Relevant bibliographies by topics / Sparse bound

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Academic literature on the topic 'Sparse bound'

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Published: 6 September 2023

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Journal articles on the topic "Sparse bound"

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Lorist, Emiel, and Zoe Nieraeth. "Sparse domination implies vector-valued sparse domination." Mathematische Zeitschrift 301, no. 1 (January 12, 2022): 1–35. http://dx.doi.org/10.1007/s00209-021-02943-z.

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AbstractWe prove that scalar-valued sparse domination of a multilinear operator implies vector-valued sparse domination for tuples of quasi-Banach function spaces, for which we introduce a multilinear analogue of the $${{\,\mathrm{UMD}\,}}$$ UMD condition. This condition is characterized by the boundedness of the multisublinear Hardy-Littlewood maximal operator and goes beyond examples in which a $${{\,\mathrm{UMD}\,}}$$ UMD condition is assumed on each individual space and includes e.g. iterated Lebesgue, Lorentz, and Orlicz spaces. Our method allows us to obtain sharp vector-valued weighted bounds directly from scalar-valued sparse domination, without the use of a Rubio de Francia type extrapolation result. We apply our result to obtain new vector-valued bounds for multilinear Calderón-Zygmund operators as well as recover the old ones with a new sharp weighted bound. Moreover, in the Banach function space setting we improve upon recent vector-valued bounds for the bilinear Hilbert transform.
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Shparlinski, Igor E., and José Felipe Voloch. "Value Sets of Sparse Polynomials." Canadian Mathematical Bulletin 63, no. 1 (September 24, 2019): 187–96. http://dx.doi.org/10.4153/s0008439519000316.

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AbstractWe obtain a new lower bound on the size of the value set $\mathscr{V}(f)=f(\mathbb{F}_{p})$ of a sparse polynomial $f\in \mathbb{F}_{p}[X]$ over a finite field of $p$ elements when $p$ is prime. This bound is uniform with respect to the degree and depends on some natural arithmetic properties of the degrees of the monomial terms of $f$ and the number of these terms. Our result is stronger than those that can be extracted from the bounds on multiplicities of individual values in $\mathscr{V}(f)$.
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Zhang, Rui, Rui Xin, Margo Seltzer, and Cynthia Rudin. "Optimal Sparse Regression Trees." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 9 (June 26, 2023): 11270–79. http://dx.doi.org/10.1609/aaai.v37i9.26334.

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Regression trees are one of the oldest forms of AI models, and their predictions can be made without a calculator, which makes them broadly useful, particularly for high-stakes applications. Within the large literature on regression trees, there has been little effort towards full provable optimization, mainly due to the computational hardness of the problem. This work proposes a dynamic programming-with-bounds approach to the construction of provably-optimal sparse regression trees. We leverage a novel lower bound based on an optimal solution to the k-Means clustering algorithm on one dimensional data. We are often able to find optimal sparse trees in seconds, even for challenging datasets that involve large numbers of samples and highly-correlated features.
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Chen, Wengu, and Huanmin Ge. "A Sharp Bound on RIC in Generalized Orthogonal Matching Pursuit." Canadian Mathematical Bulletin 61, no. 1 (March 1, 2018): 40–54. http://dx.doi.org/10.4153/cmb-2017-009-6.

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AbstractThe generalized orthogonal matching pursuit (gOMP) algorithm has received much attention in recent years as a natural extension of the orthogonal matching pursuit (OMP). It is used to recover sparse signals in compressive sensing. In this paper, a new bound is obtained for the exact reconstruction of every K-sparse signal via the gOMP algorithm in the noiseless case. That is, if the restricted isometry constant (RIC) δNK+1 of the sensing matrix A satisfiesthen the gOMP can perfectly recover every K-sparse signal x from y = Ax. Furthermore, the bound is proved to be sharp. In the noisy case, the above bound on RIC combining with an extra condition on the minimum magnitude of the nonzero components of K-sparse signals can guarantee that the gOMP selects all of the support indices of the K-sparse signals.
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Ferber, Asaf, Gweneth McKinley, and Wojciech Samotij. "Supersaturated Sparse Graphs and Hypergraphs." International Mathematics Research Notices 2020, no. 2 (March 8, 2018): 378–402. http://dx.doi.org/10.1093/imrn/rny030.

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Abstract A central problem in extremal graph theory is to estimate, for a given graph H, the number of H-free graphs on a given set of n vertices. In the case when H is not bipartite, Erd̋s, Frankl, and Rödl proved that there are 2(1+o(1))ex(n, H) such graphs. In the bipartite case, however, bounds of the form 2O(ex(n, H)) have been proven only for relatively few special graphs H. As a 1st attempt at addressing this problem in full generality, we show that such a bound follows merely from a rather natural assumption on the growth rate of n ↦ ex(n, H); an analogous statement remains true when H is a uniform hypergraph. Subsequently, we derive several new results, along with most previously known estimates, as simple corollaries of our theorem. At the heart of our proof lies a general supersaturation statement that extends the seminal work of Erd̋s and Simonovits. The bounds on the number of H-free hypergraphs are derived from it using the method of hypergraph containers.
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FELDHEIM, OHAD N., and MICHAEL KRIVELEVICH. "Winning Fast in Sparse Graph Construction Games." Combinatorics, Probability and Computing 17, no. 6 (November 2008): 781–91. http://dx.doi.org/10.1017/s0963548308009401.

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A graph construction game is a Maker–Breaker game. Maker and Breaker take turns in choosing previously unoccupied edges of the complete graphKN. Maker's aim is to claim a copy of a given target graphGwhile Breaker's aim is to prevent Maker from doing so. In this paper we show that ifGis ad-degenerate graph onnvertices andN>d1122d+9n, then Maker can claim a copy ofGin at mostd1122d+7nrounds. We also discuss a lower bound on the number of rounds Maker needs to win, and the gap between these bounds.
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Chen, Qiushi, Xin Zhang, Qiang Yang, Lei Ye, and Mengxiao Zhao. "Performance Bound for Joint Multiple Parameter Target Estimation in Sparse Stepped-Frequency Radar: A Comparison Analysis." Sensors 19, no. 9 (April 29, 2019): 2002. http://dx.doi.org/10.3390/s19092002.

