Abstract
In this paper we present a methodology to characterize elastic-plastic constitutive law of metallic materials using spherical indentation tests and **parametric** **identification** coupled with finite elements model (FEM) simulation. This procedure was applied to identify mechanical properties of aluminium, copper and titanium and the identified models show differences with experimental uniaxial tensile tests results that do not exceed 10%. A sensitivity study according to a 2 Design of Experience (DoE) was achieved to determine which data that can be extracted from pile-up is the most relevant to use in order to enhance the **identification** procedure. It appears that the maximum pile-up height seems to be the best suited for this purpose.

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Derived from the powerful plant architecture model AMAP, GreenLab is a generic plant growth model that integrates various morphological features with biomass production and allocation at organ scale [18], called GL1. The plant architecture is built based on an automaton which is analogous to writing L- system rules, and the biomass acquisition and allocation are based on source-sink relationship. GreenLab model is able to simulate plant's phenotypic plasticity that results from feedbacks among growth (biomass acquisition), differentiation (phenology, morphogenesis) and the physiological condition of the organism (e.g. stresses) [19]. At present, GreenLab has been applied to crops, e.g., cotton [20], maize [21], wheat [22], tomato [23], and trees, e.g., Chinese pine saplings [24] and beech trees [25]. However, these calibration processes were performed with deterministic architecture that represents an average topological structure from several samples. No appropriate method was developed to include topological information in the set of target data used for the procedure of **parametric** **identification**. Moreover a deterministic topological development is not realistic with regards to the high variability of branching patterns observed in tree stands. To get realistic simulations of tree growth, it is important to consider the randomness of topological development. This motivated the development of a stochastic version of GreenLab, called GL2 [26]. Beside simulation of stochastic plant sample, the theoretical mean and variance of numbers of organs at any growth stage can be calculated.

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L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignemen[r]

Digital Speckle Photography
Stress and strain homogeneity, in tested samples, is a crucial assumption during a dynamic test. Whenever this assumption is true, the conventional recovery of the mean strain and stress is valid. However, when the stress and strain ﬁelds in the sample are not homoge- neous, more sophisticated treatment must be considered. Inverse problem techniques are then proposed. Nevertheless, they may yield a non-physical result. In this paper, a non-**parametric** solution to the problem of non-homogeneity in dynamic tests is presented. The stress ﬁeld is deduced from the displacement ﬁeld measured via a Digital Speckle Pho- tography (DSP) technique and a force boundary condition.

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II. I DENTIFICATION O F T HE I NSULATION S YSTEM F ROM
E XPERIMENTAL D ATA
A. In Situ **Identification** of High Frequency Model Structures
Fig. 2 shows the technical solution carried out for the in-situ excitation of the insulation system. A pulse generator applies a high frequency and high voltage excitation to the insulation system, between phases and ground wall. The capacitive coupling box contains adaptation and measurement resistances, and the impedance of the coupling capacitances can be neglected in the high frequency range of the input/output signals used for the insulation system **identification**.

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According to the Dieudonne water retention model, the micro void ratio (e m , initial value = 0.30) increases with increase in water content or decrease in soil total suction during the [r]

This method is applied to the Orthoglide for a **parametric** stiffness analysis. The stiffness matrix elements are symbolically computed. This allows an easy analysis of the influence of the Orthoglide critical design parameters. No numerical computations are conducted until graphical results are generated. First we present the Orthoglide, then the compliant model. The results showing the influence of the parameters are presented next.

Key words: **Parametric** analysis; Stiffness; PKM design; Orhtoglide.
1 Introduction
Usually, parallel manipulators are claimed to offer good stiffness and accuracy prop- erties, as well as good dynamic performances. This makes them attractive for in- novative machine-tool structures for high speed machining [1,2,3]. When a parallel manipulator is intended to become a Parallel Kinematic Machine (PKM), stiffness becomes a very important issue in its design [4,5,6]. This paper presents a **parametric** stiffness analysis of the Orthoglide, a 3-axis translational PKM prototype developed at IRCCyN [7].

