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Academic literature on the topic 'Gradient bound'

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Published: 9 March 2023
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Journal articles on the topic "Gradient bound"

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ARONSSON, GUNNAR. "INTERPOLATION UNDER A GRADIENT BOUND." Journal of the Australian Mathematical Society 87, no. 01 (August 2009): 19. http://dx.doi.org/10.1017/s1446788709000044.

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Chang, Ting-Jui, and Shahin Shahrampour. "On Online Optimization: Dynamic Regret Analysis of Strongly Convex and Smooth Problems." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 8 (May 18, 2021): 6966–73. http://dx.doi.org/10.1609/aaai.v35i8.16858.

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The regret bound of dynamic online learning algorithms is often expressed in terms of the variation in the function sequence (V_T) and/or the path-length of the minimizer sequence after T rounds. For strongly convex and smooth functions, Zhang et al. (2017) establish the squared path-length of the minimizer sequence (C*_{2,T}) as a lower bound on regret. They also show that online gradient descent (OGD) achieves this lower bound using multiple gradient queries per round. In this paper, we focus on unconstrained online optimization. We first show that a preconditioned variant of OGD achieves O(min{C*_T,C*_{2,T}}) with one gradient query per round (C*_T refers to the normal path-length). We then propose online optimistic Newton (OON) method for the case when the first and second order information of the function sequence is predictable. The regret bound of OON is captured via the quartic path-length of the minimizer sequence (C*_{4,T}), which can be much smaller than C*_{2,T}. We finally show that by using multiple gradients for OGD, we can achieve an upper bound of O(min{C*_{2,T},V_T}) on regret.
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Li, Dong, Fan Wang, and Kai Yang. "An improved gradient bound for 2D MBE." Journal of Differential Equations 269, no. 12 (December 2020): 11165–71. http://dx.doi.org/10.1016/j.jde.2020.08.045.

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De Silva, Daniela, and David Jerison. "A gradient bound for free boundary graphs." Communications on Pure and Applied Mathematics 64, no. 4 (December 13, 2010): 538–55. http://dx.doi.org/10.1002/cpa.20354.

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Hao, Jia, Winfield Zhao, Jeong Min Oh, and Keyue Shen. "A Pillar-Free Diffusion Device for Studying Chemotaxis on Supported Lipid Bilayers." Micromachines 12, no. 10 (October 16, 2021): 1254. http://dx.doi.org/10.3390/mi12101254.

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Chemotactic cell migration plays a crucial role in physiological and pathophysiological processes. In tissues, cells can migrate not only through extracellular matrix (ECM), but also along stromal cell surfaces via membrane-bound receptor–ligand interactions to fulfill critical functions. However, there remains a lack of models recapitulating chemotactic migration mediated through membrane-bound interactions. Here, using micro-milling, we engineered a multichannel diffusion device that incorporates a chemoattractant gradient and a supported lipid bilayer (SLB) tethered with membrane-bound factors that mimics stromal cell membranes. The chemoattractant channels are separated by hydrogel barriers from SLB in the cell loading channel, which enable precise control of timing and profile of the chemokine gradients applied on cells interacting with SLB. The hydrogel barriers are formed in pillar-free channels through a liquid pinning process, which eliminates complex cleanroom-based fabrications and distortion of chemoattractant gradient by pillars in typical microfluidic hydrogel barrier designs. As a proof-of-concept, we formed an SLB tethered with ICAM-1, and demonstrated its lateral mobility and different migratory behavior of Jurkat T cells on it from those on immobilized ICAM-1, under a gradient of chemokine CXCL12. Our platform can thus be widely used to investigate membrane-bound chemotaxis such as in cancer, immune, and stem cells.
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Wang, Zhengxing, Yuke Wang, Shumao Wang, Bin Li, and Hu Wang. "Effect of Longitudinal Gradient on 3D Face Stability of Circular Tunnel in Undrained Clay." Advances in Civil Engineering 2020 (August 19, 2020): 1–12. http://dx.doi.org/10.1155/2020/5846151.

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The longitudinal gradient existed in shield-driven tunnel crossing river or channel has a longitudinal gradient, which is often ignored in most stability analyses of the tunnel face. Considering the influence of the longitudinal gradient into A(a) continuous velocity field, the present paper, conducting a limit analysis of the tunnel face in undrained clay, adopted to yield the upper-bound solutions of the limit pressure supporting on a three-dimensional tunnel face. The least upper bounds of the collapse and blow-out pressures can be obtained by conducting an optimization procedure. These upper-bound solutions are given in the design charts, which provide a simple way to assess the range of the limit pressure in practice. The influence of the longitudinal gradient becomes more significant with the increase of γD/su and C/D. The blow-out pressure for tunneling in a downward movement could be overestimated and the collapse pressure for tunneling in an upward movement could be conversely underestimated, with ignoring the influence of the longitudinal gradient.
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Bovier, Anton. "Sharp upper bounds on perfect retrieval in the Hopfield model." Journal of Applied Probability 36, no. 3 (September 1999): 941–50. http://dx.doi.org/10.1239/jap/1032374647.

