Gaussian approximations for stochastic systems with delay: chemical Langevin equation and application to a Brusselator system

We present a heuristic derivation of Gaussian approximations for stochastic chemical reaction systems with distributed delay. In particular we derive the corresponding chemical Langevin equation. Due to the non-Markovian character of the underlying dynamics these equations are integro-differential equations, and the noise in the Gaussian approximation is coloured. Following on from the chemical Langevin equation a further reduction leads to the linear-noise approximation. We apply the formalism to a delay variant of the celebrated Brusselator model, and show how it can be used to characterise noise-driven quasi-cycles, as well as noise-triggered spiking. We find surprisingly intricate dependence of the typical frequency of quasi-cycles on the delay period.Comment: 14 pages, 9 figure

Prospects for detection of Υ(1D)→Υ(1S)ππ\Upsilon(1D) \to \Upsilon(1S) \pi \pi via Υ(3S)→Υ(1D)+X\Upsilon(3S) \to \Upsilon(1D) + X

At least one state in the first family of D-wave $b \bar b$ quarkonium levels has been discovered near the predicted mass of 10.16 GeV/$c^2$. This state is probably the one with J=2. This state and the ones with J=1 and J=3 may contribute a detectable amount to the decay $\Upsilon(1D) \to \Upsilon(1S) \pi \pi$, depending on the partial widths for these decays for which predictions vary considerably. The prospects for detection of the chain $\Upsilon(3S) \to \Upsilon(1D) + X \to \Upsilon \pi \pi + X$ are discussed.Comment: 4 pages, LaTeX, 1 figure, to be published in Phys. Rev. D, comment added after Eq. (2

A new framework for consensus for discrete-time directed networks of multi-agents with distributed delays

Copyright @ 2012 Taylor & FrancisIn this article, the distributed consensus problem is considered for discrete-time delayed networks of dynamic agents with fixed topologies, where the networks under investigation are directed and the time-delays involved are distributed time delays including a single or multiple time delay(s) as special cases. By using the invariance principle of delay difference systems, a new unified framework is established to deal with the consensus for the discrete-time delayed multi-agent system. It is shown that the addressed discrete-time network with arbitrary distributed time delays reaches consensus provided that it is strongly connected. A numerical example is presented to illustrate the proposed methods.This work was supported in part by City University of Hong Kong under Grant 7008114, the Royal Society of the UK, the National Natural Science Foundation of China under Grants 60774073 and 61074129, and the Natural Science Foundation of Jiangsu Province of China under Grant BK2010313

Azimuth sidelobes suppression using multi-azimuth angle synthetic aperture radar images

A novel method is proposed for azimuth sidelobes suppression using multi-pass squinted (MPS) synthetic aperture radar (SAR) data. For MPS SAR, the radar observes the scene with different squint angles and heights on each pass. The MPS SAR mode acquisition geometry is given first. Then, 2D signals are focused and the images are registered to the master image. Based on the new signal model, elevation processing and incoherent addition are introduced in detail, which are the main parts for azimuth sidelobes suppression. Moreover, parameter design criteria in incoherent addition are derived for the best performance. With the proposed parameter optimization step, the new method has a prominent azimuth sidelobes suppression effect with a slightly better azimuth resolution, as verified by experimental results on both simulated point targets and TerraSAR-X data

Search for Bc(ns)B_c(ns) via the Bc(ns)→Bc(ms)π+π−B_c(ns)\to B_c(ms)\pi^+\pi^- transition at LHCb and Z0Z_0 factory

It is interesting to study the characteristics of the whole family of $B_c$ which contains two different heavy flavors. LHC and the proposed $Z^0$ factory provide an opportunity because a large database on the $B_c$ family will be achieved. $B_c$ and its excited states can be identified via their decay modes. As suggested by experimentalists, $B_c^*(ns)\to B_c+\gamma$ is not easy to be clearly measured, instead, the trajectories of $\pi^+$ and $\pi^-$ occurring in the decay of $B_c(ns)\to B_c(ms)+\pi^+\pi^-$ ($n>m$) can be unambiguously identified, thus the measurement seems easier and more reliable, therefore this mode is more favorable at early running stage of LHCb and the proposed $Z^0$ factory. In this work, we calculate the rate of $B_c(ns)\to B_c(ms)+\pi^+\pi^-$ in terms of the QCD multipole-expansion and the numerical results indicate that the experimental measurements with the luminosity of LHC and $Z^0$ factory are feasible.Comment: 12 pages, 1 figures and 4 tables, acceptted by SCIENCE CHINA Physics, Mechanics & Astronomy (Science in China Series G

Towards Impartial Multi-task Learning

Multi-task learning (MTL) has been widely used in representation learning. However, naively training all tasks simultaneously may lead to the partial training issue, where specific tasks are trained more adequately than others. In this paper, we propose to learn multiple tasks impartially. Specifically, for the task-shared parameters, we optimize the scaling factors via a closed-form solution, such that the aggregated gradient (sum of raw gradients weighted by the scaling factors) has equal projections onto individual tasks. For the task-specific parameters, we dynamically weigh the task losses so that all of them are kept at a comparable scale. Further, we find the above gradient balance and loss balance are complementary and thus propose a hybrid balance method to further improve the performance. Our impartial multi-task learning (IMTL) can be end-to-end trained without any heuristic hyper-parameter tuning, and is general to be applied on all kinds of losses without any distribution assumption. Moreover, our IMTL can converge to similar results even when the task losses are designed to have different scales, and thus it is scale-invariant. We extensively evaluate our IMTL on the standard MTL benchmarks including Cityscapes, NYUv2 and CelebA. It outperforms existing loss weighting methods under the same experimental settings

