), contrasting such concepts as commonality and idiosyncrasy, factors and common shocks, dynamic and static principal components. That time-domain approach emphasizes the fact that, contrary to the static factor models favored by practitioners, the so-called general dynamic factor model essentially does not impose any constraints on the data-generating process, but follows from a general representation result.     

The Behavioral Approach to Systems and Modeling

Passive and active limited-slip differentials are used in high-performance cars to optimize the torque distribution on the driving wheels for traction maximization, driving comfort, stability and active safety of the vehicle. In this paper, detailed and reduced dynamic models for the simulation of four kinds of differential are presented. The models refer to the limited-slip steering differential with two clutches. The model of the conventional differential, of the mechanical limited-slip differential and of the controlled limited-slip differential can be obtained by simplification. The detailed model allows the simulation of the internal phenomena that influence the differential dynamics. The reduced model focuses only on the main dynamic behaviour of the differential. Some simulations show the use of the reduced model to compare the effects of the four differentials on the vehicle dynamics.     

Backbone fractal dimension and fractal hybrid orbital of protein structure

Fractal geometry analysis provides a useful and desirable tool to characterize the configuration and structure of proteins. In this paper we examined the fractal properties of 750 folded proteins from four different structural classes, namely (1) the α-class (dominated by α-helices), (2) the β-class (dominated by β-pleated sheets), (3) the (α/β)-class (α-helices and β-sheets alternately mixed) and (4) the (α + β)-class (α-helices and β-sheets largely segregated) by using two fractal dimension methods, i.e. “the local fractal dimension” and “the backbone fractal dimension” (a new and useful quantitative parameter). The results showed that the protein molecules exhibit a fractal behavior in the range of 1 ? N ? 15 (N is the number of the interval between two adjacent amino acid residues), and the value of backbone fractal dimension is distinctly greater than that of local fractal dimension for the same protein. The average value of two fractal dimensions decreased in order of α > α/β > α + β > β. Moreover, the mathematical formula for the hybrid orbital model of protein based on the concept of backbone fractal dimension is in good coincidence with that of the similarity dimension. So it is a very accurate and simple method to analyze the hybrid orbital model of protein by using the backbone fractal dimension.     

Exclusion and dominance in discrete population models via the carrying simplex

This paper is devoted to show that Hirsch's results on the existence of a carrying simplex are a powerful tool to understand the dynamics of Kolmogorov models. For two and three species, we prove that there is exclusion for our models if and only if there are no coexistence states. The proof of this result is based on a result in planar topology due to Campos, Ortega and Tineo. For an arbitrary number of species, we will obtain dominance criteria following the notions of Franke and Yakubu. In this scenario, the crucial fact will be that the carrying simplex is an unordered manifold. Applications in concrete models are given.     

Global attractors for the discrete Klein–Gordon–Schrödinger type equations

The purpose of this work is to investigate the asymptotic behaviours of solutions for the discrete Klein–Gordon–Schrödinger type equations in one-dimensional lattice. We first establish the global existence and uniqueness of solutions for the corresponding Cauchy problem. According to the solution's estimate, it is shown that the semi-group generated by the solution is continuous and possesses an absorbing set. Using truncation technique, we show that there exists a global attractor for the semi-group. Finally, we extend the criteria of Zhou et al. [S. Zhou, C. Zhao, and Y. Wang, Finite dimensionality and upper semicontinuity of compact kernel sections of non-autonomous lattice systems, Discrete Contin. Dyn. Syst. A 21 (2008), pp. 1259–1277.] for finite fractal dimension of a family of compact subsets in a Hilbert space to obtain an upper bound of fractal dimension for the global attractor.     

The rank-size scaling law and entropy-maximizing principle

The rank-size regularity known as Zipf’s law is one of the scaling laws and is frequently observed in the natural living world and social institutions. Many scientists have tried to derive the rank-size scaling relation through entropy-maximizing methods, but they have not been entirely successful. By introducing a pivotal constraint condition, I present here a set of new derivations based on the self-similar hierarchy of cities. First, I derive a pair of exponent laws by postulating local entropy maximizing. From the two exponential laws follows a general hierarchical scaling law, which implies the general form of Zipf’s law. Second, I derive a special hierarchical scaling law with the exponent equal to 1 by postulating global entropy maximizing, and this implies the pure form of Zipf’s law. The rank-size scaling law has proven to be one of the special cases of the hierarchical scaling law, and the derivation suggests a certain scaling range with the first or the last data point as an outlier. The entropy maximization of social systems differs from the notion of entropy increase in thermodynamics. For urban systems, entropy maximizing suggests the greatest equilibrium between equity for parts/individuals and efficiency of the whole.     

Detecting high-dimensional determinism in time series with application to human movement data

We numerically investigate the ability of a statistic to detect determinism in time series generated by high-dimensional continuous chaotic systems. This recently introduced statistic (denoted V_E2) is derived from the averaged false nearest neighbors method for analyzing data. Using surrogate data tests, we show that the proposed statistic is able to discriminate high-dimensional chaotic data from their stochastic counterparts. By analyzing the effect of the length of the available data, we show that the proposed criterion is efficient for relatively short time series. Finally, we apply the method to real-world data from biomechanics, namely postural sway time series. In this case, the results led us to exclude the hypothesis of nonlinear deterministic underlying dynamics for the observed phenomena.     

Random coverings of the circle with i.i.d. centers

Consider the random intervals In(ω):=(ωn-ln/2,ωn+ln/2)(mod 1) with their centers ωn being i.i.d.but not necessary uniformly distributed on the circle T = R /Z and with their lengths decreasing to zero.Using the dimension theory in dynamical systems,we give conditions on which the circle is finitely or infinitely often covered by intervals In(ω)}n≥1.