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We prove a sharp upper bound on the number of patterns that can be stored in the Hopfield model if the stored patterns are required to be fixed points of the gradient dynamics. We also show corresponding bounds on the one-step convergence of the sequential gradient dynamics. The bounds coincide with the known lower bounds and confirm the heuristic expectations. The proof is based on a crucial idea of Loukianova (1997) using the negative association properties of some random variables arising in the analysis.
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Bovier, Anton. "Sharp upper bounds on perfect retrieval in the Hopfield model." Journal of Applied Probability 36, no. 03 (September 1999): 941–50. http://dx.doi.org/10.1017/s0021900200017708.

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We prove a sharp upper bound on the number of patterns that can be stored in the Hopfield model if the stored patterns are required to be fixed points of the gradient dynamics. We also show corresponding bounds on the one-step convergence of the sequential gradient dynamics. The bounds coincide with the known lower bounds and confirm the heuristic expectations. The proof is based on a crucial idea of Loukianova (1997) using the negative association properties of some random variables arising in the analysis.
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Albin, Nathan, Sergio Conti, and Vincenzo Nesi. "Improved bounds for composites and rigidity of gradient fields." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 463, no. 2084 (June 13, 2007): 2031–48. http://dx.doi.org/10.1098/rspa.2007.1863.

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We determine an improved lower bound for the conductivity of three-component composite materials. Our bound is strictly larger than the well-known Hashin–Shtrikman bound outside the regime where the latter is known to be optimal. The main ingredient of our result is a new quantitative rigidity estimate for gradient fields in two dimensions.
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Kuusi, Tuomo, and Giuseppe Mingione. "The Wolff gradient bound for degenerate parabolic equations." Journal of the European Mathematical Society 16, no. 4 (2014): 835–92. http://dx.doi.org/10.4171/jems/449.

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Dissertations / Theses on the topic "Gradient bound"

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COLOMBO, GIULIO. "GLOBAL GRADIENT BOUNDS FOR SOLUTIONS OF PRESCRIBED MEAN CURVATURE EQUATIONS ON RIEMANNIAN MANIFOLDS." Doctoral thesis, Università degli Studi di Milano, 2021. http://hdl.handle.net/2434/813095.

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This thesis is concerned with the study of qualitative properties of solutions of the minimal surface equation and of a class of prescribed mean curvature equations on complete Riemannian manifolds. We derive global gradient bounds for non-negative solutions of such equations on manifolds satisfying a uniform Ricci lower bound and we obtain Liouville-type theorems and other rigidity results on Riemannian manifolds with non-negative Ricci curvature. The proof of the aforementioned global gradient bounds for non-negative solutions u is based on the application of the maximum principle to an elliptic differential inequality satisfied by a suitable auxiliary function z=f(u,|Du|), in the spirit of Bernstein’s method of a priori estimates for nonlinear PDEs and of Yau’s proof of global gradient bounds for harmonic functions on complete Riemannian manifolds. The particular choice of the auxiliary function z parallels the one in Korevaar’s proof of a priori gradient estimates for the prescribed mean curvature equation in Euclidean space. The rigidity results obtained in the last part of the thesis include a Liouville theorem for positive solutions of the minimal surface equation on complete Riemannian manifolds with non-negative Ricci curvature, a splitting theorem for complete parabolic manifolds of non-negative sectional curvature supporting non-constant solutions with linear growth of the minimal surface equation, and a splitting theorem for domains of complete parabolic manifolds with non-negative Ricci curvature supporting non-constant solutions of overdetermined problems involving the mean curvature operator.
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Zhang, Shao-Yong. "Formulation et résolution de problèmes à variables mixtes. Application à la conception et à la modélisation de procédés chimiques." Toulouse, INPT, 1989. http://www.theses.fr/1989INPT043G.

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Presentation d'une procedure d'optimisation en variables mixtes pour la conception de procedes et l'identification de modeles de genie chimique. Developpement d'un algorithme de programmation mixte base sur un principe de decomposition, de projection et de relaxation permettant le traitement des problemes non lineaires a variables non necessairement separables. Presentation d'une procedure de decomposition de superstructure permettant de denombrer l'ensemble de toutes les variables discretes et continues du probleme. Illustration par deux exemples d'application: conception optimale d'un procede comportant un ensemble de reacteurs-separateurs et identification d'un modele de representation d'une operation de traitement d'effluents aqueux
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Nee, Colm. "Sharp gradient bounds for the diffusion semigroup." Thesis, Imperial College London, 2011. http://hdl.handle.net/10044/1/9105.

