A note on mean volume and surface densities for a class of birth-and-growth stochastic processes

Many real phenomena may be modelled as locally finite unions of $d$-dimensional time dependent random closed sets in $\mathbb{R}^d$, described by birth-and-growth stochastic processes, so that their mean volume and surface densities, as well as the so called mean \emph{extended} volume and surface densities, may be studied in terms of relevant quantities characterizing the process. We extend here known results in the Poissonian case to a wider class of birth-and-growth stochastic processes, proving in particular the absolute continuity of the random time of capture of a point $x\in\R^d$ by processes of this class.Comment: 11 pages; revised version for publication: proof simplified, added new resul

On the approximation of mean densities of random closed sets

Many real phenomena may be modelled as random closed sets in $\mathbb{R}^d$, of different Hausdorff dimensions. In many real applications, such as fiber processes and $n$-facets of random tessellations of dimension $n\leq d$ in spaces of dimension $d\geq1$, several problems are related to the estimation of such mean densities. In order to confront such problems in the general setting of spatially inhomogeneous processes, we suggest and analyze an approximation of mean densities for sufficiently regular random closed sets. We show how some known results in literature follow as particular cases. A series of examples throughout the paper are provided to illustrate various relevant situations.Comment: Published in at http://dx.doi.org/10.3150/09-BEJ186 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

On the local approximation of mean densities of random closed sets

Mean density of lower dimensional random closed sets, as well as the mean boundary density of full dimensional random sets, and their estimation are of great interest in many real applications. Only partial results are available so far in current literature, under the assumption that the random set is either stationary, or it is a Boolean model, or it has convex grains. We consider here non-stationary random closed sets (not necessarily Boolean models), whose grains have to satisfy some general regularity conditions, extending previous results. We address the open problem posed in (Bernoulli 15 (2009) 1222-1242) about the approximation of the mean density of lower dimensional random sets by a pointwise limit, and to the open problem posed by Matheron in (Random Sets and Integral Geometry (1975) Wiley) about the existence (and its value) of the so-called specific area of full dimensional random closed sets. The relationship with the spherical contact distribution function, as well as some examples and applications are also discussed.Comment: Published in at http://dx.doi.org/10.3150/12-BEJ474 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

ON MEAN DENSITIES OF INHOMOGENEOUS GEOMETRIC PROCESSES ARISING IN MATERIAL SCIENCE AND MEDICINE

The scope of this paper is to offer an overview of the main results obtained by the authors in recent literature in connection with the introduction of a Delta formalism, á la Dirac-Schwartz, for random generalized functions (distributions) associated with random closed sets, having an integer Hausdorff dimension n lower than the full dimension d of the environment space Rd. A concept of absolute continuity of random closed sets arises in a natural way in terms of the absolute continuity of suitable mean content measures, with respect to the usual Lebesgue measure on Rd. Correspondingly mean geometric densities are introduced with respect to the usual Lebesgue measure; approximating sequences are provided, that are of interest for the estimation of mean geometric densities of lower dimensional random sets such as fbre processes, surface processes, etc. Many models in material science and in biomedicine include time evolution of random closed sets, describing birthand-growth processes; the Delta formalism provides a natural framework for deriving evolution equations for mean densities at all (integer) Hausdorff dimensions, in terms of the relevant kinetic parameters

Temperature Dependent Stress–Strain Behavior and Martensite Stabilization in Magnetic Shape Memory Ni51.1Fe16.4Ga26.3Co6.2 Single Crystal

The superelastic properties and stress-induced martensite (SIM) stabilization have been studied in a shape memory Ni51.1Fe16.4Ga26.3Co6.2 single crystal. The single crystal, characterized by a thermally induced forward martensitic transformation temperature around 56 °C in the initial state, has been submitted to compression mechanical testing at different temperatures well above, near and below the martensitic transformation (MT). After each mechanical test, the characteristic MT temperatures and the transformation enthalpy have been monitored by means of differential scanning calorimetry. At temperatures below MT, the stress–strain (σ–ε) curves show a large strain, around 6.0%, resulting from the detwinning process in the martensitic microstructure, which remains accumulated after unloading in the detwinned state of the sample as a typical behavior of the shape memory alloys (SMAs). After just two “σ–ε + heating” cycles the accumulation of strain was not observed any more indicating the formation of a two-way shape memory effect which consists in a spontaneous recovery of the aforementioned detwinned state of the sample during its cooling across the forward MT. Whereas the thermally induced shape recovery in conventional SMAs occurs at the fixed value of the reverse MT temperature, the heating DSC curves of the mechanically deformed martensite in the present work show a burst-like calorimetric peak at the reverse MT arising at temperatures essentially higher than the thermally activated one. This behavior is the result of the SIM stabilization effect. After a short thermal aging in the stress-free state, this effect almost disappears, showing a slight impact on the MT characteristic temperatures and the enthalpy. At temperatures higher than the transformation one, the SIM is not stabilized, as the mechanically induced martensite fully retransforms into austenite after the unloading. From the σ–ε curves, the critical stress, σc, as well as the values of Young’s moduli of martensite and austenite are determined showing linear dependences on the temperature with a slope of 3.6 MPa/°C.This research has been carried out with the financial support of the Spanish Ministry of Science, Innovation and Universities (project RTI2018-094683-B-C53-54) and Basque Government Department of Education (project IT1245-19) and in the framework of INNOSMAD ID546749 Project, PROGRAMMA DI COOPERAZIONE INTERREG V-A ITALIA SVIZZERA CCI 2014TC16RFCB035. s

