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A bilinearisation-reduction approach is described for finding solutions for nonlocal integrable systems and is illustrated with nonlocal discrete nonlinear Schrodinger equations. In this approach we first bilinearise the coupled system before reduction and derive its double Casoratian solutions; then we impose reduction on double Casoratians so that they coincide with the nonlocal reduction on potentials. Double Caosratian solutions of the classical and nonlocal (reverse space, reverse time and reverse space-time) discrete nonlinear Schrodinger equations are presented.

Identifying spawning grounds of Asian carp is important for determining the reproductive front of invasive populations. Ichthyoplankton monitoring along the Illinois Waterway (IWW) has provided information on abundances of Asian carp eggs in the IWW's navigation pools. Post-fertilization times derived from egg development stages and water temperatures can be used to estimate spawning times of Asian carp eggs, but estimating how far these eggs have drifted requires information on river hydraulics. A Fluvial Egg Drift Simulator (FluEgg) program was designed to predict the drift of Asian carp eggs in the riverine environment with egg growth considered. This paper presents a reverse-time particle tracking (RTPT) algorithm for back-casting the spawning location of eggs from their collection site. The RTPT algorithm was implemented as a module in FluEgg. The new version of FluEgg was coupled with an unsteady hydrodynamic model of the IWW to predict the spawning locations for 530 eggs that were collected in June 2015. The results indicate that tailwater sections below the Locks and Dams (L&Ds) in each navigation pool appear to be preferred spawning locations for Silver Carp (a species of Asian carp). From the data analyzed, the most upstream spawning location for the June 2015 spawning period was in the upper Marseilles navigation pool, downstream of the Dresden Island L&D. The RTPT algorithm can efficiently estimate spawning locations for multiple egg samples.

Inspired by the idea of Ablowitz and Musslimani, a reverse-time nonlocal nonlinear self-dual network equation is proposed under certain nonlocal symmetry reduction. N -fold Darboux transformation technique is used to construct discrete unstable and stable multi-soliton solutions in zero seed background for this system. Based on the asymptotic and graphic analysis, structures of one-, two- and three-soliton solutions are shown graphically. It is found that the individual components in this nonlocal equation show unstable temporal soliton structures whereas the combined potential terms exhibit stable soliton structures. Dynamical behaviors for one-soliton solutions are investigated via numerical simulations. It is worth noting that the solutions of this nonlocal equation are clearly different from those of its corresponding local part. Results obtained in this paper may be helpful for the explanation of the propagation of electrical signals.

Coupled dispersionless equation is an important model in quantum physics. Complex coupled dispersionless equation has valuable applications in geomerty. Recently, Ablowitz and Musslimani introduced and investigated a large class of reverse space, reverse time and reverse space-time nonlocal integrable equations. In this paper, we investigate a reverse space-time nonlocal complex coupled dispersionless equation, which was proposed in our paper [1]. By means of the Darboux transformation, we obtain its multi-soliton solutions from zero seed and nonzero seed. The asymptotic behavior of these solutions is discussed.

In the commented paper the authors propose a novel three-dimensional energy-saving and emission-reduction system. They claim to prove the existence of Silnikov homoclinic orbits by using the undetermined coefficient method and, consequently, the Silnikov theorem guarantees that the system has Smale horseshoes and the horseshoe chaos. Unfortunately, their demonstration is invalid because the form of the function they assume in the series expansion for the homoclinic orbits is incorrect. Namely, they compose the homoclinic orbit of the same manifold, which is stable in forward time and unstable in reverse time.

We used reverse time capture-mark-recapture models to describe associations between rate of population change (k) and climate for northern spotted owls (Strix occidentalis caurina) at six long-term study areas in Washington and Oregon, USA. Populations in three of six areas showed strong evidence of declining populations, while populations in two additional areas were likely declining as well. At four areas, k was positively associated with wetter-than-normal conditions during the growing season, which likely affects prey availability. Lambda was also negatively associated with cold, wet winters and nesting seasons, and the number of hot summer days. The amount of annual variation in k accounted for by climate varied across study areas (3–85%). Rate of population change was more sensitive to adult survival than to recruitment; however, there was considerable variation among years and across study areas for all demographic rates. While annual survival was more closely related to regional climate conditions, recruitment was often associated with local weather. In addition to climate, declines in recruitment at four of six areas were associated with increased presence of barred owls. Climate change models predict warmer, wetter winters and hotter, drier summers for the Pacific Northwest in the first half of the 21st century. Our results indicate that these conditions have the potential to negatively affect annual survival, recruitment, and consequently population growth rates for northern spotted owls.

