Piecewise smooth systems near a co-dimension 2 discontinuity manifold: can one say what should happen?

We consider a piecewise smooth system in the neighborhood of a co-dimension 2 discontinuity manifold $\Sigma$. Within the class of Filippov solutions, if $\Sigma$ is attractive, one should expect solution trajectories to slide on $\Sigma$. It is well known, however, that the classical Filippov convexification methodology is ambiguous on $\Sigma$. The situation is further complicated by the possibility that, regardless of how sliding on $\Sigma$ is taking place, during sliding motion a trajectory encounters so-called generic first order exit points, where $\Sigma$ ceases to be attractive. In this work, we attempt to understand what behavior one should expect of a solution trajectory near $\Sigma$ when $\Sigma$ is attractive, what to expect when $\Sigma$ ceases to be attractive (at least, at generic exit points), and finally we also contrast and compare the behavior of some regularizations proposed in the literature. Through analysis and experiments we will confirm some known facts, and provide some important insight: (i) when $\Sigma$ is attractive, a solution trajectory indeed does remain near $\Sigma$, viz. sliding on $\Sigma$ is an appropriate idealization (of course, in general, one cannot predict which sliding vector field should be selected); (ii) when $\Sigma$ loses attractivity (at first order exit conditions), a typical solution trajectory leaves a neighborhood of $\Sigma$; (iii) there is no obvious way to regularize the system so that the regularized trajectory will remain near $\Sigma$ as long as $\Sigma$ is attractive, and so that it will be leaving (a neighborhood of) $\Sigma$ when $\Sigma$ looses attractivity. We reach the above conclusions by considering exclusively the given piecewise smooth system, without superimposing any assumption on what kind of dynamics near $\Sigma$ (or sliding motion on $\Sigma$) should have been taking place.Comment: 19 figure

Efficient parameter search for qualitative models of regulatory networks using symbolic model checking

Investigating the relation between the structure and behavior of complex biological networks often involves posing the following two questions: Is a hypothesized structure of a regulatory network consistent with the observed behavior? And can a proposed structure generate a desired behavior? Answering these questions presupposes that we are able to test the compatibility of network structure and behavior. We cast these questions into a parameter search problem for qualitative models of regulatory networks, in particular piecewise-affine differential equation models. We develop a method based on symbolic model checking that avoids enumerating all possible parametrizations, and show that this method performs well on real biological problems, using the IRMA synthetic network and benchmark experimental data sets. We test the consistency between the IRMA network structure and the time-series data, and search for parameter modifications that would improve the robustness of the external control of the system behavior

Molecular Distributions in Gene Regulatory Dynamics

We show how one may analytically compute the stationary density of the distribution of molecular constituents in populations of cells in the presence of noise arising from either bursting transcription or translation, or noise in degradation rates arising from low numbers of molecules. We have compared our results with an analysis of the same model systems (either inducible or repressible operons) in the absence of any stochastic effects, and shown the correspondence between behaviour in the deterministic system and the stochastic analogs. We have identified key dimensionless parameters that control the appearance of one or two steady states in the deterministic case, or unimodal and bimodal densities in the stochastic systems, and detailed the analytic requirements for the occurrence of different behaviours. This approach provides, in some situations, an alternative to computationally intensive stochastic simulations. Our results indicate that, within the context of the simple models we have examined, bursting and degradation noise cannot be distinguished analytically when present alone.Comment: 14 pages, 12 figures. Conferences: "2010 Annual Meeting of The Society of Mathematical Biology", Rio de Janeiro (Brazil), 24-29/07/2010. "First International workshop on Differential and Integral Equations with Applications in Biology and Medicine", Aegean University, Karlovassi, Samos island (Greece), 6-10/09/201

Gata2 in Embryonic Hematopoiesis

Hematopoiesis is a word originating from the two greek words αἷμα (haima) which means blood and the verb ποιεῖν (poien) which means to make/create. Hematopoiesis describes the process by which the organism creates and replenishes all the blood cell types that are required for the physiologic functions of the organism. The importance of the blood tissue can be highlighted by the many and discrete functions that it performs. These are accomplished through several different cell types forming the blood tissue (erythrocytes, platelets, macrophages, neutrophils, eosinophils, basophils, B-cells, T-cells, NK-cells). For example, the red blood cells or erythrocytes found in the circulating blood are mainly involved in the transport of O2 and CO2. Lymphocytes which are white blood cells are part of the immune system and actively participate in the defense of the organism against pathogens. In the adult organism hematopoietic cells are found not only in the blood but also in hematopoietic tissues such as the bone marrow, spleen, lymph nodes and thymus. Importantly, all mature hematopoietic cell types found in the blood tissues originate from rare hematopoietic stem cells (HSCs). These founder cells are quiescent, long-lived and are at the base of a well-studied cell differentiation hierarchy. HSCs robustly produce all the billions of mature blood cells that are required daily and throughout the entire life of the organism. HSCs are clinically relevant cells that have been used for over 50 years in transplantation and cell replacement therapies for leukemia and monogenic blood-related diseases

Global initiatives for improving quality healthcare by the Thalassaemia International Federation

In today’s health care arena, a number of issues are being raised that have received more attention either from the health care consumers or the media. The 1990s can easily be dubbed the period of “performance measurement”. Whether as a provider, a consumer or a purchaser, each was looking for ways to satisfy the other through measuring and reporting on care outcomes. Accountability was at stake in that period. Several third-party organizations attempted to produce certain measure to report on these care outcomes. A number of “indicators” were developed and measured and “report cards” were assembled. All of these activities were done in the effort to measure performance. WHO organized and facilitated a number of activities related to quality assessment, performance improvement and outcome measurement. A large number of countries and institutions participated in these activities and initiatives. And at the end, all agreed there had to be an organized mechanism to account for quality, continuous measurement and improved performance in health care organizations. In order to do this, a mechanism for certification, licensure or accreditation should be put in place. This trend continued in the 2000’s and until now where performance measurements and improvement as on the top of the agenda of any healthcare organization and country healthcare system. Related to performance is accountability. In particular professional accountability both at the individual and the institutional levels became extremely important when dealing with issues related to performance

Business model analysis of low-cost carriers on the exaple of Ryanair

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