The Homflypt polynomial and the oriented Thompson group

We show how to construct unitary representations of the oriented Thompson group $\vec{F}$ from oriented link invariants. In particular we show that the suitably normalised HOMFLYPT polynomial defines a positive definite function of $\vec{F}$.Comment: To appear in Quantum Topolog

Short-term memory and vocabulary development in children with Down syndrome and children with specific language impairment

A longitudinal comparison was made between development of verbal and visuo-spatial short-term memory and vocabulary in children with Down syndrome (DS), children with specific language impairment (SLI), and typically developing children as a control group. Participants were 12 children with DS (6 males, 6 females; mean chronological age 9y 9mo [SD 2.8 mo], range 8y 6mo to 11y 4mo); nine children with SLI (4 males, 5 females; mean chronological age 3y 9mo [SD 4.8mo], range 3y 3mo to 4y 5mo); and 12 typically developing children (5 males, 7 females; mean chronological age 4y 4mo [SD 3.9mo], range 3y 3mo to 4y 3mo). Participants were matched on mental age (mean mental age 4y 3mo). All participants completed verbal short-term memory, visuo-spatial short-term memory, and expressive and receptive vocabulary tasks on three occasions over 1 year. Similarities were seen in the clinical groups for verbal short-term memory. There was some evidence of difficulty in visuo-spatial short-term memory in the children with SLI relative to the other groups, but all three groups showed overlap in visuo-spatial short-term memory performance. At the final time-point vocabulary performance in the clinical groups was similar; the typically developing children showed higher vocabulary abilities than both clinical groups

Cognitive abilities in children with specific language impairment: consideration of visuo-spatial skills

Background: The study is concerned with the cognitive abilities of children with specific language impairment (SLI). Previous research has indicated that children with SLI demonstrate difficulties with certain cognitive tasks despite normal non‐verbal IQ scores. It has been suggested that a general processing limitation might account for the pattern of language and cognitive difficulties seen in children with SLI. The performances on a visuo‐spatial short‐term memory task and a visuo‐spatial processing task were considered in a group of young children with SLI. Verbal short‐term memory was also measured. Aims: To identify whether children with SLI demonstrate difficulties with visuo‐spatial memory as well as verbal short‐term memory. To see whether a visuo‐spatial processing task without short‐term memory requirements is problematic for children with SLI. To consider performance on these tasks over time. Methods & Procedures: Nine children with SLI (mean age 3;9 years at the study outset) and nine typically developing children (mean age 3;9 years at the study outset) were visited on three occasions over 1 year. Verbal short‐term memory, visuo‐spatial short‐term memory and visuo‐spatial processing tasks were administered to the children, and performance over time was compared between the two groups. Outcomes & Results: The children with SLI performed at a lower level than the typically developing children on the verbal short‐term memory task. Both groups showed similar development on the verbal short‐term memory task and the visuo‐spatial processing task over time. Only the visuo‐spatial short‐term memory task showed slower development over time in the children with SLI relative to the typically developing children. Conclusions: Children with SLI demonstrated slower development on a visuo‐spatial short‐term memory task relative to typically developing children of the same chronological age. This finding has implications for speech and language therapists and other professionals working with children with SLI. It may mean that only certain types of visual support are suitable, and that children with SLI will have difficulty with tasks requiring a high level of processing, or a number of mental manipulations

Evaluation and comparison of satellite precipitation estimates with reference to a local area in the Mediterranean Sea

Precipitation is one of the major variables for many applications and disciplines related to water resources and the geophysical Earth system. Satellite retrieval systems, rain-gauge networks, and radar systems are complementary to each other in terms of their coverage and capability of monitoring precipitation. Satellite-rainfall estimate systems produce data with global coverage that can provide information in areas for which data from other sources are unavailable. Without referring to ground measurements, satellite-based estimates can be biased and, although some gauge-adjusted satellite-precipitation products have been already developed, an effective way of integrating multi-sources of precipitation information is still a challenge.In this study, a specific area, the Sicilia Island (Italy), has been selected for the evaluation of satellite-precipitation products based on rain-gauge data. This island is located in the Mediterranean Sea, with a particular climatology and morphology, which can be considered an interesting test site for satellite-precipitation products in the European mid-latitude area. Four satellite products (CMORPH, PERSIANN, PERSIANN-CCS, and TMPA-RT) and two GPCP-adjusted products (TMPA and PERSIANN Adjusted) have been selected. Evaluation and comparison of selected products is performed with reference to data provided by the rain-gauge network of the Island Sicilia and by using statistical and graphical tools. Particular attention is paid to bias issues shown both by only-satellite and adjusted products. In order to investigate the current and potential possibilities of improving estimates by means of adjustment procedures using GPCC ground precipitation, the data have been retrieved separately and compared directly with the reference rain-gauge network data set of the study area.Results show that bias is still considerable for all satellite products, then some considerations about larger area climatology, PMW-retrieval algorithms, and GPCC data are discussed to address this issue, along with the spatial and seasonal characterization of results. © 2013 Elsevier B.V

Solvable Lie algebras are not that hypo

We study a type of left-invariant structure on Lie groups, or equivalently on Lie algebras. We introduce obstructions to the existence of a hypo structure, namely the 5-dimensional geometry of hypersurfaces in manifolds with holonomy SU(3). The choice of a splitting g^*=V_1 + V_2, and the vanishing of certain associated cohomology groups, determine a first obstruction. We also construct necessary conditions for the existence of a hypo structure with a fixed almost-contact form. For non-unimodular Lie algebras, we derive an obstruction to the existence of a hypo structure, with no choice involved. We apply these methods to classify solvable Lie algebras that admit a hypo structure.Comment: 21 pages; v2: presentation improved, typos corrected, notational conflicts eliminated. To appear in Transformation Group

Electron Correlation and Charge Transfer Instability in Bilayered Two Dimensional Electron Gas

We prove that the predicted charge transfer state in symmetric bilayers of two dimensional electron gases is always unstable at zero bias voltage, due to interlayer correlation and/or tunneling. This is most easily seen by resorting to a pseudospin formalism and considering coherent states obtained from the charge transfer state through rotations of the pseudospins. Evidently, the charge transfer state is stabilized by a sufficiently strong gate voltage, as found in recent experiments. We show that a simple model, in which the layers are strictly two dimensional, is able to account quantitatively for such experimental findings, when correlation is properly included.Comment: 5 pages, 3 figures. Subm. to Europhys. Let