International Journal of Modern Physics C

The least-squares support vector machine (LS-SVM) is a frequently used kernel method for non-linear regression and classification tasks. Here we discuss several approximation algorithms for the LS-SVM classifier. The proposed methods are based on randomized block kernel matrices, and we show that they provide good accuracy and reliable scaling for multi-class classification problems with relatively large data sets. Also, we present several numerical experiments that illustrate the practical applicability of the proposed methods.

In this paper, we study the pedestrian flow with an Improved Two-Process (ITP) cellular automaton model, which is originally proposed by Blue and Adler. Simulations of pedestrian counterflow have been conducted, under both periodic and open boundary conditions. The lane formation phenomenon has been reproduced without using the place exchange rule. We also present and discuss the flow-density and velocity-density relationships of both uni-directional flow and counterflow. By the comparison with the Blue-Adler model, we find the ITP model has higher values of maximum flow, critical density and completely jammed density under different conditions.

This paper undertakes a social network analysis of two science fiction television series, Stargate and Star Trek. Television series convey stories in the form of character interaction, which can be represented as “character networks”. We connect each pair of characters that exchanged spoken dialogue in any given scene demarcated in the television series transcripts. These networks are then used to characterize the overall structure and topology of each series. We find that the character networks of both series have similar structure and topology to that found in previous work on mythological and fictional networks. The character networks exhibit the small-world effects but found no significant support for power-law. Since the progression of an episode depends to a large extent on the interaction between each of its characters, the underlying network structure tells us something about the complexity of that episode’s storyline. We assessed the complexity using techniques from spectral graph theory. We found that the episode networks are structured either as (1) closed networks, (2) those containing bottlenecks that connect otherwise disconnected clusters or (3) a mixture of both.

We examine a dynamical network model of visual processing that reproduces several aspects of a well-known optical illusion, including subtle dependencies on curvature and scale. The model uses a genetic algorithm to construct the percept of an image, and we show that this percept evolves dynamically so as to produce the illusions reported. We find that the perceived illusions are hardwired into the model architecture and we propose that this approach may serve as an archetype to distinguish behaviors that are due to nature (i.e. a fixed network architecture) from those subject to nurture (that can be plastically altered through learning).

We calculate the power spectral density and velocity correlations for a turbulent flow of a fluid inside a duct. Turbulence is induced by obstructions placed near the entrance of the flow. The power spectral density is obtained for several points at cross-sections along the duct axis, and an analysis is made on the way the spectra changes according to the distance to the obstruction. We show that the differences on the power spectral density are important in the lower frequency range, while in the higher frequency range, the spectra are very similar to each other. Our results suggest the use of the changes on the low frequency power spectral density to identify the occurrence of obstructions in pipelines. Our results show some frequency regions where the power spectral density behaves according to the Kolmogorov hypothesis. At the same time, the calculation of the power spectral densities at increasing distances from the obstructions indicates an energy cascade where the spectra evolves in frequency space by spreading the frequency amplitude.

The hierarchical structure, $k$-core, is common in various complex networks, and the actual network always has successive layers from 1-core layer (the peripheral layer) to $k_m$-core layer (the core layer). The nodes within the core layer have been proved to be the most influential spreaders, but there is few work about how the depth of $k$-core layers (the value of $k_m$) can affect the robustness against cascading failures, rather than the interdependent networks. First, following the preferential attachment, a novel method is proposed to generate the scale-free network with successive $k$-core layers (KCBA network), and the KCBA network is validated more realistic than the traditional BA network. Then, with KCBA interdependent networks, the effect of the depth of $k$-core layers is investigated. Considering the load-based model, the loss of capacity on nodes is adopted to quantify the robustness instead of the number of functional nodes in the end. We conduct two attacking strategies, i.e. the RO-attack (Randomly remove only one node) and the RF-attack (Randomly remove a fraction of nodes). Results show that the robustness of KCBA networks not only depends on the depth of $k$-core layers, but also is slightly influenced by the initial load. With RO-attack, the networks with less $k$-core layers are more robust when the initial load is small. With RF-attack, the robustness improves with small $k_m$, but the improvement is getting weaker with the increment of the initial load. In a word, the lower the depth is, the more robust the networks will be.

Gravitational billiards composed of a viscoelastic frictional disk bouncing on a vibrating wedge have been studied previously, but only from the point of view of their translational behavior. In this work, the average rotational velocity of the disk is studied under various circumstances. First, an experimental realization is briefly presented, which shows sustained rotation when the wedge is tilted. Next, this phenomenon is scrutinized in close detail using a precise numerical implementation of frictional forces. We show that the bouncing disk acquires a spontaneous rotational velocity whenever the wedge angle is not bisected by the direction of gravity. Our molecular dynamics (MD) results are well reproduced by event-driven (ED) simulations. When the wedge aperture angle ${\theta }_W>\pi ∕2$, the average tangential velocity $R\bar{\omega }$ of the disk scales with the typical wedge vibration velocity $v_b$, and is in general a nonmonotonic function of the overall tilt angle ${\theta }_T$ of the wedge. The present work focuses on wedges with ${\theta }_W=2\pi ∕3$, which are relevant for the problem of spontaneous rotation in vibrated disk packings. This study makes part of the PhD Thesis of G. G. Peraza-Mues.

