Singularity confinement and algebraic integrability

Two important notions of integrability for discrete mappings are algebraic integrability and singularity confinement, have been used for discrete mappings. Algebraic integrability is related to the existence of sufficiently many conserved quantities whereas singularity confinement is associated with the local analysis of singularities. In this paper, the relationship between these two notions is explored for birational autonomous mappings. Two types of results are obtained: first, algebraically integrable mappings are shown to have the singularity confinement property. Second, a proof of the non-existence of algebraic conserved quantities of discrete systems based on the lack of confinement property is given.Comment: 18 pages, no figur

Some properties of the k-dimensional Lyness' map

This paper is devoted to study some properties of the k-dimensional Lyness' map. Our main result presentes a rational vector field that gives a Lie symmetry for F. This vector field is used, for k less or equal to 5 to give information about the nature of the invariant sets under F. When k is odd, we also present a new (as far as we know) first integral for F^2 which allows to deduce in a very simple way several properties of the dynamical system generated by F. In particular for this case we prove that, except on a given codimension one algebraic set, none of the positive initial conditions can be a periodic point of odd period.Comment: 22 pages; 3 figure

Epigenetic dysregulation of brainstem nuclei in the pathogenesis of Alzheimer's disease: looking in the correct place at the right time?

This is the final version. Available from Springer Verlag via the DOI in this record.Even though the etiology of Alzheimer's disease (AD) remains unknown, it is suggested that an interplay among genetic, epigenetic and environmental factors is involved. An increasing body of evidence pinpoints that dysregulation in the epigenetic machinery plays a role in AD. Recent developments in genomic technologies have allowed for high throughput interrogation of the epigenome, and epigenome-wide association studies have already identified unique epigenetic signatures for AD in the cortex. Considerable evidence suggests that early dysregulation in the brainstem, more specifically in the raphe nuclei and the locus coeruleus, accounts for the most incipient, non-cognitive symptomatology, indicating a potential causal relationship with the pathogenesis of AD. Here we review the advancements in epigenomic technologies and their application to the AD research field, particularly with relevance to the brainstem. In this respect, we propose the assessment of epigenetic signatures in the brainstem as the cornerstone of interrogating causality in AD. Understanding how epigenetic dysregulation in the brainstem contributes to AD susceptibility could be of pivotal importance for understanding the etiology of the disease and for the development of novel diagnostic and therapeutic strategies.Funds have been provided by the Joint Programme—Neurodegenerative Disease Research (JPND) for the EPI-AD consortium focusing on epigenetic dysregulation in the brainstem in Alzheimer’s Disease (http://www.neurodegenerationresearch.eu/wp-content/uploads/2015/10/Factsheet_EPI-AD.pdf). The project is supported through the following funding organizations under the aegis of JPND—http://www.jpnd.eu, The Netherlands, The Netherlands Organisation for Health Research and Development (ZonMw); United Kingdom, Medical Research Council; Germany, German Federal ministry of Education and Research (BMBF); Luxembourg, National Research Fund (FNR). This project has received funding from the European Union’s Horizon 2020 research and innovation programme under Grant Agreement No. 643417. Additional support has been provided by the UK Medical Research Council (MRC) Grant MR/N027973/1 (K.L), Alzheimer’s Association (US) New Investigator Research Grant NIRG-14-320878 (K.L), Alzheimer’s Society (UK) Grant AS-PG-14-038 (K.L), the Internationale Stichting Alzheimer Onderzoek (ISAO) Grants 7551 and 11532 (D.L.A vdH.), the ISAO Grant 12530 (G.K), the ISAO Grant 13515 (B.P.F.R), and the Netherlands Organization for Scientific Research (NWO) Grant 916.11.086 (Veni Award) (B.P.F.R)

Construction of Integrals of Higher-Order Mappings

We find that certain higher-order mappings arise as reductions of the integrable discrete A-type KP (AKP) and B-type KP (BKP) equations. We find conservation laws for the AKP and BKP equations, then we use these conservation laws to derive integrals of the associated reduced maps.Comment: appear to Journal of the Physical Society of Japa

Analogues of Kahan's method for higher order equations of higher degree

Kahan introduced an explicit method of discretization for systems of first order differential equations with nonlinearities of degree at most two (quadratic vector fields). Kahan's method has attracted much interest due to the fact that it preserves many of the geometrical properties of the original continuous system. In particular, a large number of Hamiltonian systems of quadratic vector fields are known for which their Kahan discretization is a discrete integrable system. In this note, we introduce a special class of explicit order-preserving discretization schemes that are appropriate for certain systems of ordinary differential equations of higher order and higher degree

Tailoring the flow of soft glasses by soft additives

We examine the vitrification and melting of asymmetric star polymers mixtures by combining rheological measurements with mode coupling theory. We identify two types of glassy states, a {\it single} glass, in which the small component is fluid in the glassy matrix of the big one and a {\it double} glass, in which both components are vitrified. Addition of small star polymers leads to melting of {\it both} glasses and the melting curve has a non-monotonic dependence on the star-star size ratio. The phenomenon opens new ways for externally steering the rheological behavior of soft matter systems.Comment: 4 pages, 4 figures, accepted in Phys. Rev. Let

Exploring the interactions of irbesartan and irbesartan–2-hydroxypropyl-β-cyclodextrin complex with model membranes

The interactions of irbesartan (IRB) and irbesartan–2-hydroxypropyl-β-cyclodextrin (HP-β-CD) complex with Dipalmitoyl Phosphatidylcholine (DPPC) bilayers have been explored utilizing an array of biophysical techniques ranging from Differential Scanning Calorimetry (DSC), Small angle X-ray Scattering (SAXS), ESI Mass-Spectrometry (ESI-MS) and solid state Nuclear Magnetic Resonance (ssNMR). Molecular Dynamics (MD) calculations have been also conducted to complement the experimental results. Irbesartan was found to be embedded in the lipid membrane core and to affect the phase transition properties of the DPPC bilayers. SAXS studies revealed that irbesartan alone does not display perfect solvation since some coexisting irbesartan crystallites are present. In its complexed form IRB gets fully solvated in the membranes showing that encapsulation of IRB in HP-β-CD may have beneficial effects in the ADME properties of this drug. MD experiments revealed the topological and orientational integration of irbesartan into the phospholipid bilayer being placed at about 1 nm from the membrane centre

The Anopheles gambiae Odorant Binding Protein 1 (AgamOBP1) Mediates Indole Recognition in the Antennae of Female Mosquitoes

Haematophagous insects are frequently carriers of parasitic diseases, including malaria. The mosquito Anopheles gambiae is the major vector of malaria in sub-Saharan Africa and is thus responsible for thousands of deaths daily. Although the role of olfaction in A. gambiae host detection has been demonstrated, little is known about the combinations of ligands and odorant binding proteins (OBPs) that can produce specific odor-related responses in vivo. We identified a ligand, indole, for an A. gambiae odorant binding protein, AgamOBP1, modeled the interaction in silico and confirmed the interaction using biochemical assays. RNAi-mediated gene silencing coupled with electrophysiological analyses confirmed that AgamOBP1 binds indole in A. gambiae and that the antennal receptor cells do not respond to indole in the absence of AgamOBP1. This case represents the first documented instance of a specific A. gambiae OBP–ligand pairing combination, demonstrates the significance of OBPs in odor recognition, and can be expanded to the identification of other ligands for OBPs of Anopheles and other medically important insects