fragmentation-death models. In particular, we prove that the two **approaches** lead to the same criterion of possible invasion, although the link between the two notions of fitness is far from obvious. This means that one can choose arbitrarily the point of view which is more suited to the particular problem or application under study. For example, the invasion fitness is simpler to characterize in the **deterministic** model, **and** is hence more convenient to study qualitative evolutionary properties of practical biological situations. It is also less costly to compute the **deterministic** invasion fitness using classical numerical approximation methods than to compute the extinction probability using Monte-Carlo or iterative methods (Fritsch et al, 2015a). In addition, the criterion of invasion is more straightforward in the **deterministic** case (sign of the eigenvalue) than in the **stochastic** one (probability of extinction equal to or different from 1). Conversely, for modeling purpose, the **stochastic** model is more convenient in small populations, which is typically the case in invasion problems. The invasion fitness also provides further information on the **stochastic** model, since the extinction probability depends of the initial state of the population.

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Doha Safieddine 1,2 , Amar Kachenoura 1,2 , Laurent Albera 1,2 , Gwénaël Birot 1,2 , Ahmad Karfoul 3 , Anca Pasnicu 4 , Arnaud Biraben 1,2,4 , Fabrice Wendling 1,2 , Lotfi Senhadji 1,2 **and** Isabelle Merlet 1,2*
Abstract
Electroencephalographic (EEG) recordings are often contaminated with muscle artifacts. This disturbing myogenic activity not only strongly affects the visual analysis of EEG, but also most surely impairs the results of EEG signal processing tools such as source localization. This article focuses on the particular context of the contamination epileptic signals (interictal spikes) by muscle artifact, as EEG is a key diagnosis tool for this pathology. In this context, our aim was to compare the ability of two **stochastic** **approaches** of blind source separation, namely independent component analysis (ICA) **and** canonical correlation analysis (CCA), **and** of two **deterministic** **approaches** namely empirical mode decomposition (EMD) **and** wavelet transform (WT) to remove muscle artifacts from EEG signals. To quantitatively compare the performance of these four algorithms, epileptic spike-like EEG signals were simulated from two different source configurations **and** artificially contaminated with different levels of real EEG-recorded myogenic activity. The efficiency of CCA, ICA, EMD, **and** WT to correct the muscular artifact was evaluated both by calculating the normalized mean-squared error between denoised **and** original signals **and** by comparing the results of source localization obtained from artifact-free as well as noisy signals, before **and** after artifact correction. Tests on real data recorded in an epileptic patient are also presented. The results obtained in the context of simulations **and** real data show that EMD outperformed the three other algorithms for the denoising of data highly contaminated by muscular activity. For less noisy data, **and** when spikes arose from a single cortical source, the myogenic artifact was best corrected with CCA **and** ICA. Otherwise when spikes originated from two distinct sources, either EMD or ICA offered the most reliable denoising result for highly noisy data, while WT offered the better denoising result for less noisy data. These results suggest that the performance of muscle artifact correction methods strongly depend on the level of data contamination, **and** of the source configuration underlying EEG signals. Eventually, some insights into the numerical complexity of these four algorithms are given.

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Two uncertain nuclear data from diﬀerent parameters types are always considered uncorrelated, as well as two radioactive decay constants or radioactive decay energies or independent ﬁssi[r]

– is co-consumed by each cell, as shown by Enjalbert et al. [ 5 ]. One goal of this work is to link both **stochastic** **and** **deterministic** **approaches** in order to explain the observations available at different scales, **and** to study the main parameters that control the length of the lag-phase.
The paper is organized as follows. First, the **stochastic** model is presented. Secondly, its behavior for large populations is approximated, allowing us to write a model consisting in a set of **deterministic** differential equations. Then, the model is used to investigate the role of a number of model parameters **and** of initial conditions on the substrate consumption dynamics **and** on the length of the lag-phases. Eventually the main conclusions **and** perspectives are drawn. An appendix provides some additional information on proofs **and** simulations.

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Recent research in the speech community has notably improved the speech synthesis quality by explicitly modelling the de- terministic **and** **stochastic** component of the glottal excitation source [5, 6]. Advanced source-filter decomposition strategies as in [7, 8, 9] address finer details defined by extended voice production models for human speech. These **approaches** ana- lyze an extended voice descriptor set to model their transfor- mation **and** synthesis. The extended voice descriptor set con- sists of: the Vocal Tract Filter (VTF), the glottal pulse positions **and** shapes, **and** energies **and** a random component described by spectral **and** temporal envelopes.

