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Let $\Omega$ be a bounded domain in $\R^n$ whose boundary is $\ka{1,\,\gamma}$ for $\gamma\in(0,\,1)$. Consider the aggregation equation in the case of the initial condition being a positive multiple of the characteristic function of $\Omega$. In this paper we prove global in time analyticity of the flow generated by the velocity field which propagates the density solution of this equation., Comment: The abstract rewritten in better English. Argument in the proof of Proposition 1 has been improved. Argument in the proof of Lemma 12 has been clarified. Several typos have been corrected

In this paper, we construct time periodic doubly connected solutions for the 3D quasi-geostrophic model in the patch setting. More specifically, we prove the existence of nontrivial $m$-fold doubly connected rotating patches bifurcating from a generic doubly connected revolution shape domain with higher symmetry $m\geq m_0$ and $m_0$ is large enough. The linearized matrix operator at the equilibrium state is with variable and singular coefficients and its spectral analysis is performed via the approach devised in [27] where a suitable symmetrization has been introduced. New difficulties emerge due to the interaction between the surfaces making the spectral problem richer and involved.

We prove the persistence of boundary smoothness of vortex patches for a non-linear transport equation in $\mathbb{R}^n$ with velocity field given by convolution of the density with an odd kernel, homogeneous of degree $-(n-1)$ and of class $C^2(\mathbb{R}^n\setminus\{0\}, \mathbb{R}^n).$ This allows the velocity field to have non-trivial divergence. The quasi-geostrophic equation in $\mathbb{R}^3$ and the Cauchy transport equation in the plane are examples., Comment: About the replacement: the main result has been significantly improved. The kernels to which the result applies are now of the more natural class conceivable. Furthermore, the proof has been adapted to the new context and an appendix has been added. About the replacement on September 2023: stylistic changes proposed by the journal

A spatial curve dynamical model framework is adopted for functional prediction of counts in a spatiotemporal log-Gaussian Cox process model. Our spatial functional estimation approach handles both wavelet-based heterogeneity analysis in time, and spectral analysis in space. Specifically, model fitting is achieved by minimising the information divergence or relative entropy between the multiscale model underlying the data and the corresponding candidates in the spatial spectral domain. A simulation study is carried out within the family of log-Gaussian Spatial Autoregressive l2-valued processes (SARl2 processes) to illustrate the asymptotic properties of the proposed spatial functional estimators. We apply our modelling strategy to spatiotemporal prediction of respiratory disease mortality., Comment: 37 pages, 17 figures

In this paper we consider nonlocal energies defined on probability measures in the plane, given by a convolution interaction term plus a quadratic confinement. The interaction kernel is $-\log|z|+\alpha\, x^2/|z|^2, \; z=x+iy,$ with $-1 < \alpha< 1.$ This kernel is anisotropic except for the Coulombic case $\alpha=0.$ We present a short compact proof of the known surprising fact that the unique minimiser of the energy is the normalised characteristic function of the domain enclosed by an ellipse with horizontal semi-axis $\sqrt{1-\alpha}$ and vertical semi-axis $\sqrt{1+\alpha}.$ Letting $\alpha \to 1^-$ we find that the semicircle law on the vertical axis is the unique minimiser of the corresponding energy, a result related to interacting dislocations, and previously obtained by some of the authors. We devote the first sections of this paper to presenting some well-known background material in the simplest way possible, so that readers unfamiliar with the subject find the proofs accessible, Comment: 17 pages, minor modifications after referee's report

We give a proof of the analiticity in time for the particle trajectories associated with the solutions of some transport equations when the initial datum is a patch. These results are obtained from a precise study of the Beurling transform, which provides estimates for the solutions of some new equations satisfied by the lagrangian flow., Comment: 59 pages, 1 figure, revised and clarified some arguments in sections 2 and 3, results unchanged

