Fr\'echet differentiability of mild solutions to SPDEs with respect to the initial datum

We establish n-th order Fr\'echet differentiability with respect to the initial datum of mild solutions to a class of jump-diffusions in Hilbert spaces. In particular, the coefficients are Lipschitz continuous, but their derivatives of order higher than one can grow polynomially, and the (multiplicative) noise sources are a cylindrical Wiener process and a quasi-left-continuous integer-valued random measure. As preliminary steps, we prove well-posedness in the mild sense for this class of equations, as well as first-order G\^ateaux differentiability of their solutions with respect to the initial datum, extending previous results in several ways. The differentiability results obtained here are a fundamental step to construct classical solutions to non-local Kolmogorov equations with sufficiently regular coefficients by probabilistic means.Comment: 30 pages, no figure

Ergodicity and Kolmogorov equations for dissipative SPDEs with singular drift: a variational approach

We prove existence of invariant measures for the Markovian semigroup generated by the solution to a parabolic semilinear stochastic PDE whose nonlinear drift term satisfies only a kind of symmetry condition on its behavior at infinity, but no restriction on its growth rate is imposed. Thanks to strong integrability properties of invariant measures $\mu$, solvability of the associated Kolmogorov equation in $L^1(\mu)$ is then established, and the infinitesimal generator of the transition semigroup is identified as the closure of the Kolmogorov operator. A key role is played by a generalized variational setting.Comment: 32 page

A variational approach to dissipative SPDEs with singular drift

We prove global well-posedness for a class of dissipative semilinear stochastic evolution equations with singular drift and multiplicative Wiener noise. In particular, the nonlinear term in the drift is the superposition operator associated to a maximal monotone graph everywhere defined on the real line, on which no continuity nor growth assumptions are imposed. The hypotheses on the diffusion coefficient are also very general, in the sense that the noise does not need to take values in spaces of continuous, or bounded, functions in space and time. Our approach combines variational techniques with a priori estimates, both pathwise and in expectation, on solutions to regularized equations.Comment: 35 page

Approximation and convergence of solutions to semilinear stochastic evolution equations with jumps

We prove that the mild solution to a semilinear stochastic evolution equation on a Hilbert space, driven by either a square integrable martingale or a Poisson random measure, is (jointly) continuous, in a suitable topology, with respect to the initial datum and all coefficients. In particular, if the leading linear operators are maximal (quasi-)monotone and converge in the strong resolvent sense, the drift and diffusion coefficients are uniformly Lipschitz continuous and converge pointwise, and the initial data converge, then the solutions converge.Comment: 28 pages, no figure

Dogs are not better than humans at detecting coherent motion

The ability to perceive motion is one of the main properties of the visual system. Sensitivity in detecting coherent motion has been thoroughly investigated in humans, where thresholds for motion detection are well below 10% of coherence, i.e. of the proportion of dots coherently moving in the same direction, among a background of randomly moving dots. Equally low thresholds have been found in other species, including monkeys, cats and seals. Given the lack of data from the domestic dog, we tested 5 adult dogs on a conditioned discrimination task with random dot displays. In addition, five adult humans were tested in the same condition for comparative purposes. The mean threshold for motion detection in our dogs was 42% of coherence, while that of humans was as low as 5%. Therefore, dogs have a much higher threshold of coherent motion detection than humans, and possibly also than phylogenetically closer species that have been tested in similar experimental conditions. Various factors, including the relative role of global and local motion processing and experience with the experimental stimuli may have contributed to this result. Overall, this finding questions the general claim on dogs' high performance in detecting motion

Ethical and medico-legal remarks on uterus transplantation: may it solve uterine factor infertility?

Uterus transplantation was firstly tested with animal trials sixty-five years ago. Despite several successful attempts in human subjects, the different procedures still lay at the experimental stage, in need of further studies and investigations before they can be considered as standard clinical practices. Uterus transplant cannot be regarded as a life-saving procedure, but rather a method to restore woman ability to procreate, when lost, thus improving her quality of life. Uterus transplant is a complex surgical procedure and presents significant health threats. Medical staff should therefore always obtain informed consent from patients, emphasizing such risks. Before that, women undergoing uterine transplants should be thoroughly informed about the hazards inherent to the procedure and especially about the dangers of immunosuppressant drugs, administered after the surgery which may injure the fetus, eventually formed in the restored organ and even lead to its death, thus nullifying the purpose of the transplant itself. Therefore, the risk-benefit ratio of uterus transplantation needs to be carefully assessed and described

Comparative study of nonideal beam effects in high gain harmonic generation and self-seeded free electron lasers

In this paper we investigate and compare the properties of two narrow-bandwidth free-electron laser (FEL) schemes, one using self-seeding and the other high gain harmonic generation (HGHG). The two systems have been thoroughly studied analytically and numerically in the past. The aim of this work is to compare their performances when the FEL is driven by an electron beam with nonideal properties, thus including effects such as shot-to-shot energy fluctuations and nonlinear energy chirp. In both cases nonlinearities produce a bandwidth larger than the Fourier transform limited value. However, our analysis indicates that, for approximately the same output power levels, the self-seeding scheme is less affected than the HGHG scheme by quadratic energy chirps in the electron beam longitudinal phase space. This is confirmed by a specific numerical example corresponding to SPARX parameters where the electron beam was optimized to minimize the FEL gain length. The work has been carried out with the aid of the time dependent FEL codes GENESIS 1.3 (3D) and PERSEO (1D)