weighted **Least** **Square**.
The Fig. 2 and Fig. 3 are obtained respectively for indoor and outdoor scenarios with the parameters described in Table III. These figures show that the estimation schemes based on the mode estimator for ranges performs better than those usually used based on median and mean estimators. Moreover, these figures show obviously that the Weighted **Least** **Square** **approximation** performs better than typical unweighted **Least** **Square** **approximation**. Nevertheless, the Weighted **Least** **Square** **approximation** is more complex and consumes more ressources since it performs the estimation of different variances before estimating the position of the MS. In order to compare the performances of these different estimation schemes in the case of hybrid RSS fusion, we carried simulations in a typical 4G scenario where the MS can be connected conjointly to cellular BSs and wireless APs (IEEE 802.15.4 or IEEE 802.11 for example). The Fig. 4 shows the performances of different estimation schemes for this scenario with l = 1000 m. This figure is obtained by reproducing the same simulations conditions assumed in Fig. 3 but with adding two indoor links into a **square** of l = 15 m. The position of MS is chosen randomly in the **square** 15 × 15 m 2

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The paper is organized as follows. Section 2 settles the general problem of **least** **square** **approximation** and gives the most fundamental results which will be useful in the sequel. In particular, it is seen how linear (or more generally, conic) values arise from **least** **square** **approximation**. Section 3 concentrates on **least** **square** values, and establishes explicit solution formulas under mild con- straints on the weights used in the **approximation** with application to the Shapley value and to an optimization problem given in Ruiz et al. [14]. (Interestingly, the weights do not necessarily have to be all positive under our constraints.) Finally, Section 4 shows how Weber’s [19] so-called probabilistic values arise naturally in our model.

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for some subcollection N 0 ⊆ N would stipulate an **approximation** of v by a game that induces an efficient value (the first equality) and, furthermore, preserves the total sum of the v(S) for some specific subsets (second equality). Observe that all equalities (4) to (6) are of the form Ax = b(v) with b linear in v. Hence, **least** **square** **approximation** problems of a game v (or of its image by a linear map c) by a game satisfying some of the above equalities (e.g., an additive game) fall under the case covered by (1). Then Lemma 1 applies, from which it follows that such approximations are linear in v.

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4.1.1 From the tensorial decomposition
It is not the unique way, but it is a convenient one: we will introduce the symmetrical and anti- symmetrical decomposition of **square** matrices from the tensor decomposition of rectangular matrices as introduced in 2.6. In this section, matrix Y is **square**, of size P × P , and its rows and columns are associated to the same series of items, so only one covariable matrix W of size P × K will be considered. In that framework, Equation (30) reads:

The individual product space was used as a reference map for basic taste stimuli in water at known concentrations. The Partial **Least** **Square** models were built on this reference data, for each taste.
Then, new physiological measurements were performed on taste stimuli (Exp2 – 2 repetitions). They have been projected on the PCA reference map (Figure 1) and their concentrations in sapid molecules was predicted from the PLS models developed previously (Table 2).

Aujourd’hui, le **Square** Viger est l’objet de nombreuses discussions. Il se situe en effet encore une fois au coeur d’une grande métamorphose urbaine, qui est celle du secteur Champ-de- Mars. La perspective de sa démolition, annoncée par la Ville de Montréal dès le début des années 2000, a donné lieu à de nombreux débats de la part de nombreux acteurs : les dé- fenseurs du patrimoine, avec, en tête, Héritage Montréal ; les élus et dirigeants représentant la Ville de Montréal ; la presse locale ; les organismes communautaires tels que le Réseau d’aide aux personnes seules et itinérantes de Montréal (RASPIM) et enfin, plus générale- ment, les citoyens. À ce jour, les parties qui militent pour sa conservation crient haut et fort, même si la démolition est inéluctable.

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Unité de recherche INRIA Lorraine, Technopôle de Nancy-Brabois, Campus scientifique, 615 rue du Jardin Botanique, BP 101, 54600 VILLERS LÈS NANCY Unité de recherche INRIA Rennes, Irisa, [r]

Objectives: Develop a new, rapid and reliable method to detect roots and crop residues in soil using Near Infrared hyperspectral imaging system (NIR- HSI) combined with predictive models based on the partial **least** **square** discriminant analysis (PLS-DA) chemometric’s tool. This is a first step aiming to a possible quantification of the different materials.
Materials: Camera: NIR Hyperspectral line scan or push-broom combined with a conveyor belt (Vermeulen & al., 2012).

Severini and Mansour introduced **square** polygons, as graphical representations of **square** permutations, that is, per- mutations such that all entries are records (left or right, minimum or maximum), and they obtained a nice formula for their number. In this paper we give a recursive construction for this class of permutations, that allows to simplify the derivation of their formula and to enumerate the subclass of **square** permutations with a simple record polygon. We also show that the generating function of these permutations with respect to the number of records of each type is algebraic, answering a question of Wilf in a particular case.