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A performance bound—Cramér-Rao lower bound (CRLB) for target estimation and detection in sparse stepped frequency radars is presented. The vector formulation of this CRLB is used to obtain a lower bound on the estimation error. The estimation performance can be transformed into different types of CRLB structures. Therefore, the expressions of bounds under three equivalent models are derived separately: time delay and Doppler stretch estimator, joint multiple parameter estimator, and sparse-based estimator. The variables to be estimated include the variances of unknown noise, range, velocity, and the real and imaginary parts of the amplitude. A general performance expression is proposed by considering the echo of the target in the line-of-sight. When the relationship between CRLB and various parameters are discussed in detail, the specific effect of waveform parameters on a single CRLB is compared and analyzed. Numerical simulations demonstrated that the resulting CRLB exhibits considerable theoretical and practical significance for the selection of optimal waveform parameters.
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Sapir, Shachar, and Asaf Shapira. "The Induced Removal Lemma in Sparse Graphs." Combinatorics, Probability and Computing 29, no. 1 (September 30, 2019): 153–62. http://dx.doi.org/10.1017/s0963548319000233.

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AbstractThe induced removal lemma of Alon, Fischer, Krivelevich and Szegedy states that if an n-vertex graph G is ε-far from being induced H-free then G contains δH(ε) · nh induced copies of H. Improving upon the original proof, Conlon and Fox proved that 1/δH(ε)is at most a tower of height poly(1/ε), and asked if this bound can be further improved to a tower of height log(1/ε). In this paper we obtain such a bound for graphs G of density O(ε). We actually prove a more general result, which, as a special case, also gives a new proof of Fox’s bound for the (non-induced) removal lemma.
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Deng, Hao, Jianghong Chen, Biqin Song, and Zhibin Pan. "Error Bound of Mode-Based Additive Models." Entropy 23, no. 6 (May 22, 2021): 651. http://dx.doi.org/10.3390/e23060651.

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Due to their flexibility and interpretability, additive models are powerful tools for high-dimensional mean regression and variable selection. However, the least-squares loss-based mean regression models suffer from sensitivity to non-Gaussian noises, and there is also a need to improve the model’s robustness. This paper considers the estimation and variable selection via modal regression in reproducing kernel Hilbert spaces (RKHSs). Based on the mode-induced metric and two-fold Lasso-type regularizer, we proposed a sparse modal regression algorithm and gave the excess generalization error. The experimental results demonstrated the effectiveness of the proposed model.
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Milani Fard, Mahdi, Yuri Grinberg, Joelle Pineau, and Doina Precup. "Compressed Least-Squares Regression on Sparse Spaces." Proceedings of the AAAI Conference on Artificial Intelligence 26, no. 1 (September 20, 2021): 1054–60. http://dx.doi.org/10.1609/aaai.v26i1.8303.

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Recent advances in the area of compressed sensing suggest that it is possible to reconstruct high-dimensional sparse signals from a small number of random projections. Domains in which the sparsity assumption is applicable also offer many interesting large-scale machine learning prediction tasks. It is therefore important to study the effect of random projections as a dimensionality reduction method under such sparsity assumptions. In this paper we develop the bias-variance analysis of a least-squares regression estimator in compressed spaces when random projections are applied on sparse input signals. Leveraging the sparsity assumption, we are able to work with arbitrary non i.i.d. sampling strategies and derive a worst-case bound on the entire space. Empirical results on synthetic and real-world datasets shows how the choice of the projection size affects the performance of regression on compressed spaces, and highlights a range of problems where the method is useful.
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Dissertations / Theses on the topic "Sparse bound"

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Shabara, Yahia. "Establishing Large-Scale MIMO Communication: Coding for Channel Estimation." The Ohio State University, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=osu1618578732285999.

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Price, Eric (Eric C. ). "Algorithms and lower bounds for sparse recovery." Thesis, Massachusetts Institute of Technology, 2010. http://hdl.handle.net/1721.1/62668.

