Slowly varying discrete system x sub /i+1/ = A sub i x sub i

Slowly varying discrete system of matrice

Direct methods for the solution of systems of linear equations with sparse coefficient matrix and related topics Final report, 1 Dec. 1967 - 31 Aug. 1970

Deriving algorithms for computations involving sparse matrice

Transient vibration analysis of linear systems using transition matrices

Transient vibration analysis of liner systems using transition matrice

Generalized Rayleigh methods with applications to finding eigenvalues of large matrices

Generalized Rayleigh quotients for calculating eigenvalues and eigenvectors of large matrice

Sharp detection of smooth signals in a high-dimensional sparse matrix with indirect observations

We consider a matrix-valued Gaussian sequence model, that is, we observe a sequence of high-dimensional $M \times N$ matrices of heterogeneous Gaussian random variables $x_{ij,k}$ for $i \in\{1,...,M\}$, $j \in \{1,...,N\}$ and $k \in \mathbb{Z}$. The standard deviation of our observations is \ep k^s for some \ep >0 and $s \geq 0$. We give sharp rates for the detection of a sparse submatrix of size $m \times n$ with active components. A component $(i,j)$ is said active if the sequence $\{x_{ij,k}\}_k$ have mean $\{\theta_{ij,k}\}_k$ within a Sobolev ellipsoid of smoothness $\tau >0$ and total energy $\sum_k \theta^2_{ij,k}$ larger than some r^2_\ep. Our rates involve relationships between $m,\, n, \, M$ and $N$ tending to infinity such that $m/M$, $n/N$ and \ep tend to 0, such that a test procedure that we construct has asymptotic minimax risk tending to 0. We prove corresponding lower bounds under additional assumptions on the relative size of the submatrix in the large matrix of observations. Except for these additional conditions our rates are asymptotically sharp. Lower bounds for hypothesis testing problems mean that no test procedure can distinguish between the null hypothesis (no signal) and the alternative, i.e. the minimax risk for testing tends to 1

Autonomous Recharging and Flight Mission Planning for Battery-operated Autonomous Drones

Autonomous drones (also known as unmanned aerial vehicles) are increasingly popular for diverse applications of light-weight delivery and as substitutions of manned operations in remote locations. The computing systems for drones are becoming a new venue for research in cyber-physical systems. Autonomous drones require integrated intelligent decision systems to control and manage their flight missions in the absence of human operators. One of the most crucial aspects of drone mission control and management is related to the optimization of battery lifetime. Typical drones are powered by on-board batteries, with limited capacity. But drones are expected to carry out long missions. Thus, a fully automated management system that can optimize the operations of battery-operated autonomous drones to extend their operation time is highly desirable. This paper presents several contributions to automated management systems for battery-operated drones: (1) We conduct empirical studies to model the battery performance of drones, considering various flight scenarios. (2) We study a joint problem of flight mission planning and recharging optimization for drones with an objective to complete a tour mission for a set of sites of interest in the shortest time. This problem captures diverse applications of delivery and remote operations by drones. (3) We present algorithms for solving the problem of flight mission planning and recharging optimization. We implemented our algorithms in a drone management system, which supports real-time flight path tracking and re-computation in dynamic environments. We evaluated the results of our algorithms using data from empirical studies. (4) To allow fully autonomous recharging of drones, we also develop a robotic charging system prototype that can recharge drones autonomously by our drone management system

