Limit theorems for continuous-state branching processes with immigration

We prove and extend some results stated by Mark Pinsky: Limit theorems for continuous state branching processes with immigration [Bull. Amer. Math. Soc. 78(1972), 242--244]. Consider a continuous-state branching process with immigration $(Y_t,t\geq 0)$ with branching mechanism $\Psi$ and immigration mechanism $\Phi$ (CBI$(\Psi,\Phi)$ for short). We shed some light on two different asymptotic regimes occurring when $\int_{0}\frac{\Phi(u)}{|\Psi(u)|}du<\infty$ or $\int_{0}\frac{\Phi(u)}{|\Psi(u)|}du=\infty$. We first observe that when $\int_{0}\frac{\Phi(u)}{|\Psi(u)|}du<\infty$, supercritical CBIs have a growth rate dictated by the branching dynamics, namely there is a renormalization $\tau(t)$, only depending on $\Psi$, such that $(\tau(t)Y_t,t\geq 0)$ converges almost-surely to a finite random variable. When $\int_{0}\frac{\Phi(u)}{|\Psi(u)|}du=\infty$, it is shown that the immigration overwhelms the branching dynamics and that no linear renormalization of the process can exist. Asymptotics in the second regime are studied in details for all non-critical CBI processes via a nonlinear time-dependent renormalization in law. Three regimes of weak convergence are then exhibited, where a misprint in Pinsky's paper is corrected. CBI processes with critical branching mechanisms subject to a regular variation assumption are also studied

Hopf bifurcation analysis and control of three-dimensional Prescott neuron model

Neurons generate different firing patterns because of different bifurcations in the dynamical viewpoint. Various nerve diseases are relevant to the bifurcation of nervous system. Therefore, it is vital to control bifurcation since it may be potential ways of treating nerve diseases. This paper focuses on the critical Hopf bifurcation analysis and the problem of Hopf bifurcation control. We investigate the effects of key parameters on critical Hopf bifurcation and obtain the Hopf bifurcation occurrence region on parameter plane. With the theory of high-dimensional Hopf bifurcation, we analytically deduce the judgement criteria of Hopf bifurcation type for the three-dimensional models and judge the Hopf bifurcation type of Prescott model by using it. With application of the Washout filter, the subcritical Hopf bifurcation of Prescott model is controlled and converted to supercritical Hopf bifurcation. In addition, we make some discussions on Hopf bifurcation analysis of a coupled neural network. The results provided in this paper could bring new ways to controlling neurological diseases

Limit theorems for continuous-state branching processes with immigration

AbstractA continuous-state branching process with immigration having branching mechanism $\Psi$ and immigration mechanism $\Phi$ , a CBI $(\Psi,\Phi)$ process for short, may have either of two different asymptotic regimes, depending on whether \int_{0}\frac{\Phi(u)}{|\Psi(u)|}\textrm{d} u<\infty or $\int_{0}\frac{\Phi(u)}{|\Psi(u)|}\textrm{d} u=\infty$ . When \int_{0}\frac{\Phi(u)}{|\Psi(u)|}\textrm{d} u<\infty , the CBI process has either a limit distribution or a growth rate dictated by the branching dynamics. When $\scriptstyle\int_{0}\tfrac{\Phi(u)}{|\Psi(u)|}\textrm{d} u=\infty$ , immigration overwhelms branching dynamics. Asymptotics in the latter case are studied via a nonlinear time-dependent renormalization in law. Three regimes of weak convergence are exhibited. Processes with critical branching mechanisms subject to a regular variation assumption are studied. This article proves and extends results stated by M. Pinsky in ‘Limit theorems for continuous state branching processes with immigration’ (Bull. Amer. Math. Soc.78, 1972).</jats:p

Underwater target detection using multichannel subband adaptive filtering and high-order correlation schemes

Includes bibliographical references.In this paper, new pre- and post-processing schemes are developed to process shallow-water sonar data to improve the accuracy of target detection. A multichannel subband adaptive filtering is applied to preprocess the data in order to isolate the potential target returns from the acoustic backscattered signals and improve the signal-to-reverberation ratio. This is done by estimating the time delays associated with the reflections in different subbands. The preprocessed results are then beamformed to generate an image for each ping of the sonar. The testing results on both the simulated and real data revealed the efficiency of this scheme in time-delay estimation and its capability in removing most of the competing reverberations and noise. To improve detection rate while significantly minimizing the incident of false detections, a high-order correlation (HOC) method for postprocessing the beamformed images is then developed. This method determines the consistency in occurrence of the target returns in several consecutive pings. The application of the HOC process to the real beamformed sonar data showed the ability of this method for removing the clutter and at the same time boosting the target returns in several consecutive pings. The algorithm is simple, fast, and easy to implement.This work was supported by the Office of Naval Research (ONR 321TS) under Contract N61331-94-K-0018

1,3-Bis(carboxy­meth­yl)imidazolium triiodide 1-carboxyl­atomethyl-3-carboxy­methyl­imidazolium

In the title compound, C7H9N2O4 +·I3 −·C7H8N2O4, the two imidazolium units are hydrogen bonded through the carboxyl groups. The units are further linked via inter­molecular O—H⋯O hydrogen bonding, resulting in a one-dimensional ladder-type structure. As a result, the two carb­oxy groups of each imidazolium unit adopt a cis configuration with respect to the imidazolium ring

Structure of the Brd4 ET domain bound to a C-terminal motif from γ-retroviral integrases reveals a conserved mechanism of interaction

The bromodomain and extraterminal domain (BET) protein family are promising therapeutic targets for a range of diseases linked to transcriptional activation, cancer, viral latency, and viral integration. Tandem bromodomains selectively tether BET proteins to chromatin by engaging cognate acetylated histone marks, and the extraterminal (ET) domain is the focal point for recruiting a range of cellular and viral proteins. BET proteins guide γ-retroviral integration to transcription start sites and enhancers through bimodal interaction with chromatin and the γ-retroviral integrase (IN). We report the NMR-derived solution structure of the Brd4 ET domain bound to a conserved peptide sequence from the C terminus of murine leukemia virus (MLV) IN. The complex reveals a protein–protein interaction governed by the binding-coupled folding of disordered regions in both interacting partners to form a well-structured intermolecular three-stranded β sheet. In addition, we show that a peptide comprising the ET binding motif (EBM) of MLV IN can disrupt the cognate interaction of Brd4 with NSD3, and that substitutions of Brd4 ET residues essential for binding MLV IN also impair interaction of Brd4 with a number of cellular partners involved in transcriptional regulation and chromatin remodeling. This suggests that γ-retroviruses have evolved the EBM to mimic a cognate interaction motif to achieve effective integration in host chromatin. Collectively, our findings identify key structural features of the ET domain of Brd4 that allow for interactions with both cellular and viral proteins

Organic Molecules in Low-Mass Protostellar Hot Cores: Submillimeter Imaging of IRAS 16293-2422

Arcsecond-resolution spectral observations toward the protobinary system IRAS 16293-2422 at 344 and 354 GHz were conducted using the Submillimeter Array. Complex organic molecules such as CH3OH and HCOOCH3 were detected. Together with the rich organic inventory revealed, it clearly indicates the existence of two, rather than one, compact hot molecular cores (smaller than or equal to 400 AU in radius) associated with each of the protobinary components identified by their dust continuum emission in the inner star-forming core.Comment: 11 pages, 3 figures, to be published in ApJ