Dynamic Scaling of Non-Euclidean Interfaces

The dynamic scaling of curved interfaces presents features that are strikingly different from those of the planar ones. Spherical surfaces above one dimension are flat because the noise is irrelevant in such cases. Kinetic roughening is thus a one-dimensional phenomenon characterized by a marginal logarithmic amplitude of the fluctuations. Models characterized by a planar dynamical exponent $z>1$, which include the most common stochastic growth equations, suffer a loss of correlation along the interface, and their dynamics reduce to that of the radial random deposition model in the long time limit. The consequences in several applications are discussed, and we conclude that it is necessary to reexamine some experimental results in which standard scaling analysis was applied

Stochastic growth equations on growing domains

The dynamics of linear stochastic growth equations on growing substrates is studied. The substrate is assumed to grow in time following the power law $t^\gamma$, where the growth index $\gamma$ is an arbitrary positive number. Two different regimes are clearly identified: for small $\gamma$ the interface becomes correlated, and the dynamics is dominated by diffusion; for large $\gamma$ the interface stays uncorrelated, and the dynamics is dominated by dilution. In this second regime, for short time intervals and spatial scales the critical exponents corresponding to the non-growing substrate situation are recovered. For long time differences or large spatial scales the situation is different. Large spatial scales show the uncorrelated character of the growing interface. Long time intervals are studied by means of the auto-correlation and persistence exponents. It becomes apparent that dilution is the mechanism by which correlations are propagated in this second case.Comment: Published versio

Microarray analysis of Foxl2 mediated gene regulation in the mouse ovary derived KK1 granulosa cell line: Over-expression of Foxl2 leads to activation of the gonadotropin releasing hormone receptor gene promoter

<p>Abstract</p> <p>Background</p> <p>The Foxl2 transcription factor is required for ovarian function during follicular development. The mechanism of Foxl2 regulation of this process has not been elucidated. Our approach to begin to understand Foxl2 function is through the identification of Foxl2 regulated genes in the ovary.</p> <p>Methods</p> <p>Transiently transfected KK1 mouse granulosa cells were used to identify genes that are potentially regulated by Foxl2. KK1 cells were transfected in three groups (mock, activated, and repressed) and twenty-four hours later RNA was isolated and submitted for <it>Affymetrix </it>microarray analysis. <it>Genesifter </it>software was used to carry out analysis of microarray data. One identified target, the gonadotropin releasing hormone receptor (GnRHR) gene, was chosen for further study and validation of Foxl2 responsiveness. Transient transfection analyses were carried out to study the effect of Foxl2 over-expression on GnRHR gene promoter-luciferase fusion activity. Data generated was analyzed with <it>GraphPad Prism </it>software.</p> <p>Results</p> <p>Microarray analysis identified 996 genes of known function that are potentially regulated by Foxl2 in mouse KK1 granulosa cells. The steroidogenic acute regulatory protein (StAR) gene that has been identified as Foxl2 responsive by others was identified in this study also, thereby supporting the effectiveness of our strategy. The GnRHR gene was chosen for further study because it is known to be expressed in the ovary and the results of previous work has indicated that Foxl2 may regulate GnRHR gene expression. Cellular levels of Foxl2 were increased via transient co-transfection of KK1 cells using a Foxl2 expression vector and a GnRHR promoter-luciferase fusion reporter vector. The results of these analyses indicate that over-expression of Foxl2 resulted in a significant increase in GnRHR promoter activity. Therefore, these transfection data validate the microarray data which suggest that Foxl2 regulates GnRHR and demonstrate that Foxl2 acts as an activator of the GnRHR gene.</p> <p>Conclusions</p> <p>Potential Foxl2 regulated ovarian genes have been identified through microarray analysis and comparison of these data to other microarray studies. The Foxl2 responsiveness of the GnRHR gene has been validated and provided evidence of Foxl2 transcriptional activation of the GnRHR gene promoter in the mouse ovary derived KK1 granulosa cell line.</p