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Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2010.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 69-71).
We consider the following k-sparse recovery problem: design a distribution of m x n matrix A, such that for any signal x, given Ax with high probability we can efficiently recover x satisfying IIx - x l, by Eric Price.
M.Eng.
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Do, Ba Khanh. "Algorithms and lower bounds in the streaming and sparse recovery models." Thesis, Massachusetts Institute of Technology, 2012. http://hdl.handle.net/1721.1/75629.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2012.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 52-56).
In the data stream computation model, input data is given to us sequentially (the data stream), and our goal is to compute or approximate some function or statistic on that data using a sublinear (in both the length of the stream and the size of the universe of items that can appear in the stream) amount of space; in particular, we can store neither the entire stream nor a counter for each possible item we might see. In the sparse recovery model (also known as compressed sensing), input data is a large but sparse vector x [epsilon] Rn, and our goal is to design an m x n matrix [Phi]D, where m << n, such that for any sufficiently sparse x we can efficiently recover a good approximation of x from [Phi]x. Although at first glance these two models may seem quite different, they are in fact intimately related. In the streaming model, most statistics of interest are order-invariant, meaning they care only about the frequency of each item in the stream and not their position. For these problems, the data in the stream can be viewed as an n-dimensional vector x, where xi is the number of occurrences of item i. Using this representation, one of the high-level tools that have proven most popular has been the linear sketch, where for some m x n matrix {Phi]we maintain {Phi]x (the sketch) for the partial vector x as we progress along the stream. The linearity of the mapping D allows us to efficiently do incremental updates on our sketch, and as in its use in sparse recovery, the linear sketch turns out to be surprisingly powerful. In this thesis, we try to answer some questions of interest in each model, illustrating both the power and the limitations of the linear sketch. In Chapter 2, we provide an efficient sketch for estimating the (planar) Earth-Mover Distance (EMD) between two multisets of points. The EMD between point sets A, B R2 of the same size is defined as the minimum cost of a perfect matching between them, with each edge contributing a cost equal to its (Euclidean) length. As immediate consequences, we give an improved algorithm for estimating EMD between point sets given over a stream, and an improved algorithm for the approximate nearest neighbor problem under EMD. In Chapter 3, we prove tight lower bounds for sparse recovery in the number of rows in the matrix [Phi] (i.e., the number of measurements) in order to achieve any of the three most studied recovery guarantees. Specifically, consider a matrix [Phi] and an algorithm R such that for any signal x, R can recover an approximation & from [Phi] satisfying ... where (1) p= q= 1 and C= O(1), (2) p= q= 2 and C = O(1), or (3) p =2, q = 1 and C = O(k-1/ 2 ). We show that any such [Phi] I must have at least [Omega](k log(n/k)) rows. This is known to be optimal in cases (1) and (2), and near optimal for (3). In Chapter 4, we propose a variant of sparse recovery that incorporates some additional knowledge about the signal that allows the above lower bound to be broken. In particular, we consider the scenario where, after measurements are taken, we are given a set S of size s < n (s is known beforehand) that is supposed to contain most of the "large" coefficients of x. The goal is then to recover i satisfying ... We refer to this formulation as the sparse recovery with partial support knowledge problem (SRPSK). We focus on the guarantees where p = q = 1 or 2 and C = 1 + e, for which we provide lower bounds as well as a method of converting algorithms for "standard" sparse recovery into ones for SRPSK. We also make use of one of the reductions to give an optimal algorithm for SRPSK for the guarantee where p = q = 2.
by Khanh Do Ba.
Ph.D.
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Brennan, Matthew (Matthew Stewart). "Reducibility and computational lower bounds for problems with planted sparse structure." Thesis, Massachusetts Institute of Technology, 2018. http://hdl.handle.net/1721.1/118062.

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Thesis: S.M. in Computer Science and Engineering, Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2018.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 145-155).
Recently, research in unsupervised learning has gravitated towards exploring statistical-computational gaps induced by sparsity. A line of work initiated by Berthet and Rigollet has aimed to explain these gaps through reductions to conjecturally hard problems from complexity theory. However, the delicate nature of average-case reductions has limited the development of techniques and often led to weaker hardness results that only apply to algorithms that are robust to different noise distributions or that do not need to know the parameters of the problem. We introduce several new techniques to give a web of average-case reductions showing strong computational lower bounds based on the planted clique conjecture for planted independent set, planted dense subgraph, biclustering, sparse rank-1 submatrix, sparse PCA and the subgraph stochastic block model. Our results demonstrate that, despite the delicate nature of average-case reductions, using natural problems as intermediates can often be beneficial, as is the case in worst-case complexity. Our main technical contribution is to introduce a set of techniques for average-case reductions that: (1) maintain the level of signal in an instance of a problem; (2) alter its planted structure; and (3) map two initial high-dimensional distributions simultaneously to two target distributions approximately under total variation. We also give algorithms matching our lower bounds and identify the information-theoretic limits of the models we consider.
by Matthew Brennan.
S.M. in Computer Science and Engineering
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Gasiorowski, Pawel. "Individual and group dynamic behaviour patterns in bound spaces." Thesis, London Metropolitan University, 2017. http://repository.londonmet.ac.uk/1447/.

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The behaviour analysis of individual and group dynamics in closed spaces is a subject of extensive research in both academia and industry. However, despite recent technological advancements the problem of implementing the existing methods for visual behaviour data analysis in production systems remains difficult and the applications are available only in special cases in which the resourcing is not a problem. Most of the approaches concentrate on direct extraction and classification of the visual features from the video footage for recognising the dynamic behaviour directly from the source. The adoption of such an approach allows recognising directly the elementary actions of moving objects, which is a difficult task on its own. The major factor that impacts the performance of the methods for video analytics is the necessity to combine processing of enormous volume of video data with complex analysis of this data using and computationally resourcedemanding analytical algorithms. This is not feasible for many applications, which must work in real time. In this research, an alternative simulation-based approach for behaviour analysis has been adopted. It can potentially reduce the requirements for extracting information from real video footage for the purpose of the analysis of the dynamic behaviour. This can be achieved by combining only limited data extracted from the original video footage with a symbolic data about the events registered on the scene, which is generated by 3D simulation synchronized with the original footage. Additionally, through incorporating some physical laws and the logics of dynamic behaviour directly in the 3D model of the visual scene, this framework allows to capture the behavioural patterns using simple syntactic pattern recognition methods. The extensive experiments with the prototype implementation prove in a convincing manner that the 3D simulation generates sufficiently rich data to allow analysing the dynamic behaviour in real-time with sufficient adequacy without the need to use precise physical data, using only a limited data about the objects on the scene, their location and dynamic characteristics. This research can have a wide applicability in different areas where the video analytics is necessary, ranging from public safety and video surveillance to marketing research to computer games and animation. Its limitations are linked to the dependence on some preliminary processing of the video footage which is still less detailed and computationally demanding than the methods which use directly the video frames of the original footage.
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Seeger, Matthias. "Bayesian Gaussian process models : PAC-Bayesian generalisation error bounds and sparse approximations." Thesis, University of Edinburgh, 2003. http://hdl.handle.net/1842/321.

