Stochastic phenotype transition of a single cell in an intermediate region of gene-state switching

Multiple phenotypic states often arise in a single cell with different gene-expression states that undergo transcription regulation with positive feedback. Recent experiments have shown that at least in E. coli, the gene state switching can be neither extremely slow nor exceedingly rapid as many previous theoretical treatments assumed. Rather it is in the intermediate region which is difficult to handle mathematically.Under this condition, from a full chemical-master-equation description we derive a model in which the protein copy-number, for a given gene state, follow a deterministic mean-field description while the protein synthesis rates fluctuate due to stochastic gene-state switching. The simplified kinetics yields a nonequilibrium landscape function, which, similar to the energy function for equilibrium fluctuation, provides the leading orders of fluctuations around each phenotypic state, as well as the transition rates between the two phenotypic states. This rate formula is analogous to Kramers theory for chemical reactions. The resulting behaviors are significantly different from the two limiting cases studied previously.Comment: 6 pages,4 figure

Numerical inversion of SRNFs for efficient elastic shape analysis of star-shaped objects.

The elastic shape analysis of surfaces has proven useful in several application areas, including medical image analysis, vision, and graphics. This approach is based on defining new mathematical representations of parameterized surfaces, including the square root normal field (SRNF), and then using the L2 norm to compare their shapes. Past work is based on using the pullback of the L2 metric to the space of surfaces, performing statistical analysis under this induced Riemannian metric. However, if one can estimate the inverse of the SRNF mapping, even approximately, a very efficient framework results: the surfaces, represented by their SRNFs, can be efficiently analyzed using standard Euclidean tools, and only the final results need be mapped back to the surface space. Here we describe a procedure for inverting SRNF maps of star-shaped surfaces, a special case for which analytic results can be obtained. We test our method via the classification of 34 cases of ADHD (Attention Deficit Hyperactivity Disorder), plus controls, in the Detroit Fetal Alcohol and Drug Exposure Cohort study. We obtain state-of-the-art results

Multispectral and Hyperspectral Image Fusion by MS/HS Fusion Net

Hyperspectral imaging can help better understand the characteristics of different materials, compared with traditional image systems. However, only high-resolution multispectral (HrMS) and low-resolution hyperspectral (LrHS) images can generally be captured at video rate in practice. In this paper, we propose a model-based deep learning approach for merging an HrMS and LrHS images to generate a high-resolution hyperspectral (HrHS) image. In specific, we construct a novel MS/HS fusion model which takes the observation models of low-resolution images and the low-rankness knowledge along the spectral mode of HrHS image into consideration. Then we design an iterative algorithm to solve the model by exploiting the proximal gradient method. And then, by unfolding the designed algorithm, we construct a deep network, called MS/HS Fusion Net, with learning the proximal operators and model parameters by convolutional neural networks. Experimental results on simulated and real data substantiate the superiority of our method both visually and quantitatively as compared with state-of-the-art methods along this line of research.Comment: 10 pages, 7 figure

Low-mass Active Galactic Nuclei on the Fundamental Plane of Black Hole Activity

It is widely known that in active galactic nuclei (AGNs) and black hole X-ray binaries (BHXBs), there is a tight correlation among their radio luminosity ($L_R$), X-ray luminosity ($L_X$) and BH mass (\mbh), the so-called `fundamental plane' (FP) of BH activity. Yet the supporting data are very limited in the \mbh regime between stellar mass (i.e., BHXBs) and 10$^{6.5}$\,\msun\ (namely, the lower bound of supermassive BHs in common AGNs). In this work, we developed a new method to measure the 1.4 GHz flux directly from the images of the VLA FIRST survey, and apply it to the type-1 low-mass AGNs in the \cite{2012ApJ...755..167D} sample. As a result, we obtained 19 new low-mass AGNs for FP research with both \mbh\ estimates (\mbh \approx 10^{5.5-6.5}\,\msun), reliable X-ray measurements, and (candidate) radio detections, tripling the number of such candidate sources in the literature.Most (if not all) of the low-mass AGNs follow the standard radio/X-ray correlation and the universal FP relation fitted with the combined dataset of BHXBs and supermassive AGNs by \citet{2009ApJ...706..404G}; the consistency in the radio/X-ray correlation slope among those accretion systems supports the picture that the accretion and ejection (jet) processes are quite similar in all accretion systems of different \mbh. In view of the FP relation, we speculate that the radio loudness $\mathcal{R}$ (i.e., the luminosity ratio of the jet to the accretion disk) of AGNs depends not only on Eddington ratio, but probably also on \mbh.Comment: ApJ accepte

Stabilizing Queuing Networks with Model Data-Independent Control

Classical queuing network control strategies typically rely on accurate knowledge of model data, i.e., arrival and service rates. However, such data are not always available and may be time-variant. To address this challenge, we consider a class of model data-independent (MDI) control policies that only rely on traffic state observation and network topology. Specifically, we focus on the MDI control policies that can stabilize multi-class Markovian queuing networks under centralized and decentralized policies. Control actions include routing, sequencing, and holding. By expanding the routes and constructing piecewise-linear test functions, we derive an easy-to-use criterion to check the stability of a multi-class network under a given MDI policy. For stabilizable multi-class networks, we show that a centralized, stabilizing MDI policy exists. For stabilizable single-class networks, we further show that a decentralized, stabilizing MDI policy exists. In addition, for both settings, we construct explicit policies that attain maximal throughput and present numerical examples to illustrate the results.Comment: Accepted by IEEE Transactions on Control of Network System