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ABSTRACT: This paper aims at comparing different analysis methods in the design of a roof subjected to buffeting wind forces. The specificity of this study is that aerodynamic pressures acting on the stadium roof are measured in a wind tunnel. Commonly a **deterministic** approach is considered in that context **and** modal superposition is applied. Uncoupled modal equations are solved either in the time domain with a step-by-step method, either in the frequency domain. As an alternative, we seek to apply the concepts of a **stochastic** analysis using the background resonant decomposition. The key idea is to fit a probabilistic model onto the measured data **and** to perform the **stochastic** analysis as a usual buffeting analysis. An important focus is put on the ultimate goal of designing the structure, i.e. of computing extreme values of representative internal forces in the structure. This is performed with dedicated **approaches** for **deterministic** **and** **stochastic** analyses.The **deterministic** approach is able to capture the non Gaussian nature of the loading **and** provides therefore positive **and** negative peak factors. On the contrary, in the **stochastic** approach limited to the second order here (Gaussian context), Rice’s formula provides a unique peak factor **and** therefore advanced techniques need to be applied in order to provide suitable estimations of extreme values. This difficulty to model extreme values is a drawback of the **stochastic** approach that could be solve by reproducing at higher statistical orders the principles of the method presented in this paper. For a number of reasons explained in the paper, the **stochastic** approach performs better than the **deterministic** one.

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The coupling of **deterministic** **and** **stochastic** models is largely used in food process engineering due to the variation of product biological properties **and** uncertain process conditions. This approach is applied, for example, heat treatment of packaged foods (Nicolaï et al. 2000, Baucour et al, 2003), Different methods have been proposed in these studies to quantify the effects of the uncertainty of model parameters on the output of the studied system. In cold chain, product is often exposed to uncertain environment such as temperature **and** duration in refrigerating equipment. Bogataj et al (2005) studied the effect of time-temperature evolution in the cold chain on product deterioration. Dabbene et al (2008a,b) proposed an approach for optimisation of fresh food quality (ripeness, microbial charge, product temperature) **and** logistic cost.

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while maintaining the same confidence in the results can be achieved by employing variance reduction techniques.
In analogue MC simulations, all neutrons are characterised by the same statistical weight. Neutron histories that are unlikely to contribute to the final tally are tracked from origin point until capture or leakage; such an approach is wasteful. Variance reduction techniques act as a filter to distinguish between neutrons contributing to the result **and** those having low or no contribution. Several **approaches** are available including splitting **and** roulette, implicit capture **and** interaction forcing. The splitting roulette approach is widely used in several MC codes. The basic idea is to split particles with expected high contribution to the result into a number of particles with same characteristics of the original particle. The split particles are tracked independently **and** share the same statistical weight. On the other hand, particles with unlikely contribution are subject to a statistical test. A random number is sampled **and** if this number falls below a predetermined threshold, the history is terminated, otherwise, tracking continues **and** the weight of the particle is increased. In the implicit capture method, no absorption reactions are allowed. When an absorption reaction is sampled from the cross section data, the neutron history is not terminated. Instead, the weight of the neutron is reduced by the probability of absorption. This approach is combined with Russian Roulette to terminate the histories of those neutrons whose weights become less than a user defined threshold. The implicit capture approach ensures that particles with low weight will have some contribution to the tallies. Finally, interaction forcing approach is used to ensure regions of high importance but small dimensions in the order of a mean free path are sampled more frequently. Sampling of the next collision site near such regions is modified to force some interactions within the region while adjusting the weight of the history. [23]

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Celine Bonnet 1 , Keltoum Chahour 2 , Fr´ ed´ erique Cl´ ement 3 , Marie Postel 4
**and** Romain Yvinec 5
Abstract. In this study, we describe different modeling **approaches** for ovarian follicle population dynamics, based on either ordinary (ODE), partial (PDE) or **stochastic** (SDE) differential equations, **and** accounting for interactions between follicles. We put a special focus on representing the population- level feedback exerted by growing ovarian follicles onto the activation of quiescent follicles. We take advantage of the timescale difference existing between the growth **and** activation processes to apply model reduction techniques in the framework of singular perturbations. We first study the linear versions of the models to derive theoretical results on the convergence to the limit models. In the nonlinear cases, we provide detailed numerical evidence of convergence to the limit behavior. We reproduce the main semi-quantitative features characterizing the ovarian follicle pool, namely a bimodal distribution of the whole population, **and** a slope break in the decay of the quiescent pool with aging.

