RECERCAT - Articles publicats en revistes (Matemàtica Aplicada i Anàlisi)
http://www.recercat.cat:80/handle/2072/48838
www.ub.eduMon, 02 Mar 2015 12:58:17 GMT2015-03-02T12:58:17ZThe Channel Imagehttp://www.recercat.cat:80/bitstream/id/26419/
http://www.recercat.cat:80/handle/2072/48838
Preferred Spatial Frequencies for Human Face Processing Are Associated with Optimal Class Discrimination in the Machine
http://www.recercat.cat:80/handle/2072/206260
Preferred Spatial Frequencies for Human Face Processing Are Associated with Optimal Class Discrimination in the Machine
Keil, Matthias S.; Lapedriza i Garcia, Àgata; Masip, David; Vitrià i Marca, Jordi
Psychophysical studies suggest that humans preferentially use a narrow band of low spatial frequencies for face recognition. Here we asked whether artificial face recognition systems have an improved recognition performance at the same spatial frequencies as humans. To this end, we estimated recognition performance over a large database of face images by computing three discriminability measures: Fisher Linear Discriminant Analysis, Non-Parametric Discriminant Analysis, and Mutual Information. In order to address frequency dependence, discriminabilities were measured as a function of (filtered) image size. All three measures revealed a maximum at the same image sizes, where the spatial frequency content corresponds to the psychophysical found frequencies. Our results therefore support the notion that the critical band of spatial frequencies for face recognition in humans and machines follows from inherent properties of face images, and that the use of these frequencies is associated with optimal face recognition performance.
http://www.recercat.cat:80/handle/2072/206260Beurling-Landau's density on compact manifolds
http://www.recercat.cat:80/handle/2072/208569
Beurling-Landau's density on compact manifolds
Ortega Cerdà, Joaquim; Pridhnani, Bharti
Given a compact Riemannian manifold $M$, we consider the subspace of $L^2(M)$ generated by the eigenfunctions of the Laplacian ofeigenvalue less than $L\geq1$. This space behaves like a space of polynomials and we have an analogy with the Paley-Wiener spaces. Westudy the interpolating and Marcinkiewicz-Zygmund (M-Z) families and provide necessary conditions for sampling and interpolation in termsof the Beurling-Landau densities. As an application, we prove the equidistribution of the Fekete arrays on some compact manifolds.
http://www.recercat.cat:80/handle/2072/208569A note on the periodic orbits and topological entropy of graph maps
http://www.recercat.cat:80/handle/2072/49445
A note on the periodic orbits and topological entropy of graph maps
Alsedà i Soler, Lluís; Juher, J.; Mumbrú i Rodriguez, Pere
This paper deals with the relationship between the periodic orbits of continuous maps on graphs and the topological entropy of the map. We show that the topological entropy of a graph map can be approximated by the entropy of its periodic orbits.
http://www.recercat.cat:80/handle/2072/49445Newton's method on bring-Jerrard polynomials
http://www.recercat.cat:80/handle/2072/246777
Newton's method on bring-Jerrard polynomials
Campos, Beatriz; Garijo, Antonio; Jarque i Ribera, Xavier; Vindel, Pura
In this paper we study the topology of the hyperbolic component of the parameter plane for the Newton's method applied to n-degree Bring<br>Jerrard polynomials given by $P_{n}(z)=z^{n}-cz +1, c \in \mathbb{C}$. For $n=5$ using the Tschirnhaus<br>Bring<br>Jerrard nonlinear transformations, this family controls, at least theoretically, the roots of all quintic polynomials. We also study a bifurcation cascade of the bifurcation locus by considering $c\in\mathbb{R}$
http://www.recercat.cat:80/handle/2072/246777On the computation of reducible invariant tori on a parallel computer
http://www.recercat.cat:80/handle/2072/206831
On the computation of reducible invariant tori on a parallel computer
Jorba i Monte, Àngel; Olmedo, Estrella
We present an algorithm for the computation of reducible invariant tori of discrete dynamical systems that is suitable for tori of dimensions larger than 1. It is based on a quadratically convergent scheme that approximates, at the same time, the Fourier series of the torus, its Floquet transformation, and its Floquet matrix. The Floquet matrix describes the linearization of the dynamics around the torus and, hence, its linear stability. The algorithm presents a high degree of parallelism, and the computational effort grows linearly with the number of Fourier modes needed to represent the solution. For these reasons it is a very good option to compute quasi-periodic solutions with several basic frequencies. The paper includes some examples (flows) to show the efficiency of the method in a parallel computer. In these flows we compute invariant tori of dimensions up to 5, by taking suitable sections.