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Non-parametric models and techniques enjoy a growing popularity in the field of machine learning, and among these Bayesian inference for Gaussian process (GP) models has recently received significant attention. We feel that GP priors should be part of the standard toolbox for constructing models relevant to machine learning in the same way as parametric linear models are, and the results in this thesis help to remove some obstacles on the way towards this goal. In the first main chapter, we provide a distribution-free finite sample bound on the difference between generalisation and empirical (training) error for GP classification methods. While the general theorem (the PAC-Bayesian bound) is not new, we give a much simplified and somewhat generalised derivation and point out the underlying core technique (convex duality) explicitly. Furthermore, the application to GP models is novel (to our knowledge). A central feature of this bound is that its quality depends crucially on task knowledge being encoded faithfully in the model and prior distributions, so there is a mutual benefit between a sharp theoretical guarantee and empirically well-established statistical practices. Extensive simulations on real-world classification tasks indicate an impressive tightness of the bound, in spite of the fact that many previous bounds for related kernel machines fail to give non-trivial guarantees in this practically relevant regime. In the second main chapter, sparse approximations are developed to address the problem of the unfavourable scaling of most GP techniques with large training sets. Due to its high importance in practice, this problem has received a lot of attention recently. We demonstrate the tractability and usefulness of simple greedy forward selection with information-theoretic criteria previously used in active learning (or sequential design) and develop generic schemes for automatic model selection with many (hyper)parameters. We suggest two new generic schemes and evaluate some of their variants on large real-world classification and regression tasks. These schemes and their underlying principles (which are clearly stated and analysed) can be applied to obtain sparse approximations for a wide regime of GP models far beyond the special cases we studied here.
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Giulini, Ilaria. "Generalization bounds for random samples in Hilbert spaces." Thesis, Paris, Ecole normale supérieure, 2015. http://www.theses.fr/2015ENSU0026/document.

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Ce travail de thèse porte sur l'obtention de bornes de généralisation pour des échantillons statistiques à valeur dans des espaces de Hilbert définis par des noyaux reproduisants. L'approche consiste à obtenir des bornes non asymptotiques indépendantes de la dimension dans des espaces de dimension finie, en utilisant des inégalités PAC-Bayesiennes liées à une perturbation Gaussienne du paramètre et à les étendre ensuite aux espaces de Hilbert séparables. On se pose dans un premier temps la question de l'estimation de l'opérateur de Gram à partir d'un échantillon i. i. d. par un estimateur robuste et on propose des bornes uniformes, sous des hypothèses faibles de moments. Ces résultats permettent de caractériser l'analyse en composantes principales indépendamment de la dimension et d'en proposer des variantes robustes. On propose ensuite un nouvel algorithme de clustering spectral. Au lieu de ne garder que la projection sur les premiers vecteurs propres, on calcule une itérée du Laplacian normalisé. Cette itération, justifiée par l'analyse du clustering en termes de chaînes de Markov, opère comme une version régularisée de la projection sur les premiers vecteurs propres et permet d'obtenir un algorithme dans lequel le nombre de clusters est déterminé automatiquement. On présente des bornes non asymptotiques concernant la convergence de cet algorithme, lorsque les points à classer forment un échantillon i. i. d. d'une loi à support compact dans un espace de Hilbert. Ces bornes sont déduites des bornes obtenues pour l'estimation d'un opérateur de Gram dans un espace de Hilbert. On termine par un aperçu de l'intérêt du clustering spectral dans le cadre de l'analyse d'images
This thesis focuses on obtaining generalization bounds for random samples in reproducing kernel Hilbert spaces. The approach consists in first obtaining non-asymptotic dimension-free bounds in finite-dimensional spaces using some PAC-Bayesian inequalities related to Gaussian perturbations and then in generalizing the results in a separable Hilbert space. We first investigate the question of estimating the Gram operator by a robust estimator from an i. i. d. sample and we present uniform bounds that hold under weak moment assumptions. These results allow us to qualify principal component analysis independently of the dimension of the ambient space and to propose stable versions of it. In the last part of the thesis we present a new algorithm for spectral clustering. It consists in replacing the projection on the eigenvectors associated with the largest eigenvalues of the Laplacian matrix by a power of the normalized Laplacian. This iteration, justified by the analysis of clustering in terms of Markov chains, performs a smooth truncation. We prove nonasymptotic bounds for the convergence of our spectral clustering algorithm applied to a random sample of points in a Hilbert space that are deduced from the bounds for the Gram operator in a Hilbert space. Experiments are done in the context of image analysis
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Cherief-Abdellatif, Badr-Eddine. "Contributions to the theoretical study of variational inference and robustness." Electronic Thesis or Diss., Institut polytechnique de Paris, 2020. http://www.theses.fr/2020IPPAG001.

