Central limit theorems and diffusion approximations for multiscale Markov chain models

Ordinary differential equations obtained as limits of Markov processes appear in many settings. They may arise by scaling large systems, or by averaging rapidly fluctuating systems, or in systems involving multiple time-scales, by a combination of the two. Motivated by models with multiple time-scales arising in systems biology, we present a general approach to proving a central limit theorem capturing the fluctuations of the original model around the deterministic limit. The central limit theorem provides a method for deriving an appropriate diffusion (Langevin) approximation.Comment: Published in at http://dx.doi.org/10.1214/13-AAP934 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Chemical systems with limit cycles

The dynamics of a chemical reaction network (CRN) is often modeled under the assumption of mass action kinetics by a system of ordinary differential equations (ODEs) with polynomial right-hand sides that describe the time evolution of concentrations of chemical species involved. Given an arbitrarily large integer K∈N , we show that there exists a CRN such that its ODE model has at least K stable limit cycles. Such a CRN can be constructed with reactions of at most second-order provided that the number of chemical species grows linearly with K. Bounds on the minimal number of chemical species and the minimal number of chemical reactions are presented for CRNs with K stable limit cycles and at most second order or seventh-order kinetics. We also show that CRNs with only two chemical species can have K stable limit cycles, when the order of chemical reactions grows linearly with K

RECONSTRUCTION OF SOCIAL SCIENCE AND HUMANITIES THROUGH NARRATIVE

Purpose: The purpose of this paper is to present new directions and research strategies through critical analysis of the academic tendencies of existing social science and humanities. The narrative theory of human experience is adopted as a theoretical rationale for critical analysing existing social sciences and humanities. Since the 1970s and 1980s, the academic tendencies of the humanities and social sciences have been transformed into the narrative turn. We focus on the new integrity of humanities and social sciences in light of the narrative theory that approaches the totality of human life. The narrative theory for academic inquiry makes use of the position of Bruner, Polkinghorne, Ricoeur Methodology: We reviewed the literature related to the research topic and took an integrated approach to the philosophical analysis of core claims. Main Findings: As a result, the narrative theory has a characteristic approach to human life and experience as a whole, and it is possible to integrate by narrative ways of knowing. Implications/Applications: Based on this narrative theory, existing humanities and social sciences need to be reconstructed into narrative science. And a narrative method or narrative inquiry is useful as its specific inquiry method. As a narrative science, humanities and social sciences can be implemented by the integration of human experience and narrative epistemology. It has the advantage of integrating the atomized sub-sciences into the narrative of human experience according to this new method. Also, in-depth research on concrete exploration strategies is expected in the future

Flow cytometric fluorescence pulse width analysis of etoposide-induced nuclear enlargement in HCT116 cells

Fluorescence pulse width can provide size information on the fluorescence-emitting particle, such as the nuclei of propidium iodide-stained cells. To analyze nuclear size in the present study, rather than perform the simple doublet discrimination approach usually employed in flow cytometric DNA content analyses, we assessed the pulse width of the propidium iodide fluorescence signal. The anti-cancer drug etoposide is reportedly cytostatic, can induce a strong G2/M arrest, and results in nuclear enlargement. Based on these characteristics, we used etoposide-treated HCT116 cells as our experimental model system. The fluorescence pulse widths (FL2-W) of etoposide-treated (10 μM, 48 h) cells were distributed at higher positions than those of vehicle control, so the peak FL2-W value of etoposide-treated cells appeared at 400 while those of vehicle control cells appeared at 200 and 270. These results were consistent with our microscopic observations. This etoposide-induced increase in FL2-W was more apparent in G2/M phase than other cell cycle phases, suggesting that etoposide-induced nuclear enlargement preferentially occurred in G2/M phase cells rather than in G0/G1 or S phase cells