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In the literature, numerical schemes for PDMP/PDP have been the subject of different papers. In [7] **and** [8], the authors introduce numerical methods to compute expectations of functionals of a PDMP **and** optimal stopping times. Their **approaches** are based on the quantization of the underlying discrete-time Markov chain. In [71] **and** [2], the authors show that a PDMP with a specific jump distribution can be represented as the solution of a **stochastic** differential equation (SDE) where the noise comes from counting processes. Consequently, they build fixed time step numerical schemes where they simulate the number of jumps within each time step rather than the jump times explicitly. The numerical schemes introduced in [27] **and** [70] explicitly simulate the jump times **and** are both based on the numerical inversion of a survival function. In [27], the authors approximate the log-survival function (i.e the integrated jump rate) of the jump times using a numerical scheme together with a linear interpolation. By doing this, they approximate the distribution of the jump times with a piecewise exponential distribution. In [70], the author reformulates the problem of the inversion of the survival function of each jump time as a hitting time problem for a system of ordinary differential equations (ODE) with random threshold. The system of ODEs is non-linear, includes an equation on the jump rate along the flow of the PDMP **and** is different for each jump time. A numerical scheme which is related to [70] can be found in [77] where the author uses a change of time in the previous system of ODEs in order to obviate the hitting time problem. None of the numerical schemes discussed above uses the thinning **and** none of them produces an exact simulation even if the flow of the PDMP is explicit.

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2.2 Classical formulation of the problem **and** practical analysis
2.2.1 Formulation of the valuation problem
We consider the practical **and** classical point of view of a supplying contract which provide to its holder the right to purchase periodically (usually daily) an amount of gas. It means that the possible exercise times are pre-dened (**and** **deterministic**). These Swing options are dierent **and** might not be confused with multiple exercises American options (in continuous time) as considered for example by Carmona **and** Touzi [27]. In present formulation, we highlight in particular volumetric local **and** global constraints involved in gas supplying contracts: the exibility is not reduced to time decisions, but also has to take into account volumes management. In addition, many other clauses than volume constraints (other constraints, penalties **and** additional rights) might be involved in gas supplying contracts, providing more or less exibility to the contract holder, see Remark 2.2.1. In the following, we restrict ourselves to basic volume constraints but on the other side, emphasize on the structure of the Swing contract strike price. Indeed, this implies a path dependance of cashows which complicates much more the valuation. Indexed strike price of the contract Let us denote by S g = (S g

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{giannitrapani, paoletti, vicino}@dii.unisi.it
Abstract—This paper addresses the energy management of a grid-connected photovoltaic plant coupled with a battery energy storage device, within the capacity firming specifications of the French Energy Regulatory Commission. The paper contributions are positioned in the continuity of the studies adopting **stochastic** models for optimizing the bids of renewable energy sources in a day-ahead market by considering a storage device. The proposed **deterministic** **and** **stochastic** **approaches** are optimization prob- lems formulated as quadratic problems with linear constraints. The case study is a real microgrid with PV production monitored on site. The results demonstrate the validity of the **stochastic** formulation by using an ideal predictor that produces unbiased PV scenarios.

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4. CONCLUSIONS
The vibroacoustic response of the fluid filled cylindrical shell coupled to two ring stiffeners **and** excited by **deterministic** (force/monopole) or **stochastic** (TBL) sources has been predicted using the circumferential admittance **and** spectral **approaches**. The calculation process has been presented considering only the radial coupling between the shell **and** the stiffeners. It can be extended to take into account the coupling in others directions (axial, tangential, rotation). This will be done in the next future, in particular to study the influence on the shell vibration of the twist stiffness of the ring stiffeners. This numerical process can be used to achieve “virtual experiments” in order to study the efficiency of vibratory monitoring techniques for detecting an acoustic source inside the pipe ([14]).

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lem into the iterative resolution of a sequence of subproblems of smaller size. The decomposition by prediction is implemented through a fixed-point algorithm that is first tested on synthetic cases. These synthetic cases have been designed so as to have a similar structure as the industrial problem **and** so that the application of the fixed-point algorithm is straightforward. The numerical experiments show that the decomposition by prediction is very efficient on the synthetic cases. The APP cannot be applied directly for the industrial problem because some integer variables are present in the model. Therefore, we design a relaxation of the sys- tem. After a careful tuning of the algorithm, the decomposition methodology is applied on a large-scale maintenance optimization problem with 80 components. The decomposition leads to a gain of 11% over the current reference algorithm, which represents more than 1, 4Me. The decomposition manages to design an efficient maintenance strategy by exploiting the fact that the components are new at the beginning of the time horizon **and** that the discount rate makes failures not too penalizing at the end of the horizon.