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Precise regularity estimates on diffusion semigroups are more than a mere theoretical curiosity. They play a fundamental role in deducing sharp error bounds for higher-order particle methods. In this thesis error bounds which are of consequence in iterated applications of Wiener space cubature (Lyons and Victoir [29]) and a related higher-order method by Kusuoka [21] are considered. Regularity properties for a wide range of diffusion semigroups are deduced. In particular, semigroups corresponding to solutions of stochastic differential equations (SDEs) with non-smooth and degenerate coefficients. Precise derivative bounds for these semigroups are derived as functions of time, and are obtained under a condition, known as the UFG condition, which is much weaker than Hormander's criterion for hypoellipticity. Moreover, very relaxed differentiability assumptions on the coefficients are imposed. Proofs of exact error bounds for the associated higher-order particle methods are deduced, where no such source already exists. In later chapters, a local version of the UFG condition - `the LFG condition' - is introduced and is used to obtain local gradient bounds and local smoothness properties of the semigroup. The condition's generality is demonstrated. In later chapters, it is shown that the V0 condition, proposed by Crisan and Ghazali [8], may be completely relaxed. Sobolev-type gradient bounds are established for the semigroup under very general differentiability assumptions of the vector fields. The problem of considering regularity properties for a semigroup which has been perturbed by a potential, and a Langrangian term are also considered. These prove important in the final chapter, in which we discuss existence and uniqueness of solutions to the Cauchy problem.
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Arlery, Fabien. "Formes d’ondes MSPSR, traitements et performances associés." Thesis, Evry, Institut national des télécommunications, 2017. http://www.theses.fr/2017TELE0005/document.

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Aujourd’hui, les systèmes MSPSR (Multi-Static Primary Surveillance Radar) passifs se sont installés de manière durable dans le paysage de la surveillance aérienne [1]. L’intérêt que suscitent ces nouveaux systèmes provient du fait qu’en comparaison aux radars mono-statiques utilisés actuellement, les systèmes MSPSR reposent sur une distribution spatiale d’émetteurs et de récepteurs offrant des avantages en termes de fiabilité (redondance), de coûts (absence de joints tournants et émetteurs moins puissants) et de performances (diversité spatiale). Toutefois, le défaut majeur du MSPSR passif réside en l’absence de formes d’ondes dédiées due à l’exploitation d’émetteurs d’opportunités tels que les émetteurs de radio FM (Frequency Modulation) et/ou de DVB-T (Digital Video Broadcasting-Terrestrial) [2]. Afin de pallier à ce défaut, il est envisagé d’utiliser des émetteurs dédiés permettant l’emploi de formes d’ondes optimisées pour une application radar, on parle alors de MSPSR actif. Cette thèse se place dans ce cadre et a pour objectif d’étudier et de définir la ou les formes d’ondes ainsi que les traitements associés permettant d’atteindre de meilleurs performances : une meilleure flexibilité sur la disposition du système (positionnement des émetteurs libres), une continuité de service (non dépendance d’un système tiers) et de meilleurs performances radars (e.g. en terme de précision des mesures, détections, …). Dans ce but, cette thèse étudie : - Les critères de sélection des codes : comportement des fonctions d’ambiguïtés, PAPR (Peak to Average Power Ratio), efficacité spectrale, etc... ; - Les formes d’ondes utilisées en télécommunication (scrambling code, OFDM) afin d’identifier leur possible réemploi pour une application radar ; - L’utilisation d’algorithmes cycliques pour générer des familles de séquences adaptées à notre problème ; - Une approche basée sur une descente de gradient afin de générer des familles de codes de manière plus efficiente ; - Et l’évaluation des performances de ces différents algorithmes à travers l’établissement d’une borne supérieure sur le niveau maximum des lobes secondaires et à travers le dépouillement des données enregistrées suite à des campagnes d’essais
Nowadays, MSPSR (Multi-Static Primary Surveillance Radar) systems are sustainably settled in air surveillance program [1]. Compared to mono-static radar currently in use, an MSPSR system is based on a sparse network of transmitters (Tx) and receivers (Rx) interconnected to a Central Unit and offers advantages in terms of reliability, cost and performance.Two kinds of MSPSR systems exist: the Passive form and the Active one. While the Passive MSPSR uses transmitters of opportunity such as radio Frequency Modulation (FM) transmitters and/or Digital Video Broadcasting-Terrestrial (DVB-T) transmitters [2], the Active MSPSR uses dedicated transmitters, which emit a waveform that is controlled and designed for a radar application. Each receiver processes the signal coming from all transmitters and reflected on the targets; and the Central Unit restores the target location by intersecting “ellipsoids” from all (transmitter, receiver) pairs. Compared to passive MSPSR, the main advantages of the active MSPSR are the use of dedicated waveforms that allow reaching better performances (like a better association of the transmitters’ contributions at the receiver level); more flexibility in the deployment of transmitters and receivers station (in order to meet the requirements in localisation accuracy and in horizontal and altitude coverages); and the guarantee of having a service continuity. On this purpose, this thesis analyses the differents codes criteria such as the ambiguity function behaviour, the PAPR (Peak to Average Power Ratio), the spectrum efficiency, etc... . Then, in order to find dedicated waveforms for MSPSR systems, one solution is to find easily-constructed families of sequences. Thus building on the works carried out by the Telecommunication field for solving multi-user issues, this document investigates the application of spreading codes and OFDM signals in MSPSR concept. Besides, another solution is to directly generate a set of sequences. Based on cyclic algorithms in [3] we derive a new algorithm that allows to optimize sets of sequences. Similarly, using a gradient descent approach, we develop a more efficient algorithm than the cyclic one. Finally, in order to evaluate the performances of the different algorithms, this thesis generalizes the Levenshtein Bound, establishes new lower bounds on the PSLR (Peak Sidelobe Level Ratio) in mismatched filter case, and studies real data recorded during some trials
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Cheng, Jianqiang. "Stochastic Combinatorial Optimization." Thesis, Paris 11, 2013. http://www.theses.fr/2013PA112261.