http://www.recercat.cat:80/handle/2072/206831Beurling-Landau densities of weighted Fekete sets and correlation kernel estimates
http://www.recercat.cat:80/handle/2072/210240
Beurling-Landau densities of weighted Fekete sets and correlation kernel estimates
Ameur, Yacin; Ortega Cerdà, Joaquim
Let $Q$ be a suitable real function on $C$. An $n$-Fekete set corresponding to $Q$ is a subset ${Z_{n1}},\dotsb, Z_{nn}}$ of $C$ which maximizes the expression $\Pi^n_i_{<j}|Z_{ni} - Z_{nj}|^2 e^-^{n(Q(Z_n_1)+\dotsb+Q(Z_{nn}))}$. It is well known that, under reasonable conditions on $Q$, there is a compact set $S$ known as the 'droplet' such that the measures $\mu_n n^{-1} (\delta_{zn1}+\dots+\delta_{znn})$ converges to the equilibrium measure $\Delta Q.1 _S$d$A$ as $n \rightarrow \infty$. In this note we prove that Fekete sets are, in a sense, maximally spread out with respect to the equilibrium measure. In general, our results apply only to a part of the Fekete set, which is at a certain distance away from the boundary of the droplet. However, for the potential $Q=|Z|^2$ we obtain results which hold globally, and we conjecture that such global results are true for a wide range of potentials.
http://www.recercat.cat:80/handle/2072/210240The Bonenblust-Hille inequality for homogeneous polynomials is hypercontractive
http://www.recercat.cat:80/handle/2072/208683
The Bonenblust-Hille inequality for homogeneous polynomials is hypercontractive
Defant, Andreas; Frerick, Leonhard; Ortega Cerdà, Joaquim; Ounaïes, Myriam; Seip, Kristian
The Bohnenblust-Hille inequality says that the $\ell^{\frac{2m}{m+1}}$ -norm of the coefficients of an $m$-homogeneous polynomial $P$ on $\Bbb{C}^n$ is bounded by $\| P \|_\infty$ times a constant independent of $n$, where $\|\cdot \|_\infty$ denotes the supremum norm on the polydisc $\mathbb{D}^n$. The main result of this paper is that this inequality is hypercontractive, i.e., the constant can be taken to be $C^m$ for some $C>1$. Combining this improved version of the Bohnenblust-Hille inequality with other results, we obtain the following: The Bohr radius for the polydisc $\mathbb{D}^n$ behaves asymptotically as $\sqrt{(\log n)/n}$ modulo a factor bounded away from 0 and infinity, and the Sidon constant for the set of frequencies $\bigl\{ \log n: n \text{a positive integer} \le N\bigr\}$ is $\sqrt{N}\exp\{(-1/\sqrt{2}+o(1))\sqrt{\log N\log\log N}\}$.
http://www.recercat.cat:80/handle/2072/208683Marcinkiewicz-Zygmund inequalities
http://www.recercat.cat:80/handle/2072/222205
Marcinkiewicz-Zygmund inequalities
Ortega Cerdà, Joaquim; Saludes i Closa, Jordi
We study a generalization of the classical Marcinkiewicz-Zygmund inequalities. We relate this problem to the sampling sequences in the Paley-Wiener space and by using this analogy we give sharp necessary and sufficient computable conditions for a family of points to satisfy the Marcinkiewicz-Zygmund inequalities.