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Cette thèse de doctorat traite de l'inférence variationnelle et de la robustesse en statistique et en machine learning. Plus précisément, elle se concentre sur les propriétés statistiques des approximations variationnelles et sur la conception d'algorithmes efficaces pour les calculer de manière séquentielle, et étudie les estimateurs basés sur le Maximum Mean Discrepancy comme règles d'apprentissage qui sont robustes à la mauvaise spécification du modèle.Ces dernières années, l'inférence variationnelle a été largement étudiée du point de vue computationnel, cependant, la littérature n'a accordé que peu d'attention à ses propriétés théoriques jusqu'à très récemment. Dans cette thèse, nous étudions la consistence des approximations variationnelles dans divers modèles statistiques et les conditions qui assurent leur consistence. En particulier, nous abordons le cas des modèles de mélange et des réseaux de neurones profonds. Nous justifions également d'un point de vue théorique l'utilisation de la stratégie de maximisation de l'ELBO, un critère numérique qui est largement utilisé dans la communauté VB pour la sélection de modèle et dont l'efficacité a déjà été confirmée en pratique. En outre, l'inférence Bayésienne offre un cadre d'apprentissage en ligne attrayant pour analyser des données séquentielles, et offre des garanties de généralisation qui restent valables même en cas de mauvaise spécification des modèles et en présence d'adversaires. Malheureusement, l'inférence Bayésienne exacte est rarement tractable en pratique et des méthodes d'approximation sont généralement employées, mais ces méthodes préservent-elles les propriétés de généralisation de l'inférence Bayésienne ? Dans cette thèse, nous montrons que c'est effectivement le cas pour certains algorithmes d'inférence variationnelle (VI). Nous proposons de nouveaux algorithmes tempérés en ligne et nous en déduisons des bornes de généralisation. Notre résultat théorique repose sur la convexité de l'objectif variationnel, mais nous soutenons que notre résultat devrait être plus général et présentons des preuves empiriques à l'appui. Notre travail donne des justifications théoriques en faveur des algorithmes en ligne qui s'appuient sur des méthodes Bayésiennes approchées.Une autre question d'intérêt majeur en statistique qui est abordée dans cette thèse est la conception d'une procédure d'estimation universelle. Cette question est d'un intérêt majeur, notamment parce qu'elle conduit à des estimateurs robustes, un thème d'actualité en statistique et en machine learning. Nous abordons le problème de l'estimation universelle en utilisant un estimateur de minimisation de distance basé sur la Maximum Mean Discrepancy. Nous montrons que l'estimateur est robuste à la fois à la dépendance et à la présence de valeurs aberrantes dans le jeu de données. Nous mettons également en évidence les liens qui peuvent exister avec les estimateurs de minimisation de distance utilisant la distance L2. Enfin, nous présentons une étude théorique de l'algorithme de descente de gradient stochastique utilisé pour calculer l'estimateur, et nous étayons nos conclusions par des simulations numériques. Nous proposons également une version Bayésienne de notre estimateur, que nous étudions à la fois d'un point de vue théorique et d'un point de vue computationnel
This PhD thesis deals with variational inference and robustness. More precisely, it focuses on the statistical properties of variational approximations and the design of efficient algorithms for computing them in an online fashion, and investigates Maximum Mean Discrepancy based estimators as learning rules that are robust to model misspecification.In recent years, variational inference has been extensively studied from the computational viewpoint, but only little attention has been put in the literature towards theoretical properties of variational approximations until very recently. In this thesis, we investigate the consistency of variational approximations in various statistical models and the conditions that ensure the consistency of variational approximations. In particular, we tackle the special case of mixture models and deep neural networks. We also justify in theory the use of the ELBO maximization strategy, a model selection criterion that is widely used in the Variational Bayes community and is known to work well in practice.Moreover, Bayesian inference provides an attractive online-learning framework to analyze sequential data, and offers generalization guarantees which hold even under model mismatch and with adversaries. Unfortunately, exact Bayesian inference is rarely feasible in practice and approximation methods are usually employed, but do such methods preserve the generalization properties of Bayesian inference? In this thesis, we show that this is indeed the case for some variational inference algorithms. We propose new online, tempered variational algorithms and derive their generalization bounds. Our theoretical result relies on the convexity of the variational objective, but we argue that our result should hold more generally and present empirical evidence in support of this. Our work presents theoretical justifications in favor of online algorithms that rely on approximate Bayesian methods. Another point that is addressed in this thesis is the design of a universal estimation procedure. This question is of major interest, in particular because it leads to robust estimators, a very hot topic in statistics and machine learning. We tackle the problem of universal estimation using a minimum distance estimator based on the Maximum Mean Discrepancy. We show that the estimator is robust to both dependence and to the presence of outliers in the dataset. We also highlight the connections that may exist with minimum distance estimators using L2-distance. Finally, we provide a theoretical study of the stochastic gradient descent algorithm used to compute the estimator, and we support our findings with numerical simulations. We also propose a Bayesian version of our estimator, that we study from both a theoretical and a computational points of view
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Lashkaripour, Rahmatollah. "Lower bounds and norms of operators on Lorentz sequence spaces." Thesis, Lancaster University, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.364315.

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Rammea, Lisema. "Computations and bounds for surfaces in weighted projective four-spaces." Thesis, University of Bath, 2009. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.507235.

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Many researchers have constructed examples of non general type surfaces in weighted projective spaces in various dimensions. Most of these constructions so far have been concentrated on complete intersections, and in the past three decades there has been a lot of success in this direction. Nowadays we have seen use of computer algebra systems to handle examples that are too cumbersome to do by hand. All smooth projective surfaces can be embedded in P5, but only few of them in P4. The most amazing fact is that the numerical invariants of any smooth surface in P4 must satisfy the double point formula. A natural question is whether there are any non general type surfaces in four dimensional weighted projective space, P4(w), which are not complete intersections. We believe that the answer is \yes, but they are not abundant". This thesis shows the �rst part, and justi�es the second part. That is, this thesis has two distinctive parts. First we prove that families of non general type surfaces in weighted projective four{space, P4(w) are rare by showing that their corresponding covers in straight P4, which are usually general type surfaces, are rare. In the second part we construct explicit examples of these rare objects in P4 using a technique involving sheaf cohomology and the Beilinson monad. We concentrate on the case of weights w = (1; 1; 1; 1; 2) for our particular examples. We present three explicit examples, one of which is symmetric. The main computer algebra system used is Macaulay2, Version 1.1 developed by D. Grayson and M. Stillman.
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Books on the topic "Sparse bound"

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Turtledove, Harry. Homeward Bound. New York: Del Rey/Ballantine Books, 2004.

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Turtledove, Harry. Homeward Bound. New York: Random House Publishing Group, 2004.

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Turtledove, Harry. Homeward bound. New York: Ballantine Books, 2005.

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Nikova, Svetla Iordanova. Bounds for designs in infinite polynomial metric spaces. [Eindhoven]: University Press Facilities, Eindhoven University of Technology, 1998.

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Schneck, Arne. Bounds for optimization of the reflection coefficient by constrained optimization in hardy spaces. Karlsruhe: Univ.-Verl. Karlsruhe, 2009.

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Public Art Development Trust (London, England), ed. The Thames archive project: Henry Bond Angela Bulloch. London: Public Art Development Trust, 2000.

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United States. Superintendent of Documents. Explorations in space: A collection of space-related publications to interest earth-bound astronauts of all ages. Washington, DC: Supt. of Docs., 1985.

