Modelling hematopoiesis mediated by growth factors with applications to periodic hematological diseases

Hematopoiesis is a complex biological process that leads to the production and regulation of blood cells. It is based upon differentiation of stem cells under the action of growth factors. A mathematical approach of this process is proposed to carry out explanation on some blood diseases, characterized by oscillations in circulating blood cells. A system of three differential equations with delay, corresponding to the cell cycle duration, is analyzed. The existence of a Hopf bifurcation for a positive steady-state is obtained through the study of an exponential polynomial characteristic equation with delay-dependent coefficients. Numerical simulations show that long period oscillations can be obtained in this model, corresponding to a destabilization of the feedback regulation between blood cells and growth factors. This stresses the localization of periodic hematological diseases in the feedback loop

Connective stability of discontinuous large scale systems

AbstractThe stability of discontinuous large scale systems under structural perturbations are studied in this paper. It is assumed that the discontinuous equations possess solutions in the sense of Filippov. The results obtained yield sufficient conditions for connective stability. The interconnected systems are treated in terms of their subsystems

THE DEVELOPMENT OF THE WEB BASED CO2SYS PROGRAM

A web-based version of CO2SYS program has been implemented to replace the current DOS based version system. The user does not have to download anything to a local computer, instead they can run the calculations online freely. For this new designed program, all the user inputs and options are displayed in one single window instead of several small black and white DOS screens. All the calculation results are listed in a single page, as well. The user can change any inputs and constants before and after the data calculation, i.e., recalculation. Much more powerful error checking has been built into this web-based system. It also provides useful directions and guidance for the user. The user can get access to the helpful information for each input and constant. Typographical error information, which is listed separately from their individual reference paper, is incorporated with the reference through the hyperlinks. Moreover, this new system presents an attractive and dynamic appearance to users

Some Physiological Effects Of Stress In The American Cockroach Periplaneta Americana (l)

The effects of different forms of stress on the American cockroach, Periplaneta americana (L.) have been systematically examined. This study demonstrated that at least two stress-related events occurred in the haemolymph of the American cockroach. First, the data clearly indicated that a large increase in hypertrehalosemic hormones occurred in the haemolymph of stressed cockroaches. Secondly, proteolytic activity in the haemolymph of stressed cockroaches was greatly increased. The increase of both hypertrehalosemic hormones and proteolytic activity in the haemolymph appeared to be a non-specific response to different forms of stress, including chemical poisoning with lindane, immobilization, forced movement, starvation, and elevated temperatures. The stress-related appearance of proteolytic activity and hypertrehalosemic hormones in the haemolymph could be blocked by neck ligation, suggesting the involvement of an unknown neurohormone or head factor in the release mechanism.;A major portion of this study deals with the isolation and in vitro characterization of the individual proteases present in the haemolymph. Two of these proteases have been purified to apparent homogeneity. The following properties of each of the isolated proteases were examined: (i) native molecular weight; (ii) optimal pH for activity; (iii) sensitivity to proteolytic inhibitors; (iv) cleavage specificity utilizing insulin B chain as substrate; (v) ability to degrade hypertrehalosemic hormones. The conclusion from these studies was that four distinct serine endoproteases appeared in the haemolymph in response to nonlethal forms of stress. These proteases were disappeared from the haemolymph when the stress was removed. One of these proteases was capable of clearing hypertrehalosemic hormones from the haemolymph both in vitro and in vivo. Under stress conditions leading to paralysis and death, two additional proteases, a serine and an aspartic endoprotease, appeared in the haemolymph, most likely of pathological origin.;These studies raise a number of important questions regarding the tissue of origin of the haemolymph proteases, the mechanisms involved in the release and/or activation of the proteases, the physiological role of these proteases, and the mechanisms involved in the clearing of these proteases from the haemolymph. The possible mechanisms involved, and the experimental approaches needed to prove or disprove such mechanisms, are discussed. The possible role of these haemolymph proteases in other stress-related events such as activation of prophenoloxidase, or clearance of FMRFamide-related peptides and proctolin, is discussed

Projectors on the generalized eigenspaces for functional differential equations using integrated semigroups

AbstractThe aim of this article is to derive explicit formulas for the projectors on the generalized eigenspaces associated to some eigenvalues for linear functional differential equations (FDE) by using integrated semigroup theory. The idea is to formulate the FDE as a non-densely defined Cauchy problem and obtain an explicit formula for the integrated solutions of the non-densely defined Cauchy problem, from which we then derive explicit formulas for the projectors on the generalized eigenspaces associated to some eigenvalues. The results are useful in studying bifurcations in some semi-linear problems

