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We consider the Cahn-Hilliard equation on manifolds with conical singularities. For appropriate initial data, we show that the solution exists in the maximal $L^q$-regularity space for all times and becomes instantaneously smooth in space and time, where the maximal $L^q$-regularity is obtained in the sense of Mellin-Sobolev spaces. Moreover, we provide precise information concerning the asymptotic behavior of the solution close to the conical tips in terms of the local geometry., Comment: 28 pages

Logical models have been successfully used to describe regulatory and signaling networks without requiring quantitative data. However, existing data is insufficient to adequately define a unique model, rendering the parametrization of a given model a difficult task. Here, we focus on the characterization of the set of Boolean functions compatible with a given regulatory structure, i.e. the set of all monotone nondegenerate Boolean functions. We then propose an original set of rules to locally explore the direct neighboring functions of any function in this set, without explicitly generating the whole set. Also, we provide relationships between the regulatory functions and their corresponding dynamics. Finally, we illustrate the usefulness of this approach by revisiting Probabilistic Boolean Networks with the model of T helper cell differentiation from Mendoza & Xenarios.

We characterize the X-ray luminosity--temperature ($L_{\rm X}-T$) relation using a sample of 353 clusters and groups of galaxies with temperatures in excess of 1 keV, spanning the redshift range $0.1 < z < 0.6$, the largest ever assembled for this purpose. All systems are part of the ${\it XMM-Newton}$ Cluster Survey (XCS), and have also been independently identified in Sloan Digital Sky Survey (SDSS) data using the redMaPPer algorithm. We allow for redshift evolution of the normalisation and intrinsic scatter of the $L_{\rm X}-T$ relation, as well as, for the first time, the possibility of a temperature-dependent change-point in the exponent of such relation. However, we do not find strong statistical support for deviations from the usual modelling of the $L_{\rm X}-T$ relation as a single power-law, where the normalisation evolves self-similarly and the scatter remains constant with time. Nevertheless, assuming {\it a priori} the existence of the type of deviations considered, then faster evolution than the self-similar expectation for the normalisation of the $L_{\rm X}-T$ relation is favoured, as well as a decrease with redshift in the scatter about the $L_{\rm X}-T$ relation. Further, the preferred location for a change-point is then close to 2 keV, possibly marking the transition between the group and cluster regimes. Our results also indicate an increase in the power-law exponent of the $L_{\rm X}-T$ relation when moving from the group to the cluster regime, and faster evolution in the former with respect to the later, driving the temperature-dependent change-point towards higher values with redshift., Comment: 19 pages, 29 figures, 7 tables, submitted to MNRAS. Comments are welcome

Several investigations of the X-ray variability of active galactic nuclei (AGN) using the normalised excess variance (${\sigma^2_{\rm NXS}}$) parameter have shown that variability has a strong anti-correlation with black hole mass ($M_{\rm BH}$) and X-ray luminosity ($L_{\rm X}$). In this study we confirm these previous correlations and find no evidence of a redshift evolution. Using observations from XMM-Newton, we determine the ${\sigma^2_{\rm NXS}}$ and $L_{\rm X}$ for a sample of 1091 AGN drawn from the XMM-Newton Cluster Survey (XCS) - making this the largest study of X-ray spectral properties of AGNs. We created light-curves in three time-scales; 10 ks, 20 ks and 40 ks and used these to derive scaling relations between ${\sigma^2_{\rm NXS}}$, $L_{\rm X}$ (2.0-10 keV range) and literature estimates of $M_{\rm BH}$ from reverberation mapping. We confirm the anti-correlation between $M_{\rm BH}$ and ${\sigma^2_{\rm NXS}}$ and find a positive correlation between $M_{\rm BH}$ and $L_{\rm X}$. The use of ${\sigma^2_{\rm NXS}}$ is practical only for pointed observations where the observation time is tens of kiloseconds. For much shorter observations one cannot accurately quantify variability to estimate $M_{\rm BH}$. Here we describe a method to derive $L_{\rm X}$ from short duration observations and used these results as an estimate for $M_{\rm BH}$. We find that it is possible to estimate $L_{\rm X}$ from observations of just a few hundred seconds and that when correlated with $M_{\rm BH}$, the relation is statistically similar to the relation of $M_{\rm BH}$-$L_{\rm X}$ derived from a spectroscopic analysis of full XMM observations. This method may be particularly useful to the eROSITA mission, an all-sky survey, which will detect $>$10$^{6}$ AGN., Comment: 19 pages, 20 figures

In this paper, we study existence, uniqueness and asymptotic behavior of the Laplace equation with dynamical boundary conditions on regular non-cylindrical domains. We write the problem as a non-autonomous Dirichlet-to-Neumann operator and use form methods in a more general framework to accomplish our goal. A class of non-autonomous elliptic problems with dynamical boundary conditions on Lipschitz domains is also considered in this same context., Comment: This is a new version of a previous paper submitted here in Arxiv. It has substantial changes from the previous one. A whole section was rewritten and some small mistakes were corrected

We prove the spectral invariance of the algebra of classical pseudodifferential boundary value problems on manifolds with conical singularities in the Lp-setting. As a consequence we also obtain the spectral invariance of the classical Boutet de Monvel algebra of zero order operators with parameters. In order to establish these results, we show the equivalence of Fredholm property and ellipticity for both cases.

We study the prisoner's dilemma model with a noisy imitation evolutionary dynamics on directed out-homogeneous and uncorrelated directed random networks. An heterogeneous pair mean-field approximation is presented showing good agreement with Monte Carlo simulations in the limit of weak selection (high noise) where we obtain analytical predictions for the critical temptations. We discuss the phase diagram as a function of temptation, intensity of noise and coordination number of the networks and we consider both the model with and without self-interaction. We compare our results with available results for non-directed lattices and networks., Comment: 18 pages, 9 figures

We present a direct measurement of the mean halo occupation distribution (HOD) of galaxies taken from the eleventh data release (DR11) of the Sloan Digital Sky Survey-III Baryon Oscillation Spectroscopic Survey (BOSS). The HOD of BOSS low-redshift (LOWZ: $0.2 < z < 0.4$) and Constant-Mass (CMASS: $0.43

We measure the evolution of the velocity dispersion--temperature ($\sigma_{\rm v}$--$T_{\rm X}$) relation up to $z = 1$ using a sample of 38 galaxy clusters drawn from the \textit{XMM} Cluster Survey. This work improves upon previous studies by the use of a homogeneous cluster sample and in terms of the number of high redshift clusters included. We present here new redshift and velocity dispersion measurements for 12 $z > 0.5$ clusters observed with the GMOS instruments on the Gemini telescopes. Using an orthogonal regression method, we find that the slope of the relation is steeper than that expected if clusters were self-similar, and that the evolution of the normalisation is slightly negative, but not significantly different from zero ($\sigma_{\rm v} \propto T^{0.86 \pm 0.14} E(z)^{-0.37 \pm 0.33}$). We verify our results by applying our methods to cosmological hydrodynamical simulations. The lack of evolution seen in our data is consistent with simulations that include both feedback and radiative cooling., Comment: Accepted to MNRAS (3 August 2016); Paper: 15 pages, 12 figures; Appendix A: 1 table; Appendix B: 34 Tables; Appendix C: 2 Figures