Extrema statistics in the dynamics of a non-Gaussian random field

When the equations that govern the dynamics of a random field are nonlinear, the field can develop with time non-Gaussian statistics even if its initial condition is Gaussian. Here, we provide a general framework for calculating the effect of the underlying nonlinear dynamics on the relative densities of maxima and minima of the field. Using this simple geometrical probe, we can identify the size of the non-Gaussian contributions in the random field, or alternatively the magnitude of the nonlinear terms in the underlying equations of motion. We demonstrate our approach by applying it to an initially Gaussian field that evolves according to the deterministic KPZ equation, which models surface growth and shock dynamics.Comment: 9 pages, 3 figure

Stochastic geometry and topology of non-Gaussian fields

Gaussian random fields pervade all areas of science. However, it is often the departures from Gaussianity that carry the crucial signature of the nonlinear mechanisms at the heart of diverse phenomena, ranging from structure formation in condensed matter and cosmology to biomedical imaging. The standard test of non-Gaussianity is to measure higher order correlation functions. In the present work, we take a different route. We show how geometric and topological properties of Gaussian fields, such as the statistics of extrema, are modified by the presence of a non-Gaussian perturbation. The resulting discrepancies give an independent way to detect and quantify non-Gaussianities. In our treatment, we consider both local and nonlocal mechanisms that generate non-Gaussian fields, both statically and dynamically through nonlinear diffusion.Comment: 8 pages, 4 figure

Phase estimation via quantum interferometry for noisy detectors

The sensitivity in optical interferometry is strongly affected by losses during the signal propagation or at the detection stage. The optimal quantum states of the probing signals in the presence of loss were recently found. However, in many cases of practical interest, their associated accuracy is worse than the one obtainable without employing quantum resources (e.g. entanglement and squeezing) but neglecting the detector's loss. Here we detail an experiment that can reach the latter even in the presence of imperfect detectors: it employs a phase-sensitive amplification of the signals after the phase sensing, before the detection. We experimentally demonstrated the feasibility of a phase estimation experiment able to reach its optimal working regime. Since our method uses coherent states as input signals, it is a practical technique that can be used for high-sensitivity interferometry and, in contrast to the optimal strategies, does not require one to have an exact characterization of the loss beforehand.Comment: 4 pages + supplementary information (10 pages), 3 + 4 figure

Monte Carlo Study of Crystalline Order and Defects on Weakly Curved Surfaces

We numerically study the ground states of particles interacting via a repulsive Yukawa potential on two rigid substrates shaped as isolated and periodically arranged bumps characterized by a spatially varying Gaussian curvature. Below a critical aspect ratio that describes the substrate deformation, the lattice is frustrated, but defect free. A further increase of the aspect ratio triggers defect unbinding transitions that lower the total potential energy by introducing dislocations either in isolation or within grain boundaries. In the presence of very strong deformations, isolated disclinations are nucleated. We show that the character and spatial distribution of defects observed in the ground state reflect the symmetries and periodicity of the two model surfaces investigated in this study

Nematic Films and Radially Anisotropic Delaunay Surfaces

We develop a theory of axisymmetric surfaces minimizing a combination of surface tension and nematic elastic energies which may be suitable for describing simple film and bubble shapes. As a function of the elastic constant and the applied tension on the bubbles, we find the analogues of the unduloid, sphere, and nodoid in addition to other new surfaces.Comment: 15 pages, 18 figure

Role of disclinations in determining the morphology of deformable fluid interfaces

We study the equilibrium shapes of vesicles, with an in-plane nematic order, using a Monte-Carlo scheme and show that highly curved shapes, like tubes and discs, with a striking similarity to the structures engendered by certain curvature sensing peripheral membrane proteins, can be spontaneously generated by anisotropic directional curvature with nematic disclinations playing and important role. We show that the coupling between nematic order and local curvature could lead to like defects moving towards each other and unlike defects moving away, in turn leading to tube formation. Thermally induced defect pair production lead to branched tubular structures. It is also shown that helical arrangement of the membrane tubes, with nematic field spiraling around it, is a dominant soft mode of the system.Comment: 6 Figures; Soft Matter, Advance Article 201

Gut microbial communities of hybridising pygmy angelfishes reflect species boundaries

Hybridisation and introgression of eukaryotic genomes can generate new species or subsume existing ones, with direct and indirect consequences for biodiversity. An understudied component of these evolutionary forces is their potentially rapid effect on host gut microbiomes, and whether these pliable microcosms may serve as early biological indicators of speciation. We address this hypothesis in a field study of angelfishes (genus Centropyge), which have one of the highest prevalence of hybridisation within coral reef fish. In our study region of the Eastern Indian Ocean, the parent fish species and their hybrids cohabit and display no differences in their diet, behaviour, and reproduction, often interbreeding in mixed harems. Despite this ecological overlap, we show that microbiomes of the parent species are significantly different from each other in form and function based on total community composition, supporting the division of parents into distinct species, despite the confounding effects of introgression acting to homogenize parent species identity at other molecular markers. The microbiome of hybrid individuals, on the other hand, are not significantly different to each of the parents, instead harbouring an intermediate community composition. These findings suggest that shifts in gut microbiomes may be an early indicator of speciation in hybridising species

Tbx1 expression in pharyngeal epithelia is necessary for pharyngeal arch artery development.

During embryonic life, the initially paired pharyngeal arch arteries (PAAs) follow a precisely orchestrated program of persistence and regression that leads to the formation of the mature aortic arch and great vessels. When this program fails, specific cardiovascular defects arise that may be life threatening or mild, according to the identity of the affected artery. Fourth PAA-derived cardiovascular defects occur commonly in DiGeorge syndrome and velocardiofacial syndrome (22q11DS), and in Tbx1(+/-) mice that model the 22q11DS cardiovascular phenotype. Tbx1 is expressed in pharyngeal mesoderm, endoderm and ectoderm, and, in addition, we show that it is expressed in precursors of the endothelial cells that line the PAAs, thus expanding the number of tissues in which Tbx1 is potentially required for fourth PAA development. In this study, we have used cell fate mapping and tissue-specific gene deletion, driven by six different Cre lines, to explore Tbx1 gene-dosage requirements in the embryonic pharynx for fourth PAA development. Through this approach, we have resolved the spatial requirements for Tbx1 in this process, and we show pharyngeal epithelia to be a critical tissue. We also thereby demonstrate conclusively that the role of Tbx1 in fourth PAA development is cell non-autonomous