Modeling the Geographic Spread of Rabies in China

Abstract In order to investigate how the movement of dogs affects the geographically inter-provincial spread of rabies in Mainland China, we propose a multi-patch model to describe the transmission dynamics of rabies between dogs and humans, in which each province is regarded as a patch. In each patch the submodel consists of susceptible, exposed, infectious, and vaccinated subpopulations of both dogs and humans and describes the spread of rabies among dogs and from infectious dogs to humans. The existence of the disease-free equilibrium is discussed, the basic reproduction number is calculated, and the effect of moving rates of dogs between patches on the basic reproduction number is studied. To investigate the rabies virus clades lineages, the two-patch submodel is used to simulate the human rabies data from Guizhou and Guangxi, Hebei and Fujian, and Sichuan and Shaanxi, respectively. It is found that the basic reproduction number of the two-patch model could be larger than one even if the isolated basic reproduction number of each patch is less than one. This indicates that the immigration of dogs may make the disease endemic even if the disease dies out in each isolated patch when there is no immigration. In order to reduce and prevent geographical spread of rabies in China, our results suggest that the management of dog markets and trades needs to be regulated, and transportation of dogs has to be better monitored and under constant surveillance. Author Summary In 1999, human rabies cases were reported in about 120 counties in Mainland China, mainly in the southern provinces. Now outbreaks of human rabies have been reported in about 1000 counties and the disease has spread geographically from the south to the north. Phylogeographic analyses of rabies virus strains indicate that prevalent strains in northern provinces are indeed related to the remote southern provinces. It is believed that the geographical spread of rabies virus is caused by the transportation of dogs. In this paper, a multi-patch model is proposed to describe the spatial transmission dynamics of rabies in China and to investigate how the immigration of dogs affects the geographical spread of rabies. The expression and sensitivity analysis of the basic reproduction number indicates that the movement of dogs plays an essential role in the spatial transmission dynamics of rabies. Numerical simulations on the effect of the immigration rate in three pairs of provinces, Guizhou and Guangxi, Hebei and Fujian, Sichuan and Shaanxi, are also performed. It is shown that the immigration of dogs is the main factor for the long-distance inter-provincial spread of rabies and it is necessary to manage such inter-provincial transportation of dogs

SciRE-Solver: Efficient Sampling of Diffusion Probabilistic Models by Score-integrand Solver with Recursive Derivative Estimation

Diffusion probabilistic models (DPMs) are a powerful class of generative models known for their ability to generate high-fidelity image samples. A major challenge in the implementation of DPMs is the slow sampling process. In this work, we bring a high-efficiency sampler for DPMs. Specifically, we propose a score-based exact solution paradigm for the diffusion ODEs corresponding to the sampling process of DPMs, which introduces a new perspective on developing numerical algorithms for solving diffusion ODEs. To achieve an efficient sampler, we propose a recursive derivative estimation (RDE) method to reduce the estimation error. With our proposed solution paradigm and RDE method, we propose the score-integrand solver with the convergence order guarantee as efficient solver (SciRE-Solver) for solving diffusion ODEs. The SciRE-Solver attains state-of-the-art (SOTA) sampling performance with a limited number of score function evaluations (NFE) on both discrete-time and continuous-time DPMs in comparison to existing training-free sampling algorithms. Such as, we achieve $3.48$ FID with $12$ NFE and $2.42$ FID with $20$ NFE for continuous-time DPMs on CIFAR10, respectively. Different from other samplers, SciRE-Solver has the promising potential to surpass the FIDs achieved in the original papers of some pre-trained models with a small NFEs. For example, we reach SOTA value of $2.40$ FID with $100$ NFE for continuous-time DPM and of $3.15$ FID with $84$ NFE for discrete-time DPM on CIFAR-10, as well as of $2.17$ ($2.02$) FID with $18$ ($50$) NFE for discrete-time DPM on CelebA 64$\times$64

Stability and Hopf bifurcation in a mathematical model of pluripotent stem cell dynamics

We study a mathematical model describing the dynamics of a pluripotent stem cell population involved in the blood production process in the bone marrow. This model is a differential equation with a time delay. The delay describes the cell cycle duration and is uniformly distributed on an interval. We obtain stability conditions independent of the delay. We also show that the distributed delay can destabilize the entire system. In particularly, it is shown that Hopf bifurcations can occur