Particle filtering in high-dimensional chaotic systems

We present an efficient particle filtering algorithm for multiscale systems, that is adapted for simple atmospheric dynamics models which are inherently chaotic. Particle filters represent the posterior conditional distribution of the state variables by a collection of particles, which evolves and adapts recursively as new information becomes available. The difference between the estimated state and the true state of the system constitutes the error in specifying or forecasting the state, which is amplified in chaotic systems that have a number of positive Lyapunov exponents. The purpose of the present paper is to show that the homogenization method developed in Imkeller et al. (2011), which is applicable to high dimensional multi-scale filtering problems, along with important sampling and control methods can be used as a basic and flexible tool for the construction of the proposal density inherent in particle filtering. Finally, we apply the general homogenized particle filtering algorithm developed here to the Lorenz'96 atmospheric model that mimics mid-latitude atmospheric dynamics with microscopic convective processes.Comment: 28 pages, 12 figure

Scaling properties of growing noninfinitesimal perturbations in space-time chaos

We study the spatiotemporal dynamics of random spatially distributed noninfinitesimal perturbations in one-dimensional chaotic extended systems. We find that an initial perturbation of finite size $\epsilon_0$ grows in time obeying the tangent space dynamic equations (Lyapunov vectors) up to a characteristic time $t_{\times}(\epsilon_0) \sim b - (1/\lambda_{max}) \ln (\epsilon_0)$, where $\lambda_{max}$ is the largest Lyapunov exponent and $b$ is a constant. For times $t < t_{\times}$ perturbations exhibit spatial correlations up to a typical distance $\xi \sim t^z$. For times larger than $t_{\times}$ finite perturbations are no longer described by tangent space equations, memory of spatial correlations is progressively destroyed and perturbations become spatiotemporal white noise. We are able to explain these results by mapping the problem to the Kardar-Parisi-Zhang universality class of surface growth.Comment: 4.5 pages LaTeX (RevTeX4) format, 3 eps figs included. Submitted to Phys Rev

Homophilic binding of PTP mu, a receptor-type protein tyrosine phosphatase, can mediate cell-cell aggregation

The receptor-like protein tyrosine phosphatase, PTPmu, displays structural similarity to cell-cell adhesion molecules of the immunoglobulin superfamily. We have investigated the ability of human PTPmu to function in such a capacity. Expression of PTPmu, with or without the PTPase domains, by recombinant baculovirus infection of Sf9 cells induced their aggregation. However, neither a chimeric form of PTPmu, containing the extracellular and transmembrane segments of the EGF receptor and the intracellular segment of PTPmu, nor the intracellular segment of PTPmu expressed as a soluble protein induced aggregation. PTPmu mediates aggregation via a homophilic mechanism, as judged by lack of incorporation of uninfected Sf9 cells into aggregates of PTPmu-expressing cells. Homophilic binding has been demonstrated between PTPmu-coated fluorescent beads (Covaspheres) and endogenously expressed PTPmu on MvLu cells. Additionally the PTPmu-coated beads specifically bound to a bacterially expressed glutathione-S-transferase fusion protein containing the extracellular segment of PTPmu (GST/PTPmu) adsorbed to petri dishes. Covaspheres coated with the GST/PTPmu fusion protein aggregated in vitro and also bound to PTPmu expressed endogenously on MvLu cells. These results suggest that the ligand for this transmembrane PTPase is another PTPmu molecule on an adjacent cell. Thus homophilic binding interactions may be an important component of the function of PTPmu in vivo

Development of Educational Programs for Retail Stores That Sell Pesticides

Although homeowners usually purchase pesticides from home and garden centers, previous surveys have shown that store employees often do not receive adequate training in pest management and pesticide safety. Educational programs were conducted for retail store employees in Illinois. Topics included pest identification, integrated pest management, pesticide safety, pesticide toxicity, and emergency spill response. Evaluations suggested a high level of satisfaction with the training. Evaluation comments also indicated concern over the high turnover of seasonal employees, the wide range of employee understanding of pest management, and time constraints that may prohibit small retail stores from participating in educational programs

Brief Communication: Breeding vectors in the phase space reconstructed from time series data

Bred vectors characterize the nonlinear instability of dynamical systems and so far have been computed only for systems with known evolution equations. In this article, bred vectors are computed from a single time series data using time-delay embedding, with a new technique, nearest-neighbor breeding. Since the dynamical properties of the standard and nearest-neighbor breeding are shown to be similar, this provides a new and novel way to model and predict sudden transitions in systems represented by time series data alone