In this paper we characterise the minimisers of a one-parameter family of nonlocal and anisotropic energies $I_\alpha$ defined on probability measures in $\R^n$, with $n\geq 3$. The energy $I_\alpha$ consists of a purely nonlocal term of convolution type, whose interaction kernel reduces to the Coulomb potential for $\alpha=0$ and is anisotropic otherwise, and a quadratic confinement. The two-dimensional case arises in the study of defects in metals and has been solved by the authors by means of complex-analysis techniques. We prove that for $\alpha\in (-1, n-2]$, the minimiser of $I_\alpha$ is unique and is the (normalised) characteristic function of a spheroid. This result is a paradigmatic example of the role of the anisotropy of the kernel on the shape of minimisers. In particular, the phenomenon of loss of dimensionality, observed in dimension $n=2$, does not occur in higher dimension at the value $\alpha=n-2$ corresponding to the sign change of the Fourier transform of the interaction potential.

We introduce a new class of spatial Cox processes driven by a Hilbert--valued random log--intensity. We adopt a parametric framework in the spectral domain, to estimate its spatial functional correlation structure. Specifically, we consider a spectral functional, based on the periodogram operator, inspired on Whittle estimation methodology. Strong-consistency of the parametric estimator is proved in the linear case. We illustrate this property in a simulation study under a Gaussian first order Spatial Autoregressive Hilbertian scenario for the log--intensity model. Our method is applied to the spatial functional prediction of respiratory disease mortality in the Spanish Iberian Peninsula, in the period 1980--2015., Comment: Submitted (25 pages, 18 figures and seven tables)

In this paper we consider a nonlocal energy $I_\alpha$ whose kernel is obtained by adding to the Coulomb potential an anisotropic term weighted by a parameter $\alpha\in \R$. The case $\alpha=0$ corresponds to purely logarithmic interactions, minimised by the celebrated circle law for a quadratic confinement; $\alpha=1$ corresponds to the energy of interacting dislocations, minimised by the semi-circle law. We show that for $\alpha\in (0,1)$ the minimiser can be computed explicitly and is the normalised characteristic function of the domain enclosed by an \emph{ellipse}. To prove our result we borrow techniques from fluid dynamics, in particular those related to Kirchhoff's celebrated result that domains enclosed by ellipses are rotating vortex patches, called \emph{Kirchhoff ellipses}. Therefore we show a surprising connection between vortices and dislocations.

This paper presents an original ABC algorithm, "ABC Shadow", that can be applied to sample posterior densities that are continuously differentiable. The proposed method uses the ideas given by the auxiliary variable MH of (M\o ller and Waagepetersen, 2004). The obtained algorithm solves the main condition to be fulfilled by any ABC algorithm, in order to be useful in practice. This condition requires enough samples in the parameter space region, induced by the observed statistics (Blum, 2010). The algorithm is tuned on the posterior of a Gaussian model which is entirely known, and then it is applied for the statistical analysis of several spatial patterns. These patterns are issued or assumed to be outcomes of point processes. The considered models are: Strauss, Candy and area-interaction., Comment: 34 pages, 8 figures, 4 tables

We explore the frequency-dependent relative permittivity of Ruddlesden-Popper series Sr(n+1)Ti(n)O(3n+1) (n =1,2,3) thin films as a function of temperature and dc electric field. Interdigitated capacitors and coplanar waveguides were used to extract the frequency response from 500 Hz to 40 GHz. At room temperature, the in-plane relative permittivities obtained for Sr(n+1)Ti(n)O(3n+1) (n =1,2,3) were 42+/-3, 54+/-3, and 77+/-2, respectively, and were independent of frequency. At low temperatures, permittivity increases and electric field tunability develops in Sr(4)Ti(3)O(10).