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Dans cette thèse, nous étudions trois types de problèmes stochastiques : les problèmes avec contraintes probabilistes, les problèmes distributionnellement robustes et les problèmes avec recours. Les difficultés des problèmes stochastiques sont essentiellement liées aux problèmes de convexité du domaine des solutions, et du calcul de l’espérance mathématique ou des probabilités qui nécessitent le calcul complexe d’intégrales multiples. A cause de ces difficultés majeures, nous avons résolu les problèmes étudiées à l’aide d’approximations efficaces.Nous avons étudié deux types de problèmes stochastiques avec des contraintes en probabilités, i.e., les problèmes linéaires avec contraintes en probabilité jointes (LLPC) et les problèmes de maximisation de probabilités (MPP). Dans les deux cas, nous avons supposé que les variables aléatoires sont normalement distribués et les vecteurs lignes des matrices aléatoires sont indépendants. Nous avons résolu LLPC, qui est un problème généralement non convexe, à l’aide de deux approximations basée sur les problèmes coniques de second ordre (SOCP). Sous certaines hypothèses faibles, les solutions optimales des deux SOCP sont respectivement les bornes inférieures et supérieures du problème du départ. En ce qui concerne MPP, nous avons étudié une variante du problème du plus court chemin stochastique contraint (SRCSP) qui consiste à maximiser la probabilité de la contrainte de ressources. Pour résoudre ce problème, nous avons proposé un algorithme de Branch and Bound pour calculer la solution optimale. Comme la relaxation linéaire n’est pas convexe, nous avons proposé une approximation convexe efficace. Nous avons par la suite testé nos algorithmes pour tous les problèmes étudiés sur des instances aléatoires. Pour LLPC, notre approche est plus performante que celles de Bonferroni et de Jaganathan. Pour MPP, nos résultats numériques montrent que notre approche est là encore plus performante que l’approximation des contraintes probabilistes individuellement.La deuxième famille de problèmes étudiés est celle relative aux problèmes distributionnellement robustes où une partie seulement de l’information sur les variables aléatoires est connue à savoir les deux premiers moments. Nous avons montré que le problème de sac à dos stochastique (SKP) est un problème semi-défini positif (SDP) après relaxation SDP des contraintes binaires. Bien que ce résultat ne puisse être étendu au cas du problème multi-sac-à-dos (MKP), nous avons proposé deux approximations qui permettent d’obtenir des bornes de bonne qualité pour la plupart des instances testées. Nos résultats numériques montrent que nos approximations sont là encore plus performantes que celles basées sur les inégalités de Bonferroni et celles plus récentes de Zymler. Ces résultats ont aussi montré la robustesse des solutions obtenues face aux fluctuations des distributions de probabilités. Nous avons aussi étudié une variante du problème du plus court chemin stochastique. Nous avons prouvé que ce problème peut se ramener au problème de plus court chemin déterministe sous certaine hypothèses. Pour résoudre ce problème, nous avons proposé une méthode de B&B où les bornes inférieures sont calculées à l’aide de la méthode du gradient projeté stochastique. Des résultats numériques ont montré l’efficacité de notre approche. Enfin, l’ensemble des méthodes que nous avons proposées dans cette thèse peuvent s’appliquer à une large famille de problèmes d’optimisation stochastique avec variables entières
In this thesis, we studied three types of stochastic problems: chance constrained problems, distributionally robust problems as well as the simple recourse problems. For the stochastic programming problems, there are two main difficulties. One is that feasible sets of stochastic problems is not convex in general. The other main challenge arises from the need to calculate conditional expectation or probability both of which are involving multi-dimensional integrations. Due to the two major difficulties, for all three studied problems, we solved them with approximation approaches.We first study two types of chance constrained problems: linear program with joint chance constraints problem (LPPC) as well as maximum probability problem (MPP). For both problems, we assume that the random matrix is normally distributed and its vector rows are independent. We first dealt with LPPC which is generally not convex. We approximate it with two second-order cone programming (SOCP) problems. Furthermore under mild conditions, the optimal values of the two SOCP problems are a lower and upper bounds of the original problem respectively. For the second problem, we studied a variant of stochastic resource constrained shortest path problem (called SRCSP for short), which is to maximize probability of resource constraints. To solve the problem, we proposed to use a branch-and-bound framework to come up with the optimal solution. As its corresponding linear relaxation is generally not convex, we give a convex approximation. Finally, numerical tests on the random instances were conducted for both problems. With respect to LPPC, the numerical results showed that the approach we proposed outperforms Bonferroni and Jagannathan approximations. While for the MPP, the numerical results on generated instances substantiated that the convex approximation outperforms the individual approximation method.Then we study a distributionally robust stochastic quadratic knapsack problems, where we only know part of information about the random variables, such as its first and second moments. We proved that the single knapsack problem (SKP) is a semedefinite problem (SDP) after applying the SDP relaxation scheme to the binary constraints. Despite the fact that it is not the case for the multidimensional knapsack problem (MKP), two good approximations of the relaxed version of the problem are provided which obtain upper and lower bounds that appear numerically close to each other for a range of problem instances. Our numerical experiments also indicated that our proposed lower bounding approximation outperforms the approximations that are based on Bonferroni's inequality and the work by Zymler et al.. Besides, an extensive set of experiments were conducted to illustrate how the conservativeness of the robust solutions does pay off in terms of ensuring the chance constraint is satisfied (or nearly satisfied) under a wide range of distribution fluctuations. Moreover, our approach can be applied to a large number of stochastic optimization problems with binary variables.Finally, a stochastic version of the shortest path problem is studied. We proved that in some cases the stochastic shortest path problem can be greatly simplified by reformulating it as the classic shortest path problem, which can be solved in polynomial time. To solve the general problem, we proposed to use a branch-and-bound framework to search the set of feasible paths. Lower bounds are obtained by solving the corresponding linear relaxation which in turn is done using a Stochastic Projected Gradient algorithm involving an active set method. Meanwhile, numerical examples were conducted to illustrate the effectiveness of the obtained algorithm. Concerning the resolution of the continuous relaxation, our Stochastic Projected Gradient algorithm clearly outperforms Matlab optimization toolbox on large graphs
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Piovano, Paulo. "Evolution and Regularity Results for Epitaxially Strained Thin Films and Material Voids." Research Showcase @ CMU, 2012. http://repository.cmu.edu/dissertations/96.

