Distributed delays stabilize negative feedback loops

Linear scalar differential equations with distributed delays appear in the study of the local stability of nonlinear differential equations with feedback, which are common in biology and physics. Negative feedback loops tend to promote oscillation around steady states, and their stability depends on the particular shape of the delay distribution. Since in applications the mean delay is often the only reliable information available about the distribution, it is desirable to find conditions for stability that are independent from the shape of the distribution. We show here that the linear equation with distributed delays is asymptotically stable if the associated differential equation with a discrete delay of the same mean is asymptotically stable. Therefore, distributed delays stabilize negative feedback loops

Optimal linear stability condition for scalar differential equations with distributed delay

Linear scalar differential equations with distributed delays appear in the study of the local stability of nonlinear differential equations with feedback, which are common in biology and physics. Negative feedback loops tend to promote oscillations around steady states, and their stability depends on the particular shape of the delay distribution. Since in applications the mean delay is often the only reliable information available about the distribution, it is desirable to find conditions for stability that are independent from the shape of the distribution. We show here that for a given mean delay, the linear equation with distributed delay is asymptotically stable if the associated differential equation with a discrete delay is asymptotically stable. We illustrate this criterion on a compartment model of hematopoietic cell dynamics to obtain sufficient conditions for stability

Taking the time

Mot de l’éditeur délégué et directeur général de l'Association québécoise de pédagogie collégialeDisponible en français dans EDUQ.info sous le titre "Prendre le temps

Multi-purpose cowpea inoculation for improved yields in small holder farms in Kenya

Introduction In Kenya, cowpea is the most important pulse crop in the dry lands of Eastern and Coastal regions where it is commonly inter cropped with maize and sorghum. The poor yields obtained in small holder farms in Kenya (150 kg ha-1) can in part be attributed to the use of poor yielding varieties, low soil fertility (mainly N and P deficiency) low presence of effective indigenous rhizobia and high occurrence of highly competitive but inefficient indigenous rhizobia strains. Biological nitrogen fixation (BNF) through exploitation of the rhizobia-legume symbiosis and use of inoculants coupled with soil amendments such as Phosphorus offers in part a means to improve cowpea yield, nutrition and soil fertility

Bounds for self-stabilization in unidirectional networks

A distributed algorithm is self-stabilizing if after faults and attacks hit the system and place it in some arbitrary global state, the systems recovers from this catastrophic situation without external intervention in finite time. Unidirectional networks preclude many common techniques in self-stabilization from being used, such as preserving local predicates. In this paper, we investigate the intrinsic complexity of achieving self-stabilization in unidirectional networks, and focus on the classical vertex coloring problem. When deterministic solutions are considered, we prove a lower bound of $n$ states per process (where $n$ is the network size) and a recovery time of at least $n(n-1)/2$ actions in total. We present a deterministic algorithm with matching upper bounds that performs in arbitrary graphs. When probabilistic solutions are considered, we observe that at least $\Delta + 1$ states per process and a recovery time of $\Omega(n)$ actions in total are required (where $\Delta$ denotes the maximal degree of the underlying simple undirected graph). We present a probabilistically self-stabilizing algorithm that uses $\mathtt{k}$ states per process, where $\mathtt{k}$ is a parameter of the algorithm. When $\mathtt{k}=\Delta+1$, the algorithm recovers in expected $O(\Delta n)$ actions. When $\mathtt{k}$ may grow arbitrarily, the algorithm recovers in expected O(n) actions in total. Thus, our algorithm can be made optimal with respect to space or time complexity

A quantitative estimate of agglutinins in three Shigella flexneri antisera.

Thesis (Ph.D.)--Boston University.The Flexner group of dysentery organisms contains a number of strains classified together because of their close physiological and serological properties. The serological relationships of this group have been determined qualitatively by Boyd and Wheeler. According to these investigators, each Flexner type is distinguished by the presence in the cell of an antigen characteristic of that type. This antigen is called the "type-specific" antigen. Those antigens, possessed in common by several types, which are responsible for the serological cross reactions are designated as "group antigens". The purpose of this investigation was to study quantitatively (using the method of Heidelberger and Kabat to measure agglutinin nitrogen) the serological cross reactions that occur among Shigella flexneri types Ia, Ib and III. In so far as it seemed practical, a quantitative serological analysis was made of types Ia, Ib and III antisera. The type-specific antibody in each serum and the group "6" antibody in types Ib and III antisera was measured. It is this "group 6" factor, possessed in common by both Ib and III cells, which is responsible for the close serological relationship of these two types. [TRUNCATED

Samuel Pennock Bernard to My Dear Fred, 9 June 1873

https://egrove.olemiss.edu/bernard/1056/thumbnail.jp

Receipt, 31 March 1875

https://egrove.olemiss.edu/bernard/1000/thumbnail.jp