The magnetic dipole transitions in the (cbˉ)(c\bar{b}) binding system

The magnetic dipole transitions between the vector mesons $B_c^*$ and their relevant pseudoscalar mesons $B_c$ ($B_c$, $B_c^*$, $B_c(2S)$, $B_c^*(2S)$, $B_c(3S)$ and $B_c^*(3S)$ etc, the binding states of $(c\bar{b})$ system) of the $B_c$ family are interesting. To see the `hyperfine' splitting due to spin-spin interaction is an important topic for understanding the spin-spin interaction and the spectrum of the the $(c\bar{b})$ binding system. The knowledge about the magnetic dipole transitions is also very useful for identifying the vector boson $B_c^*$ mesons experimentally, whose masses are just slightly above the masses of their relevant pseudoscalar mesons $B_c$ accordingly. Considering the possibility to observe the vector mesons via the transitions at $Z^0$ factory and the potentially usages of the theoretical estimate on the transitions, we fucus our efforts on calculating the magnetic dipole transitions, i.e. precisely to calculate the rates for the transitions such as decays $B_c^*\to B_c\gamma$ and $B_c^*\to B_c e^+e^-$, and particularly work in the Behte-Salpeter framework. In the estimate, as a typical example, we carefully investigate the dependance of the rate $\Gamma(B_c^*\to B_c\gamma)$ on the mass difference $\Delta M=M_{B_c^*}-M_{B_c}$ as well.Comment: 10 pages, 2 figures, 1 tabl

Discovery From Non-Parties (Third-Party Discovery) in International Arbitration

International arbitration rules and many arbitration laws usually provide procedures that permit tribunals to order parties to disclose documents and other materials to the other parties.1 More complex are the rules that determine opportunities to obtain discovery from persons that are not party to the arbitration (third-party discovery). This article will review third-party discovery under the Federal Arbitration Act (FAA) and the provisions of the US Code s.1782 that authorise US courts to act in aid of actions before foreign tribunals. Section 1782 has unique interest at this time because it figured prominently in the EU antitrust investigation of Intel that was initiated on request from Advanced Micro Devices (AMD). Early in that investigation, AMD filed a s.1782 request in the US District Court to obtain evidence from US sources for submission to the DG-Competition of the European Commission (EC). This request ultimately led to the Supreme Court’s decision in Intel Corp v Advanced Micro Devices Inc2 which appeared to significantly expand the scope of s.1782. Ironically, after AMD won on key legal issues in the Supreme Court, the District Court on remand exercised its discretion and denied the request for judicial assistance. This paper first describes the FAA non-party discovery rules and the split among the federal appellate courts concerning the authority of arbitrators to order prehearing discovery from non-parties. Next, it provides an analysis of the meaning of the terms “interested party” and “tribunal”—terms that were controversially interpreted by the Supreme Court in Intel and are essential to the application of s.1782. Finally, it discusses the “discretionary” factors used by the federal courts in deciding whether to grant a s.1782 request even when the statutory criteria are met. The opportunity to exercise this discretion seems to rebut the argument that the Supreme Court’s interpretation of s.1782 gives participants before foreign tribunals more discovery rights in the United States than are available to the parties in arbitrations covered by the FAA

Detection of promoter hypermethylation of the CpG island of E-cadherin in gastric cardiac adenocarcinoma

<p>Abstract</p> <p>Aim</p> <p>Abnormal hypermethylation of CpG islands associated with tumor suppressor genes can lead to transcriptional silencing in neoplasia. The aim of this study was to investigate the promoter methylation and expression of E-cadherin gene in gastric cardiac adenocarcinoma (GCA).</p> <p>Methods</p> <p>A nested MSP approach, immunohistochemistry method and RT-PCR were used respectively to examine the methylation status of the 5' CpG island of E-cadherin, its protein expression and mRNA expression in tumors and corresponding normal tissues.</p> <p>Results</p> <p>E-cadherin was methylated in 63 of 92 (68.5%) tumor specimens, which was significantly higher than that in corresponding normal tissues (P < 0.001). Methylation frequencies of stage III and IV tumor tissues was significantly higher than that in stage I and II tumor tissues (P = 0.01). Methylation status of poor differentiation group was significantly higher than moderate and poor-moderate differentiation groups (P < 0.01). By immunostaining 51 of 92 tumor tisssues demonstrated heterogeneous, positive immunostaining of tumor tissues (44.6%), significantly different from matched normal tissues (P < 0.001). Positive immunostaining of stage III and IV tumor tissues was significantly lower than stage I and II tumor tissues (P < 0.01). Poor differentiation group was also significantly lower than moderate and poor-moderate differentiation groups (P < 0.05). 80 percent of tumor tissues with E-cadherin gene methylated showed inactivated mRNA expression.</p> <p>Conclusions</p> <p>High methylation status of the 5' CpG island of E-cadherin gene may be one of the mechanisms in the development of gastric cardiac adenocarcinoma.</p