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In the latter case, since there is an infinite number of valuations and a finite number of **parametric** transitions, using the pigeonhole principle, there is at least one such transition that must be used as the first **parametric** transition in the run for an infinite number of valuations. The input places of its **parametric** arcs are therefore not bounded. Thus, the valuation of the input **parametric** arcs of this transition is not limiting anymore since we can generate an arbitrary large amount of tokens in the corresponding places. Therefore, we will later evaluate 2 those parameters to 0 in order to perform the verification on a classic Petri net.

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Remark 1. In this paper, we allow guards and invariants of the form x ./ P
1≤j≤M β j p j + d , which is more restrictive
than [ BL09 ] (that allows **parametric** coefficients different from 0 and 1, as well as diagonal constraints), but more permissive than [ AHV93 ], that only allows a syntax x ./ p . In fact, most papers in the literature define their own syntax (see [ And15 ] for a survey). We can adapt our proof to fit in the most restrictive syntax ( x ./ p ) as follows: transitions with y = a + 1 guards and y := 0 reset can be equivalently replaced by one transition with a “ y = 1 ” guard and a reset of some additional clock w , followed by a transition with a w = a guard and the y := 0 reset (and similarly for x and z is the decrement gadget). This also allows the proof to work without complex **parametric** expressions in guards, using three additional clocks (we conjecture that a smarter encoding can be exhibited to factor these additional clocks, so as to use a single additional clock). A similar modification can be applied to all subsequent undecidability proofs.

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still su fficient to turn a subcritical system into a dynamo with exponentially growing magnetic field even when the perturbation
amplitude remains small. This nonresonant **parametric** amplification can also be of importance for long-term variations of magnetic activity as, for example, found in the solar dynamo models of Ref. [40].
We have restricted our interest to linear models with a prescribed flow. However, it has been found that nonaxisymmetric perturbations also impact the nonlinear state of a dynamo [41] and may even change the fundamental character of the dynamo by triggering hemispheric asymmetries or cyclic changes of the large-scale magnetic field orientation known as flip-flop phe- nomenon or active longitudes [42]. We further restricted our examinations to a perturbation pattern with azimuthal wave number e

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Remark 1. We use guards with constraints y = a + 1 while our definition of PTAs, following [ AHV93 ], only allows comparisons of a clock with a single pa- rameter. Note however, and that will be true for all subsequent constructions, that transitions with y = a + 1 guards and y := 0 reset can be equivalently replaced by one transition with an y = 1 guard and a reset of some additional clock w, followed by a transition with a w = a guard and the y := 0 reset (and similarly for x and z is the decrement gadget). This allows the proof to work without complex **parametric** expressions in guards and uses only one **parametric** clock and three normal clocks, with one parameter, matching the best known results with that respect [ Mil00 ].

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Unité de recherche INRIA Rocquencourt Domaine de Voluceau - Rocquencourt - BP 105 - 78153 Le Chesnay Cedex France Unité de recherche INRIA Lorraine : LORIA, Technopôle de Nancy-Brabois -[r]

and the true density f 0 , but then the solution depends on the unknown distribution and hence
heavy bootstrap methods need to be employed.
To improve inference, there exist also other approaches than that of forming a convex com- bination between the **parametric** and nonparametric estimators. The locally **parametric** non- **parametric** estimation is developed for instance in [ 19 , 20 , 46 ], but is less appealing from the point of view of model quality assessment because they do not provide any “fitness coefficient”.