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United States. National Aeronautics and Space Administration., ed. Development of a nondestructive vibration technique for bond assessment of space shuttle tiles: Final report. Orlando, Fla: Dept. of Mechanical and Aerospace Engineering, University of Central Florida, 1994.

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United States. Environmental Protection Agency. Office of Transportation and Air Quality. Bond requirements for nonroad spark-ignition engines: Frequently asked questions. Washington, D.C.]: U.S. Environmental Protection Agency, Office of Transportation and Air Quality, 2009.

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Copyright Paperback Collection (Library of Congress), ed. Honor Bound: Day of Honor Book 6: Star Trek: Deep Space Nine #11. New York: Pocket Books, 1997.

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Book chapters on the topic "Sparse bound"

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Schmitt, Michael. "An Improved VC Dimension Bound for Sparse Polynomials." In Learning Theory, 393–407. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-27819-1_27.

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Liu, Pan, and Fenglei Wang. "Sparse Acceleration Algorithm Based on Likelihood Upper Bound." In Advances in Intelligent Systems and Computing, 171–79. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-34387-3_21.

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Chen, Xi, Tim Randolph, Rocco A. Servedio, and Timothy Sun. "A Lower Bound on Cycle-Finding in Sparse Digraphs." In Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms, 2936–52. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2020. http://dx.doi.org/10.1137/1.9781611975994.178.

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Maurer, Andreas, Massimiliano Pontil, and Luca Baldassarre. "Lower Bounds for Sparse Coding." In Measures of Complexity, 359–70. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-21852-6_24.

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de Woot, Philippe. "New Spaces: Globalization of the Market Economy." In Should Prometheus Be Bound?, 25–37. London: Palgrave Macmillan UK, 2005. http://dx.doi.org/10.1057/9780230502062_3.

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van de Geer, Sara. "Lower Bounds for Sparse Quadratic Forms." In Lecture Notes in Mathematics, 223–31. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-32774-7_15.

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Sottile, Frank. "Lower bounds for sparse polynomial systems." In Real Solutions to Equations from Geometry, 77–90. Providence, Rhode Island: American Mathematical Society, 2011. http://dx.doi.org/10.1090/ulect/057/07.

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Waghid, Yusef. "Pedagogy Within Rhizomatic Spaces." In Pedagogy Out of Bounds, 65–70. Rotterdam: SensePublishers, 2014. http://dx.doi.org/10.1007/978-94-6209-616-5_7.

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Martín Pendás, Ángel, and Julia Contreras-García. "Topological Spaces." In Topological Approaches to the Chemical Bond, 9–28. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-13666-5_2.

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Krause, Ben, and Michael T. Lacey. "Sparse Bounds for Random Discrete Carleson Theorems." In 50 Years with Hardy Spaces, 317–32. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-59078-3_16.

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Conference papers on the topic "Sparse bound"

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Guitton, A. "Sparse Radon Transforms with Bound-Constrained Optimization." In 67th EAGE Conference & Exhibition. European Association of Geoscientists & Engineers, 2005. http://dx.doi.org/10.3997/2214-4609-pdb.1.a025.

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Pajovic, Milutin. "Misspecified Bayesian Cramér-Rao Bound for Sparse Bayesian." In 2018 IEEE Statistical Signal Processing Workshop (SSP). IEEE, 2018. http://dx.doi.org/10.1109/ssp.2018.8450780.

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Florescu, Anisia, Emilie Chouzenoux, Jean-Christophe Pesquet, and Silviu Ciochina. "Cramer-Rao bound for a sparse complex model." In 2014 10th International Conference on Communications (COMM). IEEE, 2014. http://dx.doi.org/10.1109/iccomm.2014.6866673.

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Saidi, Pouria, George Atia, and Azadeh Vosoughi. "Improved Block-Sparse Recovery Bound Using Cumulative Block Coherence." In 2020 54th Asilomar Conference on Signals, Systems, and Computers. IEEE, 2020. http://dx.doi.org/10.1109/ieeeconf51394.2020.9443546.

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Friedlander, B. "On the Cramer-Rao Bound for Sparse Linear Arrays." In 2020 54th Asilomar Conference on Signals, Systems, and Computers. IEEE, 2020. http://dx.doi.org/10.1109/ieeeconf51394.2020.9443292.

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Montanari, Andrea, and Elchanan Mossel. "Smooth compression, Gallager bound and nonlinear sparse-graph codes." In 2008 IEEE International Symposium on Information Theory - ISIT. IEEE, 2008. http://dx.doi.org/10.1109/isit.2008.4595436.

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Wang, Di, and Jinhui Xu. "Lower Bound of Locally Differentially Private Sparse Covariance Matrix Estimation." In Twenty-Eighth International Joint Conference on Artificial Intelligence {IJCAI-19}. California: International Joint Conferences on Artificial Intelligence Organization, 2019. http://dx.doi.org/10.24963/ijcai.2019/665.

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In this paper, we study the sparse covariance matrix estimation problem in the local differential privacy model, and give a non-trivial lower bound on the non-interactive private minimax risk in the metric of squared spectral norm. We show that the lower bound is actually tight, as it matches a previous upper bound. Our main technique for achieving this lower bound is a general framework, called General Private Assouad Lemma, which is a considerable generalization of the previous private Assouad lemma and can be used as a general method for bounding the private minimax risk of matrix-related estimation problems.
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Hashemi, Abolfazl, and Haris Vikalo. "Recovery of sparse signals via Branch and Bound Least-Squares." In 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2017. http://dx.doi.org/10.1109/icassp.2017.7953060.

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Khan, Diba, and Kristine L. Bell. "Explicit Ziv-Zakai bound for DOA estimation with sparse linear arrays." In 2009 3rd IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP). IEEE, 2009. http://dx.doi.org/10.1109/camsap.2009.5413287.

