Distortion of surface groups in Cat (0) free-by-cyclic groups

Given a non-positively curved 2-complex with a circle-valued Morse function satisfying some extra combinatorial conditions, we describe how to locally isometrically embed this in a larger non- positively curved 2-complex with free-by-cyclic fundamental group. This embedding procedure is used to produce examples of CAT(0) free-by-cyclic groups that contain closed hyperbolic surface subgroups with polynomial distortion of arbitrary degree. We also produce examples of CAT(0) hyperbolic free-by-cyclic groups that contain closed hyperbolic surface subgroups that are exponentially distorted.

Distortion of wreath products in some finitely presented groups

"Vegeu el resum a l'inici del document del fitxer adjunt."

Distortion of Hausdorff measures and improved Painlevé removability for quasiregular mappings

"Vegeu el resum a l'inici del document del fitxer adjunt."

Quasiconformal distortion of Riesz capacities and Hausdorff measures in the plane

In this paper we prove the sharp distortion estimates for the quasiconformal mappings in the plane, both in terms of the Riesz capacities from non linear potential theory and in terms of the Hausdorff measures.

Overview of coded light projection techniques for automatic 3D profiling

Obtaining automatic 3D profile of objects is one of the most important issues in computer vision. With this information, a large number of applications become feasible: from visual inspection of industrial parts to 3D reconstruction of the environment for mobile robots. In order to achieve 3D data, range finders can be used. Coded structured light approach is one of the most widely used techniques to retrieve 3D information of an unknown surface. An overview of the existing techniques as well as a new classification of patterns for structured light sensors is presented. This kind of systems belong to the group of active triangulation method, which are based on projecting a light pattern and imaging the illuminated scene from one or more points of view. Since the patterns are coded, correspondences between points of the image(s) and points of the projected pattern can be easily found. Once correspondences are found, a classical triangulation strategy between camera(s) and projector device leads to the reconstruction of the surface. Advantages and constraints of the different patterns are discussed

Behaviours implemented using a vision system based on coded light projection

In a search for new sensor systems and new methods for underwater vehicle positioning based on visual observation, this paper presents a computer vision system based on coded light projection. 3D information is taken from an underwater scene. This information is used to test obstacle avoidance behaviour. In addition, the main ideas for achieving stabilisation of the vehicle in front of an object are presented

An overview of the advantages and constraints of coded pattern projection techniques for autonomous navigation

The absolute necessity of obtaining 3D information of structured and unknown environments in autonomous navigation reduce considerably the set of sensors that can be used. The necessity to know, at each time, the position of the mobile robot with respect to the scene is indispensable. Furthermore, this information must be obtained in the least computing time. Stereo vision is an attractive and widely used method, but, it is rather limited to make fast 3D surface maps, due to the correspondence problem. The spatial and temporal correspondence among images can be alleviated using a method based on structured light. This relationship can be directly found codifying the projected light; then each imaged region of the projected pattern carries the needed information to solve the correspondence problem. We present the most significant techniques, used in recent years, concerning the coded structured light method

Distortion theorems for quasiconformal mappings

L'any 1994, Astala publicà el reconegut teorema de distorió de l'àrea per aplicacions quasiconformes, un resultat innovador que va permetre que n'apareguessin nombrosos més dins d'aquest camp de l'anàlisi durant la darrera dècada. Ens centrem en les conseqüències que té en la distorsió de la mesura de Hausdorff. Seguim la demostració de Lacey, Sawyer i Uriarte-Tuero per la distorsió del contingut de Hausdorff, clarificant-ne alguns punts i canviant l'enfocament per l'acotació de la transformada de Beurling, on prenem les idees d'Astala, Clop, Tolsa, Uriarte-Tuero i Verdera.

Distortion control for delay-sensitive sources

We investigate the problem of finding minimum-distortion policies for streaming delay-sensitive but distortion-tolerant data. We consider cross-layer approaches which exploit the coupling between presentation and transport layers. We make the natural assumption that the distortion function is convex and decreasing. We focus on a single source-destination pair and analytically find the optimum transmission policy when the transmission is done over an error-free channel. This optimum policy turns out to be independent of the exact form of the convex and decreasing distortion function. Then, for a packet-erasure channel, we analytically find the optimum open-loop transmission policy, which is also independent of the form of the convex distortion function. We then find computationally efficient closed-loop heuristic policies and show, through numerical evaluation, that they outperform the open-loop policy and have near optimal performance.

