On the integral cohomology of smooth toric varieties

Let $X_\Sigma$ be a smooth, not necessarily compact toric variety. We show that a certain complex, defined in terms of the fan $\Sigma$, computes the integral cohomology of $X_\Sigma$, including the module structure over the homology of the torus. In some cases we can also give the product. As a corollary we obtain that the cycle map from Chow groups to integral Borel-Moore homology is split injective for smooth toric varieties. Another result is that the differential algebra of singular cochains on the Borel construction of $X_\Sigma$ is formal.Comment: 10 page

Continuous Spectrum of Automorphism Groups and the Infraparticle Problem

This paper presents a general framework for a refined spectral analysis of a group of isometries acting on a Banach space, which extends the spectral theory of Arveson. The concept of continuous Arveson spectrum is introduced and the corresponding spectral subspace is defined. The absolutely continuous and singular-continuous parts of this spectrum are specified. Conditions are given, in terms of the transposed action of the group of isometries, which guarantee that the pure-point and continuous subspaces span the entire Banach space. In the case of a unitarily implemented group of automorphisms, acting on a $C^*$-algebra, relations between the continuous spectrum of the automorphisms and the spectrum of the implementing group of unitaries are found. The group of spacetime translation automorphisms in quantum field theory is analyzed in detail. In particular, it is shown that the structure of its continuous spectrum is relevant to the problem of existence of (infra-)particles in a given theory.Comment: 31 pages, LaTeX. As appeared in Communications in Mathematical Physic

Global bifurcation of homoclinic trajectories of discrete dynamical systems

We prove the existence of an unbounded connected branch of nontrivial homoclinic trajectories of a family of discrete nonautonomous asymptotically hyperbolic systems parametrized by a circle under assumptions involving the topological properties of the asymptotic stable bundles.Comment: 28 pages. arXiv admin note: text overlap with arXiv:1111.140

Topology and Homoclinic Trajectories of Discrete Dynamical Systems

We show that nontrivial homoclinic trajectories of a family of discrete, nonautonomous, asymptotically hyperbolic systems parametrized by a circle bifurcate from a stationary solution if the asymptotic stable bundles Es(+{\infty}) and Es(-{\infty}) of the linearization at the stationary branch are twisted in different ways.Comment: 19 pages, canceled the appendix (Properties of the index bundle) in order to avoid any text overlap with arXiv:1005.207

Prediction of peptide and protein propensity for amyloid formation

Understanding which peptides and proteins have the potential to undergo amyloid formation and what driving forces are responsible for amyloid-like fiber formation and stabilization remains limited. This is mainly because proteins that can undergo structural changes, which lead to amyloid formation, are quite diverse and share no obvious sequence or structural homology, despite the structural similarity found in the fibrils. To address these issues, a novel approach based on recursive feature selection and feed-forward neural networks was undertaken to identify key features highly correlated with the self-assembly problem. This approach allowed the identification of seven physicochemical and biochemical properties of the amino acids highly associated with the self-assembly of peptides and proteins into amyloid-like fibrils (normalized frequency of β-sheet, normalized frequency of β-sheet from LG, weights for β-sheet at the window position of 1, isoelectric point, atom-based hydrophobic moment, helix termination parameter at position j+1 and ΔGº values for peptides extrapolated in 0 M urea). Moreover, these features enabled the development of a new predictor (available at http://cran.r-project.org/web/packages/appnn/index.html) capable of accurately and reliably predicting the amyloidogenic propensity from the polypeptide sequence alone with a prediction accuracy of 84.9 % against an external validation dataset of sequences with experimental in vitro, evidence of amyloid formation

Search for heavy gauge W ' bosons in events with an energetic lepton and large missing transverse momentum at root s=13TeV

Peer reviewe

Search for light bosons in decays of the 125 GeV Higgs boson in proton-proton collisions at root s=8 TeV

Peer reviewe