http://www.recercat.cat:80/handle/2072/222205On the Connectivity of the Julia sets of meromorphic functions
http://www.recercat.cat:80/handle/2072/246776
On the Connectivity of the Julia sets of meromorphic functions
Baranski, Krzysztof; Fagella Rabionet, Núria; Jarque i Ribera, Xavier; Karpinska, Boguslava
We prove that every transcendental meromorphic map $f$ with disconnected Julia set has a weakly repelling fixed point. This implies that the Julia set of Newton's method for finding zeroes of an entire map is connected. Moreover, extending a result of Cowen for holomorphic self-maps of the disc, we show the existence of absorbing domains for holomorphic self-maps of hyperbolic regions, whose iterates tend to a boundary point. In particular, the results imply that periodic Baker domains of Newton's method for entire maps are simply connected, which solves a well-known open question.
http://www.recercat.cat:80/handle/2072/246776Social network extraction and analysis based on multimodal dyadic interaction
http://www.recercat.cat:80/handle/2072/227932
Social network extraction and analysis based on multimodal dyadic interaction
Escalera Guerrero, Sergio; Baró i Solé, Xavier; Vitrià i Marca, Jordi; Radeva, Petia; Raducanu, Bogdan
Social interactions are a very important component in people"s lives. Social network analysis has become a common technique used to model and quantify the properties of social interactions. In this paper, we propose an integrated framework to explore the characteristics of a social network extracted from multimodal dyadic interactions. For our study, we used a set of videos belonging to New York Times" Blogging Heads opinion blog. The Social Network is represented as an oriented graph, whose directed links are determined by the Inﬂuence Model. The links" weights are a measure of the"inﬂuence" a person has over the other. The states of the Inﬂuence Model encode automatically extracted audio/visual features from our videos using state-of-the art algorithms. Our results are reported in terms of accuracy of audio/visual data fusion for speaker segmentation and centrality measures used to characterize the extracted social network.
http://www.recercat.cat:80/handle/2072/227932Stable sampling and Fourier multipliers
http://www.recercat.cat:80/handle/2072/237228
Stable sampling and Fourier multipliers
Matei, Basarab; Meyer, Yves; Ortega Cerdà, Joaquim
We study the relationship between stable sampling sequences for bandlimited functions in $L^p(\R^n)$ and the Fourier multipliers in $L^p$. In the case that the sequence is a lattice and the spectrum is a fundamental domain for the lattice the connection is complete. In the case of irregular sequences there is still a partial relationship.
http://www.recercat.cat:80/handle/2072/237228On Lundh's percolation diffusion
http://www.recercat.cat:80/handle/2072/208568
On Lundh's percolation diffusion
Carroll, Tom; O'Donovan, Julie; Ortega Cerdà, Joaquim
A collection of spherical obstacles in the unit ball in Euclidean space is said to be avoidable for Brownian motion if there is a positive probability that Brownian motion diffusing from some point in the ball will avoid all the obstacles and reach the boundary of the ball. The centres of the spherical obstacles are generated according to a Poisson point process while the radius of an obstacle is a deterministic function. If avoidable configurations are generated with positive probability, Lundh calls this percolation diffusion. An integral condition for percolation diffusion is derived in terms of the intensity of the point process and the function that determines the radii of the obstacles.
http://www.recercat.cat:80/handle/2072/208568The maximum voltage drop in an on-chip power distribution network: analysis of square, triangular and hexagonal power pad arrangements
http://www.recercat.cat:80/handle/2072/241485
The maximum voltage drop in an on-chip power distribution network: analysis of square, triangular and hexagonal power pad arrangements
Carroll, Tom; Ortega Cerdà, Joaquim
A mathematical model of the voltage drop which arises in on-chip power distribution networks is used to compare the maximum voltage drop in the case of different geometric arrangements of the pads supplying power to the chip. These include the square or Manhattan power pad arrangement, which currently predominates, as well as equilateral triangular and hexagonal arrangements. In agreement with the findings in the literature and with physical and SPICE models, the equilateral triangular power pad arrangement is found to minimize the maximum voltage drop. This headline finding is a consequence of relatively simple formulas for the voltage drop, with explicit error bounds, which are established using complex analysis techniques, and elliptic functions in particular.
