Stability of cluster solutions in a cooperative consumer chain model

This is the author's accepted manuscript. The final published article is available from the link below. Copyright @ Springer-Verlag Berlin Heidelberg 2012.We study a cooperative consumer chain model which consists of one producer and two consumers. It is an extension of the Schnakenberg model suggested in Gierer and Meinhardt [Kybernetik (Berlin), 12:30-39, 1972] and Schnakenberg (J Theor Biol, 81:389-400, 1979) for which there is only one producer and one consumer. In this consumer chain model there is a middle component which plays a hybrid role: it acts both as consumer and as producer. It is assumed that the producer diffuses much faster than the first consumer and the first consumer much faster than the second consumer. The system also serves as a model for a sequence of irreversible autocatalytic reactions in a container which is in contact with a well-stirred reservoir. In the small diffusion limit we construct cluster solutions in an interval which have the following properties: The spatial profile of the third component is a spike. The profile for the middle component is that of two partial spikes connected by a thin transition layer. The first component in leading order is given by a Green's function. In this profile multiple scales are involved: The spikes for the middle component are on the small scale, the spike for the third on the very small scale, the width of the transition layer for the middle component is between the small and the very small scale. The first component acts on the large scale. To the best of our knowledge, this type of spiky pattern has never before been studied rigorously. It is shown that, if the feedrates are small enough, there exist two such patterns which differ by their amplitudes.We also study the stability properties of these cluster solutions. We use a rigorous analysis to investigate the linearized operator around cluster solutions which is based on nonlocal eigenvalue problems and rigorous asymptotic analysis. The following result is established: If the time-relaxation constants are small enough, one cluster solution is stable and the other one is unstable. The instability arises through large eigenvalues of order O(1). Further, there are small eigenvalues of order o(1) which do not cause any instabilities. Our approach requires some new ideas: (i) The analysis of the large eigenvalues of order O(1) leads to a novel system of nonlocal eigenvalue problems with inhomogeneous Robin boundary conditions whose stability properties have been investigated rigorously. (ii) The analysis of the small eigenvalues of order o(1) needs a careful study of the interaction of two small length scales and is based on a suitable inner/outer expansion with rigorous error analysis. It is found that the order of these small eigenvalues is given by the smallest diffusion constant ε22.RGC of Hong Kon

Existence and Stability of a Spike in the Central Component for a Consumer Chain Model

We study a three-component consumer chain model which is based on Schnakenberg type kinetics. In this model there is one consumer feeding on the producer and a second consumer feeding on the first consumer. This means that the first consumer (central component) plays a hybrid role: it acts both as consumer and producer. The model is an extension of the Schnakenberg model suggested in \cite{gm,schn1} for which there is only one producer and one consumer. It is assumed that both the producer and second consumer diffuse much faster than the central component. We construct single spike solutions on an interval for which the profile of the first consumer is that of a spike. The profiles of the producer and the second consumer only vary on a much larger spatial scale due to faster diffusion of these components. It is shown that there exist two different single spike solutions if the feed rates are small enough: a large-amplitude and a small-amplitude spike. We study the stability properties of these solutions in terms of the system parameters. We use a rigorous analysis for the linearized operator around single spike solutions based on nonlocal eigenvalue problems. The following result is established: If the time-relaxation constants for both producer and second consumer vanish, the large-amplitude spike solution is stable and the small-amplitude spike solution is unstable. We also derive results on the stability of solutions when these two time-relaxation constants are small. We show a new effect: if the time-relaxation constant of the second consumer is very small, the large-amplitude spike solution becomes unstable. To the best of our knowledge this phenomenon has not been observed before for the stability of spike patterns. It seems that this behavior is not possible for two-component reaction-diffusion systems but that at least three components are required. Our main motivation to study this system is mathematical since the novel interaction of a spike in the central component with two other components results in new types of conditions for the existence and stability of a spike. This model is realistic if several assumptions are made: (i) cooperation of consumers is prevalent in the system, (ii) the producer and the second consumer diffuse much faster than the first consumer, and (iii) there is practically an unlimited pool of producer. The first assumption has been proven to be correct in many types of consumer groups or populations, the second assumption occurs if the central component has a much smaller mobility than the other two, the third assumption is realistic if the consumers do not feel the impact of the limited amount of producer due to its large quantity. This chain model plays a role in population biology, where consumer and producer are often called predator and prey. This system can also be used as a model for a sequence of irreversible autocatalytic reactions in a container which is in contact with a well-stirred reservoir

Learning 3D Human Pose from Structure and Motion

3D human pose estimation from a single image is a challenging problem, especially for in-the-wild settings due to the lack of 3D annotated data. We propose two anatomically inspired loss functions and use them with a weakly-supervised learning framework to jointly learn from large-scale in-the-wild 2D and indoor/synthetic 3D data. We also present a simple temporal network that exploits temporal and structural cues present in predicted pose sequences to temporally harmonize the pose estimations. We carefully analyze the proposed contributions through loss surface visualizations and sensitivity analysis to facilitate deeper understanding of their working mechanism. Our complete pipeline improves the state-of-the-art by 11.8% and 12% on Human3.6M and MPI-INF-3DHP, respectively, and runs at 30 FPS on a commodity graphics card.Comment: ECCV 2018. Project page: https://www.cse.iitb.ac.in/~rdabral/3DPose

What do γ\gamma-ray bursts look like?

