Robust Moment Closure Method for the Chemical Master Equation

The Chemical Master Equation (CME) is used to stochastically model biochemical reaction networks, under the Markovian assumption. The low-order statistical moments induced by the CME are often the key quantities that one is interested in. However, in most cases, the moments equation is not closed; in the sense that the first $n$ moments depend on the higher order moments, for any positive integer $n$. In this paper, we develop a moment closure technique in which the higher order moments are approximated by an affine function of the lower order moments. We refer to such functions as the affine Moment Closure Functions (MCF) and prove that they are optimal in the worst-case context, in which no a priori information on the probability distribution is available. Furthermore, we cast the problem of finding the optimal affine MCF as a linear program, which is tractable. We utilize the affine MCFs to derive a finite dimensional linear system that approximates the low-order moments. We quantify the approximation error in terms of the $$ induced norm of some linear system. Our results can be effectively used to approximate the low-order moments and characterize the noise properties of the biochemical network under study

Boolean versus continuous dynamics on simple two-gene modules

We investigate the dynamical behavior of simple modules composed of two genes with two or three regulating connections. Continuous dynamics for mRNA and protein concentrations is compared to a Boolean model for gene activity. Using a generalized method, we study within a single framework different continuous models and different types of regulatory functions, and establish conditions under which the system can display stable oscillations. These conditions concern the time scales, the degree of cooperativity of the regulating interactions, and the signs of the interactions. Not all models that show oscillations under Boolean dynamics can have oscillations under continuous dynamics, and vice versa.Comment: 8 pages, 10 figure

Solitons and nonsmooth diffeomorphisms in conformal nets

We show that any solitonic representation of a conformal (diffeomorphism covariant) net on S^1 has positive energy and construct an uncountable family of mutually inequivalent solitonic representations of any conformal net, using nonsmooth diffeomorphisms. On the loop group nets, we show that these representations induce representations of the subgroup of loops compactly supported in S^1 \ {-1} which do not extend to the whole loop group. In the case of the U(1)-current net, we extend the diffeomorphism covariance to the Sobolev diffeomorphisms D^s(S^1), s > 2, and show that the positive-energy vacuum representations of Diff_+(S^1) with integer central charges extend to D^s(S^1). The solitonic representations constructed above for the U(1)-current net and for Virasoro nets with integral central charge are continuously covariant with respect to the stabilizer subgroup of Diff_+(S^1) of -1 of the circle.Comment: 33 pages, 3 TikZ figure

On tests of general relativity with binary radio pulsars

The timing of radio pulsars in binary systems provides a superb testing ground of general relativity. Here we propose a Bayesian approach to carry out these tests, and a relevant efficient numerical implementation, that has several conceptual and practical advantages with respect to traditional methods based on least-square-fits that have been used so far: (i) it accounts for the actual structure of the likelihood function - and it is not predicated on the Laplace approximation which is implicitly built in least-square fits that can potentially bias the inference - (ii) it provides the ratio of the evidences of any two models under consideration as the statistical quantity to compare different theories, and (iii) it allows us to put joint constraints from the monitoring of multiple systems, that can be expressed in terms of ratio of evidences or probability intervals of global (thus not system-dependent) parameters of the theory, if any exists. Our proposed approach optimally exploits the progress in timing of radio pulsars and the increase in the number of observed systems. We demonstrate the power of this framework using simulated data sets that are representative of current observations.Comment: Accepted for publication on MNRAS Letter

Testing general relativity with compact coalescing binaries: comparing exact and predictive methods to compute the Bayes factor

The second generation of gravitational-wave detectors is scheduled to start operations in 2015. Gravitational-wave signatures of compact binary coalescences could be used to accurately test the strong-field dynamical predictions of general relativity. Computationally expensive data analysis pipelines, including TIGER, have been developed to carry out such tests. As a means to cheaply assess whether a particular deviation from general relativity can be detected, Cornish et al. and Vallisneri recently proposed an approximate scheme to compute the Bayes factor between a general-relativity gravitational-wave model and a model representing a class of alternative theories of gravity parametrised by one additional parameter. This approximate scheme is based on only two easy-to-compute quantities: the signal-to-noise ratio of the signal and the fitting factor between the signal and the manifold of possible waveforms within general relativity. In this work, we compare the prediction from the approximate formula against an exact numerical calculation of the Bayes factor using the lalinference library. We find that, using frequency-domain waveforms, the approximate scheme predicts exact results with good accuracy, providing the correct scaling with the signal-to-noise ratio at a fitting factor value of 0.992 and the correct scaling with the fitting factor at a signal-to-noise ratio of 20, down to a fitting factor of $\sim$ 0.9. We extend the framework for the approximate calculation of the Bayes factor which significantly increases its range of validity, at least to fitting factors of $\sim$ 0.7 or higher.Comment: 13 pages, 4 figures, accepted for publication in Classical and Quantum Gravit

El derecho natural como fundamento de la sociedad ( Il diritto naturale como fundamento della societá)

Fil: Ubertone, Fermín Pedro. Universidad de Buenos Aires. Facultad de Derecho. Buenos Aires, ArgentinaLa. versión original en italiano de este articulo apareció en "Dinámica Social", N° 141 ps. 25 y 26 (Centro de Estudios Económico-Sociales, Buenos Aires, 1963

Principi di funzionamento dei sistemi di pianificazione e controllo per il settore della moda

Gestione Erp all'interno di una azienda del settore mod