http://www.recercat.cat:80/handle/2072/241485A lower bound in Nehari's theorem on the polydisc
http://www.recercat.cat:80/handle/2072/209638
A lower bound in Nehari's theorem on the polydisc
Ortega Cerdà, Joaquim; Seip, Kristian
By theorems of Ferguson and Lacey ($d=2$) and Lacey and Terwilleger ($d>2$), Nehari's theorem is known to hold on the polydisc $\D^d$ for $d>1$, i.e., if $H_\psi$ is a bounded Hankel form on $H^2(\D^d)$ with analytic symbol $\psi$, then there is a function $\varphi$ in $L^\infty(\T^d)$ such that $\psi$ is the Riesz projection of $\varphi$. A method proposed in Helson's last paper is used to show that the constant $C_d$ in the estimate $\|\varphi\|_\infty\le C_d \|H_\psi\|$ grows at least exponentially with $d$; it follows that there is no analogue of Nehari's theorem on the infinite-dimensional polydisc.
http://www.recercat.cat:80/handle/2072/209638Trust region versus line search for computing the optical flow
http://www.recercat.cat:80/handle/2072/239334
Trust region versus line search for computing the optical flow
Kalmoun, El Mostafa; Garrido Ostermann, Lluís
We consider the numerical treatment of the optical flow problem by evaluating the performance of the trust region method versus the line search method. To the best of our knowledge, the trust region method is studied here for the first time for variational optical flow computation. Four different optical flow models are used to test the performance of the proposed algorithm combining linear and nonlinear data terms with quadratic and TV regularization. We show that trust region often performs better than line search; especially in the presence of non-linearity and non-convexity in the model.
http://www.recercat.cat:80/handle/2072/239334Relation between plaque type, plaque thickness, blood shear stress, and plaque stress in coronary arteries assessed by X-ray Angiography and Intravascular Ultrasound
http://www.recercat.cat:80/handle/2072/238746
Relation between plaque type, plaque thickness, blood shear stress, and plaque stress in coronary arteries assessed by X-ray Angiography and Intravascular Ultrasound
Balocco, Simone; Gatta, Carlo; Alberti, Marina; Carrillo, Xavier; Rigla, Juan; Radeva, Petia
Purpose: Atheromatic plaque progression is affected, among others phenomena, by biomechanical, biochemical, and physiological factors. In this paper, the authors introduce a novel framework able to provide both morphological (vessel radius, plaque thickness, and type) and biomechanical (wall shear stress and Von Mises stress) indices of coronary arteries. Methods: First, the approach reconstructs the three-dimensional morphology of the vessel from intravascular ultrasound(IVUS) and Angiographic sequences, requiring minimal user interaction. Then, a computational pipeline allows to automatically assess fluid-dynamic and mechanical indices. Ten coronary arteries are analyzed illustrating the capabilities of the tool and confirming previous technical and clinical observations. Results: The relations between the arterial indices obtained by IVUS measurement and simulations have been quantitatively analyzed along the whole surface of the artery, extending the analysis of the coronary arteries shown in previous state of the art studies. Additionally, for the first time in the literature, the framework allows the computation of the membrane stresses using a simplified mechanical model of the arterial wall. Conclusions: Circumferentially (within a given frame), statistical analysis shows an inverse relation between the wall shear stress and the plaque thickness. At the global level (comparing a frame within the entire vessel), it is observed that heavy plaque accumulations are in general calcified and are located in the areas of the vessel having high wall shear stress. Finally, in their experiments the inverse proportionality between fluid and structural stresses is observed.
