The curve shortening flow with density of a spherical curve in codimension two

In the present paper we carry out a systematic study about the flow of a spherical curve by the mean curvature flow with density in a 3-dimensional rotationally symmetric space with density (M3 w, gw,ξ) where the density ξ decomposes as sum of a radial part ϕ and an angular part ψ. We analyse how either the parabolicity or the hyperbolicity of (M3 w, gw) conditions the behaviour of the flow when the solution goes to infinity

Broadband and efficient plasmonic control in the near-infrared and visible via strong interference of surface plasmon polaritons

This paper was published in Optics Letters and is made available as an electronic reprint with the permission of OSA. The paper can be found at the following URL on the OSA website: http://dx.doi.org/10.1364/OL.38.004453 Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law.Copyright © 2013 Optical Society of AmericaBroadband and tunable control of surface plasmon polaritons in the near-infrared and visible spectrum is demonstrated theoretically and numerically with a pair of phased nanoslits. We establish, with simulations supported by a coupled wave model, that by dividing the incident power equally between two input channels, the maximum plasmon intensity deliverable to either side of the nanoslit pair is twice that for an isolated slit. For a broadband source, a compact device with nanoslit separation of the order of a tenth of the wavelength is shown to steer nearly all the generated plasmons to one side for the same phase delay, thereby achieving a broadband unidirectional plasmon launcher. The reported effect can be applied to the design of ultra-broadband and efficient tunable plasmonic devices.Engineering and Physical Sciences Research Council (EPSRC

El problema del acortamiento de curvas asociado a una densidad

A lo largo de la presente Tesis, se estudia el flujo por la curvatura media asociado a una densidad (FCMpsi) de una hipersuperficie, en una variedad riemanniana con densidad. Los principales resultados se obtienen para el caso particular en el que la dimensión de la variedad ambiente es dos y las subvariedades son curvas. A dicho problema, se le llamará problema del acortamiento de curvas asociado a una densidad (PACpsi). En el capítulo uno, se presentan los conceptos básicos para desarrollar y comprender el trabajo de la Tesis. Se da la definición del problema a abordar, se introducen las herramientas necesarias para su estudio y se calculan las fórmulas de variación de las cantidades geométricas asociadas a las subvariedades que constituyen la solución del flujo. A su vez, se incluyen en esta sección los primeros resultados originales. En el capítulo siguiente, se estudia el PACpsi en el caso particular en que la densidad es diferenciable en la región donde se da la evolución de la curva. Los resultados principales de esta sección se refieren a la descripción de la evolución, bajo el PACpsi, de una curva cerrada y embebida en el plano con una densidad radial, y a un resultado de subconvergencia a una curva cerrada y psi-mínima en una superficie bajo algunas circunstancias generales, cuando el tiempo máximo de existencia para la solución es infinito. Dicho resultado de subconvergencia, junto al trabajo desarrollado por Angenent, Oaks y Xi-Ping Zhu, generaliza al caso con densidad los resultados obtenidos por Gage, Grayson y Hamilton en la década de los ochenta para el problema del acortamiento de curvas. En el capítulo tres, se definen las singularidades de tipo I para el flujo por la curvatura media asociado a una densidad, psi, y se describe el blow-up en el tiempo máximo en el que se dan estas singularidades. En esta parte de la Tesis se pone especial atención al caso donde la singularidad se produce por la parte de la psi-curvatura debida a la densidad. Atendiendo a este objetivo, se describe una familia de curvas cuya evolución bajo el PACpsi (en una superficie riemanniana de curvatura de Gauss no negativa y con una densidad que es singular en una geodésica de la superficie) produce únicamente singularidades de tipo I y se procede a estudiar los límites de estos blow-up. Como consecuencia de este estudio, y gracias a la relación entre submersiones riemannianas y geometría con densidad, se obtiene un resultado para el flujo por la curvatura media de hipersuperficies de revolución en espacios rotacionalmente simétricos con curvatura seccional no negativa. Este resultado generaliza ciertos resultados obtenidos por Huisken, Altschuler, Angenent y Giga para superficies de revolución en el espacio euclídeo. Los resultados del segundo capítulo junto a algunos de los del primer capítulo constituyen el contenido del artículo: Miquel, V., and Viñado-Lereu, F. The curve shortening problem associated to a density. Calculus of Variations and Partial Differential Equations 55:61, 3 (June 2016), 1 - 30. Los resultados del tercer capítulo junto a algunos de los del primer capítulo constituyen el contenido del preprint: Miquel, V., and Viñado-Lereu, F. Type I singularities in the curve shortening flow associated to a density. Preprint arXiv.org: 1607.08402v1 (2016)

