Parametrization of local biholomorphisms of real analytic hypersurfaces

Let $M$ be a real analytic hypersurface in \bC^N which is finitely nondegenerate, a notion that can be viewed as a generalization of Levi nondegenerate, at $p_0\in M$. We show that if $M'$ is another such hypersurface and $p'_0\in M'$, then the set of germs at $p_0$ of biholomorphisms $H$ with $H(M)\subset M'$ and $H(p_0)=p'_0$, equipped with its natural topology, can be naturally embedded as a real analytic submanifold in the complex jet group of \bC^N of the appropriate order. We also show that this submanifold is defined by equations that can be explicitly computed from defining equations of $M$ and $M'$. Thus, $(M,p_0)$ and $(M',p'_0)$ are biholomorphically equivalent if and only if this (infinite) set of equations in the complex jet group has a solution. Another result obtained in this paper is that any invertible formal map $H$ that transforms $(M,p_0)$ to $(M',p'_0)$ is convergent. As a consequence, $(M,p_0)$ and $(M',p'_0)$ are biholomorphically equivalent if and only if they are formally equivalent

Surfaces Meeting Porous Sets in Positive Measure

Let n>2 and X be a Banach space of dimension strictly greater than n. We show there exists a directionally porous set P in X for which the set of C^1 surfaces of dimension n meeting P in positive measure is not meager. If X is separable this leads to a decomposition of X into a countable union of directionally porous sets and a set which is null on residually many C^1 surfaces of dimension n. This is of interest in the study of certain classes of null sets used to investigate differentiability of Lipschitz functions on Banach spaces

Analytic and Gevrey Hypoellipticity for Perturbed Sums of Squares Operators

We prove a couple of results concerning pseudodifferential perturbations of differential operators being sums of squares of vector fields and satisfying H\"ormander's condition. The first is on the minimal Gevrey regularity: if a sum of squares with analytic coefficients is perturbed with a pseudodifferential operator of order strictly less than its subelliptic index it still has the Gevrey minimal regularity. We also prove a statement concerning real analytic hypoellipticity for the same type of pseudodifferential perturbations, provided the operator satisfies to some extra conditions (see Theorem 1.2 below) that ensure the analytic hypoellipticity

Post- and peritraumatic stress in disaster survivors: An explorative study about the influence of individual and event characteristics across different types of disasters

Background: Examination of existing research on posttraumatic adjustment after disasters suggests that survivors’ posttraumatic stress levels might be better understood by investigating the influence of the characteristics of the event experienced on how people thought and felt, during the event as well as afterwards. Objective: To compare survivors’ perceived post- and peritraumatic emotional and cognitive reactions across different types of disasters. Additionally, to investigate individual and event characteristics. Design: In a European multi-centre study, 102 survivors of different disasters terror attack, flood, fire and collapse of a building were interviewed about their responses during the event. Survivors’ perceived posttraumatic stress levels were assessed with the Impact of Event Scale-Revised (IES-R). Peritraumatic emotional stress and risk perception were rated retrospectively. Influences of individual characteristics, such as socio-demographic data, and event characteristics, such as time and exposure factors, on post- and peritraumatic outcomes were analyzed. Results: Levels of reported post- and peritraumatic outcomes differed significantly between types of disasters. Type of disaster was a significant predictor of all three outcome variables but the factors gender, education, time since event, injuries and fatalities were only significant for certain outcomes. Conclusion: Results support the hypothesis that there are differences in perceived post- and peritraumatic emotional and cognitive reactions after experiencing different types of disasters. However, it should be noted that these findings were not only explained by the type of disaster itself but also by individual and event characteristics. As the study followed an explorative approach, further research paths are discussed to better understand the relationships between variables

A eukaryote assemblage intercalated with Marinoan glacial deposits in South Australia

Video of digital X-ray tomographs (µCT) in longitudinal plane through cylinder of siltstone, maximum diameter seen (left to right when viewing movie) is 5.4m

Programmability and Performance of Parallel ECS-based Simulation of Multi-Agent Exploration Models

While the traditional objective of parallel/distributed simulation techniques has been mainly in improving performance and making very large models tractable, more recent research trends targeted complementary aspects, such as the “ease of programming”. Along this line, a recent proposal called Event and Cross State (ECS) synchronization, stands as a solution allowing to break the traditional programming rules proper of Parallel Discrete Event Simulation (PDES) systems, where the application code processing a specific event is only allowed to access the state (namely the memory image) of the target simulation object. In fact with ECS, the programmer is allowed to write ANSI-C event-handlers capable of accessing (in either read or write mode) the state of whichever simulation object included in the simulation model. Correct concurrent execution of events, e.g., on top of multi-core machines, is guaranteed by ECS with no intervention by the programmer, who is in practice exposed to a sequential-style programming model where events are processed one at a time, and have the ability to access the current memory image of the whole simulation model, namely the collection of the states of any involved object. This can strongly simplify the development of specific models, e.g., by avoiding the need for passing state information across concurrent objects in the form of events. In this article we investigate on both programmability and performance aspects related to developing/supporting a multi-agent exploration model on top of the ROOT-Sim PDES platform, which supports ECS

Apparent non-canonical trans-splicing is generated by reverse transcriptase in vitro

Trans-splicing, the in vivo joining of two RNA molecules, is well characterized in several groups of simple organisms but was long thought absent from fungi, plants and mammals. However, recent bioinformatic analyses of expressed sequence tag (EST) databases suggested widespread trans-splicing in mammals^1-2^. Splicing, including the characterised trans-splicing systems, involves conserved sequences at the splice junctions. Our analysis of a yeast non-coding RNA revealed that around 30% of the products of reverse transcription lacked an internal region of 117 nt, suggesting that the RNA was spliced. The junction sequences lacked canonical splice-sites but were flanked by direct repeats, and further analyses indicated that the apparent splicing actually arose because reverse transcriptase can switch templates during transcription^3^. Many newly identified, apparently trans-spliced, RNAs lacked canonical splice sites but were flanked by short regions of homology, leading us to question their authenticity. Here we report that all reported categories of non-canonical splicing could be replicated using an in vitro reverse transcription system with highly purified RNA substrates. We observed the reproducible occurrence of ostensible trans-splicing, exon shuffling and sense-antisense fusions. The latter generate apparent antisense non-coding RNAs, which are also reported to be abundant in humans^4^. Different reverse transcriptases can generate different products of template switching, providing a simple diagnostic. Many reported examples of splicing in the absence of canonical splicing signals may be artefacts of cDNA preparation