http://www.recercat.cat:80/handle/2072/238746Sherali-Adams Relaxations and Indistinguishability in Counting Logics
http://www.recercat.cat:80/handle/2072/207067
Sherali-Adams Relaxations and Indistinguishability in Counting Logics
Atserias, Albert; Maneva, Elitza
Two graphs with adjacency matrices $\mathbf{A}$ and $\mathbf{B}$ are isomorphic if there exists a permutation matrix $\mathbf{P}$ for which the identity $\mathbf{P}^{\mathrm{T}} \mathbf{A} \mathbf{P} = \mathbf{B}$ holds. Multiplying through by $\mathbf{P}$ and relaxing the permutation matrix to a doubly stochastic matrix leads to the linear programming relaxation known as fractional isomorphism. We show that the levels of the Sherali--Adams (SA) hierarchy of linear programming relaxations applied to fractional isomorphism interleave in power with the levels of a well-known color-refinement heuristic for graph isomorphism called the Weisfeiler--Lehman algorithm, or, equivalently, with the levels of indistinguishability in a logic with counting quantifiers and a bounded number of variables. This tight connection has quite striking consequences. For example, it follows immediately from a deep result of Grohe in the context of logics with counting quantifiers that a fixed number of levels of SA suffice to determine isomorphism of planar and minor-free graphs. We also offer applications in both finite model theory and polyhedral combinatorics. First, we show that certain properties of graphs, such as that of having a flow circulation of a prescribed value, are definable in the infinitary logic with counting with a bounded number of variables. Second, we exploit a lower bound construction due to Cai, Fürer, and Immerman in the context of counting logics to give simple explicit instances that show that the SA relaxations of the vertex-cover and cut polytopes do not reach their integer hulls for up to $\Omega(n)$ levels, where $n$ is the number of vertices in the graph.
http://www.recercat.cat:80/handle/2072/207067Reliable computation of robust response tori on the verge of breakdown
http://www.recercat.cat:80/handle/2072/207066
Reliable computation of robust response tori on the verge of breakdown
Figueras Romero, Jordi-Lluís; Haro, Àlex
We prove the existence and local uniqueness of invariant tori on the verge of breakdown for two systems: the quasi-periodically driven logistic map and the quasi-periodically forced standard map. These systems exemplify two scenarios: the Heagy-Hammel route for the creation of strange non- chaotic attractors and the nonsmooth bifurcation of saddle invariant tori. Our proofs are computer- assisted and are based on a tailored version of the Newton-Kantorovich theorem. The proofs cannot be performed using classical perturbation theory because the two scenarios are very far from the perturbative regime, and fundamental hypotheses such as reducibility or hyperbolicity either do not hold or are very close to failing. Our proofs are based on a reliable computation of the invariant tori and a careful study of their dynamical properties, leading to the rigorous validation of the numerical results with our novel computational techniques.
http://www.recercat.cat:80/handle/2072/207066Standardized evaluation methodology and reference database for evaluating IVUS image segmentation
http://www.recercat.cat:80/handle/2072/227933
Standardized evaluation methodology and reference database for evaluating IVUS image segmentation
Balocco, Simone; Gatta, Carlo; Ciompi, Francesco; Wahle, Andreas; Radeva, Petia; Carlier, Stéphane; Ünal, Gözde B.; Sanidas, Elias; Mauri, Josepa; Carrillo, Xavier; Kovarnik, Tomas; Wang, Ching-Wei; Chen, Hsiang-Chou; Exarchos, Themis P.; Fotiadis, Dimitrios I.; Destrempes, François; Cloutier, Guy; Pujol Vila, Oriol; Alberti, Marina; E. Gerardo Mendizabal-Ruiz
This paper describes an evaluation framework that allows a standardized and quantitative comparison of IVUS lumen and media segmentation algorithms. This framework has been introduced at the MICCAI 2011 Computing and Visualization for (Intra)Vascular Imaging (CVII) workshop, comparing the results of eight teams that participated. We describe the available data-base comprising of multi-center, multi-vendor and multi-frequency IVUS datasets, their acquisition, the creation of the reference standard and the evaluation measures. The approaches address segmentation of the lumen, the media, or both borders; semi- or fully-automatic operation; and 2-D vs. 3-D methodology. Three performance measures for quantitative analysis have been proposed. The results of the evaluation indicate that segmentation of the vessel lumen and media is possible with an accuracy that is comparable to manual annotation when semi-automatic methods are used, as well as encouraging results can be obtained also in case of fully-automatic segmentation. The analysis performed in this paper also highlights the challenges in IVUS segmentation that remains to be solved.