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Koochakzadeh, Ali, and Piya Pal. "On saturation of the Cramér Rao Bound for Sparse Bayesian Learning." In 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2017. http://dx.doi.org/10.1109/icassp.2017.7952723.

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Reports on the topic "Sparse bound"

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Clark, Donald L., Stefan M. Kirby, and Charles G. Oviatt. Geologic Map of the Rush Valley 30' X 60' Quadrangle, Tooele, Utah, and Salt Lake Counties, Utah. Utah Geological Survey, August 2023. http://dx.doi.org/10.34191/m-294dm.

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The Rush Valley 30' x 60' quadrangle extends southwest and west from the greater Salt Lake City–Provo metropolitan area with land use varied between public, military, Indian reservation, and private. This 1:62,500-scale geologic map will aid the proper management of land, water, and other resources. The map area lies within the eastern Basin and Range Province. Mountain ranges are composed of unexposed basement rocks overlain by exposed Neoproterozoic through Triassic rocks that are about 10.4 miles (16.8 km) thick, and by numerous Tertiary sedimentary and volcanic units (~47 to 20 Ma). The intervening valleys include bedrock covered with Miocene-Pliocene? rocks (~11 to 4 Ma) and Neogene-Quaternary surficial deposits. The map area is on the southern flank of the Uinta-Tooele structural zone. This area is in the Charleston-Nebo (Provo) salient of the Sevier fold-thrust belt and some thrust faults are exposed, but the overall Sevier belt geometry is obscured by extensive Cenozoic cover and later faulting. Following Sevier deformation, calk-alkaline volcanism occurred from several Paleogene volcanic centers (42 to 25 Ma). Extensional tectonism created the distinctive basin and range topography from about 20 Ma to the present. Early extensional basin fill includes Miocene sedimentary and volcanic rocks followed by Pliocene-Holocene surficial deposits primarily from lacustrine and alluvial depositional environments. Valley areas were covered by late Pleistocene Lake Bonneville, and deposits are associated with three levels of regional shorelines. Normal faults cut the ranges and are known to bound some valley margins where not concealed. Although deep drill hole data are relatively sparse, gravity data were used to help constrain basin geometries.
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Mezzacappa, Anthony, Eirik Endeve, Cory D. Hauck, and Yulong Xing. Bound-Preserving Discontinuous Galerkin Methods for Conservative Phase Space Advection in Curvilinear Coordinates. Office of Scientific and Technical Information (OSTI), February 2015. http://dx.doi.org/10.2172/1394128.

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Jacobs, Timothy, and Jacob Hedrick. PR-457-14201-R03 Variable NG Composition Effects in LB 2S Compressor Engines - Prediction Enhancement. Chantilly, Virginia: Pipeline Research Council International, Inc. (PRCI), August 2017. http://dx.doi.org/10.55274/r0011406.

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Phase II of the project has focused on improving the initial analysis performed in the first phase by enhancing the various aspects of predictive combustion for lean burn spark ignition natural gas engines under variable composition fueling. These enhancements have incorporated validation data from a Cooper-Bessemer GMVH-10C3 engine located in New Jersey, which improves upon the lack of field data to bound the scope of composition variation. In simulation related endeavors, effort was made to improve the fundamental combustion physics related parameters, namely laminar flame speed, by developing a code base for distributed computing of the chemical kinetics solver, Cantera, and was key to improving upon the chemistry modeling used in the previous phase. Methods to improve numerical convergence were employed to reduce the time to solve large mechanisms, such as the Saudi Aramco Mechanism (v1.3). Modeling of pre-chamber combustion from first principles, common input experimental heat release analysis and simulated heat release generation were additional components of improving model matching with pre-chambered engines. In its current state, manual optimization is required to tune the heat release curves based on guesses about the initial charge mass state, scavenging efficiency, fuel delivery and thereby the trapped equivalence ratio.
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Oliynyk, Kateryna, and Matteo Ciantia. Application of a finite deformation multiplicative plasticity model with non-local hardening to the simulation of CPTu tests in a structured soil. University of Dundee, December 2021. http://dx.doi.org/10.20933/100001230.

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In this paper an isotropic hardening elastoplastic constitutive model for structured soils is applied to the simulation of a standard CPTu test in a saturated soft structured clay. To allow for the extreme deformations experienced by the soil during the penetration process, the model is formulated in a fully geometric non-linear setting, based on: i) the multiplicative decomposition of the deformation gradient into an elastic and a plastic part; and, ii) on the existence of a free energy function to define the elastic behaviour of the soil. The model is equipped with two bonding-related internal variables which provide a macroscopic description of the effects of clay structure. Suitable hardening laws are employed to describe the structure degradation associated to plastic deformations. The strain-softening associated to bond degradation usually leads to strain localization and consequent formation of shear bands, whose thickness is dependent on the characteristics of the microstructure (e.g, the average grain size). Standard local constitutive models are incapable of correctly capturing this phenomenon due to the lack of an internal length scale. To overcome this limitation, the model is framed using a non-local approach by adopting volume averaged values for the internal state variables. The size of the neighbourhood over which the averaging is performed (characteristic length) is a material constant related to the microstructure which controls the shear band thickness. This extension of the model has proven effective in regularizing the pathological mesh dependence of classical finite element solutions in the post-localization regime. The results of numerical simulations, conducted for different soil permeabilities and bond strengths, show that the model captures the development of plastic deformations induced by the advancement of the cone tip; the destructuration of the clay associated with such plastic deformations; the space and time evolution of pore water pressure as the cone tip advances. The possibility of modelling the CPTu tests in a rational and computationally efficient way opens a promising new perspective for their interpretation in geotechnical site investigations.
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Bano, Masooda, and Zeena Oberoi. Embedding Innovation in State Systems: Lessons from Pratham in India. Research on Improving Systems of Education (RISE), December 2020. http://dx.doi.org/10.35489/bsg-rise-wp_2020/058.

