Connections between ∞-Poincaré inequality, quasi-convexity, and N1,∞

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Automated Segmentation of Cerebral Vasculature with Aneurysms in 3DRA and TOF-MRA using Geodesic Active Regions: an Evaluation Study

Purpose: To evaluate the suitability of an improved version of an automatic segmentation method based on geodesic active regions (GAR) for segmenting cerebral vasculature with aneurysms from 3D X-ray reconstruc-tion angiography (3DRA) and time of °ight magnetic resonance angiography (TOF-MRA) images available in the clinical routine.Methods: Three aspects of the GAR method have been improved: execution time, robustness to variability in imaging protocols and robustness to variability in image spatial resolutions. The improved GAR was retrospectively evaluated on images from patients containing intracranial aneurysms in the area of the Circle of Willis and imaged with two modalities: 3DRA and TOF-MRA. Images were obtained from two clinical centers, each using di®erent imaging equipment. Evaluation included qualitative and quantitative analyses ofthe segmentation results on 20 images from 10 patients. The gold standard was built from 660 cross-sections (33 per image) of vessels and aneurysms, manually measured by interventional neuroradiologists. GAR has also been compared to an interactive segmentation method: iso-intensity surface extraction (ISE). In addition, since patients had been imaged with the two modalities, we performed an inter-modality agreement analysis with respect to both the manual measurements and each of the two segmentation methods. Results: Both GAR and ISE di®ered from the gold standard within acceptable limits compared to the imaging resolution. GAR (ISE, respectively) had an average accuracy of 0.20 (0.24) mm for 3DRA and 0.27 (0.30) mm for TOF-MRA, and had a repeatability of 0.05 (0.20) mm. Compared to ISE, GAR had a lower qualitative error in the vessel region and a lower quantitative error in the aneurysm region. The repeatabilityof GAR was superior to manual measurements and ISE. The inter-modality agreement was similar between GAR and the manual measurements. Conclusions: The improved GAR method outperformed ISE qualitatively as well as quantitatively and is suitable for segmenting 3DRA and TOF-MRA images from clinical routine.

Contractions in the 2-wasserstein lenght space and thermalization of granular media

An algebraic decay rate is derived which bounds the time required for velocities to equilibrate in a spatially homogeneous flow-through model representing the continuum limit of a gas of particles interacting through slightly inelastic collisions. This rate is obtained by reformulating the dynamical problem as the gradient flow of a convex energy on an infinite-dimensional manifold. An abstract theory is developed for gradient flows in length spaces, which shows how degenerate convexity (or even non-convexity) | if uniformly controlled | will quantify contractivity (limit expansivity) of the flow.

Increasing quasiconcave production and utility functions with diminishing returns to scale

In microeconomic analysis functions with diminishing returns to scale (DRS) have frequently been employed. Various properties of increasing quasiconcave aggregator functions with DRS are derived. Furthermore duality in the classical sense as well as of a new type is studied for such aggregator functions in production and consumer theory. In particular representation theorems for direct and indirect aggregator functions are obtained. These involve only small sets of generator functions. The study is carried out in the contemporary framework of abstract convexity and abstract concavity.

Reduction, Linearization and stability of relative equilibria for mechanical systems on riemannian manifolds

Consider a Riemannian manifold equipped with an infinitesimal isometry. For this setup, a unified treatment is provided, solely in the language of Riemannian geometry, of techniques in reduction, linearization, and stability of relative equilibria. In particular, for mechanical control systems, an explicit characterization is given for the manner in which reduction by an infinitesimal isometry, and linearization along a controlled trajectory "commute." As part of the development, relationships are derived between the Jacobi equation of geodesic variation and concepts from reduction theory, such as the curvature of the mechanical connection and the effective potential. As an application of our techniques, fiber and base stability of relative equilibria are studied. The paper also serves as a tutorial of Riemannian geometric methods applicable in the intersection of mechanics and control theory.

A parameter-free approach for solving combinatorial optimization problems through biased randomization of efficient heuristics

This paper discusses the use of probabilistic or randomized algorithms for solving combinatorial optimization problems. Our approach employs non-uniform probability distributions to add a biased random behavior to classical heuristics so a large set of alternative good solutions can be quickly obtained in a natural way and without complex conguration processes. This procedure is especially useful in problems where properties such as non-smoothness or non-convexity lead to a highly irregular solution space, for which the traditional optimization methods, both of exact and approximate nature, may fail to reach their full potential. The results obtained are promising enough to suggest that randomizing classical heuristics is a powerful method that can be successfully applied in a variety of cases.

Creació d'un Sistema d'Informació Geogràfic per a la consulta i gestió de la base de vèrtexs geodèsics de Catalunya amb Geomedia PRO 6.0©

L'objectiu és realitzar una explicació dels passos i les tasques realitzades per a la construcció d'un Sistema d'Informació Geogràfica (SIG) que permeti la gestió de vèrtex geodèsics de Catalunya i la implementació de l'algorisme de Delaunay sobre un conjunt de vèrtex seleccionats.