3.2 **Parametric** t-Distributed Stochastic Exemplar-centered Embedding
To address the instability, sensitivity, and unscalability is- sues of pt-SNE, we present deep t-distributed stochastic exemplar-centered embedding (dt-SEE) and high-order t- distributed stochastic exemplar-centered embedding (hot- SEE) building upon pt-SNE and hot-SNE for **parametric** data embedding described earlier. The resulting objective function has linear computational complexity with respect to the size of training set. The underlying intuition is that, instead of comparing pairwise training data points, we com- pare training data only with a small number of representa- tive exemplars in the training set for neighborhood proba- bility computations. To this end, we simply precompute the exemplars by running a fixed number of iterations of k- means with scalable k-means++ seeding on the training set, which has at most linear computational complexity with re- spect to the size of training set [1].

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Introduction
We consider the evolution of a network of neurons, focus- ing on the asymptotic behavior of spikes dynamics instead of membrane potential dynamics. The spike response is not sought as a deterministic response in this context, but as a conditional probability: "Reading the code" consists in inferring this probability [1]. Since one has experimentally only access to finite time raster plots and since the convergence of the empirical statistics to their average can be quite slow, we use a **parametric** statis- tical model using a thermodynamic formalism. The natu- ral candidate for spike train statistics is a Gibbs measure [2]. Our work generalizes this seminal and profound work of Bialek and collaborators. This model allows us to pre- dict the conditional probability of rank R Markovian spike patterns and is strongly linked with the thermodynamic formalism [3]. It generalizes most spike patterns statistical models (e.g. Poisson, correlated Poisson, etc.).

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is assumed to be compact in L ∞ .
Although elementary, the above example gathers important features that are present in other relevant examples of **parametric** PDEs. In particular, the solution map a 7→ u(a) acts from an infinite dimensional space into another infinite dimensional space. Also note that, while the operator P of (1.6) is linear both in a and u (up to the constant additive term f ) the solution map is nonlinear. Because of the high dimensionality of the parameter space X, such problems represent a significant challenge when trying to capture this map numerically. One objective of this article is to understand which properties of this map allow for a successful numerical treatment. Concepts such as holomorphy, sparsity, and adaptivity are at the heart of our development.

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As in the previous subsection, to investigate the contagion’s phenomena, we use both methods based on non **parametric** tools and on multivariate switch- ing models.
1 - Second order measures. The linear correlation’s coeﬃcient between these two returns is equal to 0.10. Thus, it is very small. In table 11, we give the conditional correlation’s coeﬃcient for the two series. We condition using the quantiles of the empirical distribution of each series. We do not observe a U-shape. It seems that no relevant information is obtained from this statistic concerning a possible contamination of the volatility behavior from one series to the other one, in presence of shocks.

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Therefore, a typical parameter range is a set A ⊂ {a ∈ L ∞ (D) : a ≥ r}, which in addition is assumed to be compact in L ∞ .
Although elementary, the above example gathers important features that are present in other relevant examples of **parametric** PDEs. In particular, the solution map a 7→ u(a) acts from an infinite dimensional space into another infinite dimensional space. Also note that, while the operator P of (1.6) is linear both in a and u (up to the constant additive term f ) the solution map is nonlinear. Because of the high dimensionality of the parameter space X, such problems represent a significant challenge when trying to capture this map numerically. One objective of this article is to understand which properties of this map allow for a successful numerical treatment. Concepts such as holomorphy, sparsity, and adaptivity are at the heart of our development.

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1 Introduction
Finding high-level structure in scores is one of the fundamental research chal- lenges in music information retrieval. Listeners are capable of discerning struc- ture in music through the **identification** of common parts and their relative organization. Capturing musical structure with formal grammars is an old idea, taking roots in linguistics [1, 12, 18–20]. A grammar consists of a collection of productions, transforming non-terminal symbols into other symbols, and even- tually producing terminal symbols that can be the actual notes or other elements of the musical surface. Grammars can be used as a music analysis tool, to find the right grammar modeling a piece, as well as a composition tool, to generate pieces following a grammar. Typically, for a grammar to be used as a generating tool, the productions are additionally labeled with probabilities [3].

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