Spatially-separated foci can also be useful for spectrally-resolved experiments. Here we demonstrate a direct application of the XUV beam properties control by performing XUV **spectral** **filtering** without using any XUV optics. This is realized by comparing the spatially- resolved HHG spectrum obtained with a 140-µm-diameter pinhole centered on the pathway of the harmonics and the reference obtained without the pinhole, as shown in Fig. 3(a) and (b) for z jet = -58 mm. The transmission factor (T) is then defined as the ratio of the HHG spectra

we perform direct numerical simulations of Eq. (1) using the split-step Fourier code. We first consider in Fig. 4 the propagation of four types of solitons perturbed initially by a weak dispersive field nearby. It is clearly seen that two types of Hamiltonian solitons suffer from strong fluctua- tions in both their soliton part and background [see panels (a) and (b)], whereas AA solitons can recover very cleanly from such perturbation [see panels (c) and (d)]. We argue that it is the effect of **spectral** **filtering** that suppresses the instabilities induced by the dispersive field, as revealed in our linear stability analysis above. Additionally, we con- sider perturbations such as U 0 exp(i0.5τ ) and find that

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6 CONC LUSIO N
A picosecond optical parametric oscillator is demonstrated without any **spectral** **filtering** element. Based on a stoechio- metric PPSLT nonlinear crystal, it provides tunable transform limited picosecond pulses in the 1550-1640 nm region for sig- nal, and 1300-1375 nm for idler radiations respectively. The influence of the cavity length detuning on the **spectral** and temporal dynamic of the output radiation was analyzed in de- tail. The possibility of continuous tuning of the pulse duration in the 9-17 ps region for the 80% output coupler, and the 12- 20 ps region for the 90% output coupler is demonstrated by reduction of the OPO cavity length. Moreover the possibility of signal pulse compression by a factor of 5 to 10 is shown

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Fourier transformed picosecond OPO based on PPSLT without **spectral** **filtering** element
A. Ryasnyanskiy, N. Dubreuil, Ph. Delaye, R. Frey, G. Roosen Laboratoire Charles Fabry de l'Institut d'Optique, Centre National de la Recherche Scientifique et Université Paris-Sud, Campus Polytechnique,

different optical methods based on non-linear effects in optical fibers have been proposed; for example: the use of non-linear optical loop mirrors (NOLMs) [4], four-wave mixing [5], or self-phase modulation (SPM) [6]. The latest method is based on **spectral** broadening followed by an offset **spectral** **filtering** and has been proposed in 1998 by P.V. Mamyshev. Many works, both experimental [7-13] and theoretical [9, 11, 14-19], have dealt with the possibilities of such a device known as the Mamyshev regenerator. For example, its capacity of multi-wavelength regeneration [8, 17], the existence of eigen-pulses in concatenated regenerators [19] or its inclusion in a set-up compatible with DPSK signals [20] have been recently reported.

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Ultrasound modulated optical tomography (UOT) is a powerful imaging technique to discriminate healthy from unhealthy biological tissues based on their optical signature. Among the numerous detection techniques developed for acousto-optic imaging, only those based on **spectral** **filtering** are intrinsically immune to speckle decorrelation. This paper reports on UOT imaging based on **spectral** hole burning in Tm:YAG crystal under a moderate magnetic field (200G) with a well-defined orientation. The deep and long-lasting holes translate into a more efficient UOT imaging with a higher contrast and faster imaging frame rate. We demonstrate the potential of this method by imaging calibrated phantom scattering gels.

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Collaborative **Filtering** (CF) is the most successful approach to Recommender Systems (RS). In this paper, we suggest methods for global and personalized visualization of CF data. Users and items are first embedded into a high-dimensional latent feature space according to a predictor function particularly designated to conform with visu- alization requirements. The data is then projected into 2-dimensional space by Principal Component Analysis (PCA) and Curvilinear Com- ponent Analysis (CCA). Each projection technique targets a different application, and has its own advantages. PCA places all items on a Global Item Map (GIM) such that the correlation between their latent features is revealed optimally. CCA draws personalized Item Maps (PIMs) representing a small subset of items to a specific user. Unlike in GIM, a user is present in PIM and items are placed closer or fur- ther to her based on their predicted ratings. The intra-item semantic correlations are inherited from the high-dimensional space as much as possible. The algorithms are tested on three versions of the MovieLens dataset and the Netflix dataset to show they combine good accuracy with satisfactory visual properties. We rely on a few examples to argue our methods can reveal links which are hard to be extracted, even if explicit item features are available.