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1.3 Application to some neuron models with numerical re-
sults
In this section, we apply the reduction results of Section 1.2.2 to some widely used models **and** support our theoretical results with numerical results. These theoretical results regard the ChR2-3-states model **and** we also investigate numerically the associated ChR2- 4-states models. The numerical results are obtained by direct methods based on the ipopt routine [WB06] to solve nonlinear optimization problems, **and** implemented with the ampl language [FGK02]. For a survey on numerical methods in optimal control, see [Tré12]. The numerical values used for the ChR2-3-states **and** 4-states models are those of Appendices 1.C.1 **and** 1.C.2. For each neuron model that we study, namely the FitzHugh-Nagumo model, the Morris-Lecar model **and** the reduced **and** complete Hodgkin-Huxley models, we implement the direct method for the ChR2-3-states **and** 4-states models **and** compare them. We repeat the computation for several values of the the maximum control value in order to try **and** detect possible singular optimal controls. Indeed, it would be possible that a singular optimal control only appears above some threshold of the maximal control value. Nevertheless, no model numerically displays such controls. We then compare the neuron models between them in terms of their behavior with respect to optogenetic control. Physiologically, Channelrhdopsin has a depolarizing effect on a neuron membrane so that it is physiologically intuitive to expect that we need to switch on the light to obtain a spike, **and** the more light we put in the system, the faster the spike will occur. We propose to distinguish between two classes of models. The first class comprises neuron models that display the intuitive physiological response to optogenetic stimulation **and** the second class comprises neuron models that display an unexpected response.

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PERES (LGP Tarbes) et H´el`ene ROUX (IMFT) pour m’avoir accueilli au sein du groupe Syst`emes D´ecisionnels et Cognitifs (SDC) de LGP Tarbes et au sein du.. groupe Hydrologie, ´ecoHydrau[r]

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A whole 2D core calculation is undertaken, with a refined pin description **and** a flux calculation scheme in two steps. First, each individual assembly geometry in an infinite lattice is described. After that, self-shielded 281 SHEM [ 15 ] energy groups cross sections are produced. Then, the neutron flux is calculated thanks to the method of characteristics onto the whole geometry. Even though the computational power has been steadily growing with time, yet the CPU time needed in order to have flux convergence is still too high. That is why several assumptions are made in order to reduce CPU time cost. Given that the steady state Boltzmann equation is discretized in space **and** energy, we decided to vary the calculation parameters from APOLLO2.8 reference calcu- lation scheme used at CEA [ 16 ]:

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Figure 7 shows the real **and** imaginary parts of the coherence functions pairing sensor 1 to sen- sors 2, **and** 3, located in the alongwind direction. Although standards usually neglect the imagi- nary part of the coherence **and** model the real part as a decreasing exponential (at least concern- ing the wind velocity) (Dyrbye **and** Hansen, 1997), we may observe that this model (adopted from free field turbulence) is far from reality. The global decrease of the real part rather indicates first a short plateau, then a rapid decrease, followed by a somewhat significant noise. The imagi- nary part is of the same order of magnitude as the real part. Notice Figure 7 indicates, for both the real **and** imaginary parts, more coherence between sensors 1 **and** 2, than 1 **and** 3 which is of course expected because of proximity.

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Besides the initial account value has been set to 1 000 000$, which is very low as compared to usual equity capitals of insurance companies. Guess what would be the actual loss of the insurer in such a casual situation...
The size of the company is also a key-factor: let us extract the part of Ta- ble 2 concerning the “soft” context **and** study the impact of the number of policyholders in the portfolio. Initially, there were 17657 policyholders. Some huge insurance companies may think that their size prevents them from ex- perimenting such scenario because of mutualization. The analysis of Table 3 demonstrates that the number of policyholders does not have a strong in- fluence on the computation of the risk margin. To reserve enough money to cover the correlation risk of surrender behaviors is very important in predicting capital needs: underestimating this risk could make shareholders dissatisfied because of unexpected important margin calls. Because undiversifiable risks are present, increasing the size of the portfolio would not reduce the impact of a correlation crisis on the considered quantities.

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