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Viet-Anh Nguyen

Publications and source records attributed to Viet-Anh Nguyen.

At least 37 records · Page 2Linked to original sources
arXiv2016

Equidistribution speed for Fekete points associated with an ample line bundle

Let K be the closure of a bounded open set with smooth boundary in C^n. A Fekete configuration of order p for K is a finite subset of K maximizing the Vandermonde determinant associated with polynomials of degree at most p. A recent theorem by Berman, Boucksom and Witt Nystrom implies that Fekete configurations for K are asymptotically equidistributed with respect to a canonical equilibrium measure, as p tends to infinite. We give here an explicit estimate for the speed of convergence. The result also holds in a general setting of Fekete points associated with an ample line bundle over a projective manifold. Our approach requires a new estimate on Bergman kernels for line bundles and quantitative results in pluripotential theory which are of independent interest.

math.CV↗
arXiv2016

Large deviations principle for some beta-ensembles

Let L be a positive line bundle over a projective complex manifold X. Consider the space of holomorphic sections of the tensor power of order p of L. The determinant of a basis of this space, together with some given probability measure on a weighted compact set in X, induces naturally a beta-ensemble, i.e., a random point process on the compact set. Physically, this general setting corresponds to a gas of free fermions in X and may admit some random matrix models. The empirical measures, associated with such beta-ensembles, converge almost surely to an equilibrium measure when p goes to infinity. We establish a large deviations principle (LDP) with an effective speed of convergence for these empirical measures. Our study covers the case of some beta-ensembles on a compact subset of a real sphere or of a real Euclidean space.

math.CV↗
arXiv2016

On the asymptotic behavior of Bergman kernels for positive line bundles

Let L be a positive line bundle on a projective complex manifold. We study the asymptotic behavior of Bergman kernels associated with the tensor powers L^p of L as p tends to infinity. The emphasis is the dependence of the uniform estimates on the positivity of the Chern form of the metric on L. This situation appears naturally when we approximate a semi-positive singular metric by smooth positively curved metrics.

math.CV↗
arXiv2016

Growth of the number of periodic points for meromorphic maps

We show that any dominant meromorphic self-map f of a compact Kaehler manifold X is an Artin-Mazur map. More precisely, if P_n(f) is the number of its isolated periodic points of period n (counted with multiplicity), then P_n(f) grows at most exponentially fast with respect to n and the exponential rate is at most equal to the algebraic entropy of f. Further estimates are given when X is a surface. Among the techniques introduced in this paper, the h-dimension of the density between two arbitrary positive closed currents on a compact Kaehler surface is obtained.

math.DS↗
arXiv2015

Oseledec multiplicative ergodic theorem for laminations

Given a n-dimensional lamination endowed with a Riemannian metric, we introduce the notion of a multiplicative cocycle of rank d, where n and d are arbitrary positive integers. The holonomy cocycle of a foliation and its exterior powers as well as its tensor powers provide examples of multiplicative cocycles. Next, we define the Lyapunov exponents of such a cocycle with respect to a harmonic probability measure directed by the lamination. We also prove an Oseledec multiplicative ergodic theorem in this context. This theorem implies the existence of an Oseledec decomposition almost everywhere which is holonomy invariant. Moreover, in the case of differentiable cocycles, we establish effective integral estimates for the Lyapunov exponents. These results find applications in the geometric and dynamical theory of laminations. They are also applicable to (not necessarily closed) laminations with singularities. Interesting holonomy properties of a generic leaf of a foliation are obtained. The main ingredients of our method are the theory of Brownian motion, the analysis of the heat diffusions on Riemannian manifolds, the ergodic theory in discrete dynamics and a geometric study of laminations.

math.DS↗
arXiv2015

Weakly Supervised Fine-Grained Image Categorization

In this paper, we categorize fine-grained images without using any object / part annotation neither in the training nor in the testing stage, a step towards making it suitable for deployments. Fine-grained image categorization aims to classify objects with subtle distinctions. Most existing works heavily rely on object / part detectors to build the correspondence between object parts by using object or object part annotations inside training images. The need for expensive object annotations prevents the wide usage of these methods. Instead, we propose to select useful parts from multi-scale part proposals in objects, and use them to compute a global image representation for categorization. This is specially designed for the annotation-free fine-grained categorization task, because useful parts have shown to play an important role in existing annotation-dependent works but accurate part detectors can be hardly acquired. With the proposed image representation, we can further detect and visualize the key (most discriminative) parts in objects of different classes. In the experiment, the proposed annotation-free method achieves better accuracy than that of state-of-the-art annotation-free and most existing annotation-dependent methods on two challenging datasets, which shows that it is not always necessary to use accurate object / part annotations in fine-grained image categorization.

cs.CV↗
arXiv2014

ITEM: Immersive Telepresence for Entertainment and Meetings - A Practical Approach