On Barabási–Albert networks (BA) and variations as well as on Erdös–Rényi (ER) random graphs, we study the occurrence of a gap in the neighbor numbers $k(i)$ versus node index $i$ (with $i=1,2,\dots ,N$) at $m=2$, 4, 6, 10, 50, 100 and 150 and with up to $N=1000000$ nodes. Here, we call “gap” a jump in the neighbor numbers $k(i)$ when $i$ equals the initial number $m$ of neighbors; $m$ is also the number of neighbors randomly selected by a newly added node. The size of the gap depends on the value of $m$ and causes a deformation in the structure $k(i)$ of the networks studied here. We give a systematic investigation of the gap in all types of BA networks known to us, and only the undirected BA (UBA) network and the ER graphs show no gap for $m>4$.

In this work, we study a model of tax evasion. We considered a fixed population divided in three compartments, namely honest tax payers, tax evaders and a third class between the mentioned two, which we call susceptibles to become evaders. The transitions among those compartments are ruled by probabilities, similarly to a model of epidemic spreading. These probabilities model social interactions among the individuals, as well as the government’s fiscalization. We simulate the model on fully-connected graphs, as well as on scale-free and random complex networks. For the fully-connected and random graph cases, we observe that the emergence of tax evaders in the population is associated with an active-absorbing nonequilibrium phase transition, that is absent in scale-free networks.

The friendship paradox (FP) is a sociological phenomenon stating that most people have fewer friends than their friends do. It is to say that in a social network, the number of friends that most individuals have is smaller than the average number of friends of friends. This has been verified by Feld. We call this interpreting method mean value version. But is it the best choice to portray the paradox? In this paper, we propose a probability method to reinterpret this paradox, and we illustrate that the explanation using our method is more persuasive. An individual satisfies the FP if his (her) randomly chosen friend has more friends than him (her) with probability not less than $1∕2$. Comparing the ratios of nodes satisfying the FP in networks, $r_p$, we can see that the probability version is stronger than the mean value version in real networks both online and offline. We also show some results about the effects of several parameters on $r_p$ in random network models. Most importantly, $r_p$ is a quadratic polynomial of the power law exponent $\gamma$ in Price model, and $r_p$ is higher when the average clustering coefficient is between $0.4$ and $0.5$ in Petter–Beom (PB) model. The introduction of the probability method to FP can shed light on understanding the network structure in complex networks especially in social networks.

Analyzing the pedestrian subconscious behavior and walking environment in the passage, right-moving preference subconscious strength and overtaking subconscious strength are introduced into the pedestrian simulation model which is based on lattice gas model. Two pedestrian subconscious behavior simulation models, which are distinguished by whether considering pedestrian flow ratio of two directions or not, are established respectively. With the platform of MATLAB software, the simulations of pedestrian counter flow subconscious behavior are realized. The simulations indicate that compared with the pedestrian subconscious behavior simulation model without considering the pedestrian flow ratio of two directions, the model that considers the pedestrian flow ratio of two directions is better in simulating the pedestrian subconscious behavior.

The probability density distribution of the traffic density is analyzed based on the empirical data. It is found that the beta distribution can fit the result obtained from the measured traffic density perfectly. Then a modified traffic model is proposed to simulate the microscopic traffic flow, in which the probability density distribution of the traffic density is taken into account. The model also contains the behavior of drivers’ speed adaptation by taking into account the driving behavior difference and the dynamic headway. Accompanied by presenting the flux-density diagrams, the velocity evolution diagrams and the spatial-temporal profiles of vehicles are also given. The synchronized flow phase and the wide moving jam phase are indicated, which is the challenge for the cellular automata traffic model. Furthermore the phenomenon of the high speed car-following is exhibited, which has been observed in the measured data previously. The results set demonstrate the effectiveness of the proposed model in detecting the complicated dynamic phenomena of the traffic flow.

In this work, a detailed study of the structural, electronic and absorption properties of crystalline 2,6-dimethyl-4-(diphenylmethylene)-2,5-cyclohexadienone with $\alpha$ form ($\alpha$-DDCD) in the pressure range of 0–250GPa is performed by density-functional theory (DFT) calculations. The particular analysis of the variation tendencies of the lattice constants, bond lengths and bond angles under different pressures shows that there occur complex transformations in $\alpha$-DDCD under compression. In addition, it can be see that the $b$-direction is much stiffer than the $a$- and $c$-axes in the structure of $\alpha$-DDCD, suggesting the compressible crystal of $\alpha$-DDCD has anisotropy. Then, by analyzing the bandgap and density of states (DOS) of $\alpha$-DDCD, it is found that the crystal undergoes a phase transformation from semiconductor to metal at 90GPa and it becomes more sensitive under compression. Besides, in the pressure range 110–170GPa, repeated transformations between metal and semiconductor occur four times, suggesting the structural instability of $\alpha$-DDCD in this pressure range. Finally, the relatively high optical activity with the pressure increases of $\alpha$-DDCD is seen from the absorption spectra, and two obvious structural transformations are also observed at 130GPa and 140GPa, respectively.

This paper introduces a multiscale multifractal multiproperty analysis based on Rényi entropy (3MPAR) method to analyze short-range and long-range characteristics of financial time series, and then applies this method to the five time series of five properties in four stock indices. Combining the two analysis techniques of Rényi entropy and multifractal detrended fluctuation analysis (MFDFA), the 3MPAR method focuses on the curves of Rényi entropy and generalized Hurst exponent of five properties of four stock time series, which allows us to study more universal and subtle fluctuation characteristics of financial time series. By analyzing the curves of the Rényi entropy and the profiles of the logarithm distribution of MFDFA of five properties of four stock indices, the 3MPAR method shows some fluctuation characteristics of the financial time series and the stock markets. Then, it also shows a richer information of the financial time series by comparing the profile of five properties of four stock indices. In this paper, we not only focus on the multifractality of time series but also the fluctuation characteristics of the financial time series and subtle differences in the time series of different properties. We find that financial time series is far more complex than reported in some research works using one property of time series.