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

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

Palaeoenvironmental implications of a marine geoarchaeological survey conducted in the SW Argosaronic gulf, Greece

AbstractA marine geoarcheological survey was conducted at the southwestern end of the Argosaronic gulf in Greece, an area of archaeological importance. The survey was initiated by the discovery of a Late Bronze Age (LBA) shipwreck off Modi Islet. The survey which employed echo-sounding, sub-bottom profiling, side scan sonar systems and sediment coring extended to the area between Poros Island, Modi Islet and Argolid peninsula, aiming to evaluate the changes of the coastal zone extent in the past. The evolution of the palaeo-shoreline over the last 20ka is proposed based on the interpretation of the acquired bathymetric and seismic records, the estimation of the thickness of the marine sediments and the examination of existing datasets of the relative sea level changes in the area.The produced scenarios suggest that major changes marked the extent of the coastal zone since the Paleolithics. During the Upper Paleolithic period, the coast was larger by at least 11km2 and Poros and Modi islands were connected to the Peloponnesus. The sea level rise during the Mesolithic period formed a well-protected bay between Poros Island and Peloponessus and disconnected the Modi Islet from Poros Island. The coastal zone reached the present configuration around Late Bronze Age. The detection and mapping of scarps on the seismic profiles imply that the sea level rise presented standstills at least from the Last Glacial maximum until the onset of Holocene. However, the submerged coasts could be potential areas of archaeological interest since the examined area is habited continuously from the Paleolithic period.The acoustic data sets produced high resolution geomorphological maps at the wreck site which constitute data base for the monitoring of the site. In addition, the examination of the seafloor texture at the wreck site suggests that the seafloor characteristics were unfavorable for the preservation of the shipwreck

Genome-wide DNA Methylation Meta-analysis in the Brains of Suicide Completers

Suicide is the second leading cause of death globally among young people representing a significant global health burden. Although the molecular correlates of suicide remains poorly understood, it has been hypothesised that epigenomic processes may play a role. The objective of this study was to identify suicide-associated DNA methylation changes in the human brain by utilising previously published and unpublished methylomic datasets. We analysed prefrontal cortex (PFC, n = 211) and cerebellum (CER, n = 114) DNA methylation profiles from suicide completers and non-psychiatric, sudden-death controls, meta-analysing data from independent cohorts for each brain region separately. We report evidence for altered DNA methylation at several genetic loci in suicide cases compared to controls in both brain regions with suicide-associated differentially methylated positions enriched among functional pathways relevant to psychiatric phenotypes and suicidality, including nervous system development (PFC) and regulation of long-term synaptic depression (CER). In addition, we examined the functional consequences of variable DNA methylation within a PFC suicide-associated differentially methylated region (PSORS1C3 DMR) using a dual luciferase assay and examined expression of nearby genes. DNA methylation within this region was associated with decreased expression of firefly luciferase but was not associated with expression of nearby genes, PSORS1C3 and POU5F1. Our data suggest that suicide is associated with DNA methylation, offering novel insights into the molecular pathology associated with suicidality

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