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In this dissertation we study free boundary problems that model the evolution of interfaces in the presence of elasticity, such as thin film profiles and material void boundaries. These problems are characterized by the competition between the elastic bulk energy and the anisotropic surface energy. First, we consider the evolution equation with curvature regularization that models the motion of a two-dimensional thin film by evaporation-condensation on a rigid substrate. The film is strained due to the mismatch between the crystalline lattices of the two materials and anisotropy is taken into account. We present the results contained in [62] where the author establishes short time existence, uniqueness and regularity of the solution using De Giorgi’s minimizing movements to exploit the L2 -gradient flow structure of the equation. This seems to be the first analytical result for the evaporation-condensation case in the presence of elasticity. Second, we consider the relaxed energy introduced in [20] that depends on admissible pairs (E, u) of sets E and functions u defined only outside of E. For dimension three this energy appears in the study of the material voids in solids, where the pairs (E, u) are interpreted as the admissible configurations that consist of void regions E in the space and of displacements u of the atoms of the crystal. We provide the precise mathematical framework that guarantees the existence of minimal energy pairs (E, u). Then, we establish that for every minimal configuration (E, u), the function u is C 1,γ loc -regular outside an essentially closed subset of E. No hypothesis of starshapedness is assumed on the voids and all the results that are contained in [18] hold true for every dimension d ≥ 2.
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Adhikari, Shishir Raj. "STATISTICAL PHYSICS OF CELL ADHESION COMPLEXES AND MACHINE LEARNING." Case Western Reserve University School of Graduate Studies / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=case1562167640484477.

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Chinot, Geoffrey. "Localization methods with applications to robust learning and interpolation." Electronic Thesis or Diss., Institut polytechnique de Paris, 2020. http://www.theses.fr/2020IPPAG002.

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Cette thèse de doctorat est centrée sur l'apprentissage supervisé. L'objectif principal est l'utilisation de méthodes de localisation pour obtenir des vitesses rapides de convergence, c'est-à-dire, des vitesse de l'ordre O(1/n), où n est le nombre d'observations. Ces vitesses ne sont pas toujours atteignables. Il faut imposer des contraintes sur la variance du problème comme une condition de Bernstein ou de marge. Plus particulièrement, dans cette thèse nous tentons d'établir des vitesses rapides de convergences pour des problèmes de robustesse et d'interpolation.On dit qu'un estimateur est robuste si ce dernier présente certaines garanties théoriques, sous le moins d'hypothèses possibles. Cette problématique de robustesse devient de plus en plus populaire. La raison principale est que dans l'ère actuelle du “big data", les données sont très souvent corrompues. Ainsi, construire des estimateurs fiables dans cette situation est essentiel. Dans cette thèse nous montrons que le fameux minimiseur du risque empirique (regularisé) associé à une fonction de perte Lipschitz est robuste à des bruits à queues lourde ainsi qu'a des outliers dans les labels. En revanche si la classe de prédicteurs est à queue lourde, cet estimateur n'est pas fiable. Dans ce cas, nous construisons des estimateurs appelé estimateur minmax-MOM, optimal lorsque les données sont à queues lourdes et possiblement corrompues.En apprentissage statistique, on dit qu'un estimateur interpole, lorsque ce dernier prédit parfaitement sur un jeu d'entrainement. En grande dimension, certains estimateurs interpolant les données peuvent être bons. En particulier, cette thèse nous étudions le modèle linéaire Gaussien en grande dimension et montrons que l'estimateur interpolant les données de plus petite norme est consistant et atteint même des vitesses rapides
This PhD thesis deals with supervized machine learning and statistics. The main goal is to use localization techniques to derive fast rates of convergence, with a particular focus on robust learning and interpolation problems.Localization methods aim to analyze localized properties of an estimator to obtain fast rates of convergence, that is rates of order O(1/n), where n is the number of observations. Under assumptions, such as the Bernstein condition, such rates are attainable.A robust estimator is an estimator with good theoretical guarantees, under as few assumptions as possible. This question is getting more and more popular in the current era of big data. Large dataset are very likely to be corrupted and one would like to build reliable estimators in such a setting. We show that the well-known regularized empirical risk minimizer (RERM) with Lipschitz-loss function is robust with respect to heavy-tailed noise and outliers in the label. When the class of predictor is heavy-tailed, RERM is not reliable. In this setting, we show that minmax Median of Means estimators can be a solution. By construction minmax-MOM estimators are also robust to an adversarial contamination.Interpolation problems study learning procedure with zero training error. Surprisingly, in large dimension, interpolating the data does not necessarily implies over-fitting. We study a high dimensional Gaussian linear model and show that sometimes the over-fitting may be benign
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Abdelhamid, Ahmed. "A non-gradient heuristic topology optimization approach using bond-based peridynamic theory." Thesis, 2017. https://dspace.library.uvic.ca//handle/1828/8452.