Empirical correction of a toy climate model

Improving the accuracy of forecast models for physical systems such as the atmosphere is a crucial ongoing effort. Errors in state estimation for these often highly nonlinear systems has been the primary focus of recent research, but as that error has been successfully diminished, the role of model error in forecast uncertainty has duly increased. The present study is an investigation of a particular empirical correction procedure that is of special interest because it considers the model a "black box", and therefore can be applied widely with little modification. The procedure involves the comparison of short model forecasts with a reference "truth" system during a training period in order to calculate systematic (1) state-independent model bias and (2) state-dependent error patterns. An estimate of the likelihood of the latter error component is computed from the current state at every timestep of model integration. The effectiveness of this technique is explored in two experiments: (1) a perfect model scenario, in which models have the same structure and dynamics as the true system, differing only in parameter values; and (2) a more realistic scenario, in which models are structurally different (in dynamics, dimension, and parameterization) from the target system. In each case, the results suggest that the correction procedure is more effective for reducing error and prolonging forecast usefulness than parameter tuning. However, the cost of this increase in average forecast accuracy is the creation of substantial qualitative differences between the dynamics of the corrected model and the true system. A method to mitigate the structural damage caused by empirical correction and further increase forecast accuracy is presented.Comment: 16 pages, 12 figure

Using Synchronization for Prediction of High-Dimensional Chaotic Dynamics

We experimentally observe the nonlinear dynamics of an optoelectronic time-delayed feedback loop designed for chaotic communication using commercial fiber optic links, and we simulate the system using delay differential equations. We show that synchronization of a numerical model to experimental measurements provides a new way to assimilate data and forecast the future of this time-delayed high-dimensional system. For this system, which has a feedback time delay of 22 ns, we show that one can predict the time series for up to several delay periods, when the dynamics is about 15 dimensional.Comment: 10 pages, 4 figure

VLBI measurement of the secular aberration drift

While analyzing decades of very long baseline interferometry (VLBI) data, we detected the secular aberration drift of the extragalatic radio source proper motions caused by the rotation of the Solar System barycenter around the Galactic center. Our results agree with the predicted estimate to be 4-6 micro arcseconds per year ({\mu}as/yr) towards {\alpha} = 266\circ and {\delta} = -29\circ. In addition, we tried to detect the quadrupole systematics of the velocity field. The analysis method consisted of three steps. First, we analyzed geodetic and astrometric VLBI data to produce radio source coordinate time series. Second, we fitted proper motions of 555 sources with long observational histories over the period 1990-2010 to their respective coordinate time series. Finally, we fitted vector spherical harmonic components of degrees 1 and 2 to the proper motion field. Within the error bars, the magnitude and the direction of the dipole component agree with predictions. The dipole vector has an amplitude of 6.4 \pm 1.5 {\mu}as/yr and is directed towards equatorial coordinates {\alpha} = 263\circ and {\delta} = -20\circ. The quadrupole component has not been detected. The primordial gravitational wave density, integrated over a range of frequencies less than 10-9 Hz, has a limit of 0.0042 h-2 where h is the normalized Hubble constant is H0/(100 km s-1)

Genomic structure and alternative splicing of murine R2B receptor protein tyrosine phosphatases (PTPκ, μ, ρ and PCP-2)

BACKGROUND: Four genes designated as PTPRK (PTPκ), PTPRL/U (PCP-2), PTPRM (PTPμ) and PTPRT (PTPρ) code for a subfamily (type R2B) of receptor protein tyrosine phosphatases (RPTPs) uniquely characterized by the presence of an N-terminal MAM domain. These transmembrane molecules have been implicated in homophilic cell adhesion. In the human, the PTPRK gene is located on chromosome 6, PTPRL/U on 1, PTPRM on 18 and PTPRT on 20. In the mouse, the four genes ptprk, ptprl, ptprm and ptprt are located in syntenic regions of chromosomes 10, 4, 17 and 2, respectively. RESULTS: The genomic organization of murine R2B RPTP genes is described. The four genes varied greatly in size ranging from ~64 kb to ~1 Mb, primarily due to proportional differences in intron lengths. Although there were also minor variations in exon length, the number of exons and the phases of exon/intron junctions were highly conserved. In situ hybridization with digoxigenin-labeled cRNA probes was used to localize each of the four R2B transcripts to specific cell types within the murine central nervous system. Phylogenetic analysis of complete sequences indicated that PTPρ and PTPμ were most closely related, followed by PTPκ. The most distant family member was PCP-2. Alignment of RPTP polypeptide sequences predicted putative alternatively spliced exons. PCR experiments revealed that five of these exons were alternatively spliced, and that each of the four phosphatases incorporated them differently. The greatest variability in genomic organization and the majority of alternatively spliced exons were observed in the juxtamembrane domain, a region critical for the regulation of signal transduction. CONCLUSIONS: Comparison of the four R2B RPTP genes revealed virtually identical principles of genomic organization, despite great disparities in gene size due to variations in intron length. Although subtle differences in exon length were also observed, it is likely that functional differences among these genes arise from the specific combinations of exons generated by alternative splicing