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9 Conclusions
We proposed a simple and efficient mechanism to control the trade-off between privacy and recommendation quality in decentralized collaborative **filtering**. Our mechanism relies on two components : (i) an original obfuscation mechanism revealing only the least sensitive informa- tion in the profiles of users, and (ii) a randomization-based dissemination algorithm ensuring differential privacy during the dissemination process. In addition, we also proposed a fully diffe- rentially private alternative which can be viewed as a contribution in its own right. Interestingly, our mechanism achieves similar results as this differentially private alternative in terms of recom- mendation quality while protecting the sensitive information of users more efficiently and being more resilient to censorship attacks.

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the shape of the amoeba is the result of a standard Gaussian lter of size. 3 on the original image, and the distan
e d pixel is the absolute dieren
e of gray-levels[r]

mean
Figure 5. Results of a “classic” median **filtering** and two amoeba-based filterings: a median and a mean on Edouard Manet’s painting “Le fifre”.
The choice of the color space and the distance has an impact on the quality of the result. However the most noticeable impact is that of the choice of the pilot image. For the images in figure 6, we have used a gaussian filter of size 3 on each R,G and B component, and recombined the three channels.

By assuming each of the preconditioners is derived from a splitting of A, the explicit forms of the composite preconditioners are discussed. Based on the ex- plicit form and certain assumptions, we show that the preconditioned matrix by using each of the composite preconditioner is symmetric with respect to certain non-standard inner product. This is potentially useful if the property can be exploited in the iterative methods, see references [13, 18, 19]. Spectrum analysis shows that the composite preconditioners benefit from each of the precondition- ers, and tend to make the spectrum clustered at one. Several examples are given to illustrate the spectrum distribution of the preconditioned matrices by using different preconditioners. On the two combination approaches, we reveal that there is little difference between them. Particularly, For the preconditioned fixed point iteration, we proved that the two combination approaches produce the same convergence rate. For the Krylov subspace methods, e.g. FGMRES method employed in this paper, we find that there is at most one step differ- ence between the two combination preconditioning approaches. Finally, some challenging linear system problems arising from discretization of boundary prob- lems are tested. The results show that the composite preconditioners proposed in this paper are efficient, and converge much faster than the classical ILU(0) preconditioner, and similar type of composite preconditioners by using different **filtering** vectors.

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tion was used to study the following **filtering** problem: if {X n } and {Y n } are
two independent stationary sequences of real-valued random variables, {X n }
being the emitted signal and {Y n } the noise, is it possible to recover {X n }
from the received signal {X n + Y n }? More precisely, the problem was to de-

Institute of Electrical Engineering, EPFL, Lausanne, Switzerland
ABSTRACT
We build upon recent advances in graph signal processing to propose a faster **spectral** clustering algorithm. Indeed, clas- sical **spectral** clustering is based on the computation of the first k eigenvectors of the similarity matrix’ Laplacian, whose computation cost, even for sparse matrices, becomes pro- hibitive for large datasets. We show that we can estimate the **spectral** clustering distance matrix without computing these eigenvectors: by graph **filtering** random signals. Also, we take advantage of the stochasticity of these random vectors to estimate the number of clusters k. We compare our method to classical **spectral** clustering on synthetic data, and show that it reaches equal performance while being faster by a factor at least two for large datasets.

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Whilst early recommender systems based on matrix factorisation aimed to recover the complete matrix of ratings, recent advances focus on optimising scoring losses designed for LTR proble[r]

In this report, we mostly focus on the first stage of the model, which performs linear spatio-temporal **filtering** on the input image. We view this stage as a linear application from a 2D space (the image) to a 2D+T space (the temporal response of the retina), which bears an optimal inverse transformation in terms of robustness to noise: the pseudo-inverse of Moore-Penrose. We study the particular structure of this pseudo- inverse, due to the structure of retinal **filtering** with a delayed surround component. As a result, the pseudo-inverse-based image reconstruction reconstructs low spatial frequencies before high spatial frequencies. This property could have psychophysical correlates, for example during perception of very short image presentations.