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Peridynamics (PD), a reformulation of the Classical Continuum Mechanics (CCM), is a new and promising meshless and nonlocal computational method in solid mechanics. To permit discontinuities, the PD integro-differential equation contains spatial integrals and time derivatives. PD can be considered as the continuum version of molecular dynamics. This feature of PD makes it a good candidate for multi-scale analysis of materials. Concurrently, the topology optimization has also been rapidly growing in view of the need to design lightweight and high performance structures. Therefore, this thesis presents the potential for a peridynamics-based topology optimization approach. To avoid the gradient calculations, a heuristic topology optimization method is employed. The minimization of the PD strain energy density is set as the objective function. The structure is optimized based on a modified solid isotropic material with a penalization approach and a projection scheme is utilized to obtain distinct results. Several test cases have been studied to analyze the suitability of the proposed method in topology optimization.
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Jain, Puneet. "Error Estimation for Solutions of Linear Systems in Bi-Conjugate Gradient Algorithm." Thesis, 2016. http://hdl.handle.net/2005/2922.

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Books on the topic "Gradient bound"

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Branch, Mary Ann. A subspace, interior, and conjugate gradient method for large-scale bound-constrained minimization problems. Ithaca, N.Y: Cornell Theory Center, Cornell University, 1995.

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Sawyer, Richard. Accuracy of self-reported high school courses and grades of college-bound students. Iowa City: American College Testing Program, 1988.

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Sawyer, Richard. Accuracy of self-reported high school courses and grades of college-bound students. Iowa City: American College Testing Program, 1988.

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Appelbaum, Paul S. Reflections on culture-bound syndromes. Edited by Kenneth S. Kendler and Josef Parnas. Oxford University Press, 2017. http://dx.doi.org/10.1093/med/9780198796022.003.0021.

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This chapter presents a commentary on culture-bound syndromes, as discussed in the previous chapter. It explores how cultural preconceptions can shape the symptomatic manifestations of physical or mental disease, as well as the concept of a gradient of cultural-responsiveness.
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Isett, Philip. Transport Estimates. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691174822.003.0017.

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This chapter derives estimates for quantities which are transported by the coarse scale flow and for their derivatives. It first considers the phase functions which satisfy the Transport equation, with the goal of choosing the lifespan parameter τ‎ sufficiently small so that all the phase functions which appear in the analysis can be guaranteed to remain nonstationary in the time interval, and so that the Stress equation can be solved. In order for these requirements to be met, τ‎ small enough is chosen so that the gradients of the phase functions do not depart significantly from their initial configurations. The chapter presents a proposition that bounds the separation of the phase gradients from their initial values in terms of b (b is less than or equal to 1, a form related to τ‎). Finally, it gathers estimates for relative velocity and relative acceleration.
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Book chapters on the topic "Gradient bound"

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Floater, Michael S. "Optimality of a Gradient Bound for Polyhedral Wachspress Coordinates." In Curves and Surfaces, 210–15. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-22804-4_16.

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Kothari, Anita, and Maxwell J. Smith. "Public Health Policymaking, Politics, and Evidence." In Integrating Science and Politics for Public Health, 59–74. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-98985-9_4.

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AbstractThis chapter explores the gradient of public health engagement and relationships with politics and political science. On one hand, public health values evidence-based decision-making grounded in orthodox hierarchies of evidence, while on the other, by nature of the issues, there are challenges to obtaining this data and to omitting values and contextual considerations. Additionally, public health competes with other health sectors for time and funding which makes political spheres difficult to break into as public health researchers. Apart from some critical public health scholars, many public health researchers have limited knowledge of policy-related concepts. This chapter describes a gradual shift from evidence-based to evidence-informed decision-making in policy, and what this means for conceptualizing policymaking and politics from a public health lens. Most importantly, the chapter describes the importance of the community as the space from which issues are identified, evidence is generated, and solutions are contextually bound.
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Lange, Magdalena Swiatek-de, Bernd Müller, and Marius Ueffing. "Native Fractionation: Isolation of Native Membrane-Bound Protein Complexes from Porcine Rod Outer Segments Using Isopycnic Density Gradient Centrifugation." In Functional Proteomics, 161–75. Totowa, NJ: Humana Press, 2008. http://dx.doi.org/10.1007/978-1-59745-398-1_11.