Plasticity, elasticity, and adhesion energy of plant cell walls: nanometrology of lignin loss using atomic force microscopy

International audienceThe complex organic polymer, lignin, abundant in plants, prevents the efficient extraction of sugars from the cell walls that is required for large scale biofuel production. Because lignin removal is crucial in overcoming this challenge, the question of how the nanoscale properties of the plant cell ultrastructure correlate with delignification processes is important. Here, we report how distinct molecular domains can be identified and how physical quantities of adhesion energy, elasticity, and plasticity undergo changes, and whether such quantitative observations can be used to characterize delignification. By chemically processing biomass, and employing nanometrology, the various stages of lignin removal are shown to be distinguished through the observed morphochemical and nanomechanical variations. Such spatially resolved correlations between chemistry and nanomechanics during deconstruction not only provide a better understanding of the cell wall architecture but also is vital for devising optimum chemical treatments

End-systole and end-diastole detection in short axis cine MRI using a fully convolutional neural network with dilated convolutions

[EN] The correct assessment and characterization of heart anatomy and functionality is usually done through inspection of magnetic resonance image cine sequences. In the clinical setting it is especially important to determine the state of the left ventricle. This requires the measurement of its volume in the end-diastolic and end-systolic frames within the sequence trough segmentation methods. However, the first step required for this analysis before any segmentation is the detection of the end-systolic and end-diastolic frames within the image acquisition. In this work we present a fully convolutional neural network that makes use of dilated convolutions to encode and process the temporal information of the sequences in contrast to the more widespread use of recurrent networks that are usually employed for problems involving temporal information. We trained the network in two different settings employing different loss functions to train the network: the classical weighted cross-entropy, and the weighted Dice loss. We had access to a database comprising a total of 397 cases. Out of this dataset we used 98 cases as test set to validate our network performance. The final classification on the test set yielded a mean frame distance of 0 for the end-diastolic frame (i.e.: the selected frame was the correct one in all images of the test set) and 1.242 (relative frame distance of 0.036) for the end-systolic frame employing the optimum setting, which involved training the neural network with the Dice loss. Our neural network is capable of classifying each frame and enables the detection of the end-systolic and end-diastolic frames in short axis cine MRI sequences with high accuracy.Funding sources This work was partially supported by the Conselleria d'Innovació, Universitats, Ciència i Societat Digital, Generalitat Valenciana (grants AEST/2020/029 and AEST/2021/050) .Pérez-Pelegrí, M.; Monmeneu, JV.; López-Lereu, MP.; Maceira, AM.; Bodi, V.; Moratal, D. (2022). End-systole and end-diastole detection in short axis cine MRI using a fully convolutional neural network with dilated convolutions. Computerized Medical Imaging and Graphics. 99:1-8. https://doi.org/10.1016/j.compmedimag.2022.102085189

Automatic left ventricle volume calculation with explainability through a deep learning weak-supervision methodology