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çªÞáQã¬éQ-ã zÏyÐIã +MÏ"ÐhÖ â"ÛmãqÞÏÝQÙ`ä|ãMåcæä|ãMåUæ Ü~ÛÖ.[r]

In this section, we study the effect of the smoothness of the reward function on the perfor- mance of **spectral** algorithms. We use a BA graph on 500 nodes for the experiment with time horizon 100 and the parameters of the algorithms are set according to table 3 . The value of effective dimension is close to 8. We controll the smoothness by explicitly setting the number of eigenvectors used for constructing the reward function by letting 5, 25, 100, or 500 elements of α to be nonzero. Note that the value of the effective dimension is the same for every reward function we used, since the definition of the effective dimension is independent of the reward function. Table 4 shows how the smoothness changes with the number of nonzero elements of α and Figures 6a and 6b confirm that the **spectral** algo- rithms are able to leverage **spectral** properties of underlying graph better when the reward function is smoother. This is also supported by our analysis, since in our experiment, the smoothness of the reward function decreases with a smaller number of eigenvectors and the regret bounds of the **spectral** algorithms are decreasing with smoothness as well.

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Figures 5-7 show a comparison of the estimation errors produced from the filter only, the concurrent **filtering** and smoothing system, and a full batch optimization. The **filtering** only solution uses the inertial strapdown with the visual odometry aiding; no loop closures are incorporated. This rep- resents a typical navigation **filtering** solution. The concurrent **filtering** and smoothing results use the inertial strapdown with the visual odometry aiding on the **filtering** side, while loop closure constraints are provided to the smoother. Unlike the **filtering** solution, long-term loop closures at arbitrary positions along the trajectory can be incorporated without affecting the time of the filter. Finally, a series of full batch optimizations have been performed. Each state estimate within the batch trajectory results from a full, nonlinear optimization of all measurements up to the current time. This trajectory captures the best possible state estimate at each time instant using only measurements available up to that time.

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Index Terms— **filtering**, denoising, edge-enhancement, stochastic **filtering**, shock filter
1. INTRODUCTION
Diffusion processes have been applied with great success to image processing for more than 30 years. Koenderink first noted the equivalence between Gaussian **filtering** and the isotropic heat partial differential equation (PDE) [1], upon which Witkin built the scale-space theory [2]. In the early 1990s Perona and Malik paved the way for a new class of successful edge preserving denoising filters using nonlin- ear heat PDEs, in which the diffusion coefficient depend on the local edge content [3]. Nonlinear filters demonstrated state of the art denoising results during 15 years. They were then outperformed in the middle of the last decade by non- local, patch-based approaches for the additive white gaussian noise (AWGN) degradation model. State of the art include, in chronological order, non-local means (NLM) [4], K-SVD [5], BM3D [6], graph Laplacian regularization [7] and DnCNN [8]. It has been suggested that the very good performances attained by these new filters could be close to approaching theoretical limits in terms of maximization of the signal-to- noise ratio (SNR) [9].

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as data for which no vectorial representation is available but for which a similarity function between objects can be computed, as in the MDS (multi-dimensional scaling) algorithms (Cox and Cox, 1994).
There are of course several dimensionality reduction methods that do not fall in the **spectral** framework described here, but which may have interesting connections nonethe- less. For example, the principal curves algorithms (Hastie and Stuetzle, 1989; Kegl and Krzyzak, 2002) have been introduced based on geometric grounds, mostly for 1- dimensional manifolds. Although they optimize a different type of criterion, their spirit is close to that of LLE and Isomap. Another very interesting family of algorithms is the Self-Organizing Map (Kohonen, 1990). With these algorithms, the low dimensional embedding space is discretized (into topologically organized centers) and one learns the coordinates in the raw high-dimensional space of each of these centers. Another neural network like approach to dimensionality reduction is the auto-associative neural network (Rumelhart, Hinton and Williams, 1986; Saund, 1989), in which one trains a multi-layer neural network to predict its input, but forcing the intermediate repre- sentation of the hidden units to be a compact code. In section 2.7 we discuss in more detail a family of density estimation algorithms that can be written as mixtures of Gaus- sians with low-rank covariance matrices, having intimate connections with the LLE and Isomap algorithms.

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