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Gilbarg, David, and Neil S. Trudinger. "Global and Interior Gradient Bounds." In Elliptic Partial Differential Equations of Second Order, 359–87. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-642-61798-0_15.

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Yu, Nai-Kang, Rong Hu, Bin Qian, Zi-Qi Zhang, and Ling Wang. "Improved Sub-gradient Algorithm for Solving the Lower Bound of No-Wait Flow-Shop Scheduling with Sequence-Dependent Setup Times and Release Dates." In Intelligent Computing Methodologies, 93–101. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-95957-3_11.

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Chappell, M. J. "Bounds for average Lyapunov exponents of gradient stochastic systems." In Lecture Notes in Mathematics, 308–21. Berlin, Heidelberg: Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/bfb0076850.

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Jackson, J. B. "An Introduction and Overview to the Section on Electrochemical Gradients Across Membranes." In Molecular Biology of Membrane-Bound Complexes in Phototrophic Bacteria, 389–92. Boston, MA: Springer US, 1990. http://dx.doi.org/10.1007/978-1-4757-0893-6_46.

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Roy, Kaushik, Qi Zhang, Manas Gaur, and Amit Sheth. "Knowledge Infused Policy Gradients with Upper Confidence Bound for Relational Bandits." In Machine Learning and Knowledge Discovery in Databases. Research Track, 35–50. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-86486-6_3.

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Consoli, Sergio, Luca Tiozzo Pezzoli, and Elisa Tosetti. "Using the GDELT Dataset to Analyse the Italian Sovereign Bond Market." In Machine Learning, Optimization, and Data Science, 190–202. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-64583-0_18.

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AbstractThe Global Data on Events, Location, and Tone (GDELT) is a real time large scale database of global human society for open research which monitors worlds broadcast, print, and web news, creating a free open platform for computing on the entire world’s media. In this work, we first describe a data crawler, which collects metadata of the GDELT database in real-time and stores them in a big data management system based on Elasticsearch, a popular and efficient search engine relying on the Lucene library. Then, by exploiting and engineering the detailed information of each news encoded in GDELT, we build indicators capturing investor’s emotions which are useful to analyse the sovereign bond market in Italy. By using regression analysis and by exploiting the power of Gradient Boosting models from machine learning, we find that the features extracted from GDELT improve the forecast of country government yield spread, relative that of a baseline regression where only conventional regressors are included. The improvement in the fitting is particularly relevant during the period government crisis in May-December 2018.
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Baudoin, Fabrice, and Cheng Ouyang. "Gradient Bounds for Solutions of Stochastic Differential Equations Driven by Fractional Brownian Motions." In Malliavin Calculus and Stochastic Analysis, 413–26. Boston, MA: Springer US, 2013. http://dx.doi.org/10.1007/978-1-4614-5906-4_18.

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Conference papers on the topic "Gradient bound"

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Awad, M. M., and Y. S. Muzychka. "Bounds on Two-Phase Frictional Pressure Gradient in Minichannels and Microchannels." In ASME 4th International Conference on Nanochannels, Microchannels, and Minichannels. ASMEDC, 2006. http://dx.doi.org/10.1115/icnmm2006-96174.

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Simple rules are developed for obtaining rational bounds for two-phase frictional pressure gradient in minichannels and microchannels. The lower bound is based on Ali et al. correlation for laminar-laminar flow. This correlation is based on modification of simplified stratified flow model derived from the theoretical approach of Taitel and Dukler for the case of two-phase flow in a narrow channel. The upper bound is based on Chisholm correlation for laminar-laminar flow. The model is verified using published experimental data of two-phase frictional pressure gradient in circular and non-circular shapes. The published data include different working fluids such as air-water mixture and nitrogen-water mixture, and different channel diameters. The bounds models are also presented in a dimensionless form as two-phase frictional multiplier (φl and φg) versus Lockhart-Martinelli parameter (X) for different working fluids such as air-water mixture and nitrogen-water mixture. It is shown that the published data can be well bounded.
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Awad, M. M., and Y. S. Muzychka. "Bounds on Two-Phase Flow: Part I — Frictional Pressure Gradient in Circular Pipes." In ASME 2005 International Mechanical Engineering Congress and Exposition. ASMEDC, 2005. http://dx.doi.org/10.1115/imece2005-81493.

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Simple rules are developed for obtaining rational bounds for two-phase frictional pressure gradient. Both the lower and upper bounds are based on the separate cylinders formulation. The lower bound is based on turbulent-turbulent flow that uses the Blasius equation to represent the Fanning friction factor. The upper bound is based on an equation that represents well the Lockhart-Martinelli correlation for turbulent-turbulent flow. The model is verified using published experimental data of two-phase frictional pressure gradient versus mass flux at constant mass quality. The published data include different working fluids such as R-12 and R-22 at different mass qualities, different pipe diameters, and different saturation temperatures. It is shown that the published data can be well bounded for a wide range of mass fluxes, mass qualities, pipe diameters and saturation temperatures. The bounds models are also presented in a dimensionless form as two-phase frictional multiplier (φl and φg) versus Lockhart-Martinelli parameter (X) for different working fluids such as R-12, R-22, air-oil and air-water mixtures.
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Zhijian Luo, Danping Liao, and Yuntao Qian. "Bound analysis of natural gradient descent in stochastic optimization setting." In 2016 23rd International Conference on Pattern Recognition (ICPR). IEEE, 2016. http://dx.doi.org/10.1109/icpr.2016.7900287.