[EN] Background and objective: Magnetic resonance imaging is the most reliable imaging technique to assess the heart. More specifically there is great importance in the analysis of the left ventricle, as the main pathologies directly affect this region. In order to characterize the left ventricle, it is necessary to extract its volume. In this work we present a neural network architecture that is capable of directly estimating the left ventricle volume in short axis cine Magnetic Resonance Imaging in the end-diastolic frame and provide a segmentation of the region which is the basis of the volume calculation, thus offering explain-ability to the estimated value. Methods: The network was designed to directly target the volumes to estimate, not requiring any labeled segmentation on the images. The network was based on a 3D U-net with extra layers defined in a scan-ning module that learned features like the circularity of the objects and the volumes to estimate in a weakly-supervised manner. The only targets defined were the left ventricle volumes and the circularity of the object detected through the estimation of the pi value derived from its shape. We had access to 397 cases corresponding to 397 different subjects. We randomly selected 98 cases to use as test set. Results: The results show a good match between the real and estimated volumes in the test set, with a mean relative error of 8% and a mean absolute error of 9.12 ml with a Pearson correlation coefficient of 0.95. The derived segmentations obtained by the network achieved Dice coefficients with a mean value of 0.79. Conclusions: The proposed method is capable of obtaining the left ventricle volume biomarker in the end-diastole and offer an explanation of how it obtains the result in the form of a segmentation mask without the need of segmentation labels to train the algorithm, making it a potentially more trustworthy method for clinicians and a way to train neural networks more easily when segmentation labels are not readily available.The authors acknowledge financial support from the Consel-leria d'Educacio, Investigacio, Cultura i Esport, Generalitat Valenciana (grants AEST/2019/037 and AEST/2020/029) , from the Agencia Valenciana de la Innovacion, Generalitat Valenciana (ref. INNCAD00/19/085) , and from the Centro para el Desarrollo Tecnologico Industrial (Programa Eurostars2, actuacion Interempresas Internacional) , Spanish Ministerio de Ciencia, Innovacion y Universidades (ref. CIIP-20192020) .Pérez-Pelegrí, M.; Monmeneu, JV.; López-Lereu, MP.; Pérez-Pelegrí, L.; Maceira, AM.; Bodi, V.; Moratal, D. (2021). Automatic left ventricle volume calculation with explainability through a deep learning weak-supervision methodology. Computer Methods and Programs in Biomedicine. 208:1-8. https://doi.org/10.1016/j.cmpb.2021.106275S1820

PSPU-Net for Automatic Short Axis Cine MRI Segmentation of Left and Right Ventricles

[EN] Characterization of the heart anatomy and function is mostly done with magnetic resonance image cine series. To achieve a correct characterization, the volume of the right and left ventricle need to be segmented, which is a timeconsuming task. We propose a new convolutional neural network architecture that combines U-net with PSP modules (PSPU-net) for the segmentation of left and right ventricle cavities and left ventricle myocardium in the diastolic frame of short-axis cine MRI images and compare its results against a classic 3D U-net architecture. We used a dataset containing 399 cases in total. The results showed higher quality results in both segmentation and final volume estimation for a test set of 99 cases in the case of the PSPU-net, with global dice metrics of 0.910 and median absolute relative errors in volume estimations of 0.026 and 0.039 for the left ventricle cavity and myocardium and 0.051 for the right ventricles cavity.DM acknowledges financial support from the Conselleria d'Educacio, Investigacio, Cultura i Esport, Generalitat Valenciana (grants AEST/2019/037 and AEST/2020/029), from the Agencia Valenciana de la Innovacion, Generalitat Valenciana (ref. INNCAD00/19/085), and from the Centro para el Desarrollo Tecnologico Industrial (Programa Eurostars-2, actuacion Interempresas Internacional), Spanish Ministerio de Ciencia, Innovacion y Universidades (ref. CIIP20192020). We are grateful to Andres Larroza for his valuable technical assistance in the project.Pérez-Pelegrí, M.; Monmeneu, JV.; López-Lereu, MP.; Ruiz-España, S.; Del-Canto, I.; Bodi, V.; Moratal, D. (2020). PSPU-Net for Automatic Short Axis Cine MRI Segmentation of Left and Right Ventricles. IEEE Computer Society. 1048-1053. https://doi.org/10.1109/BIBE50027.2020.00177S1048105