Facilitated movement of inertial Brownian motors driven by a load under an asymmetric potential

Based on recent work [L. Machura, M. Kostur, P. Talkner, J. Luczka, and P. Hanggi, Phys. Rev. Lett. 98, 040601 (2007)], we extend the study of inertial Brownian motors to the case of an asymmetric potential. It is found that some transport phenomena appear in the presence of an asymmetric potential. Within tailored parameter regimes, there exists two optimal values of the load at which the mean velocity takes its maximum, which means that a load can facilitate the transport in the two parameter regimes. In addition, the phenomenon of multiple current reversals can be observed when the load is increased.Comment: 7 pages, 3 figure

Practical stability and controllability for nonlinear discrete time-delay systems

In this paper we study the practical asymptotic stability for a class of discrete-time time-delay systems via Razumikhin-type Theorems. Further estimations of the solution boundary and arrival time of the solution are also investigated based on practical stability. In addition, the proposed theorems are used to analyze the practical controllability of a general class of nonlinear discrete systems with input time delay. Some easy testing criteria for the uniform practical asymptotical stability are derived via Lyapunov function and Razumikhin technique. Finally a numerical example is given to illustrate the effectiveness of the proposed results

Dissipativity Analysis of Descriptor Systems Using Image Space Characterization

In this paper, we analyze the dissipativity for descriptor systems with impulsive behavior based on image space analysis. First, a new image space is used to characterize state responses for descriptor systems. Based on such characterization and an integral property of delta function, a new necessary and sufficient condition for the dissipativity of descriptor systems is derived using the linear matrix inequality (LMI) approach. Also, some of the earlier related results on dissipativity for linear systems are investigated in the framework proposed in this paper. Finally, two examples are given to show the validity of the derived results

A new class of efficient piecewise nonlinear chaotic maps for secure cryptosystems

In this paper we construct a new class of nonlinear chaotic maps for secure cryptosystems. These maps can overcome the security holes brought by the "piecewise linearity" of the previous Piecewise Linear Chaotic Maps (PWLCM) due to a fact that the chaotic sequences generated by the derived iterative system based on the proposed maps are proved to have perfect dynamic properties, such as uniform invariant distribution, d-like autocorrelation function etc. Furthermore, the relative quantized two-value sequences also have perfect secure statistical characteristics. In terms of computing speed, the proposed maps have faster speed than the recently proposed nonlinear "piecewise-square-root" maps (PSRM), and they actually have equivalently the same computing speed with the linear PWLCM

Geometric entanglement from matrix product state representations

An efficient scheme to compute the geometric entanglement per lattice site for quantum many-body systems on a periodic finite-size chain is proposed in the context of a tensor network algorithm based on the matrix product state representations. It is systematically tested for three prototypical critical quantum spin chains, which belong to the same Ising universality class. The simulation results lend strong support to the previous claim [Q.-Q. Shi, R. Or\'{u}s, J. O. Fj{\ae}restad, and H.-Q. Zhou, New J. Phys \textbf{12}, 025008 (2010); J.-M. St\'{e}phan, G. Misguich, and F. Alet, Phys. Rev. B \textbf{82}, 180406R (2010)] that the leading finite-size correction to the geometric entanglement per lattice site is universal, with its remarkable connection to the celebrated Affleck-Ludwig boundary entropy corresponding to a conformally invariant boundary condition.Comment: 4+ pages, 3 figure

A Cellular Automata Model with Probability Infection and Spatial Dispersion

In this article, we have proposed an epidemic model by using probability cellular automata theory. The essential mathematical features are analyzed with the help of stability theory. We have given an alternative modelling approach for the spatiotemporal system which is more realistic and satisfactory from the practical point of view. A discrete and spatiotemporal approach are shown by using cellular automata theory. It is interesting to note that both size of the endemic equilibrium and density of the individual increase with the increasing of the neighborhood size and infection rate, but the infections decrease with the increasing of the recovery rate. The stability of the system around the positive interior equilibrium have been shown by using suitable Lyapunov function. Finally experimental data simulation for SARS disease in China and a brief discussion conclude the paper

The Euler Number of Bloch States Manifold and the Quantum Phases in Gapped Fermionic Systems

We propose a topological Euler number to characterize nontrivial topological phases of gapped fermionic systems, which originates from the Gauss-Bonnet theorem on the Riemannian structure of Bloch states established by the real part of the quantum geometric tensor in momentum space. Meanwhile, the imaginary part of the geometric tensor corresponds to the Berry curvature which leads to the Chern number characterization. We discuss the topological numbers induced by the geometric tensor analytically in a general two-band model. As an example, we show that the zero-temperature phase diagram of a transverse field XY spin chain can be distinguished by the Euler characteristic number of the Bloch states manifold in a (1+1)-dimensional Bloch momentum space

Persistence, extinction and spatio-temporal synchronization of SIRS cellular automata models

Spatially explicit models have been widely used in today's mathematical ecology and epidemiology to study persistence and extinction of populations as well as their spatial patterns. Here we extend the earlier work--static dispersal between neighbouring individuals to mobility of individuals as well as multi-patches environment. As is commonly found, the basic reproductive ratio is maximized for the evolutionary stable strategy (ESS) on diseases' persistence in mean-field theory. This has important implications, as it implies that for a wide range of parameters that infection rate will tend maximum. This is opposite with present results obtained in spatial explicit models that infection rate is limited by upper bound. We observe the emergence of trade-offs of extinction and persistence on the parameters of the infection period and infection rate and show the extinction time having a linear relationship with respect to system size. We further find that the higher mobility can pronouncedly promote the persistence of spread of epidemics, i.e., the phase transition occurs from extinction domain to persistence domain, and the spirals' wavelength increases as the mobility increasing and ultimately, it will saturate at a certain value. Furthermore, for multi-patches case, we find that the lower coupling strength leads to anti-phase oscillation of infected fraction, while higher coupling strength corresponds to in-phase oscillation.Comment: 12page

A novel hypoxia gene signature indicates prognosis and immune microenvironments characters in patients with hepatocellular carcinoma

Due to the lack of a suitable gene signature, it is difficult to assess the hypoxic exposure of HCC tissues. The clinical value of assessing hypoxia in HCC is short of tissue-level evidence. We tried to establish a robust and HCC-suitable hypoxia signature using microarray analysis and a robust rank aggregation algorithm. Based on the hypoxia signature, we obtained a hypoxia-associated HCC subtypes system using unsupervised hierarchical clustering and a hypoxia score system was provided using gene set variation analysis. A novel signature containing 21 stable hypoxia-related genes was constructed to effectively indicate the exposure of hypoxia in HCC tissues. The signature was validated by qRT-PCR and compared with other published hypoxia signatures in multiple large-size HCC cohorts. The subtype of HCC derived from this signature had different prognosis and other clinical characteristics. The hypoxia score obtained from the signature could be used to indicate clinical characteristics and predict prognoses of HCC patients. Moreover, we reveal a landscape of immune microenvironments in patients with different hypoxia score. In conclusion, we identified a novel HCC-suitable 21-gene hypoxia signature that could be used to estimate the hypoxia exposure in HCC tissues and indicated prognosis and a series of important clinical features in HCCs. It may enable the development of personalized counselling or treatment strategies for HCC patients with different levels of hypoxia exposure