http://www.recercat.cat:80/handle/2072/227933Sierpinski curve Julia sets for quadratic rational maps
http://www.recercat.cat:80/handle/2072/239335
Sierpinski curve Julia sets for quadratic rational maps
Devaney, Robert L.; Fagella Rabionet, Núria; Garijo Real, Antonio; Jarque i Ribera, Xavier
We investigate under which dynamical conditions the Julia set of a quadratic rational map is a Sierpiński curve.
http://www.recercat.cat:80/handle/2072/239335The univalent Bloch-Landau constant, harmonic symmetry and conformal glueing
http://www.recercat.cat:80/handle/2072/211599
The univalent Bloch-Landau constant, harmonic symmetry and conformal glueing
Carroll, Tom; Ortega Cerdà, Joaquim
By modifying a domain first suggested by Ruth Goodman in 1935 and by exploiting the explicit solution by Fedorov of the Polyá-Chebotarev problem in the case of four symmetrically placed points, an improved upper bound for the univalent Bloch-Landau constant is obtained. The domain that leads to this improved bound takes the form of a disk from which some arcs are removed in such a way that the resulting simply connected domain is harmonically symmetric in each arc with respect to the origin. The existence of domains of this type is established, using techniques from conformal welding, and some general properties of harmonically symmetric arcs in this setting are established.
http://www.recercat.cat:80/handle/2072/211599Pointwise estimates for the Bergman kernel of the weighted Fock space
http://www.recercat.cat:80/handle/2072/222204
Pointwise estimates for the Bergman kernel of the weighted Fock space
Marzo Sánchez, Jordi; Ortega Cerdà, Joaquim
We prove upper pointwise estimates for the Bergman kernel of the weighted Fock space of entire functions in $L^{2}(e^{-2\phi}) $ where $\phi$ is a subharmonic function with $\Delta\phi$ a doubling measure. We derive estimates for the canonical solution operator to the inhomogeneous Cauchy-Riemann equation and we characterize the compactness of this operator in terms of $\Delta\phi$.
http://www.recercat.cat:80/handle/2072/222204A parameterization method for the computation of invariant tori and their whiskers in quasi-periodic maps: explorations and mechanisms for the breakdown of hyperbolicity
http://www.recercat.cat:80/handle/2072/206763
A parameterization method for the computation of invariant tori and their whiskers in quasi-periodic maps: explorations and mechanisms for the breakdown of hyperbolicity
Haro, Àlex; Llave, Rafael de la
In two previous papers [J. Differential Equations, 228 (2006), pp. 530 579; Discrete Contin. Dyn. Syst. Ser. B, 6 (2006), pp. 1261 1300] we have developed fast algorithms for the computations of invariant tori in quasi‐periodic systems and developed theorems that assess their accuracy. In this paper, we study the results of implementing these algorithms and study their performance in actual implementations. More importantly, we note that, due to the speed of the algorithms and the theoretical developments about their reliability, we can compute with confidence invariant objects close to the breakdown of their hyperbolicity properties. This allows us to identify a mechanism of loss of hyperbolicity and measure some of its quantitative regularities. We find that some systems lose hyperbolicity because the stable and unstable bundles approach each other but the Lyapunov multipliers remain away from 1. We find empirically that, close to the breakdown, the distances between the invariant bundles and the Lyapunov multipliers which are natural measures of hyperbolicity depend on the parameters, with power laws with universal exponents. We also observe that, even if the rigorous justifications in [J. Differential Equations, 228 (2006), pp. 530-579] are developed only for hyperbolic tori, the algorithms work also for elliptic tori in Hamiltonian systems. We can continue these tori and also compute some bifurcations at resonance which may lead to the existence of hyperbolic tori with nonorientable bundles. We compute manifolds tangent to nonorientable bundles.