There have been great and rapid progresses in the field of $\gamma$-ray bursts (denoted as GRBs) since BeppoSAX and other telescopes discovered their afterglows in 1997. Here, we will first give a brief review on the observational facts of GRBs and direct understanding from these facts, which lead to the standard fireball model. The dynamical evolution of the fireball is discussed, especially a generic model is proposed to describe the whole dynamical evolution of GRB remnant from highly radiative to adiabatic, and from ultra-relativistic to non-relativistic phase. Then, Various deviations from the standard model are discussed to give new information about GRBs and their environment. In order to relax the energy crisis, the beaming effects and their possible observational evidences are also discussed in GRB's radiations.Comment: 10 pages, Latex. Invited talk at the Pacific Rim Conference on Stellar Astrophysics, Hong Kong, China, Aug. 199

Experimental Determination of the Key Heat Transfer Mechanisms in Pharmaceutical Freeze Drying

Freeze-drying is often used in manufacture of pharmaceuticals to remove a solvent in such a way that the sensitive molecular structure of the active substance of a drug is least disturbed, and to provide a sterile powder that can be quickly and completely rehydrated. In this work heat transfer rates in a laboratory-scale freeze-dryer have been measured to investigate the contribution of different heat transfer modes. Pure water was partially dried under low-pressure conditions and sublimation rates were determined gravimetrically. The heat transfer rates were observed to be independent of the separation distance between a product vial and a dryer shelf and linearly dependent on the pressure in the free molecular limit. However, under higher pressures the heat transfer rates were independent of pressure and inversely proportional to the separation distance. Previous heat transfer studies in conventional freeze-drying cycles have attributed a dominant portion of the total heat transfer to radiation, the rest to conduction, whereas the convection has been found insignificant. While the measurements revealed the significance of the radiative and gas conduction components, the convective component was found to be comparable to the gas conduction contribution at pressures greater than 100mTorr. The current investigation suggests that the convective component of the heat transfer cannot be ignored at typical laboratory-scale freeze-drying conditions

Impact of Phenanthrene on Organic Acids Secretion and Accumulation by Perennial Ryegrass, Lolium perenne L., Root

A solution culture experiment was performed to investigate the impact of phenanthrene (PHE) on organic acids secretion and accumulation by Lolium perenne L. root. Data showed that, oxalic acid was the dominant composition of organic acids in root and root exudates. In root exudates, increased levels of PHE resulted in higher oxalic acid and its secrete proportion; oxalic acid arranged from 3.00 to 4.72 mg/g FW under spiked PHE treatments, in control, it was 2.33 mg/g FW. In root, oxalic acid rose to 25.61 mg/g FW at 1 mg/L PHE treatment, while the PHE concentration was continuously increasing, organic acids in root decreased

The comparative effectiveness of statin therapy in selected chronic diseases compared with the remaining population

Total cholesterol (TC) concentration is the most commonly used measure of statin efficacy in the UK. This study aimed to evaluate the effectiveness of statins in lowering TC, cardiovascular events (CV) and mortality five common chronic diseases (chronic obstructive pulmonary disease (COPD), osteoarthritis (OA), rheumatoid arthritis (RA), chronic kidney disease (CKD), and diabetes mellitus (DM)) and to compare effectiveness with the rest of the population not recorded as having these diseases

Emerging pharmacotherapy of tinnitus

Tinnitus, the perception of sound in the absence of an auditory stimulus, is perceived by about 1 in 10 adults, and for at least 1 in 100, tinnitus severely affects their quality of life. Because tinnitus is frequently associated with irritability, agitation, stress, insomnia, anxiety and depression, the social and economic burdens of tinnitus can be enormous. No curative treatments are available. However, tinnitus symptoms can be alleviated to some extent. The most widespread management therapies consist of auditory stimulation and cognitive behavioral treatment, aiming at improving habituation and coping strategies. Available clinical trials vary in methodological rigor and have been performed for a considerable number of different drugs. None of the investigated drugs have demonstrated providing replicable long-term reduction of tinnitus impact in the majority of patients in excess of placebo effects. Accordingly, there are no FDA or European Medicines Agency approved drugs for the treatment of tinnitus. However, in spite of the lack of evidence, a large variety of different compounds are prescribed off-label. Therefore, more effective pharmacotherapies for this huge and still growing market are desperately needed and even a drug that produces only a small but significant effect would have an enormous therapeutic impact. This review describes current and emerging pharmacotherapies with current difficulties and limitations. In addition, it provides an estimate of the tinnitus market. Finally, it describes recent advances in the tinnitus field which may help overcome obstacles faced in the pharmacological treatment of tinnitus. These include incomplete knowledge of tinnitus pathophysiology, lack of well-established animal models, heterogeneity of different forms of tinnitus, difficulties in tinnitus assessment and outcome measurement and variability in clinical trial methodology. © 2009 Informa UK Ltd.Fil: Langguth, Berthold. Universitat Regensburg; AlemaniaFil: Salvi, Richard. State University of New York; Estados UnidosFil: Elgoyhen, Ana Belen. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Investigaciones en Ingeniería Genética y Biología Molecular "Dr. Héctor N. Torres"; Argentin