Specific heat studies of pure Nb3Sn single crystals at low temperature

Specific heat measurements performed on high purity vapor-grown Nb$_3$Sn crystals show clear features related to both the martensitic and superconducting transitions. Our measurements indicate that the martensitic anomaly does not display hysteresis, meaning that the martensitic transition could be a weak first or a second order thermodynamic transition. Careful measurements of the two transition temperatures display an inverse correlation between both temperatures. At low temperature specific heat measurements show the existence of a single superconducting energy gap feature.Comment: Accepted in Journal of Physics: Condensed Matte

Two species coagulation approach to consensus by group level interactions

We explore the self-organization dynamics of a set of entities by considering the interactions that affect the different subgroups conforming the whole. To this end, we employ the widespread example of coagulation kinetics, and characterize which interaction types lead to consensus formation and which do not, as well as the corresponding different macroscopic patterns. The crucial technical point is extending the usual one species coagulation dynamics to the two species one. This is achieved by means of introducing explicitly solvable kernels which have a clear physical meaning. The corresponding solutions are calculated in the long time limit, in which consensus may or may not be reached. The lack of consensus is characterized by means of scaling limits of the solutions. The possible applications of our results to some topics in which consensus reaching is fundamental, like collective animal motion and opinion spreading dynamics, are also outlined

Cell adhesion on ti surface with controlled roughness

In this report, the in situ interaction between Saos-2 osteoblast cells and a smooth Ti surface was examined over time. The adhesion kinetics and mechanisms of cellular proliferation were monitored by quartz crystal microbalance (QCM) and electrochemical impedance spectroscopy (EIS). The rate of Saos-2 attachment on Ti surfaces, obtained from the measurements performed with the QCM, is a first-order reaction, with k=2.103 min1. The impedance measurements indicate that in the absence of cells, the Ti resistance diminishes over time (7 days), due to the presence of amino acids and proteins from the culture medium that have been a dsorbed, while in the presence of osteoblasts, this decrease is much greater because of the compounds generated by the cells that accelerate the dissolution of TiAdhesión de osteoblastos sobre una superficie de Ti de rugosidad controlada. En este trabajo, se ha estudiado la interacción in situ entre células osteoblásticas Saos-2 y una superficie de Ti de rugosidad controlada a lo largo del tiempo. El estudio de la cinética y los mecanismos de proliferación celular de adhesión se ha realizado a través de la microbalanza de cristal de cuarzo (QCM) y espectroscopía de impedancia electroquímica (EIS). La velocidad de adhesión de los osteoblastos sobre la superficie de Ti obtenida a través de medidas con la QCM, sigue una reacción de primer orden, con k=2×10−3 min−1. Los ensayos de impedancia indican que, en ausencia de las células, la resistencia del Ti disminuye con el tiempo (7 días), debido a la presencia de aminoácidosy proteínas del medio de cultivo que se han adsorbido, mientras que en presencia de células, esta disminución es mucho mayor debido a los productos metabólicos generados por las células que aceleran la disolución del TiThe authors thank the financial support under projects MAT 2008-06719-C03-01, CTQ2008-05775/ BQU and by the Comunidad Autónoma de Madrid (CAM) through AVANSENS S2009/PPQ-164

Constrained parsimonious model-based clustering

A new methodology for constrained parsimonious model-based clustering is introduced, where some tuning parameter allows to control the strength of these constraints. The methodology includes the 14 parsimonious models that are often applied in model-based clustering when assuming normal components as limit cases. This is done in a natural way by filling the gap among models and providing a smooth transition among them. The methodology provides mathematically well-defined problems and is also useful to prevent us from obtaining spurious solutions. Novel information criteria are proposed to help the user in choosing parameters. The interest of the proposed methodology is illustrated through simulation studies and a real-data application on COVID data