Difference systems of sets based on cosets partitions

Difference systems of sets （DSS） are combinatorial configurations that arise in connection with code synchronization. This paper proposes a new method to construct DSSs, which uses known DSSs to partition some of the cosets of Zv relative to subgroup of order k, where v = km is a composite number. As applications, we obtain some new optimal DSSs.     

Bounded invariant verification for time-delayed nonlinear networked dynamical systems

We present a technique for bounded invariant verification of nonlinear networked dynamical systems with delayed interconnections. The underlying problem in precise bounded-time verification lies with computing bounds on the sensitivity of trajectories (or solutions) to changes in initial states and inputs of the system. For large networks, computing this sensitivity with precision guarantees is challenging. We introduce the notion of input-to-state (IS) discrepancy of each module or subsystem in a larger nonlinear networked dynamical system. The IS discrepancy bounds the distance between two solutions or trajectories of a module in terms of their initial states and their inputs. Given the IS discrepancy functions of the modules, we show that it is possible to effectively construct a reduced (low dimensional) time-delayed dynamical system, such that the trajectory of this reduced model precisely bounds the distance between the trajectories of the complete network with changed initial states. Using the above results we develop a sound and relatively complete algorithm for bounded invariant verification of networked dynamical systems consisting of nonlinear modules interacting through possibly delayed signals. Finally, we introduce a local version of IS discrepancy and show that it is possible to compute them using only the Lipschitz constant and the Jacobian of the dynamic function of the modules.     

Multiple bifurcation trees of period-1 motions to chaos in a periodically forced,time-delayed,hardening Duffing oscillator

In this paper, bifurcation trees of periodic motions in a periodically forced, time-delayed, hardening Duffing oscillator are analytically predicted by a semi-analytical method. Such a semi-analytical method is based on the differential equation discretization of the time-delayed, nonlinear dynamical system. Bifurcation trees for the stable and unstable solutions of periodic motions to chaos in such a time-delayed, Duffing oscillator are achieved analytically. From the finite discrete Fourier series, harmonic frequency-amplitude curves for stable and unstable solutions of period-1 to period-4 motions are developed for a better understanding of quantity levels, singularity and catastrophes of harmonic amplitudes in the frequency domain. From the analytical prediction, numerical results of periodic motions in the time-delayed, hardening Duffing oscillator are completed. Through the numerical illustrations, the complexity and asymmetry of period-1 motions to chaos in nonlinear dynamical systems are strongly dependent on the distributions and quantity levels of harmonic amplitudes. With the quantity level increases of specific harmonic amplitudes, effects of the corresponding harmonics on the periodic motions become strong, and the certain complexity and asymmetry of periodic motion and chaos can be identified through harmonic amplitudes with higher quantity levels.     

Discrete fractional logistic map and its chaos

A discrete fractional logistic map is proposed in the left Caputo discrete delta’s sense. The new model holds discrete memory. The bifurcation diagrams are given and the chaotic behaviors are numerically illustrated.     

Three‐unit semicircles curve: A compact 3D graphical representation of DNA sequences based on classifications of nucleotides

A new three‐dimensional graphical representation of DNA sequences, three‐unit semicircles (TUS)‐curve, which maps a given sequence into a dot sequences embedded in three‐unit semicircles, is proposed based on three biclassifications of nucleotides. TUS‐curve has the merit of compactness and could avoid the degeneracy and loss of information. The geometrical center of the curve, which indicates the distribution of base frequencies of the corresponding DNA sequence, is extracted and applied to analyze the similarity of various species. Phylogenetic tree of 11 species based on their first exons of β‐globin genes showed that the TUS‐curve is a powerful tool to get valuable biological information. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Numerical simulation of solitons switching and propagating in asymmetric directional couplers

A numerical investigation, based on the use of split step Fourier transformation algorithm, of all-optical solitons switching in asymmetric directional couplers is presented. The numerical algorithm is described in details. The analysis highlights the influence of the different effective mode area, the phase- and group–velocity mismatch, the different dispersion between two cores on the switching and propagation of short pulses. The investigation indicates that the phase velocity mismatch and the different effective mode area can reduce the coupling length while the different group velocity and the different dispersion between two cores do not change the coupling length. We have also found that the increase of effective mode area ratio can lead to an increase of the switching threshold power but improve significantly the switching steepness, the increase of the phase velocity mismatch can cause a decrease of the switching threshold power but degrade the switching steepness, the increase of the ratio of dispersion can result in a decrease of the switching threshold power and vary the switching steepness, the increase of group velocity mismatch can give rise to an increase of the switching threshold power but improve obviously the switching steepness. Furthermore, the group velocity mismatch can induce solitons pulse to walk off or stretch in the asymmetric directional coupler.     

Offline Arbitrated Quantum Blind Dual-Signature Protocol with Better Performance in Resisting Existential Forgery Attack

In this paper, we present an offline arbitrated quantum blind dual-signature protocol by using four-particle entangled Greenberger-Horne-Zeilinger(GHZ) states. By using the special relationship of four-particle GHZ states, we can not only support the security of quantum signature, but also guarantee the anonymity of the message owner. In our protocol, the authority of the arbitrator has been reduced, i.e., he will not help the receiver verify the signature in the verification. Compared with the previous quantum blind signature protocols, the presented arbitrator is offline. Finally, the security analysis and discussion are proposed.     

Learning-based compressed sensing for infrared image super resolution

This paper presents an infrared image super-resolution method based on compressed sensing (CS). First, the reconstruction model under the CS framework is established and a Toeplitz matrix is selected as the sensing matrix. Compared with traditional learning-based methods, the proposed method uses a set of sub-dictionaries instead of two coupled dictionaries to recover high resolution (HR) images. And Toeplitz sensing matrix allows the proposed method time-efficient. Second, all training samples are divided into several feature spaces by using the proposed adaptive k-means classification method, which is more accurate than the standard k-means method. On the basis of this approach, a complex nonlinear mapping from the HR space to low resolution (LR) space can be converted into several compact linear mappings. Finally, the relationships between HR and LR image patches can be obtained by multi-sub-dictionaries and HR infrared images are reconstructed by the input LR images and multi-sub-dictionaries. The experimental results show that the proposed method is quantitatively and qualitatively more effective than other state-of-the-art methods.