This paper presents an Immersive Telepresence system for Entertainment and Meetings (ITEM). The system aims to provide a radically new video communication experience by seamlessly merging participants into the same virtual space to allow a natural interaction among them and shared collaborative contents. With the goal to make a scalable, flexible system for various business solutions as well as easily accessible by massive consumers, we address the challenges in the whole pipeline of media processing, communication, and displaying in our design and realization of such a system. Particularly, in this paper we focus on the system aspects that maximize the end-user experience, optimize the system and network resources, and enable various teleimmersive application scenarios. In addition, we also present a few key technologies, i.e. fast object-based video coding for real world data and spatialized audio capture and 3D sound localization for group teleconferencing. Our effort is to investigate and optimize the key system components and provide an efficient end-to-end optimization and integration by considering user needs and preferences. Extensive experiments show the developed system runs reliably and comfortably in real time with a minimal setup requirement (e.g. a webcam and/or a depth camera, an optional microphone array, a laptop/desktop connected to the public Internet) for teleimmersive communication. With such a really minimal deployment requirement, we present a variety of interesting applications and user experiences created by ITEM.

cs.MM↗
arXiv2013

Equidistribution for meromorphic maps with dominant topological degree

Let f be a meromorphic self-map on a compact Kaehler manifold whose topological degree is strictly larger than the other dynamical degrees. We show that repelling periodic points are equidistributed with respect to the equilibrium measure of f. We also describe the exceptional set of points whose backward orbits are not equidistributed.

math.DS↗
arXiv2012

Characterization of Monge-Ampere measures with Holder continuous potentials

We show that the complex Monge-Ampere equation on a compact Kaehler manifold (X,ω) of dimension n admits a Holder continuous omega-psh solution if and only if its right-hand side is a positive measure with Holder continuous super-potential. This property is true in particular when the measure has locally Holder continuous potentials or when it belongs to the Sobolev space W^{2n/p-2+epsilon,p}(X) or to the Besov space B^{epsilon-2}_{\infty,\infty}(X) for some epsilon>0 and p>1.

math.CV↗
arXiv2011

Green currents for quasi-algebraically stable meromorphic self-maps of CP^k

We construct a canonical Green current T_f for every quasi-algebraically stable meromorphic self-map f of CP^k such that its first dynamical degree λ_1(f) is a simple root of its characteristic polynomial and that λ_1(f) > 1. We establish a functional equation for T_f and show that the support of T_f is contained in the Julia set of f, which is thus non empty.

math.CV↗
arXiv2011

Corrigendum: Conical plurisubharmonic measure and new cross theorems

In the previous version of this paper we prove a theorem on the boundary behavior of the conical plurisubharmonic measure. However, the proof turns out to be incomplete. In the present version we give a corrected proof of this theorem. We next apply it to the theory of separately holomorphic functions. These applications are presented in a more accessible way than in the previous version.

math.CV↗
arXiv2011

Entropy for hyperbolic Riemann surface laminations II

Consider a Brody hyperbolic foliation by Riemann surfaces with linearizable isolated singularities on a compact complex surface. We show that its hyperbolic entropy is finite. We also estimate the modulus of continuity of the Poincare metric on leaves. The estimate holds for foliations on manifolds of higher dimension.

math.DS↗
arXiv2011

On the dynamical degrees of meromorphic maps preserving a fibration

Let f be a dominant meromorphic self-map on a compact Kaehler manifold X which preserves a fibration given by a meromorphic map from X to a compact Kaehler manifold Y. We compute the dynamical degrees of f in term of its dynamical degrees relative to the fibration and the dynamical degrees of the map g on Y which is induced by f. We derive from this result new properties of some fibrations intrinsically associated to X when this manifold admits an interesting dynamical system.

math.DS↗
arXiv2011

Entropy for hyperbolic Riemann surface laminations I

We develop a notion of entropy, using hyperbolic time, for laminations by hyperbolic Riemann surfaces. When the lamination is compact and transversally smooth, we show that the entropy is finite and the Poincare metric on leaves is transversally Holder continuous. A notion of metric entropy is also introduced for harmonic measures.

math.DS↗
arXiv2010

Heat equation and ergodic theorems for Riemann surface laminations

We introduce the heat equation relative to a positive dd-bar-closed current and apply it to the invariant currents associated with Riemann surface laminations possibly with singularities. The main examples are holomorphic foliations by Riemann surfaces in projective spaces. We prove two kinds of ergodic theorems for such currents: one associated to the heat diffusion and one close to Birkhoff's averaging on orbits of a dynamical system. The heat diffusion theorem with respect to a harmonic measure is also developed for real laminations.

math.DS↗
arXiv2010

Noise and nonlinearities in high-throughput data

High-throughput data analyses are becoming common in biology, communications, economics and sociology. The vast amounts of data are usually represented in the form of matrices and can be considered as knowledge networks. Spectra-based approaches have proved useful in extracting hidden information within such networks and for estimating missing data, but these methods are based essentially on linear assumptions. The physical models of matching, when applicable, often suggest non-linear mechanisms, that may sometimes be identified as noise. The use of non-linear models in data analysis, however, may require the introduction of many parameters, which lowers the statistical weight of the model. According to the quality of data, a simpler linear analysis may be more convenient than more complex approaches. In this paper, we show how a simple non-parametric Bayesian model may be used to explore the role of non-linearities and noise in synthetic and experimental data sets.

q-bio.QM↗
arXiv2009

Comparison of dynamical degrees for semi-conjugate meromorphic maps

Let f be a dominant meromorphic self-map on a projective manifold X which preserves a meromorphic fibration pi: X --> Y of X over a projective manifold Y. We establish formulas relating the dynamical degrees of f, the dynamical degrees of f relative to the fibration and the dynamical degrees of the self-map g on Y induced by f. Applications are given.

math.DS↗