Regular triangulations of dynamic sets of points

The Delaunay triangulations of a set of points are a class of triangulations which play an important role in a variety of different disciplines of science. Regular triangulations are a generalization of Delaunay triangulations that maintain both their relationship with convex hulls and with Voronoi diagrams. In regular triangulations, a real value, its weight, is assigned to each point. In this paper a simple data structure is presented that allows regular triangulations of sets of points to be dynamically updated, that is, new points can be incrementally inserted in the set and old points can be deleted from it. The algorithms we propose for insertion and deletion are based on a geometrical interpretation of the history data structure in one more dimension and use lifted flips as the unique topological operation. This results in rather simple and efficient algorithms. The algorithms have been implemented and experimental results are given.Postprint (published version

Pere Vieta (1779–1856), promoter of free public teaching of physics in Catalonia

Free public teaching of physics in Catalonia started in the early 19th century, even if the interest in experimental physics goes back to the 18th century, where this discipline was discussed at various learned societies. The first chair of Physics in Barcelona was not a university chair but that of the Junta de Comerç de Barcelona (Trade Board of Barcelona), which had several scientific-technical Schools. In fact, at that time, Barcelona had no university, because it had been supressed by King Felipe V after the War of the Spanish Succession (ended in 1714). The promoter of free public teaching of experimental physics was Pere (Pedro) Vieta i Gibert (17791856), who was the first professor of that subject both at the School of the Trade Board and at the University of Barcelona, once it was restored in 1842. Vieta, who was a surgeon in the Army, combined his two professions and his interest in meteorology, he having recorded meteorological observations in Barcelona for many years. Many of his students were influential people in the scientific, intellectual, political and economic history of the 19th century in Catalonia and Spain. [Contrib Sci 11:237-247 (2015)]Postprint (published version

Cell Detection by Functional Inverse Diffusion and Non-negative Group Sparsity−-Part I: Modeling and Inverse Problems

In this two-part paper, we present a novel framework and methodology to analyze data from certain image-based biochemical assays, e.g., ELISPOT and Fluorospot assays. In this first part, we start by presenting a physical partial differential equations (PDE) model up to image acquisition for these biochemical assays. Then, we use the PDEs' Green function to derive a novel parametrization of the acquired images. This parametrization allows us to propose a functional optimization problem to address inverse diffusion. In particular, we propose a non-negative group-sparsity regularized optimization problem with the goal of localizing and characterizing the biological cells involved in the said assays. We continue by proposing a suitable discretization scheme that enables both the generation of synthetic data and implementable algorithms to address inverse diffusion. We end Part I by providing a preliminary comparison between the results of our methodology and an expert human labeler on real data. Part II is devoted to providing an accelerated proximal gradient algorithm to solve the proposed problem and to the empirical validation of our methodology.Comment: published, 15 page

R-summed form of adiabatic expansions in curved spacetime

The Feynman propagator in curved spacetime admits an asymptotic (Schwinger-DeWitt) series expansion in derivatives of the metric. Remarkably, all terms in the series containing the Ricci scalar R can be summed exactly. We show that this (non-perturbative) property of the Schwinger-DeWitt series has a natural and equivalent counterpart in the adiabatic (Parker-Fulling) series expansion of the scalar modes in an homogeneous cosmological spacetime. The equivalence between both R-summed adiabatic expansions can be further extended when a background scalar field is also present.Comment: 13 pages. Minor changes. Misprints corrected. To appear in Phys. Rev.

New approaches to texture coding in segmentation and feature-based image coding schemes

Peer ReviewedPostprint (published version

Coding of details in very low bit-rate video systems

In this paper, the importance of including small image features at the initial levels of a progressive second generation video coding scheme is presented. It is shown that a number of meaningful small features called details should be coded, even at very low data bit-rates, in order to match their perceptual significance to the human visual system. We propose a method for extracting, perceptually selecting and coding of visual details in a video sequence using morphological techniques. Its application in the framework of a multiresolution segmentation-based coding algorithm yields better results than pure segmentation techniques at higher compression ratios, if the selection step fits some main subjective requirements. Details are extracted and coded separately from the region structure and included in the reconstructed images in a later stage. The bet of considering the local background of a given detail for its perceptual selection breaks the concept ofPeer ReviewedPostprint (published version

Microgravity acoustic mixing for particle cloud combustors

Experimental and theoretical investigations of acoustic mixing procedures designed to uniformly distribute fuel particles in a combustion tube for application in the proposed Particle Cloud Combustion Experiment (PCCE) are described. Two acoustic mixing methods are investigated: mixing in a cylindrical tube using high frequency spinning modes generated by suitably phased, or quadrature speakers, and acoustic premixing in a sphere. Quadrature mixing leads to rapid circumferential circulation of the powder around the tube. Good mixing is observed in the circulating regions. However, because axial inhomogeneities are necessarily present in the acoustic field, this circulation does not extend throughout the tube. Simultaneous operation of the quadrature-speaker set and the axial-speaker was observed to produce considerably enhanced mixing compared to operation of the quadrature-speaker set alone. Mixing experiments using both types of speakers were free of the longitudinal powder drift observed using axial-speakers alone. Vigorous powder mixing was obtained in the sphere for many normal modes: however, in no case was the powder observed to fill the sphere entirely. Theoretical analysis indicated that mixing under steady conditions cannot fill more than a hemisphere except under very unusual conditions. Premixing in a hemisphere may be satisfactory; otherwise, complete mixing in microgravity might be possible by operating the speaker in short bursts. A general conclusion is that acoustic transients are more likely to produce good mixing than steady state conditions. The reason is that in steady conditions, flow structures like nodal planes are possible and often even unavoidable. These tend to separate the mixing region into cells across which powder cannot be transferred. In contrast, transients not only are free of such structures, they also have the characteristics, desirable for mixing, of randomness and disorder. This conclusion is corroborated by mixing experiments using axial waves

A phylogenetic comparative analysis on the evolution of sequential hermaphroditism in seabreams (Teleostei : Sparidae)

The Sparids are an ideal group of fish in which to study the evolution of sexual systems since they exhibit a great sexual diversity, from gonochorism (separate sexes) to protandrous (male-first) and protogynous (female-first) sequential hermaphroditism (sex-change). According to the size-advantage model (SAM), selection should favour sex change when the second sex achieves greater reproductive success at a larger body size than the first sex. Using phylogenetic comparative methods and a sample of 68 sparid species, we show that protogyny and protandry evolve from gonochorism but evolutionary transitions between these two forms of sequential hermaphroditism are unlikely to happen. Using male gonadosomatic index (GSI) as a measure of investment in gametes and proxy for sperm competition, we find that, while gonochoristic and protogynous species support the predictions of SAM, protandrous species do not, as they exhibit higher GSI values than expected even after considering mating systems and spawning modes. We suggest that small males of protandrous species have to invest disproportionally more in sperm production than predicted not only when spawning in aggregations with high levels of sperm competition, but also when spawning in pairs due to the need to fertilize highly fecund females, much larger than themselves. We propose that this compensatory mechanism, together with Bateman’s principles in sequential hermaphrodites, should be formally incorporated in the SAM