Eliminating fast reactions in stochastic simulations of biochemical networks: a bistable genetic switch

In many stochastic simulations of biochemical reaction networks, it is desirable to "coarse grain" the reaction set, removing fast reactions while retaining the correct system dynamics. Various coarse-graining methods have been proposed, but it remains unclear which methods are reliable and which reactions can safely be eliminated. We address these issues for a model gene regulatory network that is particularly sensitive to dynamical fluctuations: a bistable genetic switch. We remove protein-DNA and/or protein-protein association-dissociation reactions from the reaction set using various coarse-graining strategies. We determine the effects on the steady-state probability distribution function and on the rate of fluctuation-driven switch flipping transitions. We find that protein-protein interactions may be safely eliminated from the reaction set, but protein-DNA interactions may not. We also find that it is important to use the chemical master equation rather than macroscopic rate equations to compute effective propensity functions for the coarse-grained reactions.     

Baouendi–Trèves approximation theorem for CR functions with values in a complex Fréchet space

We study CR functions with values in a complex Fréchet space X. We prove a vector valued analog to a result by Baouendi and Trèves (Ann Math 113:387–421, 1981), i.e. any X-valued CR function of Teodorescu class B ¹ may be locally approximated by X-valued holomorphic functions on ${{\mathbb C}^n}$ . We show that any CR function ${u \in C^\omega (M, X)}$ on a real analytic CR hypersurface ${M \subset {\mathbb {C}}^n}$ admits a unique holomorphic extension ${f \in {\mathcal {O}}(\Omega, X)}$ to some open neighborhood ${\Omega \supset M}$ .     

Strong asymptotic convergence of evolution equations governed by maximal monotone operators with Tikhonov regularization

We consider the Tikhonov-like dynamics where A is a maximal monotone operator on a Hilbert space and the parameter function ε(t) tends to 0 as t→∞ with . When A is the subdifferential of a closed proper convex function f, we establish strong convergence of u(t) towards the least-norm minimizer of f. In the general case we prove strong convergence towards the least-norm point in A⁻¹(0) provided that the function ε(t) has bounded variation, and provide a counterexample when this property fails.     

Micro-analytical and microbiological investigation of selected book papers from the nineteenth century

Books represent a very important part of the cultural heritage, due to their double characteristics: first, as a man-made material and secondly, due to the information they store. The characterization of book paper represents a very important step in developing solutions for better conservation procedures, as well as for fully understanding their provenance. The present paper describes the analytical and microbiological evaluation of a collection of books from the nineteenth century, belonging to the authors’ private collections. The samples consisted of four books printed in Romania and five printed in France. The analytical characterization was performed using optical microscopy, thermal analysis, spectroscopic methods (X-ray fluorescence, X-ray diffraction, inductively coupled plasma atomic emission spectroscopy, Fourier transform infrared spectroscopy), as well as by the evaluation of the degree of polymerization and the color change. The analyses were chosen in order to be either non-destructive or, at least, micro-destructive. The fungal loading determination was performed by plating the samples on the potato dextrose agar and Sabouraud with chloramphenicol agar media, for 28 days, followed by macroscopically and microscopically identification of mold species. The present study offers a complex methodology regarding the use of non- or micro-invasive techniques for evaluating the composition, state of degradation and potential risks related to microorganism colonization of paper artifacts.     

Detonation diffraction through different geometries

We performed the study of the diffraction of a self-sustained detonation from a cylindrical tube (of inner diameter d) through different geometric configurations in order to characterise the transmission processes and to quantify the transmission criteria to the reception chamber. For the diffraction from a tube to the open space the transmission criteria is expressed by d _c  = k _c ·λ (with λ the detonation cell size and k _c depending on the mixture and on the operture configuration, classically 13 for alkane mixtures with oxygen). The studied geometries are: (a) a sharp increase of diameter (D/d > 1) with and without a central obstacle in the diffracting section, (b) a conical divergent with a central obstacle in the diffracting section and (c) an inversed intermediate one end closed tube insuring a double reflection before a final diffraction between the initiator tube and the reception chamber. The results for case A show that the reinitiation process depends on the ratio d/λ. For ratios below k _c the re-ignition takes place at the receptor tube wall and at a fixed distance from the step, i.e. closely after the diffracted shock reflection shows a Mach stem configuration. For ratios below a limit ratio k _lim (which depends on D/d) the re-ignition distance increases with the decrease of d/λ. For both case A and B the introduction of a central obstacle (of blockage ratio BR = 0.5) at the exit of the initiator tube decreases the critical transmission ratio k _c by 50%. The results in configuration C show that the re-ignition process depends both on d/λ and the geometric conditions. Optimal configuration is found that provides the transmission through the two successive reflections (from d = 26 mm to D _ch = 200 mm) at as small d/λ as 2.2 whatever the intermediate diameter D is. This configuration provides a significant improvement in the detonation transmission conditions.

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This paper was based on work that was partly presented at the International Conference on Combustion and Detonation, Zel’dovich Memorial II, Moscow, Russia, 30 August–3 September 2004, and at the 20th International Colloquium on the Dynamics of Explosions and Reactive systems, Montreal, Canada, 31 July–5 August 2005.     

Fluctuation forces in a three-layer medium with rough boundaries. IV. Calculations in the second order of perturbation theory (Casimir range)

The perturbation theory developed in the previous paper of the series is used to calculate the correction to the Casimir force due to the surface roughness.Scientific Council on the Problem Complex Kibernetika, USSR Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 92, No. 1, pp. 113–118, July, 1992.     

A new constraint qualification for the formula of the subdifferential of composed convex functions in infinite dimensional spaces

In this paper we work in separated locally convex spaces where we give equivalent statements for the formulae of the conjugate function of the sum of a convex lower‐semicontinuous function and the precomposition of another convex lower‐semicontinuous function which is also K ‐increasing with a K ‐convex K ‐epi‐closed function, where K is a nonempty closed convex cone. These statements prove to be the weakest constraint qualifications given so far under which the formulae for the subdifferential of the mentioned sum of functions are valid. Then we deliver constraint qualifications inspired from them that guarantee some conjugate duality assertions. Two interesting special cases taken from the literature conclude the paper. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simple models of firms emergence

We present a dynamical model of the emergence of firms as opposed to a flat labour market where entrepreneurs would recruit workers for each business opportunity. The model uses a preferential choice of partners based on previous collaborations experience. A sharp transition in the parameter space separates an ordered regime, where preferential links establish, from a disordered regime corresponding to a fast turnover of employees.