The minimax distortion redundancy in empirical quantizer design

We obtain minimax lower and upper bounds for the expected distortionredundancy of empirically designed vector quantizers. We show that the meansquared distortion of a vector quantizer designed from $n$ i.i.d. datapoints using any design algorithm is at least $\Omega (n^{-1/2})$ awayfrom the optimal distortion for some distribution on a bounded subset of${\cal R}^d$. Together with existing upper bounds this result shows thatthe minimax distortion redundancy for empirical quantizer design, as afunction of the size of the training data, is asymptotically on the orderof $n^{1/2}$. We also derive a new upper bound for the performance of theempirically optimal quantizer.

Solving heterogeneous-agent models by projection and perturbation

The paper proposes a numerical solution method for general equilibrium models with a continuum of heterogeneous agents, which combines elements of projection and of perturbation methods. The basic idea is to solve first for the stationary solutionof the model, without aggregate shocks but with fully specified idiosyncratic shocks. Afterwards one computes a first-order perturbation of the solution in the aggregate shocks. This approach allows to include a high-dimensional representation of the cross-sectional distribution in the state vector. The method is applied to a model of household saving with uninsurable income risk and liquidity constraints. The model includes not only productivity shocks, but also shocks to redistributive taxation, which cause substantial short-run variation in the cross-sectional distribution of wealth. If those shocks are operative, it is shown that a solution method based on very few statistics of the distribution is not suitable, while the proposed method can solve the model with high accuracy, at least for the case of small aggregate shocks. Techniques are discussed to reduce the dimension of the state space such that higher order perturbations are feasible.Matlab programs to solve the model can be downloaded.

Dimerization of polyacetylene treated as a spin-Peierls distortion of the Heisenberg Hamiltonian

Extracting a bond-length-dependent Heisenberg-like Hamiltonian from the potential-energy surfaces of the two lowest states of ethylene, it is possible to study the geometry of polyacetylene by minimization of the cohesive energy, using both variational-cluster and Rayleigh-Schrödinger perturbative expansions. The dimerization amplitude is satisfactorily reproduced. Optimizing the variational-cluster-expansion total energy with the equal-bond-length constraint, the barrier to reversal of alternation is obtained. The alternating-to-regular phase transition is treated from the Néel-state starting function and appears to be of second order.

Preface: Forecast and projection in climate scenario of Mediterranean intense events: uncertainties and propagation on environment (the MEDUP project)

The Mediterranean basin is a particularly vulnerable region to climate change, partly due to its quite unique character that results both from physiographic conditions and societal development. The region features indeed a near-closed sea surrounded by very urbanised littorals and mountains from which numerous rivers originate. This results in a lot of interactions and feedbacks between oceanic-atmospheric-hydrological processes that play a predominant role on climate and extreme events that frequently cause heavy dam- ages and human losses in the Mediterranean ...

Blind Inversion of Wiener System using a minimization-projection (MP) approach

In this paper, a new algorithm for blind inversion of Wiener systems is presented. The algorithm is based on minimization of mutual information of the output samples. This minimization is done through a Minimization-Projection (MP) approach, using a nonparametric “gradient” of mutual information.

Beyond Value-at-Risk : GlueVaR Distortion Risk Measures

We propose a new family of risk measures, called GlueVaR, within the class of distortion risk measures. Analytical closed-form expressions are shown for the most frequently used distribution functions in financial and insurance applications. The relationship between Glue-VaR, Value-at-Risk (VaR) and Tail Value-at-Risk (TVaR) is explained. Tail-subadditivity is investigated and it is shown that some GlueVaR risk measures satisfy this property. An interpretation in terms of risk attitudes is provided and a discussion is given on the applicability in non-financial problems such as health, safety, environmental or catastrophic risk management