El videojuego, un nuevo relato

Il s'agit d'une étude de la structure et du contrat du lecture établi dans le vidéo-jeu, d'après les principes opératifs de la Téorie Littéraire et de la Sémiotique. En tant que texte narratif, il donne lieu a un contrat de lecture caractérisé par une série de stratégies qui configurent l'adolescent comme lecteur idéal. La fiction (en rapport avec le registre du récit traditionnel)et la condition interactive (accentuée par des stratégies clefs qui font un effet de vraisemblance) sont les arguments pour expliquer sa consommation.A study of the structure and the contract of reading established in the videogame according to the operating principles in Literary Theory aod Semiotics. As a narrative text it gives rise to the contract of reading typified by a acquience of strategies which shape adolescents as a pattern of readers. Fiction(related to the already known register of the traditional tale)and the interactive condition (stressed by key strategies which develop effects of verisimilitude) are the arguments to explain consumption.Publicad

TRANSFORMATION KINETICS FOR NUCLEATION ON RANDOM PLANES AND LINES

Birth and growth processes are known in materials science as nucleation and growth processes. In crystalline materials nucleation almost always takes place in an internal crystalline defect. These defects are classified according to their dimensionality: point, line or planar defects. Therefore, investigating nucleation on sets of dimensionality lower than the set in which the transformation takes place is of paramount importance. Cahn (1956) in a classical work derived expressions for transformation kinetics when nucleation took place on random planes and on random straight lines. He used these expressions to describe nucleation in polycrystalline materials. He considered that nucleation on grain faces could be treated as nucleation on random planes and, likewise, nucleation on grain edges could be treated as nucleation on random lines. The present work revisits and generalizes Cahn's treatment of nucleation on planes and lines. First a general expression for the case of nucleation on lower dimensional sets is obtained. After that general expressions for nucleation on random planes and random lines are given. This paper provides the mathematical basis for the development of more specific expressions to be used in practical applications. Although this work has been done bearing applications to materials science in mind the results obtained here may be applied to birth and growth processes in any field of science

The Role of MicroRNAs in Dilated Cardiomyopathy: New Insights for an Old Entity

Dilated cardiomyopathy (DCM) is a clinical diagnosis characterized by left ventricular or biventricular dilation and systolic dysfunction. In most cases, DCM is progressive, leading to heart failure (HF) and death. This cardiomyopathy has been considered a common and final phenotype of several entities. DCM occurs when cellular pathways fail to maintain the pumping function. The etiology of this disease encompasses several factors, such as ischemia, infection, autoimmunity, drugs or genetic susceptibility. Although the prognosis has improved in the last few years due to red flag clinical follow-up, early familial diagnosis and ongoing optimization of treatment, due to its heterogeneity, there are no targeted therapies available for DCM based on each etiology. Therefore, a better understanding of the mechanisms underlying the pathophysiology of DCM will provide novel therapeutic strategies against this cardiac disease and their different triggers. MicroRNAs (miRNAs) are a group of small noncoding RNAs that play key roles in post-transcriptional gene silencing by targeting mRNAs for translational repression or, to a lesser extent, degradation. A growing number of studies have demonstrated critical functions of miRNAs in cardiovascular diseases (CVDs), including DCM, by regulating mechanisms that contribute to the progression of the disease. Herein, we summarize the role of miRNAs in inflammation, endoplasmic reticulum (ER) stress, oxidative stress, mitochondrial dysfunction, autophagy, cardiomyocyte apoptosis and fibrosis, exclusively in the context of DCM.European Regional Development Fund (ERDF) Integrated Territorial Initiative ITI PI0048-2017 ITI0017_2019Spanish Society of Cardiology for Basic Research in Cardiology PI0012_2019Foundation Progreso y Salud PEER 2020-01