This paper studies mathematical properties of h-index sequences as developed by Liang [Liang, L. (2006). h-Index sequence and h-index matrix: Constructions and applications. Scientometrics,69(1), 153-159]. For practical reasons, Liming studies such sequences where the time goes backwards while it is more logical to use the time going forward (real career periods). Both type of h-index sequences are studied here and their interrelations are revealed. We show cases where these sequences are convex, linear and concave. We also show that, when one of the sequences is convex then the other one is concave, showing that the reverse-time sequence, in general, cannot be used to derive similar properties of the (difficult to obtain) forward time sequence. We show that both sequences are the same if and only if the author produces the same number of papers per year. If the author produces an increasing number of papers per year, then Liang's h-sequences are above the ''normal'' ones. All these results are also valid for g- and R-sequences. The results are confirmed by the h-, g- and R-sequences (forward and reverse time) of the author.

This paper introduces a new interval observer based on direct and reverse time estimates. The observer is designed on the basis of the optimal observer proposed in (Moisan et al., 2007). We show that running the observer backwards in reverse time can be very efficient under specific assumptions. The method improves dramatically the convergence rate through a discontinuous interval estimation procedure. Simulation results considering a two dimensional bioreactor model are shown.

The present work introduces a new design to replace the (Finnish make) reverse time of flight (RTOF) analyzer used for the Fourier diffractometer facilities. The new design applies a data acquisition system, a special interface card and software program installed in a PC computer, to perform the cross-correlation functions between signals received from the chopper-decoder and detector. It has been found from test measurements performed with the Cairo Fourier diffractometer facility (CFDF) and the similar high resolution one at JINR (Dubna-Russia) that the new design can successfully replace the Finnish make RTOF analyzer.

We present and discuss an inherent shortcoming of neural networks used as discrete-time models in system identification, time series processing, and prediction. Trajectories of nonlinear ordinary differential equations (ODEs) can, under reasonable assumptions, be integrated uniquely backward in time. Discrete-time neural network mappings derived from time series, on the other hand, can give rise to multiple trajectories when followed backward in time: they are in principle noninvertible. This fundamental difference can lead to model predictions that are not only slightly quantitatively different, but qualitatively inconsistent with continuous time series. We discuss how noninvertibility arises, present key analytical concepts and some of its phenomenology. Using two illustrative examples (one experimental and one computational), we demonstrate when noninvertibility becomes an important factor in the validity of artificial neural network (ANN) predictions, and show some of the overall complexity of the predicted pathological dynamical behavior. These concepts can be used to probe the validity of ANN time series models, as well as provide guidelines for the acquisition of additional training data.

This paper is dealing with the problem of general conditions for the existence of the anticausal stabilizing solution to the discrete reverse-time Riccati equation. The connection between the γ-contracting property of the l2-input-output operator of a linear internally stable system and the existence of the anticausal stabilizing solution to the above-mentioned equation are pointed out.

The statistical accuracy between two neutron time-of-flight (TOF) diffraction techniques, the classic “forward” TOF and the “reverse” TOF technique, are compared. This problem is discussed in dependence on the diffracted spectrum, the background and some special device parameters. In general the “reverse” TOF method yields better statistics in the spectrum's range above the medium channel content; by the classic TOF method this is achieved in the lower area. For that reason, the reverse TOF measurement is especially recommendable for structure problems and the forward TOF technique for studying the background (e.g. the inelastic scattered portion).

1. 1. The turnover of phosphorus by RNA and phosphorus accumulation by DNA were measured with 32P at varying times after infection of E. coli with bacteriophage T2. The turnover rate of RNA is greatest shortly after infection and decreases at later times. The reverse time dependency is found for phosphorus accumulation by DNA. 2. 2. Comparison of RNA turnover in broth and in synthetic medium reveals that the RNA of infected cells in broth is much more quickly responsive to changes in specific radioactivity of orthophosphate in the medium. 3. 3. When isotope is presented to uninfected cells, the RNA mononucleotides always attain uniform specific radioactivity, whereas within 1 to 4 min after phage infection, the RNA mononucleotides of infected cells have nouniform specific activities in that adenylic and uridylic acids have about twice the activities of guanylic and cytidlic acids. 4. 4. When, after a period of 32P incorporation, infected cells are washed to reduce the acid-soluble 32P pool, further incubation results in a nearly quantitative transfer of radioactivity from RNA to DNA.