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Prasun, Parijat, Sunidhi Pandey, Shyam Kamal, Sandip Ghosh, Devender Singh, and Debdas Ghosh. "Predefined Upper Bound of Settling Time based Convergent Gradient Flow Systems." In IECON 2022 – 48th Annual Conference of the IEEE Industrial Electronics Society. IEEE, 2022. http://dx.doi.org/10.1109/iecon49645.2022.9968332.

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Leclerc, Yvan, and Pascal Fua. "Finding Object Boundaries Using Guided Gradient Ascent1." In Machine Vision. Washington, D.C.: Optica Publishing Group, 1987. http://dx.doi.org/10.1364/mv.1987.fd3.

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In real world images, physical event discontinuities cannot be detected solely by their local statistical signature in the image due to the presence of noise and various photometric anomalies. Therefore all methods for finding discontinuities that use purely local statistical criteria are bound to make mistakes and miss some of the weaker parts of edges.
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Dziwoki, Grzegorz. "An upper bound of the step size for the gradient constant modulus algorithm." In SPIE Proceedings, edited by Ryszard S. Romaniuk. SPIE, 2006. http://dx.doi.org/10.1117/12.674971.

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Sundararaghavan, Harini G., Gary A. Monteiro, and David I. Shreiber. "Microfluidic Generation of Adhesion Gradients Through 3D Collagen Gels: Implications for Neural Tissue Engineering." In ASME 2008 Summer Bioengineering Conference. American Society of Mechanical Engineers, 2008. http://dx.doi.org/10.1115/sbc2008-192987.

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During development, neurites are directed by gradients of attractive and repulsive soluble (chemotactic) cues and substrate-bound adhesive (haptotactic) cues. Many of these cues have been extensively researched in vitro, and incorporated into strategies for nerve and spinal cord regeneration, primarily to improve the regenerative environment. To enhance and direct growth, we have developed a system to create 1D gradients of adhesion through a 3D collagen gel using microfluidics. We test our system using collagen grafted with bioactive peptide sequences, IKVAV and YIGSR, from laminin — an extra-cellular matrix (ECM) protein known to strongly influence neurite outgrowth [1, 2]. Gradients are established from 0.14 mg/ml–0, and 0.07 mg/ml–0 of each peptide and tested using chick dorsal root ganglia (DRG). Neurite growth is evaluated 5 days after gradient formation. Neurites show increased growth in the gradient system when compared to control and biased growth up the gradient of peptides. These results demonstrate that neurite growth can be enhanced and directed by controlled, immobilized, haptotactic gradients through 3D scaffolds, and suggest that including these gradients in regenerative therapies may accelerate nerve and spinal cord regeneration.
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Qin, Chengie, and Florin Rusu. "Scalable I/O-bound parallel incremental gradient descent for big data analytics in GLADE." In the Second Workshop. New York, New York, USA: ACM Press, 2013. http://dx.doi.org/10.1145/2486767.2486771.

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Sundararaghavan, Harini G., Gary A. Monteiro, and David I. Shreiber. "Guided Axon Growth by Gradients of Adhesion in Collagen Gels." In ASME 2008 International Mechanical Engineering Congress and Exposition. ASMEDC, 2008. http://dx.doi.org/10.1115/imece2008-69124.

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During development, neurites are directed by gradients of attractive and repulsive soluble (chemotactic) cues and substrate-bound adhesive (haptotactic) cues. Many of these cues have been extensively researched in vitro, and incorporated into strategies for nerve and spinal cord regeneration, primarily to improve the regenerative environment. To enhance and direct growth, we have developed a system to create 1D gradients of adhesion through a 3D collagen gel using microfluidics. We test our system using collagen grafted with bioactive peptide sequences, IKVAV and YIGSR, from laminin — an extra-cellular matrix (ECM) protein known to strongly influence neurite outgrowth. Gradients are established from ∼0.37mg peptide/mg collagen – 0, and ∼0.18 mg peptide/mg collagen – 0 of each peptide and tested using chick dorsal root ganglia (DRG). Neurite growth is evaluated 5 days after gradient formation. Neurites show increased growth in the gradient system when compared to control and biased growth up the gradient of peptides. Growth in YIGSR-grafted collagen increased with steeper gradients, whereas growth in IKVAV-grafted collagen decreased with steeper gradients. These results demonstrate that neurite growth can be enhanced and directed by controlled, immobilized, haptotactic gradients through 3D scaffolds, and suggest that including these gradients in regenerative therapies may accelerate nerve and spinal cord regeneration.
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Lu, Songtao, Ziping Zhao, Kejun Huang, and Mingyi Hong. "Perturbed Projected Gradient Descent Converges to Approximate Second-order Points for Bound Constrained Nonconvex Problems." In ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2019. http://dx.doi.org/10.1109/icassp.2019.8683241.

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Reports on the topic "Gradient bound"

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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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