SIG per a la gestió dels vèrtexs geodèsics de Catalunya amb Geomedia

L¿objectiu del projecte es estudiar el que és i el que no és un sistema d¿informació geogràfica,conèixer la tecnologia associada a aquests sistemes, així com el tipus i format de les dades que fan servir. Tanmateix, l¿estudi no és només teòric i, per conèixer els mecanismes de automatització que ofereix GeoMedia, s¿implementa una petita eina de gestió de vèrtexs geodèsics centrada al territori de Catalunya que fa servir Oracle, com a gestor de bases de dades.

Bargaining, coalitions and competition

We study a decentralized matching model in a large exchange economy,in which trade takes place through non--cooperative bargaining in coalitionsof finite size. Under essentially the same conditions of core equivalence, we show that the strategic equilibrium outcomes of our model coincide with theWalrasian allocations of the economy. Our method of proof exploits equivalenceresults between the core and Walrasian equilibria. Our model relaxes differentiability and convexity of preferences thereby covering the caseof indivisible goods.

Variable Kernel estimates: On the impossibility of tuning the parameters

For the standard kernel density estimate, it is known that one can tune the bandwidth such that the expected L1 error is within a constant factor of the optimal L1 error (obtained when one is allowed to choose the bandwidth with knowledge of the density). In this paper, we pose the same problem for variable bandwidth kernel estimates where the bandwidths are allowed to depend upon the location. We show in particular that for positive kernels on the real line, for any data-based bandwidth, there exists a densityfor which the ratio of expected L1 error over optimal L1 error tends to infinity. Thus, the problem of tuning the variable bandwidth in an optimal manner is ``too hard''. Moreover, from the class of counterexamples exhibited in the paper, it appears thatplacing conditions on the densities (monotonicity, convexity, smoothness) does not help.

On payoff heterogeneity in games with strategic complementarities

Payoff heterogeneity weakens positive feedback in binary choice models intwo ways. First, heterogeneity drives individuals to corners where theyare unaffected by strategic complementarities. Second, aggregate behaviouris smoother than individual behaviour when individuals are heterogeneous.However, this smoothing does not necessarily eliminate positive feedbackor guarantee a unique equilibrium. In games with an unbounded, continuouschoice space, heterogeneity may either weaken or strengthen positive feedback,depending on a simple convexity/concavity condition. We conclude that positivefeedback phenomena derived in representative agent models will often be robustto heterogeneity.

A Note on Shapley's convex measure games

L. S. Shapley, in his paper 'Cores of Convex Games', introduces Convex Measure Games, those that are induced by a convex function on R, acting over a measure on the coalitions. But in a note he states that if this function is a function of several variables, then convexity for the function does not imply convexity of the game or even superadditivity. We prove that if the function is directionally convex, the game is convex, and conversely, any convex game can be induced by a directionally convex function acting over measures on the coalitions, with as many measures as players

Robustness of entanglement

In the quest to completely describe entanglement in the general case of a finite number of parties sharing a physical system of finite-dimensional Hilbert space an entanglement magnitude is introduced for its pure and mixed states: robustness. It corresponds to the minimal amount of mixing with locally prepared states which washes out all entanglement. It quantifies in a sense the endurance of entanglement against noise and jamming. Its properties are studied comprehensively. Analytical expressions for the robustness are given for pure states of two-party systems, and analytical bounds for mixed states of two-party systems. Specific results are obtained mainly for the qubit-qubit system (qubit denotes quantum bit). As by-products local pseudomixtures are generalized, a lower bound for the relative volume of separable states is deduced, and arguments for considering convexity a necessary condition of any entanglement measure are put forward.

Massless minimally coupled fields in de Sitter space: O(4)-symmetric states versus de Sitter invariant vacuum

The issue of de Sitter invariance for a massless minimally coupled scalar field is examined. Formally, it is possible to construct a de Sitterinvariant state for this case provided that the zero mode of the field is quantized properly. Here we take the point of view that this state is physically acceptable, in the sense that physical observables can be computed and have a reasonable interpretation. In particular, we use this vacuum to derive a new result: that the squared difference between the field at two points along a geodesic observers spacetime path grows linearly with the observers proper time for a quantum state that does not break de Sitter invariance. Also, we use the Hadamard formalism to compute the renormalized expectation value of the energy-momentum tensor, both in the O(4)-invariant states introduced by Allen and Follaci, and in the de Sitterinvariant vacuum. We find that the vacuum energy density in the O(4)-invariant case is larger than in the de Sitterinvariant case.

Self-organized criticality and synchronization in a coupled map lattice model of integrate-and-fire oscillators

We introduce two coupled map lattice models with nonconservative interactions and a continuous nonlinear driving. Depending on both the degree of conservation and the convexity of the driving we find different behaviors, ranging from self-organized criticality, in the sense that the distribution of events (avalanches) obeys a power law, to a macroscopic synchronization of the population of oscillators, with avalanches of the size of the system.