Computational inference in systems biology

Parameter inference in mathematical models of biological pathways, expressed as coupled ordinary differential equations (ODEs), is a challenging problem. The computational costs associated with repeatedly solving the ODEs are often high. Aimed at reducing this cost, new concepts using gradient matching have been proposed. This paper combines current adaptive gradient matching approaches, using Gaussian processes, with a parallel tempering scheme, and conducts a comparative evaluation with current methods used for parameter inference in ODEs

Triggering synchronized oscillations through arbitrarily weak diversity in close-to-threshold excitable media

It is shown that arbitrarily weak (frozen) heterogeneity can induce global synchronized oscillations in excitable media close to threshold. The work is carried out on networks of coupled van der Pol-FitzHugh-Nagumo oscillators. The result is shown to be robust against the presence of internal dynamical noise.Comment: 4 pages (RevTeX 3 style), 5 EPS figures, submitted to Phys. Rev. E (16 aug 2001

Limits and dynamics of stochastic neuronal networks with random heterogeneous delays

Realistic networks display heterogeneous transmission delays. We analyze here the limits of large stochastic multi-populations networks with stochastic coupling and random interconnection delays. We show that depending on the nature of the delays distributions, a quenched or averaged propagation of chaos takes place in these networks, and that the network equations converge towards a delayed McKean-Vlasov equation with distributed delays. Our approach is mostly fitted to neuroscience applications. We instantiate in particular a classical neuronal model, the Wilson and Cowan system, and show that the obtained limit equations have Gaussian solutions whose mean and standard deviation satisfy a closed set of coupled delay differential equations in which the distribution of delays and the noise levels appear as parameters. This allows to uncover precisely the effects of noise, delays and coupling on the dynamics of such heterogeneous networks, in particular their role in the emergence of synchronized oscillations. We show in several examples that not only the averaged delay, but also the dispersion, govern the dynamics of such networks.Comment: Corrected misprint (useless stopping time) in proof of Lemma 1 and clarified a regularity hypothesis (remark 1

Steady and Stable: Numerical Investigations of Nonlinear Partial Differential Equations

Excerpt: Mathematics is a language which can describe patterns in everyday life as well as abstract concepts existing only in our minds. Patterns exist in data, functions, and sets constructed around a common theme, but the most tangible patterns are visual. Visual demonstrations can help undergraduate students connect to abstract concepts in advanced mathematical courses. The study of partial differential equations, in particular, benefits from numerical analysis and simulation

Classification of occupational activity categories using accelerometry: NHANES 2003–2004

Background An individual’s occupational activity (OA) may contribute significantly to daily physical activity (PA) and sedentary behavior (SB). However, there is little consensus about which occupational categories involve high OA or low OA, and the majority of categories are unclassifiable with current methods. The purpose of this study was to present population estimates of accelerometer-derived PA and SB variables for adults (n = 1112, 20–60 years) working the 40 occupational categories collected during the 2003–2004 National Health and Nutrition Examination Survey (NHANES). Methods ActiGraph accelerometer-derived total activity counts/day (TAC), activity counts/minute, and proportion of wear time spent in moderate-to-vigorous PA [MVPA], lifestyle, and light PA organized by occupational category were ranked in ascending order and SB was ranked in descending order. Summing the ranks of the six accelerometer-derived variables generated a summary score for each occupational category, which was re-ranked in ascending order. Higher rankings indicated higher levels of OA, lower rankings indicated lower levels of OA. Tertiles of the summary score were used to establish three mutually exclusive accelerometer-determined OA groupings: high OA, intermediate OA, and low OA. Results According to their summary score, ‘farm and nursery workers’ were classified as high OA and ‘secretaries, stenographers, and typists’ were classified as low OA. Consistent with previous research, some low OA occupational categories (e.g., ‘engineers, architects, and scientists’, ‘technicians and related support occupations’, ‘management related occupations’, ‘executives, administrators, and managers’, ‘protective services’, and ‘writers, artists, entertainers, and athletes’) associated with higher education and income had relatively greater amounts of MVPA compared to other low OA occupational categories, likely due to the greater percentage of men in those occupations and/or the influence of higher levels of leisure time PA. Men had more TAC, activity counts/minute and time in MVPA, but similar proportions of SB compared to women in all three OA groupings. Conclusions Objectively measured PA allowed for a more precise estimate of the amount of PA and SB associated with different occupations and facilitated systematic classification of the 40 different occupational categories into three distinct OA groupings. This information provides new opportunities to explore the relationship between OA and health outcomes

General theory of instabilities for patterns with sharp interfaces in reaction-diffusion systems

An asymptotic method for finding instabilities of arbitrary $d$-dimensional large-amplitude patterns in a wide class of reaction-diffusion systems is presented. The complete stability analysis of 2- and 3-dimensional localized patterns is carried out. It is shown that in the considered class of systems the criteria for different types of instabilities are universal. The specific nonlinearities enter the criteria only via three numerical constants of order one. The performed analysis explains the self-organization scenarios observed in the recent experiments and numerical simulations of some concrete reaction-diffusion systems.Comment: 21 pages (RevTeX), 8 figures (Postscript). To appear in Phys. Rev. E (April 1st, 1996

Dynamics of lattice spins as a model of arrhythmia

We consider evolution of initial disturbances in spatially extended systems with autonomous rhythmic activity, such as the heart. We consider the case when the activity is stable with respect to very smooth (changing little across the medium) disturbances and construct lattice models for description of not-so-smooth disturbances, in particular, topological defects; these models are modifications of the diffusive XY model. We find that when the activity on each lattice site is very rigid in maintaining its form, the topological defects - vortices or spirals - nucleate a transition to a disordered, turbulent state.Comment: 17 pages, revtex, 3 figure

Emergent global oscillations in heterogeneous excitable media: The example of pancreatic beta cells

Using the standard van der Pol-FitzHugh-Nagumo excitable medium model I demonstrate a novel generic mechanism, diversity, that provokes the emergence of global oscillations from individually quiescent elements in heterogeneous excitable media. This mechanism may be operating in the mammalian pancreas, where excitable beta cells, quiescent when isolated, are found to oscillate when coupled despite the absence of a pacemaker region.Comment: See home page http://lec.ugr.es/~julya