Weak Poisson structures on infinite dimensional manifolds and hamiltonian actions

We introduce a notion of a weak Poisson structure on a manifold $M$ modeled on a locally convex space. This is done by specifying a Poisson bracket on a subalgebra \cA \subeq C^\infty(M) which has to satisfy a non-degeneracy condition (the differentials of elements of \cA separate tangent vectors) and we postulate the existence of smooth Hamiltonian vector fields. Motivated by applications to Hamiltonian actions, we focus on affine Poisson spaces which include in particular the linear and affine Poisson structures on duals of locally convex Lie algebras. As an interesting byproduct of our approach, we can associate to an invariant symmetric bilinear form $\kappa$ on a Lie algebra \g and a $\kappa$-skew-symmetric derivation $D$ a weak affine Poisson structure on \g itself. This leads naturally to a concept of a Hamiltonian $G$-action on a weak Poisson manifold with a \g-valued momentum map and hence to a generalization of quasi-hamiltonian group actions

Closed forms and multi-moment maps

We extend the notion of multi-moment map to geometries defined by closed forms of arbitrary degree. We give fundamental existence and uniqueness results and discuss a number of essential examples, including geometries related to special holonomy. For forms of degree four, multi-moment maps are guaranteed to exist and are unique when the symmetry group is (3,4)-trivial, meaning that the group is connected and the third and fourth Lie algebra Betti numbers vanish. We give a structural description of some classes of (3,4)-trivial algebras and provide a number of examples.Comment: 36 page

Invariants of Lie algebras extended over commutative algebras without unit

We establish results about the second cohomology with coefficients in the trivial module, symmetric invariant bilinear forms and derivations of a Lie algebra extended over a commutative associative algebra without unit. These results provide a simple unified approach to a number of questions treated earlier in completely separated ways: periodization of semisimple Lie algebras (Anna Larsson), derivation algebras, with prescribed semisimple part, of nilpotent Lie algebras (Benoist), and presentations of affine Kac-Moody algebras.Comment: v3: added a footnote on p.10 about a wrong derivation of the correct statemen

Search for the exotic Ξ−−(1860)\Xi^{--}(1860) Resonance in 340GeV/c Σ−\Sigma^--Nucleus Interactions

We report on a high statistics search for the $\Xi^{--}(1860)$ resonance in $\Sigma^-$-nucleus collisions at 340GeV/c. No evidence for this resonance is found in our data sample which contains 676000 $\Xi^-$ candidates above background. For the decay channel $\Xi^{--}(1860) \to \Xi^-\pi^-$ and the kinematic range 0.15$<x_F<$0.9 we find a 3$\sigma$ upper limit for the production cross section of 3.1 and 3.5 $\mu$b per nucleon for reactions with carbon and copper, respectively.Comment: 5 pages, 4 figures, modification of ref. 43 and 4

A non-coding RNA balancing act: miR-346-induced DNA damage is limited by the long non-coding RNA NORAD in prostate cancer

Background: miR‑346 was identified as an activator of Androgen Receptor (AR) signalling that associates with DNA damage response (DDR)‑linked transcripts in prostate cancer (PC). We sought to delineate the impact of miR‑346 on DNA damage, and its potential as a therapeutic agent. Methods: RNA‑IP, RNA‑seq, RNA‑ISH, DNA fibre assays, in vivo xenograft studies and bioinformatics approaches were used alongside a novel method for amplification‑free, single nucleotide‑resolution genome‑wide mapping of DNA breaks (INDUCE‑seq). Results: miR‑346 induces rapid and extensive DNA damage in PC cells ‑ the first report of microRNA‑induced DNA damage. Mechanistically, this is achieved through transcriptional hyperactivation, R‑loop formation and replication stress, leading to checkpoint activation and cell cycle arrest. miR‑346 also interacts with genome‑protective lncRNA NORAD to disrupt its interaction with PUM2, leading to PUM2 stabilisation and its increased turnover of DNA damage response (DDR) transcripts. Confirming clinical relevance, NORAD expression and activity strongly correlate with poor PC clinical outcomes and increased DDR in biopsy RNA‑seq studies. In contrast, miR‑346 is associated with improved PC survival. INDUCE‑seq reveals that miR‑346‑induced DSBs occur preferentially at binding sites of the most highly‑transcriptionally active transcription factors in PC cells, including c‑Myc, FOXA1, HOXB13, NKX3.1, and importantly, AR, resulting in target transcript downregulation. Further, RNA‑seq reveals widespread miR‑346 and shNORAD dysregulation of DNA damage, replication and cell cycle processes. NORAD drives target‑directed miR decay (TDMD) of miR‑346 as a novel genome protection mechanism: NORAD silencing increases mature miR‑346 levels by several thousand‑fold, and WT but not TDMD‑mutant NORAD rescues miR‑346‑induced DNA damage. Importantly, miR‑346 sensitises PC cells to DNA‑damaging drugs including PARP inhibitor and chemotherapy, and induces tumour regression as a monotherapy in vivo, indicating that targeting miR‑346:NORAD balance is a valid therapeutic strategy

