Nonlinear relaxation time and the detection of weak signals

Laser systems can be used to detect very weak optical signals. The physical mechanism is the dynamical process of the relaxation of a laser from an unstable state to a steady stable state. We present an analysis of this process based on the study of the nonlinear relaxation time. Our analytical results are compared with numerical integration of the stochastic differential equations that model this process.

The problem of physical coordinates in predictive Hamiltonian systems

In the Hamiltonian formulation of predictive relativistic systems, the canonical coordinates cannot be the physical positions. The relation between them is given by the individuality differential equations. However, due to the arbitrariness in the choice of Cauchy data, there is a wide family of solutions for these equations. In general, those solutions do not satisfy the condition of constancy of velocities moduli, and therefore we have to reparametrize the world lines into the proper time. We derive here a condition on the Cauchy data for the individuality equations which ensures the constancy of the velocities moduli and makes the reparametrization unnecessary.

Mean first-passage time of continuous non-Markovian processes driven by colored noise

An equation for mean first-passage times of non-Markovian processes driven by colored noise is derived through an appropriate backward integro-differential equation. The equation is solved in a Bourret-like approximation. In a weak-noise bistable situation, non-Markovian effects are taken into account by an effective diffusion coefficient. In this situation, our results compare satisfactorily with other approaches and experimental data.

Criteria for hitting probabilities with applications to systems of stochastic wave equations

We develop several results on hitting probabilities of random fields which highlight the role of the dimension of the parameter space. This yields upper and lower bounds in terms of Hausdorff measure and Bessel-Riesz capacity, respectively. We apply these results to a system of stochastic wave equations in spatial dimension k >- 1 driven by a d-dimensional spatially homogeneous additive Gaussian noise that is white in time and colored in space.

Approximation and support theorem for a wave equation in two space dimensions

We prove a characterization of the support of the law of the solution for a stochastic wave equation with two-dimensional space variable, driven by a noise white in time and correlated in space. The result is a consequence of an approximation theorem, in the convergence of probability, for equations obtained by smoothing the random noise. For some particular classes of coefficients, approximation in the Lp-norm for p¿1 is also proved.

Local model predictive control experiences with differential driven wheeled mobile robots

This work extends a previously developed research concerning about the use of local model predictive control in differential driven mobile robots. Hence, experimental results are presented as a way to improve the methodology by considering aspects as trajectory accuracy and time performance. In this sense, the cost function and the prediction horizon are important aspects to be considered. The aim of the present work is to test the control method by measuring trajectory tracking accuracy and time performance. Moreover, strategies for the integration with perception system and path planning are briefly introduced. In this sense, monocular image data can be used to plan safety trajectories by using goal attraction potential fields

Fast Approximation of Nonlinearities for improving inversion algorithms of PNL mixtures and Wiener systems

This paper proposes a very fast method for blindly approximating a nonlinear mapping which transforms a sum of random variables. The estimation is surprisingly good even when the basic assumption is not satisfied.We use the method for providing a good initialization for inverting post-nonlinear mixtures and Wiener systems. Experiments show that the algorithm speed is strongly improved and the asymptotic performance is preserved with a very low extra computational cost.

On the approximation of the subgrid scale for systems of equations

Postprint (published version)

Biased diffusion in confined media: Test of the Fick-Jacobs approximation and validity criteria

We study biased, diffusive transport of Brownian particles through narrow, spatially periodic structures in which the motion is constrained in lateral directions. The problem is analyzed under the perspective of the Fick-Jacobs equation, which accounts for the effect of the lateral confinement by introducing an entropic barrier in a one-dimensional diffusion. The validity of this approximation, based on the assumption of an instantaneous equilibration of the particle distribution in the cross section of the structure, is analyzed by comparing the different time scales that characterize the problem. A validity criterion is established in terms of the shape of the structure and of the applied force. It is analytically corroborated and verified by numerical simulations that the critical value of the force up to which this description holds true scales as the square of the periodicity of the structure. The criterion can be visualized by means of a diagram representing the regions where the Fick-Jacobs description becomes inaccurate in terms of the scaled force versus the periodicity of the structure.

Detection of metabolite induction in fungal co-cultures on solid media by high-throughput differential ultra-high pressure liquid chromatography-time-of-flight mass spectrometry fingerprinting.

Access to new biological sources is a key element of natural product research. A particularly large number of biologically active molecules have been found to originate from microorganisms. Very recently, the use of fungal co-culture to activate the silent genes involved in metabolite biosynthesis was found to be a successful method for the induction of new compounds. However, the detection and identification of the induced metabolites in the confrontation zone where fungi interact remain very challenging. To tackle this issue, a high-throughput UHPLC-TOF-MS-based metabolomic approach has been developed for the screening of fungal co-cultures in solid media at the petri dish level. The metabolites that were overexpressed because of fungal interactions were highlighted by comparing the LC-MS data obtained from the co-cultures and their corresponding mono-cultures. This comparison was achieved by subjecting automatically generated peak lists to statistical treatments. This strategy has been applied to more than 600 co-culture experiments that mainly involved fungal strains from the Fusarium genera, although experiments were also completed with a selection of several other filamentous fungi. This strategy was found to provide satisfactory repeatability and was used to detect the biomarkers of fungal induction in a large panel of filamentous fungi. This study demonstrates that co-culture results in consistent induction of potentially new metabolites.