http://www.recercat.cat:80/handle/2072/206763Bandlimited Lipschitz functions
http://www.recercat.cat:80/handle/2072/237229
Bandlimited Lipschitz functions
Lyubarskii, Yurii; Ortega Cerdà, Joaquim
We study the space of bandlimited Lipschitz functions in one variable. In particular we provide a geometrical description of interpolating and sampling sequences for this space. We also give a description of the trace of such functions to sequences of critical density in terms of a cancellation condition.
http://www.recercat.cat:80/handle/2072/237229The maximum voltage drop in an on-chip power distribution network: analysis of square, triangular and hexagonal power pad arrangements
http://www.recercat.cat:80/handle/2072/234164
The maximum voltage drop in an on-chip power distribution network: analysis of square, triangular and hexagonal power pad arrangements
Carroll, Tom; Ortega Cerdà, Joaquim
A mathematical model of the voltage drop which arises in on-chip power distribution networks is used to compare the maximum voltage drop in the case of different geometric arrangements of the pads supplying power to the chip. These include the square or Manhattan power pad arrangement, which currently predominates, as well as equilateral triangular and hexagonal arrangements. In agreement with the findings in the literature and with physical and SPICE models, the equilateral triangular power pad arrangement is found to minimize the maximum voltage drop. This headline finding is a consequence of relatively simple formulas for the voltage drop, with explicit error bounds, which are established using complex analysis techniques, and elliptic functions in particular.
http://www.recercat.cat:80/handle/2072/234164Approximate polytope ensemble for one-class classification
http://www.recercat.cat:80/handle/2072/228272
Approximate polytope ensemble for one-class classification
Casale, Pierluigi; Pujol Vila, Oriol; Radeva, Petia
In this work, a new one-class classification ensemble strategy called approximate polytope ensemble is presented. The main contribution of the paper is threefold. First, the geometrical concept of convex hull is used to define the boundary of the target class defining the problem. Expansions and contractions of this geometrical structure are introduced in order to avoid over-fitting. Second, the decision whether a point belongs to the convex hull model in high dimensional spaces is approximated by means of random projections and an ensemble decision process. Finally, a tiling strategy is proposed in order to model non-convex structures. Experimental results show that the proposed strategy is significantly better than state of the art one-class classification methods on over 200 datasets.
http://www.recercat.cat:80/handle/2072/228272Relation between plaque type, plaque thickness, blood shear stress, and plaque stress in coronary arteries assessed by X-ray Angiography and Intravascular Ultrasound
http://www.recercat.cat:80/handle/2072/227931
Relation between plaque type, plaque thickness, blood shear stress, and plaque stress in coronary arteries assessed by X-ray Angiography and Intravascular Ultrasound
Balocco, Simone; Gatta, Carlo; Alberti, Marina; Carrillo, Xavier; Rigla, Juan; Radeva, Petia
Purpose: Atheromatic plaque progression is affected, among others phenomena, by biomechanical, biochemical, and physiological factors. In this paper, the authors introduce a novel framework able to provide both morphological (vessel radius, plaque thickness, and type) and biomechanical (wall shear stress and Von Mises stress) indices of coronary arteries. Methods: First, the approach reconstructs the three-dimensional morphology of the vessel from intravascular ultrasound(IVUS) and Angiographic sequences, requiring minimal user interaction. Then, a computational pipeline allows to automatically assess fluid-dynamic and mechanical indices. Ten coronary arteries are analyzed illustrating the capabilities of the tool and confirming previous technical and clinical observations. Results: The relations between the arterial indices obtained by IVUS measurement and simulations have been quantitatively analyzed along the whole surface of the artery, extending the analysis of the coronary arteries shown in previous state of the art studies. Additionally, for the first time in the literature, the framework allows the computation of the membrane stresses using a simplified mechanical model of the arterial wall. Conclusions: Circumferentially (within a given frame), statistical analysis shows an inverse relation between the wall shear stress and the plaque thickness. At the global level (comparing a frame within the entire vessel), it is observed that heavy plaque accumulations are in general calcified and are located in the areas of the vessel having high wall shear stress. Finally, in their experiments the inverse proportionality between fluid and structural stresses is observed.