Estimating the apparent transverse relaxation time (R2*) from images with different contrasts (ESTATICS) reduces motion artifacts

Relaxation rates provide important information about tissue microstructure. Multi-parameter mapping (MPM) estimates multiple relaxation parameters from multi-echo FLASH acquisitions with different basic contrasts, i.e., proton density (PD), T1 or magnetization transfer (MT) weighting. Motion can particularly affect maps of the apparent transverse relaxation rate R2*, which are derived from the signal of PD-weighted images acquired at different echo times. To address the motion artifacts, we introduce ESTATICS, which robustly estimates R2* from images even when acquired with different basic contrasts. ESTATICS extends the fitted signal model to account for inherent contrast differences in the PDw, T1w and MTw images. The fit was implemented as a conventional ordinary least squares optimization and as a robust fit with a small or large confidence interval. These three different implementations of ESTATICS were tested on data affected by severe motion artifacts and data with no prominent motion artifacts as determined by visual assessment or fast optical motion tracking. ESTATICS improved the quality of the R2* maps and reduced the coefficient of variation for both types of data—with average reductions of 30% when severe motion artifacts were present. ESTATICS can be applied to any protocol comprised of multiple 2D/3D multi-echo FLASH acquisitions as used in the general research and clinical setting

Causal structures and causal boundaries

We give an up-to-date perspective with a general overview of the theory of causal properties, the derived causal structures, their classification and applications, and the definition and construction of causal boundaries and of causal symmetries, mostly for Lorentzian manifolds but also in more abstract settings.Comment: Final version. To appear in Classical and Quantum Gravit

Characterisation of Gut Microbiota in Ossabaw and Göttingen Minipigs as Models of Obesity and Metabolic Syndrome

Recent evidence suggests that the gut microbiota is an important contributing factor to obesity and obesity related metabolic disorders, known as the metabolic syndrome. The aim of this study was to characterise the intestinal microbiota in two pig models of obesity namely Göttingen minipigs and the Ossabaw minipigs.The cecal, ileal and colonic microbiota from lean and obese Osabaw and Göttingen minipigs were investigated by Illumina-based sequencing and by high throughput qPCR, targeting the 16S rRNA gene in different phylogenetic groups of bacteria. The weight gain through the study was significant in obese Göttingen and Ossabaw minipigs. The lean Göttingen minipigs' cecal microbiota contained significantly higher abundance of Firmicutes (P<0.006), Akkermensia (P<0.01) and Methanovibribacter (P<0.01) than obese Göttingen minipigs. The obese Göttingen cecum had higher abundances of the phyla Spirochaetes (P<0.03), Tenericutes (P<0.004), Verrucomicrobia (P<0.005) and the genus Bacteroides (P<0.001) compared to lean minipigs. The relative proportion of Clostridium cluster XIV was 7.6-fold higher in cecal microbiota of obese Göttingen minipigs as compared to lean. Obese Ossabaw minipigs had a higher abundance of Firmicutes in terminal ileum and lower abundance of Bacteroidetes in colon than lean Ossabaw minipigs (P<0.01). Obese Ossabaws had significantly lower abundances of the genera Prevotella and Lactobacillus and higher abundance of Clostridium in their colon than the lean Ossabaws. Overall, the Göttingen and Ossabaw minipigs displayed different microbial communities in response to diet-induced obesity in the different sections of their intestine.Obesity-related changes in the composition of the gut microbiota were found in lean versus obese Göttingen and Ossabaw minipigs. In both pig models diet seems to be the defining factor that shapes the gut microbiota as observed by changes in different bacteria divisions between lean and obese minipigs

Properties of field functionals and characterization of local functionals

Functionals (i.e. functions of functions) are widely used in quantum field theory and solid-state physics. In this paper, functionals are given a rigorous mathematical framework and their main properties are described. The choice of the proper space of test functions (smooth functions) and of the relevant concept of differential (Bastiani differential) are discussed. The relation between the multiple derivatives of a functional and the corresponding distributions is described in detail. It is proved that, in a neighborhood of every test function, the support of a smooth functional is uniformly compactly supported and the order of the corresponding distribution is uniformly bounded. Relying on a recent work by Yoann Dabrowski, several spaces of functionals are furnished with a complete and nuclear topology. In view of physical applications, it is shown that most formal manipulations can be given a rigorous meaning. A new concept of local functionals is proposed and two characterizations of them are given: the first one uses the additivity (or Hammerstein) property, the second one is a variant of Peetre's theorem. Finally, the first step of a cohomological approach to quantum field theory is carried out by proving a global Poincar\'e lemma and defining multi-vector fields and graded functionals within our framework.Comment: 32 pages, no figur