In vivo time-resolved spectroscopy of the human bronchial early cancer autofluorescence.

Time-resolved measurements of tissue autofluorescence (AF) excited at 405 nm were carried out with an optical-fiber-based spectrometer in the bronchi of 11 patients. The objectives consisted of assessing the lifetime as a new tumor/normal (T/N) tissue contrast parameter and trying to explain the origin of the contrasts observed when using AF-based cancer detection imaging systems. No significant change in the AF lifetimes was found. AF bronchoscopy performed in parallel with an imaging device revealed both intensity and spectral contrasts. Our results suggest that the spectral contrast might be due to an enhanced blood concentration just below the epithelial layers of the lesion. The intensity contrast probably results from the thickening of the epithelium in the lesions. The absence of T/N lifetime contrast indicates that the quenching is not at the origin of the fluorescence intensity and spectral contrasts. These lifetimes (6.9 ns, 2.0 ns, and 0.2 ns) were consistent for all the examined sites. The fact that these lifetimes are the same for different emission domains ranging between 430 and 680 nm indicates that there is probably only one dominant fluorophore involved. The measured lifetimes suggest that this fluorophore is elastin.

Estimating parameters for generalized mass action models using constraint propagation.

As modern molecular biology moves towards the analysis of biological systems as opposed to their individual components, the need for appropriate mathematical and computational techniques for understanding the dynamics and structure of such systems is becoming more pressing. For example, the modeling of biochemical systems using ordinary differential equations (ODEs) based on high-throughput, time-dense profiles is becoming more common-place, which is necessitating the development of improved techniques to estimate model parameters from such data. Due to the high dimensionality of this estimation problem, straight-forward optimization strategies rarely produce correct parameter values, and hence current methods tend to utilize genetic/evolutionary algorithms to perform non-linear parameter fitting. Here, we describe a completely deterministic approach, which is based on interval analysis. This allows us to examine entire sets of parameters, and thus to exhaust the global search within a finite number of steps. In particular, we show how our method may be applied to a generic class of ODEs used for modeling biochemical systems called Generalized Mass Action Models (GMAs). In addition, we show that for GMAs our method is amenable to the technique in interval arithmetic called constraint propagation, which allows great improvement of its efficiency. To illustrate the applicability of our method we apply it to some networks of biochemical reactions appearing in the literature, showing in particular that, in addition to estimating system parameters in the absence of noise, our method may also be used to recover the topology of these networks.

A matter of time: delayed mate encounter postpones mating window initiation and reduces the strength of female choosiness

Reproductive success is determined by the presence and timing of encounter of mates. The latter depends on species-specific reproductive characteristics (e.g. initiation/duration of the mating window), season, and reproductive strategies (e.g. intensity of choosiness) that may potentially mitigate constraints imposed by mating windows. Despite their potentially crucial role for fitness and population dynamics, limited evidence exists about mating window initiation, duration and reproductive strategies. Here, we experimentally tested the mechanisms of initiation and the duration of the common lizard's Zootoca vivipara mating window, by manipulating the timing of mate encounter and analyzing its effect on (re-)mating probability. We furthermore tested treatment effects on female reproductive strategies, by measuring female choosiness. The timing of mate encounter and season did not significantly affect mating probability. However, a longer delay until mate encounter reduced female choosiness. Re-mating probability decreased with re-mating delay and was independent of mating delay. This indicates that mating window initiation depends on mate encounter, that its duration is fixed, and that plastic reproductive strategies exist. These findings contrast with previous beliefs and shows that mating windows per se may not necessarily constrain reproductive success, which is congruent with rapid range expansion and absence of positive density-effects on reproductive success (Allee effects). In summary, our results show that predicting the effect of mating windows on reproduction is complex and that experimental evidence is essential for evaluating their effect on reproduction and reproductive strategies, both being important determinants of population dynamics and the colonization of new habitats.

Spatial processing for frequency diversity schemes

A novel technique to obtain optimum blind spatialprocessing for frequency diversity spread spectrum (FDSS) communicationsystems is introduced. The sufficient statistics for alinear combiner, which prove ineffective due to the interferers frequencycharacteristics, are modified to yield improved detectionunder partial jamming in the spectral domain. Robustness to partialtime jamming is achieved by extending the notion of replicasover the frequency axis to a repetition over the time variable. Analysisand simulations are provided, showing the advantages of usingFDSS with spatial diversity to combat the interference when it isconfined to a narrow frequency band or short time interval relativeto the desired signal extent in either domain.