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2 Valorisation of Agricultural Products Department, Walloon Agricultural Research Centre (CRA-W),
Gembloux, Belgium
Introduction
In studies on tillage, monitoring of root systems development and crop residues decomposition is very important. However, it is only possible if these different constituents can be discriminated from soil and then quantified. Current methods, based on soil coring, need to wash cores to extract individual elements (roots and straws), then to manually separate and to weight them (Gao-Bao et al., 2012). These methods are time consuming and dependent of the operator. In this work, we propose the use of Near Infrared combined with Hyperspectral Imaging (NIR-HSI) and chemometric tools (Partial **Least** **Square** Discriminant Analysis - PLS-DA) as a new rapid and reliable procedure to discriminate soil, roots and straws after wheat crop (Triticum aestivum L.). NIR-HSI provides simultaneously spectral and spatial information and PLS-DA allows discrimination between classes based on spectra of each pixel linked to chemical nature of sample constituents on the image (Dale et al., 2012; Fernández Pierna et al., 2012). Materials and Methods

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Aspergillus niger
A B S T R A C T
Plug ﬂow bioreactor (PFB) used in solid state fermentation gives the possibility to have semicontinuous culture. However, it is complicated to follow a single particle during its residence inside the bioreactor and to therefore study precisely the culture process all along the device. In this study, semicontinuous production of fungal compounds was successfully obtained by cultivating Aspergillus niger with a PFB prototype. Kinetic productions of the same metabolites along the bioreactor were obtained at laboratory scale to predict the residence time of the particles inside the PFB from Partial **Least** **Square** (PLS). This original methodology allowed (1) the com- parison between the production kinetics at the two production scales (pilot and laboratory) and (2) the ob- servation of eventual changes following the scale-up of the process o ﬀering a good overall insight of the PFB performance.

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The controllability of nonlinear partial differential equations has attracted a large number of works in the last decades. We refer to the monography [4] and the references therein. However, as far as we know, very few are concerned with the **approximation** of exact controls for nonlinear partial differential equa- tions, so that the construction of convergent control approximations for controllable nonlinear equation remains a challenges.

2.2 **Least** Squares Identification of the Dynamic Parameters (IDIM-LS)
The off-line identification of the base dynamic parameters
is considered, given measured or estimated off-line data for τ and q, q, q , collected while the robot is tracking some planned trajectories. The model (4) is sampled and low pass filtered in order to get an over-determined linear system of

2001 ) and is highly flexible: it can handle very general lin- ear structure on errors, including arbitrary weights (chang- ing noise for different entries), patterns of observed and un- observed errors, Toeplitz and Hankel structures, and even norms other than the Frobenius norm. The nuclear norm relaxation has been successfully used for a range of ma- chine learning problems involving rank constraints, includ- ing low-rank matrix completion, low-order system approx- imation, and robust PCA ( Cai et al. , 2010 ; Chandrasekaran et al. , 2011 ). The STLS problem is conceptually differ- ent in that we do not seek low-rank solutions, but on the contrary nearly full-rank solutions. We show both theoreti- cally and experimentally that while the plain nuclear norm formulation incurs large **approximation** errors, these can be dramatically improved by using the re-weighted nuclear norm. We suggest fast first-order methods based on Aug- mented Lagrangian multipliers ( Bertsekas , 1982 ) to com- pute the STLS solution. As part of ALM we derive new updates for the re-weighted nuclear-norm based on solv- ing the Sylvester’s equation, which can also be used for many other machine learning tasks relying on matrix-rank, including matrix completion and robust PCA.

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Tabulate and Multiply presented in Section VI-A performs
well up to 24 bits. With higher precision one can observe the increase in memory blocks for this architecture. Finally, for 32-bits we compare the requirements and performance of a Newton-Raphson-based implementation bootstrapped by a bipartite **approximation**, a higher-order Taylor based imple- mentation, and two variations of Halley’s method: first boot- strapped by a table, and the second bootstrapped by a bipartite **approximation**. These implementations show interesting trade- offs: Newton-Raphson+ bipartite shows the highest number of memory blocks (5) but the lowest number of DSPs (2), an average-low number of ALMs, and a short latency; Taylor uses the most ALMs, but fewest memory blocks, highest number of DSPs and highest latency; Halley bootstrapped by a table has the lowest ALM and latency but highest DSP and memory; Halley bootstrapped by bipartite reduces the number of memory blocks to minimum, but slightly increases the number of ALMs.

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Morgan Kaufmann Publishers, San Francisco, USA, 1994 Appendix A
The following table contains all the data for all problem instances from [BD92]. The fields describe the problem number, the number of squares, the size of the master **square** and a list of the **square** sizes. The problem number corresponds to the page number in [BD92]. Problems 166 and 167, 168 and 169, 182 and 183 are identical, but have two non-isomorphic solutions.

Que l'art et le politique s'associent pour inscrire le poème dans la Cité est salutaire. La sensuelle sobriété de ces formes géométriques auraient certainement plu à François Jacqmin. Aurait-il vu dans les arêtes des socles celles de la pensée, dans la rondeur des sphères celle du réel sensible ? Il est maintenant à nouveau permis aux Liégeois d'y rêver, dans le calme du **square** François Jacqmin.

The **least** core is closely related to some other solution concepts from cooperative game theory. For example, Maschler et al. [32] studied the relationship between the **least** core and the nucleolus [44]. Given a cost allocation x 2 R N , the excess vector .x/ is defined as the 2 n 2 dimensional vector whose components are e.x; S / for all S N such that S ¤ ;; N , in nonincreasing order. The nucleolus is the cost allocation that lexicographically minimizes the excess vector .x/. Maschler et al. [32] showed that for a cooperative game .N; v/, the nucleolus can be computed by solving jN j linear programs of the form (LC). On a different note, Einy et al. [12] showed that the **least** core is always contained in the Mas-Colell bargaining set [31]. The Mas-Colell bargaining set of a cooperative game, like the classical bargaining set [1], is the set of all cost allocations that are stable with respect to a particular system of objections and counterobjections.

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