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The learning crisis in many developing countries has led to searches for innovative teaching models. Adoption of innovation, however, disrupts routine and breaks institutional inertia, requiring government employees to change their way of working. Introducing and embedding innovative methods for improving learning outcomes within state institutions is thus a major challenge. For NGO-led innovation to have largescale impact, we need to understand: (1) what factors facilitate its adoption by senior bureaucracy and political elites; and (2) how to incentivise district-level field staff and school principals and teachers, who have to change their ways of working, to implement the innovation? This paper presents an ethnographic study of Pratham, one of the most influential NGOs in the domain of education in India today, which has attracted growing attention for introducing an innovative teaching methodology— Teaching at the Right Level (TaRL) – with evidence of improved learning outcomes among primary-school students and adoption by a number of states in India. The case study suggests that while a combination of factors, including evidence of success, ease of method, the presence of a committed bureaucrat, and political opportunity are key to state adoption of an innovation, exposure to ground realities, hand holding and confidence building, informal interactions, provision of new teaching resources, and using existing lines of communication are core to ensuring the co-operation of those responsible for actual implementation. The Pratham case, however, also confirms existing concerns that even when NGO-led innovations are successfully implemented at a large scale, their replication across the state and their sustainability remain a challenge. Embedding good practice takes time; the political commitment leading to adoption of an innovation is often, however, tied to an immediate political opportunity being exploited by the political elites. Thus, when political opportunity rather than a genuine political will creates space for adoption of an innovation, state support for that innovation fades away before the new ways of working can replace the old habits. In contexts where states lack political will to improve learning outcomes, NGOs can only hope to make systematic change in state systems if, as in the case of Pratham, they operate as semi-social movements with large cadres of volunteers. The network of volunteers enables them to slow down and pick up again in response to changing political contexts, instead of quitting when state actors withdraw. Involving the community itself does not automatically lead to greater political accountability. Time-bound donor-funded NGO projects aiming to introduce innovation, however large in scale, simply cannot succeed in bringing about systematic change, because embedding change in state institutions lacking political will requires years of sustained engagement.
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Litaor, Iggy, James Ippolito, Iris Zohar, and Michael Massey. Phosphorus capture recycling and utilization for sustainable agriculture using Al/organic composite water treatment residuals. United States Department of Agriculture, January 2015. http://dx.doi.org/10.32747/2015.7600037.bard.

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Objectives: 1) develop a thorough understanding of the sorption mechanisms of Pi and Po onto the Al/O- WTR; 2) determine the breakthrough range of the composite Al/O-WTR during P capturing from agro- wastewaters; and 3) critically evaluate the performance of the composite Al/O-WTR as a fertilizer using selected plants grown in lysimeters and test-field studies. Instead of lysimeters we used pots (Israel) and one- liter cone-tainers (USA). We conducted one field study but in spite of major pretreatments the soils still exhibited high enough P from previous experiments so no differences between control and P additions were noticeable. Due to time constrains the field study was discontinued. Background: Phosphorous, a non-renewable resource, has been applied extensively in fields to increase crop yield, yet consequently has increased the potential of waterway eutrophication. Our proposal impetus is the need to develop an innovative method of P capturing, recycling and reuse that will sustain agricultural productivity while concurrently reducing the level of P discharge from and to agricultural settings. Major Conclusions & Achievements: An innovative approach was developed for P removal from soil leachate, dairy wastewater (Israel), and swine effluents (USA) using Al-based water treatment residuals (Al- WTR) to create an organic-Al-WTR composite (Al/O-WTR), potentially capable of serving as a P fertilizer source. The Al-WTR removed 95% inorganic-P, 80% to 99.9% organic P, and over 60% dissolved organic carbon from the agro-industrial waste streams. Organic C accumulation on particles surfaces possibly enhanced weak P bonding and facilitated P desorption. Analysis by scanning electron microscope (SEM- EDS), indicated that P was sparsely sorbed on both calcic and Al (hydr)oxide surfaces. Sorption of P onto WW-Al/O-WTR was reversible due to weak Ca-P and Al-P bonds induced by the slight alkaline nature and in the presence of organic moieties. Synchrotron-based microfocused X-ray fluorescence (micro-XRF) spectrometry, bulk P K-edge X-ray absorption near edge structure spectroscopy (XANES), and P K-edge micro-XANES spectroscopy indicated that adsorption was the primary P retention mechanism in the Al- WTR materials. However, distinct apatite- or octocalciumphosphatelike P grains were also observed. Synchrotron micro-XRF mapping further suggested that exposure of the aggregate exteriors to wastewater caused P to diffuse into the porous Al-WTR aggregates. Organic P species were not explicitly identified via P K-edge XANES despite high organic matter content, suggesting that organic P may have been predominantly associated with mineral surfaces. In screen houses experiments (Israel) we showed that the highest additions of Al/O-WTR (5 and 7 g kg⁻¹) produced the highest lettuce (Lactuca sativa L. var. longifolial) yield. Lettuce yield and P concentration were similar across treatments, indicating that Al/O- WTR can provide sufficient P to perform similarly to common fertilizers. A greenhouse study (USA) was utilized to compare increasing rates of swine wastewater derived Al/O-WTR and inorganic P fertilizer (both applied at 33.6, 67.3, and 134.5 kg P₂O₅ ha⁻¹) to supply plant-available P to spring wheat (TriticumaestivumL.) in either sandy loam or sandy clay loam soil. Spring wheat straw and grain P uptake were comparable across all treatments in the sandy loam, while Al/O-WTR application to the sandy clay loam reduced straw and grain P uptake. The Al/O-WTR did not affect soil organic P concentrations, but did increase phosphatase activity in both soils; this suggests that Al/O-WTR application stimulated microorganisms and enhance the extent to which microbial communities can mineralize Al/O-WTR-bound organic P. Implications: Overall, results suggest that creating a new P fertilizer from Al-WTR and agro-industrial waste sources may be a feasible alternative to mining inorganic P fertilizer sources, while protecting the environment from unnecessary waste disposal.
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