Stochastic analysis of recurrence plots with applications to the detection of deterministic signals

Recurrence plots have been widely used for a variety of purposes such as analyzing dynamical systems, denoising, as well as detection of deterministic signals embedded in noise. Though it has been postulated previously that recurrence plots contain time correlation information here we make the relationship between unthresholded recurrence plots and the covariance of a random process more precise. Computations using examples from harmonic processes, autoregressive models, and outputs from nonlinear systems are shown to illustrate this relationship. Finally, the use of recurrence plots for detection of deterministic signals in the presence of noise is investigated and compared to traditional signal detection methods based on the likelihood ratio test. Results using simulated data show that detectors based on certain statistics derived from recurrence plots are sub-optimal when compared to well-known detectors based on the likelihood ratio.     

Comment on “Synchronization in dynamic networks with nonsymmetrical time-delay coupling based on linear feedback controllers” [Physica A 387 (2008) 2111-2119]

In this paper, we point out two problems in synchronization of dynamic networks based on linear feedback controllers presented by Wu and Jiao [J. Wu, L. Jiao, Synchronization in dynamic networks with nonsymmetrical time-delay coupling based on linear feedback controllers, Physica A 387 (2008) 2111-2119]. Furthermore, an amendatory version on global exponential synchronization is given and proved in this paper.     

Comment on “Negative refraction in 1D photonic crystals” [Solid State Communications 147 (2008) 157-160]

It can be shown that negative refraction cannot occur in one-dimensional photonic crystals oriented as in Srivastava et al. (2008) [1].     

Erratum and addendum to “A variational theory of hyperbolic Lagrangian coherent structures” [Physica D 240 (2011) 574-598]

This brief note corrects a minor error in the statement of the main result in Haller (2011) [1] on a variational approach to Lagrangian coherent structures. We also show that the corrected formulation leads to a substantial simplification of LCS criteria for two-dimensional flows.     

Comment on ‘An optimal algorithm for counting networks motifs’ [Physica A 381 (2007) 482-490]

Network motifs in a given network are small connected subnetworks that occur at significantly higher frequencies than would be expected for a random network. In their 2007 article “An optimal algorithm for counting network motifs”, Itzhack, Mogilevski, and Louzoun present an algorithm for detecting network motifs. Based on an experimental comparison with a motif detection software called FANMOD, they claim that their algorithm is “more than a thousand times faster” than any previous motif detection algorithm. We show that this claim is not correct and based on a significant flaw in the experimental setup. Once the experimental data of Itzhack et al. is corrected for this flaw, the implementation of their algorithm actually turns out to be a little slower than FANMOD for random Erd?s-Rényi graphs. For random scale-free networks, the implementation of Itzhack et al. is faster only by a factor of ∼1.5, not the orders of magnitude claimed by Itzhack et al.     

Comments on “Electronic and thermodynamic properties of B2-FeSi from first principles” [Physica B 406 (2011) 363-367]

Iron monosilicides (FeSi) is an important material with very interesting properties that can be harnessed for technological applications. Our attention has been drawn to the so-called first principle study of the electronic and thermodynamic properties of B2-FeSi by Zhao et al. (Physica B 406 (2011) 363-367) using pseudopotential plane wave method. They reported that FeSi in B2 phase is a narrow band gap material with a band gap of 0.05 eV using a generalized gradient approximation (GGA) potential implemented within the density functional theory (DFT) approximation. This comment comes to address an important oversight by these authors in the interpretation of their results.     

Comment on “Modified Baptista type chaotic cryptosystem via matrix secret key” [Phys. Lett. A 372 (2008) 5427]

In this comment, we analyze a recently proposed Baptista-like cryptosystem and show that it is not invertible. Others weaknesses are also reported. A modified version of this cryptosystem is proposed to show how to overcome the non-invertibility.     

Comment on: “Efficient high-capacity quantum secret sharing with two-photon entanglement” [Phys. Lett. A 372 (2008) 1957]

In a recent Letter [F.G. Deng, X.H. Li, H.Y. Zhou, Phys. Lett. A 372 (2008) 1957], an efficient high-capacity quantum secret sharing scheme was proposed. However, in this comment, it is shown that the protocol does not complete the task of secret sharing well when the message sender uses the nonorthogonal entangled states as the quantum information carriers. Finally a feasible improvement of this quantum secret sharing protocol is proposed.     

Reply to: “Comment on: ‘Efficient high-capacity quantum secret sharing with two-photon entanglement’ [Phys. Lett. A 372 (2008) 1957]” [Phys. Lett. A 373 (2009) 396]

A corresponding Comment, raised by Yang and Wen, claimed that (i) our scheme cannot complete the task of secret sharing well even if the agents obtain the information about their measuring bases; (ii) they give a feasible improvement of our protocol. In this Reply, we show that their first judgment is wrong and their improvement is insecure.     

Reply to: “Comment on: ‘Epidemic spreading on heterogeneous networks with identical infectivity’ [Phys. Lett. A 364 (2007) 189]” [Phys. Lett. A 372 (2008) 1722]

In a recent Letter [R. Yang, B.H. Wang, J. Ren, W.J. Bai, Z.W. Shi, W.X. Wang, T. Zhou, Phys. Lett. A 364 (2007) 189], we proposed a modified susceptible-infected-recovered (SIR) model, in which each node is assigned with an identical capability of active contact, A, at each time step. We found a threshold value λc=1/A in uncorrelated and unlocalized networks. A corresponding Comment, raised by Alberto d'Onofrio, claimed that (i) our model is not biologically relevant; (ii) our model does not have a threshold behavior for recovered population; (iii) the analytical result λc=1/A is incorrect being considered as a threshold for epidemic outbreak, because of an improper approximation of the initial configuration. In this Reply, I show that, by debating from point to point, our analysis and conclusion are solid and reasonable.     

Comment on “Thermal radiation effects on MHD flow of a micropolar fluid over a stretching surface with variable thermal conductivity”, by Mostafa A.A. Mahmoud [Physica A 375 (2007) 401-410]

In the present comment we point out some errors found in the above referenced paper.