Periodic oscillation in delayed gene networks with SUM regulatory logic and small perturbations

In this paper, we derive new criteria for evaluating the global stability of periodic oscillation in delayed gene networks with SUM regulatory logic and small perturbation, which appear in many biological systems at biomolecular or cellular levels due to the weak coupling and signal diffusion (or transport) process. Our results rely on the Lipschtiz conditions of Hill function, topology of gene networks and delay kernels. In particular, Our method based on the proposed model transforms the original network into matrix analysis problem, thereby not only significantly reducing the computational complexity but also making analysis of periodic oscillation tractable for even large-scale nonlinear networks.     

K-mer natural vector and its application to the phylogenetic analysis of genetic sequences

Based on the well-known k-mer model, we propose a k-mer natural vector model for representing a genetic sequence based on the numbers and distributions of k-mers in the sequence. We show that there exists a one-to-one correspondence between a genetic sequence and its associated k-mer natural vector. The k-mer natural vector method can be easily and quickly used to perform phylogenetic analysis of genetic sequences without requiring evolutionary models or human intervention. Whole or partial genomes can be handled more effective with our proposed method. It is applied to the phylogenetic analysis of genetic sequences, and the obtaining results fully demonstrate that the k-mer natural vector method is a very powerful tool for analysing and annotating genetic sequences and determining evolutionary relationships both in terms of accuracy and efficiency.     

Navigating in the Storm: Using Astrolabe to Adaptively Configure Web Services and Their Clients

The dramatic growth of distributed computing applications is creating both an opportunity and a daunting challenge for users seeking to build applications that will play critical roles in their organization. Here, we discuss the use of a new system, Astrolabe, to automate self-configuration, monitoring, and to control adaptation. Astrolabe operates by creating a virtual system-wide hierarchical database, which evolves as the underlying information changes. Astrolabe is secure, robust under a wide range of failure and attack scenarios, and imposes low loads even under stress. To focus the discussion, we structure it around a hypothetical Web Services scenario. One of the major opportunities created by Astrolabe is to allow Web Services client systems to autonomically adapt when a data center becomes slow or unreachable. The authors were supported by Intel Corporation, DARPA/AFRL grant RADC F30602-99-1-0532, by AFOSR/MURI grant F49620-02-1-0233, Microsoft Research BARC and the Cornell/AFRL Information Assurance Institute.     

Stability in a class of cyclic epidemic models with delay

A detailed analysis of a general class of SIRS epidemic models is given. Sufficient conditions are derived which guarantee the global stability of the endemic equilibrium solution. Further conditions are found which ensure instability for the equilibrium. Finally, the dependence of the stability on the contact number and the ratio of the mean length of infection to the mean removed time is considered.     

A bivariate median test

A bivariate median test is proposed which makes use of the geometric median or mediancentre. Simulations have shown that the resulting test statistic is X²-distributed. The test may be extended to more than two groups, but not to more than two variates.     

Notes on paradigm economy

It is shown that assuming instances of syncretism to be systematic in the unmarked case may significantly reduce the number of possible inflection classes that can be generated on the basis of a given inventory of markers, without recourse to specific constraints like Carstairs’ (Allomorphy in Inflection, Croom Helm 1987) Paradigm Economy Principle or Carstairs-McCarthy’s (Language 70:737–787, 1994) No Blur Principle. If there is always one radically underspecified (i.e., elsewhere) marker per morphological domain, and if there is always one unique marker that is chosen in cases of marker competition, it turns out that there can be at most 2 ⁿ  − 1 inflection classes for n markers, independently of the number of instantiations of the grammatical category that the markers have to distribute over. The argument relies on the notion of marker deactivation combinations.     

Degeneracy: A design principle for achieving robustness and evolvability

Robustness, the insensitivity of some of a biological system's functionalities to a set of distinct conditions, is intimately linked to fitness. Recent studies suggest that it may also play a vital role in enabling the evolution of species. Increasing robustness, so is proposed, can lead to the emergence of evolvability if evolution proceeds over a neutral network that extends far throughout the fitness landscape. Here, we show that the design principles used to achieve robustness dramatically influence whether robustness leads to evolvability. In simulation experiments, we find that purely redundant systems have remarkably low evolvability while degenerate, i.e. partially redundant, systems tend to be orders of magnitude more evolvable. Surprisingly, the magnitude of observed variation in evolvability can neither be explained by differences in the size nor the topology of the neutral networks. This suggests that degeneracy, a ubiquitous characteristic in biological systems, may be an important enabler of natural evolution. More generally, our study provides valuable new clues about the origin of innovations in complex adaptive systems.     

Stability analysis for models of diseases without immunity

Summary A cyclic, constant parameter epidemiological model is described for a closed population divided into susceptible, exposed and infectious classes. Distributed delays are introduced and the model is formulated as two coupled Volterra integral equations. The delays do not change the general nature of thresholds or asymptotic stability; in all cases considered the disease either dies out, or approaches an endemic steady state.This work was partially supported by NIH Grant AI 13233 and NSERC Grant A-4645