Robust filtering for gene expression time series data with variance constraints

This is the post print version of the article. The official published version can be obtained from the link below - Copyright 2007 Taylor & Francis Ltd.In this paper, an uncertain discrete-time stochastic system is employed to represent a model for gene regulatory networks from time series data. A robust variance-constrained filtering problem is investigated for a gene expression model with stochastic disturbances and norm-bounded parameter uncertainties, where the stochastic perturbation is in the form of a scalar Gaussian white noise with constant variance and the parameter uncertainties enter both the system matrix and the output matrix. The purpose of the addressed robust filtering problem is to design a linear filter such that, for the admissible bounded uncertainties, the filtering error system is Schur stable and the individual error variance is less than a prespecified upper bound. By using the linear matrix inequality (LMI) technique, sufficient conditions are first derived for ensuring the desired filtering performance for the gene expression model. Then the filter gain is characterized in terms of the solution to a set of LMIs, which can easily be solved by using available software packages. A simulation example is exploited for a gene expression model in order to demonstrate the effectiveness of the proposed design procedures.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grants GR/S27658/01 and EP/C524586/1, the Biotechnology and Biological Sciences Research Council (BBSRC) of the UK under Grants BB/C506264/1 and 100/EGM17735, the Nuffield Foundation of the UK under Grant NAL/00630/G, and the Alexander von Humboldt Foundation of Germany

Recovery of the orbital parameters and pulse evolution of V0332+53 during a huge outburst

The high mass X-ray binary (HMXB) V0332+53 became active at the end of 2004 and the outburst was observed at hard X-rays by RXTE and INTEGRAL. Based on these hard X-ray observations, the orbital parameters are measured through fitting the Doppler-shifted spin periods. The derived orbital period and eccentricity are consistent with those of Stella et al. (1985) obtained from EXOSAT observations, whereas the projected semimajor axis and the periastron longitude are found to have changed from 48$\pm$4 to 86$^{+6}_{-10}$ lt-s and from 313$^{\circ}$$\pm$10 to 283$^{\circ}$$\pm$14, respectively. This would indicate an angular speed of $\geq$ 1.5$^{\circ}$$\pm$0.8 yr$^{-1}$ for rotation of the orbit over the past 21 years. The periastron passage time of MJD 53367$\pm$1 is just around the time when the intensity reached maximum and an orbital period earlier is the time when the outburst started. This correlation resembles the behavior of a Type I outburst. During outburst the source spun up with a rate of 8.01$^{+1.00}_{-1.14}$$\times10^{-6}$ s day$^{-1}$. The evolution of pulse profile is highly intensity dependent. The separation of double pulses remained almost constant ($\sim$ 0.47) when the source was bright, and dropped to 0.37 within $\leq$ 3 days as the source became weaker. The pulse evolution of V0332+53 may correlate to the change in dominance of the emission between fan-beam and pencil-beam mechanisms.Comment: 13 pages, 3 figures, accepted for publication in ApJ

Low Mach number effect in simulation of high Mach number flow

In this note, we relate the two well-known difficulties of Godunov schemes: the carbuncle phenomena in simulating high Mach number flow, and the inaccurate pressure profile in simulating low Mach number flow. We introduced two simple low-Mach-number modifications for the classical Roe flux to decrease the difference between the acoustic and advection contributions of the numerical dissipation. While the first modification increases the local numerical dissipation, the second decreases it. The numerical tests on the double-Mach reflection problem show that both modifications eliminate the kinked Mach stem suffered by the original flux. These results suggest that, other than insufficient numerical dissipation near the shock front, the carbuncle phenomena is strongly relevant to the non-comparable acoustic and advection contributions of the numerical dissipation produced by Godunov schemes due to the low Mach number effect.Comment: 9 pages, 1 figur

Highlights from Five Years at the B Factories

The highlights and conflicts at the B Factories are briefly reviewed. $CP$ violation was established in 2001 in $B^0 \to J/\psi K_S$ and related modes, which has now become a precision measurement of CP violation in $B^0$-$\bar B^0$ mixing. However, the situation for the $B^0 \to \pi^+\pi^-$ and charmless $b\to s$ modes, which probe also CP violation in the {\it decay} amplitude, are not quite settled yet. They could be hinting at presence of both strong (CP conserving) and new physics (CP violating) phases. We critically assess the developments and discuss some related discrepancies and highlights, such as observation of direct CP violation, and make a projection towards the next few years.Comment: 16 pages, 5 figures, to appear as Brief Review in Mod. Phys. Lett.

Making the corona and the fast solar wind: a self-consistent simulation for the low-frequency Alfven waves from photosphere to 0.3AU

We show that the coronal heating and the fast solar wind acceleration in the coronal holes are natural consequence of the footpoint fluctuations of the magnetic fields at the photosphere, by performing one-dimensional magnetohydrodynamical simulation with radiative cooling and thermal conduction. We initially set up a static open flux tube with temperature 10^4K rooted at the photosphere. We impose transverse photospheric motions corresponding to the granulations with velocity = 0.7km/s and period between 20 seconds and 30 minutes, which generate outgoing Alfven waves. We self-consistently treat these waves and the plasma heating. After attenuation in the chromosphere by ~85% of the initial energy flux, the outgoing Alfven waves enter the corona and contribute to the heating and acceleration of the plasma mainly by the nonlinear generation of the compressive waves and shocks. Our result clearly shows that the initial cool and static atmosphere is naturally heated up to 10^6K and accelerated to 800km/s.Comment: 4 pages, 3 figures, ApJL, 632, L49, corrections of mistypes in eqs.(3) & (5), Mpeg movie for fig.1 (simulation result) is available at http://www-tap.scphys.kyoto-u.ac.jp/~stakeru/research/suzuki_200506.mp