http://www.recercat.cat:80/handle/2072/227931Equidistribution of Fekete Points on the Sphere
http://www.recercat.cat:80/handle/2072/227733
Equidistribution of Fekete Points on the Sphere
Marzo Sánchez, Jordi; Ortega Cerdà, Joaquim
Fekete points are the points that maximize a Vandermonde-type determinant that appears in the polynomial Lagrange interpolation formula. They are well suited points for interpolation formulas and numerical integration. We prove the asymptotic equidistribution of Fekete points in the sphere. The way we proceed is by showing their connection to other arrays of points, the so-called Marcinkiewicz-Zygmund arrays and interpolating arrays, that have been studied recently.
http://www.recercat.cat:80/handle/2072/227733Sierpinski curve Julia sets for quadratic rational maps
http://www.recercat.cat:80/handle/2072/227340
Sierpinski curve Julia sets for quadratic rational maps
Devaney, Robert L.; Fagella Rabionet, Núria; Garijo Real, Antonio; Jarque i Ribera, Xavier
We investigate under which dynamical conditions the Julia set of a quadratic rational map is a Sierpiński curve.
http://www.recercat.cat:80/handle/2072/227340Disminució de la sobreproducció en una empresa d’estampació mitjançant eines del Lean Manufacturing
http://www.recercat.cat:80/handle/2072/225834
Disminució de la sobreproducció en una empresa d’estampació mitjançant eines del Lean Manufacturing
Villagrasa Perulero, Victor
Aquest projecte s'ha dut a terme en una empresa d'estampació de peces per al sector de l'automòbil on, al tancament de l'any 2012, tot i haver disminuït la facturació, els costos de personal havien crescut degut a un augment del treball en hores extres. D’altra banda, l'empresa tenia una gran acumulació d'estocs de peces fabricades que ocupaven espai al magatzem, i de peces en curs que dificultaven les tasques a les estacions de treball. Després d'una primera anàlisi, es va veure que una de les causes principals de la sobreproducció era el temps de canvis de producte (TCP), que requeria entre hora i mitja i dues hores.Després d'aquesta primera anàlisi, es va realitzar un estudi del procés productiu d'una de les peces més importants per aquesta empresa, amb l'objectiu d'identificar altres causes de la sobreproducció. Per fer això, es va utilitzar la cartografia de la cadena de valor (Value Stream Map), el que va permetre també identificar malbarataments i punts de millora per a la proposta de solucions per aconseguir un flux productiu més continu.La primera solució, la qual ha estat implementada, és l'ordenació i la neteja de les naus mitjançant la tècnica de les 5S amb l'objectiu d'eliminar o reduir malbarataments en la producció, com per exemple, moviments innecessaris de cerca d'eines o temps d'espera de matèria primera per fabricar.Posteriorment, després d’analitzar les operacions de canvi de producte mitjançant la tècnica SMED per tal de disminuir el TCP, s'ha reestructurat i estandarditzat tot el procés, fent que algunes activitats que s'han de realitzar durant el canvi es realitzin quan la màquina encara està funcionant. A més, s'ha reordenat el lloc de treball per guanyar temps, i s'ha proposat realitzar, en paral·lel, algunes de les operacions del procés de canvi. En conjunt, s'ha estimat una reducció significativa del TCP, passant a ser de 42,5 minuts, sense tenir en compte la utilització de tecnologies proposades per a realitzar canvis ràpids en les màquines.Finalment, per a la reducció dels estocs entre processos, es proposa un sistema de targetes Kanban, per garantir un flux productiu més continu i eficient, i amb el qual es podrien reduir el material en un curs del producte analitzat de 28800 peces a 14400 peces.En definitiva, tot i que el conjunt de solucions proposades provenen de l’estudi i millora del procés d’una de les peces més importants de l’empresa, les mesures plantejades beneficien al conjunt de processos de l’empresa. Tot i això, seria convenient realitzar les mateixes millores en la resta de productes per tal d'aconseguir reduir completament la sobreproducció i així augmentar l’eficiència de l’empresa.
http://www.recercat.cat:80/handle/2072/225834