Analisi di mobillità pedonale mediante dati di telefonia georeferenziati

Al fine di organizzare al meglio le città del futuro occorrono nuovi strumenti in grado di analizzare e comprendere il comportamento delle persone nelle aree urbane. In questo elaborato viene illustrata la costruzione di un modello teorico relativo alla mobilità pedonale nella città di Venezia a partire dall'analisi di dati di telefonia mobile, rilevati nella giornata del 26 Febbraio 2017. Vengono in seguito mostrate le differenti fasi necessarie alla realizzazione del modello a partire dall'elaborazione preliminare dei data set a disposizione e focalizzando poi l'attenzione sugli algoritmi di georeferenziazione disponibili in letteratura. Una volta ultimata l'analisi dati, vengono esposti i concetti teorici che stanno alla base del modello realizzato ponendo l'accento sul carattere stocastico del fenomeno osservato si rivolge lo sguardo al risultato ottenuto portando alla luce le verifiche a cui viene sottoposto e le criticità che emergono nell'affrontare questo studio

Fine Structure of the Zeros of Orthogonal Polynomials, II. OPUC With Competing Exponential Decay

We present a complete theory of the asymptotics of the zeros of OPUC with Verblunsky coefficients $\alpha_n = \sum_{\ell=1}^L C_\ell b_\ell^n + O((b\Delta)^n)$ where $\Delta <1$ and \abs{b_\ell} = b<1.Comment: Keywords: orthogonal polynomials, Jacobi matrices, CMV matrice

Hyperspectral images segmentation: a proposal

Hyper-Spectral Imaging (HIS) also known as chemical or spectroscopic imaging is an emerging technique that combines imaging and spectroscopy to capture both spectral and spatial information from an object. Hyperspectral images are made up of contiguous wavebands in a given spectral band. These images provide information on the chemical make-up profile of objects, thus allowing the differentiation of objects of the same colour but which possess make-up profile. Yet, whatever the application field, most of the methods devoted to HIS processing conduct data analysis without taking into account spatial information.Pixels are processed individually, as an array of spectral data without any spatial structure. Standard classification approaches are thus widely used (k-means, fuzzy-c-means hierarchical classification...). Linear modelling methods such as Partial Least Square analysis (PLS) or non linear approaches like support vector machine (SVM) are also used at different scales (remote sensing or laboratory applications). However, with the development of high resolution sensors, coupled exploitation of spectral and spatial information to process complex images, would appear to be a very relevant approach. However, few methods are proposed in the litterature. The most recent approaches can be broadly classified in two main categories. The first ones are related to a direct extension of individual pixel classification methods using just the spectral dimension (k-means, fuzzy-c-means or FCM, Support Vector Machine or SVM). Spatial dimension is integrated as an additionnal classification parameter (Markov fields with local homogeneity constrainst [5], Support Vector Machine or SVM with spectral and spatial kernels combination [2], geometrically guided fuzzy C-means [3]...). The second ones combine the two fields related to each dimension (spectral and spatial), namely chemometric and image analysis. Various strategies have been attempted. The first one is to rely on chemometrics methods (Principal Component Analysis or PCA, Independant Component Analysis or ICA, Curvilinear Component Analysis...) to reduce the spectral dimension and then to apply standard images processing technics on the resulting score images i.e. data projection on a subspace. Another approach is to extend the definition of basic image processing operators to this new dimensionality (morphological operators for example [1, 4]). However, the approaches mentioned above tend to favour only one description either directly or indirectly (spectral or spatial). The purpose of this paper is to propose a hyperspectral processing approach that strikes a better balance in the treatment of both kinds of information....Cet article présente une stratégie de segmentation d’images hyperspectrales liant de façon symétrique et conjointe les aspects spectraux et spatiaux. Pour cela, nous proposons de construire des variables latentes permettant de définir un sous-espace représentant au mieux la topologie de l’image. Dans cet article, nous limiterons cette notion de topologie à la seule appartenance aux régions. Pour ce faire, nous utilisons d’une part les notions de l’analyse discriminante (variance intra, inter) et les propriétés des algorithmes de segmentation en région liées à celles-ci. Le principe générique théorique est exposé puis décliné sous la forme d’un exemple d’implémentation optimisé utilisant un algorithme de segmentation en région type split and merge. Les résultats obtenus sur une image de synthèse puis réelle sont exposés et commentés