A new model for the double well potential

A new model for the double well potential is presented in the paper. In the new potential, the exchanging rate could be easily calculated by the perturbation method in supersymmetric quantum mechanics. It gives good results whether the barrier is high or sallow. The new model have many merits and may be used in the double well problem.Comment: 3pages, 3figure

Two-body charmed baryon decays involving decuplet baryon in the quark-diagram scheme

In the quark-diagram scheme, we study the charmed baryon decays of ${\bf B}_c\to {\bf B}^* M$, where ${\bf B}_c$ is $\Lambda_c^+$ or $\Xi_c^{+(0)}$, together with ${\bf B}^*$ ($M$) the decuplet baryon (pseudoscalar meson). It is found that only two $W$-exchange processes are allowed to contribute to ${\bf B}_c\to {\bf B}^* M$. Particularly, we predict ${\cal B}(\Lambda_c^+ \to \Sigma^{*0(+)} \pi^{+(0)})=(2.8\pm 0.4)\times 10^{-3}$, which respects the isospin symmetry. Besides, we take into account the $SU(3)$ flavor symmetry breaking, in order to explain the observation of ${\cal B}(\Lambda_c^+\to \Sigma^{*+}\eta)$. For the decays involving $\Delta^{++}(uuu)$, we predict ${\cal B}(\Lambda_c^+\to \Delta^{++} \pi^-,\Xi_c^+ \to \Delta^{++} K^-) =(7.0\pm 1.4,13.5\pm 2.7)\times 10^{-4}$ as the largest branching fractions in the singly Cabibbo-suppressed $\Lambda_c^+,\Xi_c^+\to{\bf B}^*M$ decay channels, respectively, which are accessible to the LHCb, BELLEII and BESIII experiments.Comment: 12 pages, 1 figure, 3 tables, version to appear in EPJ

Vorticity Budget of Weak Thermal Convection in Keplerian disks

By employing the equations of mean-square vorticity (enstrophy) fluctuations in strong shear flows, we demonstrate that unlike energy production of turbulent vorticity in nonrotating shear flows, the turbulent vorticity of weak convection in Keplerian disks cannot gain energy from vortex stretching/tilting by background shear unless the asscoiated Reynolds stresses are negative. This is because the epicyclic motion is an energy sink of the radial component of mean-square turbulent vorticity in Keplerian disks when Reynolds stresses are positive. Consequently, weak convection cannot be self-sustained in Keplerian flows. This agrees with the results implied from the equations of mean-square velocity fluctuations in strong shear flows. Our analysis also sheds light on the explanation of the simulation result in which positive kinetic helicity is produced by the Balbus-Hawley instability in a vertically stratified Keplerian disk. We also comment on the possibility of outward angular momentum transport by strong convection based on azimuthal pressure perturbations and directions of energy cascade.Comment: 8 pages, 1 figure, emulateapj.sty, revised version in response to referee's comments, accepted by Ap

Semi-Supervised Data Summarization: Using Spectral Libraries to Improve Hyperspectral Clustering

Hyperspectral imagers produce very large images, with each pixel recorded at hundreds or thousands of different wavelengths. The ability to automatically generate summaries of these data sets enables several important applications, such as quickly browsing through a large image repository or determining the best use of a limited bandwidth link (e.g., determining which images are most critical for full transmission). Clustering algorithms can be used to generate these summaries, but traditional clustering methods make decisions based only on the information contained in the data set. In contrast, we present a new method that additionally leverages existing spectral libraries to identify materials that are likely to be present in the image target area. We find that this approach simultaneously reduces runtime and produces summaries that are more relevant to science goals

The Evolution of Cosmic Magnetic Fields: From the Very Early Universe, to Recombination, to the Present

(abridged) A detailed examination of the evolution of stochastic magnetic fields between high cosmic temperatures and the present epoch is presented. A simple analytical model matching the results of the 3D MHD simulations allows for the prediction of present day magnetic field correlation lengths and energy. Our conclusions are multi fold. (a) Initial primordial fields with only a small amount of helicity are evolving into maximally helical fields. (b) There exists a correlation between the strength of the magnetic field, B, at the peak of it's spectrum and the location of the peak, given at the present epoch by: B ~ 5x10^{-12} (L/kpc) Gauss, where L is the correlation length determined by the initial magnetic field. (c) Concerning studies of generation of cosmic microwave background (CMBR) anisotropies due to primordial magnetic fields of B~10^{-9} Gauss on ~ 10 Mpc scales, such fields are not only impossible to generate in early causal magnetogenesis scenarios but also seemingly ruled out by distortions of the CMBR spectrum due to magnetic field dissipation on smaller scales and the overproduction of cluster magnetic fields. (d) The most promising detection possibility of CMBR distortions due to primordial magnetic fields may be on much smaller scales at higher multipoles l~10^6 where the signal is predicted to be the strongest. (e) It seems possible that magnetic fields in clusters of galaxies are entirely of primordial origin, without invoking dynamo amplification. Such fields would be of (pre-collapse) strength 10^{-12} - 10^{-11} Gauss with correlation lengths in the kpc range, and would also exist in voids of galaxies.Comment: 35 pages, 22 figures, revtex style, submitted to PR