On supersimple groups

International audienceAn infinite group with supersimple theory has a finite series of definable groups whose factors are infinite and either virtually-FC or virtually-simple modulo a finite FC-centre. A group which is type-definable in a supersimple theory has a finite series of relatively definable groups whose factors are either abelian or simple groups. In this decomposition, the non-abelian simple factors are unique up to isomorphism

Hyperbolically embedded subgroups and rotating families in groups acting on hyperbolic spaces

We introduce and study the notions of hyperbolically embedded and very rotating families of subgroups. The former notion can be thought of as a generalization of the peripheral structure of a relatively hyperbolic group, while the later one provides a natural framework for developing a geometric version of small cancellation theory. Examples of such families naturally occur in groups acting on hyperbolic spaces including hyperbolic and relatively hyperbolic groups, mapping class groups, $Out(F_n)$, and the Cremona group. Other examples can be found among groups acting geometrically on $CAT(0)$ spaces, fundamental groups of graphs of groups, etc. We obtain a number of general results about rotating families and hyperbolically embedded subgroups; although our technique applies to a wide class of groups, it is capable of producing new results even for well-studied particular classes. For instance, we solve two open problems about mapping class groups, and obtain some results which are new even for relatively hyperbolic groups.Comment: Revision, corrections and improvement of the expositio

Data-Driven Stabilizing and Robust Control of Discrete-Time Linear Systems with Error in Variables

This work presents a sum-of-squares (SOS) based framework to perform data-driven stabilization and robust control tasks on discrete-time linear systems where the full-state observations are corrupted by L-infinity bounded input, measurement, and process noise (error in variable setting). Certificates of state-feedback superstability or quadratic stability of all plants in a consistency set are provided by solving a feasibility program formed by polynomial nonnegativity constraints. Under mild compactness and data-collection assumptions, SOS tightenings in rising degree will converge to recover the true superstabilizing controller, with slight conservatism introduced for quadratic stabilizability. The performance of this SOS method is improved through the application of a theorem of alternatives while retaining tightness, in which the unknown noise variables are eliminated from the consistency set description. This SOS feasibility method is extended to provide worst-case-optimal robust controllers under H2 control costs. The consistency set description may be broadened to include cases where the data and process are affected by a combination of L-infinity bounded measurement, process, and input noise. Further generalizations include varying noise sets, non-uniform sampling, and switched systems stabilization.Comment: 27 pages, 1 figure, 9 table

Studies on the purification and characteristization of ribitol dehydrogenase messenger RNA from Klebsiella aerogenes

Imperial Users onl

ESPRESSO: The next European exoplanet hunter

The acronym ESPRESSO stems for Echelle SPectrograph for Rocky Exoplanets and Stable Spectroscopic Observations; this instrument will be the next VLT high resolution spectrograph. The spectrograph will be installed at the Combined-Coud\'e Laboratory of the VLT and linked to the four 8.2 m Unit Telescopes (UT) through four optical Coud\'e trains. ESPRESSO will combine efficiency and extreme spectroscopic precision. ESPRESSO is foreseen to achieve a gain of two magnitudes with respect to its predecessor HARPS, and to improve the instrumental radial-velocity precision to reach the 10 cm/s level. It can be operated either with a single UT or with up to four UTs, enabling an additional gain in the latter mode. The incoherent combination of four telescopes and the extreme precision requirements called for many innovative design solutions while ensuring the technical heritage of the successful HARPS experience. ESPRESSO will allow to explore new frontiers in most domains of astrophysics that require precision and sensitivity. The main scientific drivers are the search and characterization of rocky exoplanets in the habitable zone of quiet, nearby G to M-dwarfs and the analysis of the variability of fundamental physical constants. The project passed the final design review in May 2013 and entered the manufacturing phase. ESPRESSO will be installed at the Paranal Observatory in 2016 and its operation is planned to start by the end of the same year.Comment: 12 pages, figures included, accepted for publication in Astron. Nach

Resolving intrinsically disordered proteins of the cancer genome with ion mobility mass spectrometry

For proteins the link between their structure and their function is a central tenet of biology. A common approach to understanding protein function is to ‘solve’ its structure and subsequently probe interactions between the protein and its binding partners. The first part of this approach is non-trivial for proteins where localised regions or even their entire structure fail to fold into a three-dimensional structure and yet they possess function. These so called intrinsically or inherently disordered proteins (IDP’s) or intrinsically disordered regions (IDR’s) constitute up to 40% of all expressed proteins. IDPs which have crucial roles in molecular recognition, assembly, protein modification and entropic chain activities, are often dynamic with respect to both conformation and interaction, so in the course of a protein’s ‘lifespan’ it will sample many configurations and bind to several targets. For these proteins, there is a need to develop new methods for structure characterization which exploit their biophysical properties. The solvent free environment of a mass spectrometer is ideally suited to the study of intrinsic interactions and how they contribute to structure. Ion mobility mass spectrometry is uniquely able to observe the range of structures an IDP can occupy, and also the effect of selected binding partners on altering this conformational space. This thesis details the technique of ion mobility mass spectrometry and illustrates its use in assessing the relative disorder of p53 protein. The tumour suppressor p53 is at the hub of a plethora of signalling pathways that maintain the integrity of the human genome and regulate the cell cycle. Deregulation of this protein has a great effect on carcinogenesis as mutated p53 can induce an amplified epigenetic instability of tumour cells, facilitating and accelerating the evolution of the tumour. Herein mass spectrometry provides a compelling, detailed insight into the conformational flexibility of the p53 DNA-binding domain. The plasticity of the p53 DNA-binding domain is reflected in the existence of more than one conformation, independent of any conformational changes prompted by binding. The in vacuo conformational phenotypes exhibited by common cancer-associated mutations are determined and the second-site suppressor mutation from loop L1, H115N, is probed whether it could trigger conformational changes in p53 hotspot cancer mutations. The structural basis of the binding promiscuity of p53 protein is investigated; of particular interest is the molecular interaction of the p53 N-terminus with the oncoprotein murine double minute 2, as well as with the antiapoptotic factor B-cell lymphoma-extralarge