Classical Tensors and Quantum Entanglement I: Pure States

The geometrical description of a Hilbert space asociated with a quantum system considers a Hermitian tensor to describe the scalar inner product of vectors which are now described by vector fields. The real part of this tensor represents a flat Riemannian metric tensor while the imaginary part represents a symplectic two-form. The immersion of classical manifolds in the complex projective space associated with the Hilbert space allows to pull-back tensor fields related to previous ones, via the immersion map. This makes available, on these selected manifolds of states, methods of usual Riemannian and symplectic geometry. Here we consider these pulled-back tensor fields when the immersed submanifold contains separable states or entangled states. Geometrical tensors are shown to encode some properties of these states. These results are not unrelated with criteria already available in the literature. We explicitly deal with some of these relations.Comment: 16 pages, 1 figure, to appear in Int. J. Geom. Meth. Mod. Phy

The genetic contribution of the NO system at the glutamatergic post-synapse to schizophrenia : further evidence and meta-analysis

NO is a pleiotropic signaling molecule and has an important role in cognition and emotion. In the brain, NO is produced by neuronal nitric oxide synthase (NOS-I, encoded by NOS1) coupled to the NMDA receptor via PDZ. interactions; this protein-protein interaction is disrupted upon binding of NOS1 adapter protein (encoded by NOS1AP) to NOS-I. As both NOS1 and NOS1AP were associated with schizophrenia, we here investigated these genes in greater detail by genotyping new samples and conducting a meta-analysis of our own and published data. In doing so, we confirmed association of both genes with schizophrenia and found evidence for their interaction in increasing risk towards disease. Our strongest finding was the NOS1 promoter SNP rs41279104, yielding an odds ratio of 1.29 in the meta-analysis. As findings from heterologous cell systems have suggested that the risk allele decreases gene expression, we studied the effect of the variant on NOS1 expression in human post-mortem brain samples and found that the risk allele significantly decreases expression of NOS1 in the prefrontal cortex. Bioinformatic analyses suggest that this might be due the replacement of six transcription factor binding sites by two new binding sites as a consequence of proxy SNPs. Taken together, our data argue that genetic variance in NOS1 resulting in lower prefrontal brain expression of this gene contributes to schizophrenia liability, and that NOS1 interacts with NOS1AP in doing so. The NOS1-NOS1AP PDZ interface may thus well constitute a novel target for small molecules in at least some forms of schizophrenia. PostprintPeer reviewe

Scanning-helium-ion-beam lithography with hydrogen silsesquioxane resist

A scanning-helium-ion-beam microscope is now commercially available. This microscope can be used to perform lithography similar to, but of potentially higher resolution than, scanning electron-beam lithography. This article describes the control of this microscope for lithography via beam steering/blanking electronics and evaluates the high-resolution performance of scanning helium-ion-beam lithography. The authors found that sub-10 nm-half-pitch patterning is feasible. They also measured a point-spread function that indicates a reduction in the micrometer-range proximity effect typical in electron-beam lithography.National Science Foundation (U.S.). Graduate Research Fellowship Progra

Boolean Dynamics with Random Couplings

This paper reviews a class of generic dissipative dynamical systems called N-K models. In these models, the dynamics of N elements, defined as Boolean variables, develop step by step, clocked by a discrete time variable. Each of the N Boolean elements at a given time is given a value which depends upon K elements in the previous time step. We review the work of many authors on the behavior of the models, looking particularly at the structure and lengths of their cycles, the sizes of their basins of attraction, and the flow of information through the systems. In the limit of infinite N, there is a phase transition between a chaotic and an ordered phase, with a critical phase in between. We argue that the behavior of this system depends significantly on the topology of the network connections. If the elements are placed upon a lattice with dimension d, the system shows correlations related to the standard percolation or directed percolation phase transition on such a lattice. On the other hand, a very different behavior is seen in the Kauffman net in which all spins are equally likely to be coupled to a given spin. In this situation, coupling loops are mostly suppressed, and the behavior of the system is much more like that of a mean field theory. We also describe possible applications of the models to, for example, genetic networks, cell differentiation, evolution, democracy in social systems and neural networks.Comment: 69 pages, 16 figures, Submitted to Springer Applied Mathematical Sciences Serie

Nutrition and dementia care: developing an evidence-based model for nutritional care in nursing homes.

BACKGROUND: There is a growing volume of research to offer improvements in nutritional care for people with dementia living in nursing homes. Whilst a number of interventions have been identified to support food and drink intake, there has been no systematic research to understand the factors for improving nutritional care from the perspectives of all those delivering care in nursing homes. The aim of this study was to develop a research informed model for understanding the complex nutritional problems associated with eating and drinking for people with dementia. METHODS: We conducted nine focus groups and five semi-structured interviews with those involved or who have a level of responsibility for providing food and drink and nutritional care in nursing homes (nurses, care workers, catering assistants, dietitians, speech and language therapists) and family carers. The resulting conceptual model was developed by eliciting care-related processes, thus supporting credibility from the perspective of the end-users. RESULTS: The seven identified domain areas were person-centred nutritional care (the overarching theme); availability of food and drink; tools, resources and environment; relationship to others when eating and drinking; participation in activities; consistency of care and provision of information. CONCLUSIONS: This collaboratively developed, person-centred model can support the design of new education and training tools and be readily translated into existing programmes. Further research is needed to evaluate whether these evidence-informed approaches have been implemented successfully and adopted into practice and policy contexts and can demonstrate effectiveness for people living with dementia

Cast aluminium single crystals cross the threshold from bulk to size-dependent stochastic plasticity

Metals are known to exhibit mechanical behaviour at the nanoscale different to bulk samples. This transition typically initiates at the micrometre scale, yet existing techniques to produce micrometre-sized samples often introduce artefacts that can influence deformation mechanisms. Here, we demonstrate the casting of micrometre-scale aluminium single-crystal wires by infiltration of a salt mould. Samples have millimetre lengths, smooth surfaces, a range of crystallographic orientations, and a diameter D as small as 6 μm. The wires deform in bursts, at a stress that increases with decreasing D. Bursts greater than 200 nm account for roughly 50% of wire deformation and have exponentially distributed intensities. Dislocation dynamics simulations show that single-arm sources that produce large displacement bursts halted by stochastic cross-slip and lock formation explain microcast wire behaviour. This microcasting technique may be extended to several other metals or alloys and offers the possibility of exploring mechanical behaviour spanning the micrometre scale