The theory of quasi-arithmetic means is a powerful tool in the study of covariance functions across space-time. In the present study we use quasi-arithmetic functionals to make inferences about the permissibility of averages of functions that are not, in general, permissible covariance functions. This is the case, e.g., of the geometric and harmonic averages, for which we obtain permissibility criteria. Also, some important inequalities involving covariance functions and preference relations as well as algebraic properties can be derived by means of the proposed approach. In particular, we show that quasi-arithmetic covariances allow for ordering and preference relations, for a Jensen-type inequality and for a minimal and maximal element of their class. The general results shown in this paper are then applied to study of spatial and spatiotemporal random fields. In particular, we discuss the representation and smoothness properties of a weakly stationary random field with a quasi-arithmetic covariance function. Also, we show that the generator of the quasi-arithmetic means can be used as a link function in order to build a space-time nonseparable structure starting from the spatial and temporal margins, a procedure that is technically sound for those working with copulas. Several examples of new families of stationary covariances obtainable with this procedure are shown. Finally, we use quasi-arithmetic functionals to generalise existing results concerning the construction of nonstationary spatial covariances and discuss the applicability and limits of this generalisation., Comment: 33 pages. Submitted

We have measured the periods and light curves of 148 RR Lyrae variables from V=13.5 to 19.7 from the first 100 sq. degrees of the QUEST RR Lyrae survey. Approximately 55% of these stars belong to the clump of stars detected earlier by the Sloan Digital Sky Survey. According to our measurements, this feature has ~10 times the background density of halo stars, spans at least 37.5 deg by 3.5 deg in right ascension and declination (>=30 by >=3 kpc), lies ~50 kpc from the Sun, and has a depth along the line of sight of ~5 kpc (1 sigma). These properties are consistent with the recent models that suggest it is a tidal stream from the Sgr dSph galaxy. The mean period of the type ab variables, 0.58 d, is also consistent. In addition, we have found two smaller over-densities in the halo, one of which may be related to the globular cluster Pal 5., Comment: 12 pages (including 4 figures). Accepted for publication in the ApJ Letters

We describe the discovery circumstances and photometric properties of 2000 EB173, now one of the brightest trans-Neptunian objects (TNOs) with opposition magnitude m_R=18.9 and also one of the largest Plutinos, found with the drift-scanning camera of the QUEST Collaboration, attached to the 1-m Schmidt telescope of the National Observatory of Venezuela. We measure B-V = 0.99 +/- 0.14 and V-R = 0.57 +/- 0.05, a red color observed for many fainter TNOs. At our magnitude limit m_R = 20.1 +/- 0.20, our single detection reveals a sky density of 0.015 (+0.034, -0.012) TNOs per deg^2 (the error bars are 68% confidence limits), consistent with fainter surveys showing a cumulative number proportional to 10^0.5m_R. Assuming an inclination distribution of TNOs with FWHM exceeding 30 deg, it is likely that one hundred to several hundred objects brighter than m_R=20.1 remain to be discovered.

The optical transient of the faint Gamma Ray Burst 990308 was detected by the QUEST camera on the Venezuelan 1-m Schmidt telescope starting 3.28 hours after the burst. Our photometry gives $V = 18.32 \pm 0.07$, $R = 18.14 \pm 0.06$, $B = 18.65 \pm 0.23$, and $R = 18.22 \pm 0.05$ for times ranging from 3.28 to 3.47 hours after the burst. The colors correspond to a spectral slope of close to $f_{\nu} \propto \nu^{1/3}$. Within the standard synchrotron fireball model, this requires that the external medium be less dense than $10^{4} cm^{-3}$, the electrons contain $> 20%$ of the shock energy, and the magnetic field energy must be less than 24% of the energy in the electrons for normal interstellar or circumstellar densities. We also report upper limits of $V > 12.0$ at 132 s (with LOTIS), $V > 13.4$ from 132-1029s (with LOTIS), $V > 15.3$ at 28.2 min (with Super-LOTIS), and a 8.5 GHz flux of $< 114 \mu Jy$ at 110 days (with the Very Large Array). WIYN 3.5-m and Keck 10-m telescopes reveal this location to be empty of any host galaxy to $R > 25.7$ and $K > 23.3$. The lack of a host galaxy likely implies that it is either substantially subluminous or more distant than a red shift of $\sim 1.2$., Comment: ApJ Lett submitted, 5 pages, 2 figures, no space for 12 coauthors