Quantum Error Correcting Codes Using Qudit Graph States

Graph states are generalized from qubits to collections of $n$ qudits of arbitrary dimension $D$, and simple graphical methods are used to construct both additive and nonadditive quantum error correcting codes. Codes of distance 2 saturating the quantum Singleton bound for arbitrarily large $n$ and $D$ are constructed using simple graphs, except when $n$ is odd and $D$ is even. Computer searches have produced a number of codes with distances 3 and 4, some previously known and some new. The concept of a stabilizer is extended to general $D$, and shown to provide a dual representation of an additive graph code.Comment: Version 4 is almost exactly the same as the published version in Phys. Rev.

Topology of amorphous tetrahedral semiconductors on intermediate lengthscales

Using the recently-proposed ``activation-relaxation technique'' for optimizing complex structures, we develop a structural model appropriate to a-GaAs which is almost free of odd-membered rings, i.e., wrong bonds, and possesses an almost perfect coordination of four. The model is found to be superior to structures obtained from much more computer-intensive tight-binding or quantum molecular-dynamics simulations. For the elemental system a-Si, where wrong bonds do not exist, the cost in elastic energy for removing odd-membered rings is such that the traditional continuous-random network is appropriate. Our study thus provides, for the first time, direct information on the nature of intermediate-range topology in amorphous tetrahedral semiconductors.Comment: 4 pages, Latex and 2 postscript figure

Chiral rhodium complexes covalently anchored on carbon nanotubes for enantioselective hydrogenation

Chiral rhodium hybrid nanocatalysts have been prepared by covalent anchorage of pyrrolidine-based diphosphine ligands onto functionalized CNTs. This work constitutes the first attempt at covalent anchoring of homogeneous chiral catalysts on CNTs. The catalysts, prepared with two different chiral phosphines, were characterized by ICP, XPS, N2 adsorption and TEM, and have been tested in the asymmetric hydrogenation of two different substrates: methyl 2-acetamidoacrylate and α-acetamidocinnamic acid. The hybrid nanocatalysts have shown to be active and enantioselective in the hydrogenation of α-acetamidocinnamic acid. A good recyclability of the catalysts with low leaching and without loss of activity and enantioselectivity was observed.The authors acknowledge the financial support from the Institut National Polytechnique de Toulouse (ENSIACET), the Centre National de la Recherche Scientifique, MICINN, Project MAT2012-32832, GVA and FEDER, Project Prometeo 2009/047, and MEC for the FPU scholarship of C.C.G

Global shape processing involves a hierarchy of integration stages. Vision Res

a b s t r a c t Radial Frequency (RF) patterns can be used to study the processing of familiar shapes, e.g. triangles and squares. Opinion is divided over whether the mechanisms that detect these shapes integrate local orientation and position information directly, or whether local orientations and positions are first combined to represent extended features, such as curves, and that it is local curvatures that the shape mechanism integrates. The latter view incorporates an intermediate processing stage, the former does not. To differentiate between these hypotheses we studied the processing of micro-patch sampled RF patterns as a function of the luminance polarity of successive elements on the contour path. Our first study measures shape after effects involving suprathreshold amplitude RF shapes and shows that alternating the luminance polarity of successive micro-patch elements disrupts adaptation of the global shape. Our second study shows that polarity alternations also disrupt sensitivity to threshold-amplitude RF patterns. These results suggest that neighbouring points of the contour shape are integrated into extended features by a polarity selective mechanism, prior to global shape processing, consistent with the view that for both threshold amplitude and suprathreshold amplitude patterns, global processing of RF shapes involves an intermediate stage of processing. Crow

Hold Your Methods! How Multineuronal Firing Ensembles Can Be Studied Using Classical Spike-Train Analysis Techniques

Responses of neuronal populations play an important role in the encoding of stimulus related information. However, the inherent multidimensionality required to describe population activity has imposed significant challenges and has limited the applicability of classical spike train analysis techniques. Here, we show that these limitations can be overcome. We first quantify the collective activity of neurons as multidimensional vectors (patterns). Then we characterize the behavior of these patterns by applying classical spike train analysis techniques: peri-stimulus time histograms, tuning curves and auto- and cross-correlation histograms. We find that patterns can exhibit a broad spectrum of properties, some resembling and others substantially differing from those of their component neurons. We show that in some cases pattern behavior cannot be intuitively inferred from the activity of component neurons. Importantly, silent neurons play a critical role in shaping pattern expression. By correlating pattern timing with local-field potentials, we show that the method can reveal fine temporal coordination of cortical circuits at the mesoscale. Because of its simplicity and reliance on well understood classical analysis methods the proposed approach is valuable for the study of neuronal population dynamics

Modeling the non-Markovian, non-stationary scaling dynamics of financial markets

A central problem of Quantitative Finance is that of formulating a probabilistic model of the time evolution of asset prices allowing reliable predictions on their future volatility. As in several natural phenomena, the predictions of such a model must be compared with the data of a single process realization in our records. In order to give statistical significance to such a comparison, assumptions of stationarity for some quantities extracted from the single historical time series, like the distribution of the returns over a given time interval, cannot be avoided. Such assumptions entail the risk of masking or misrepresenting non-stationarities of the underlying process, and of giving an incorrect account of its correlations. Here we overcome this difficulty by showing that five years of daily Euro/US-Dollar trading records in the about three hours following the New York market opening, provide a rich enough ensemble of histories. The statistics of this ensemble allows to propose and test an adequate model of the stochastic process driving the exchange rate. This turns out to be a non-Markovian, self-similar process with non-stationary returns. The empirical ensemble correlators are in agreement with the predictions of this model, which is constructed on the basis of the time-inhomogeneous, anomalous scaling obeyed by the return distribution.Comment: Throughout revision. 15 pages, 6 figures. Presented by A.L. Stella in a Talk at the "Econophysics - Kolkata V'' International Workshop, March 2010, Saha Institute of Nuclear Physics, Kolkata, Indi

Line orientation adaptation: local or global?

Prolonged exposure to an oriented line shifts the perceived orientation of a subsequently observed line in the opposite direction, a phenomenon known as the tilt aftereffect (TAE). Here we consider whether the TAE for line stimuli is mediated by a mechanism that integrates the local parts of the line into a single global entity prior to the site of adaptation, or the result of the sum of local TAEs acting separately on the parts of the line. To test between these two alternatives we used the fact the TAE transfers almost completely across luminance contrast polarity [1]. We measured the TAE using adaptor and test lines that (1) either alternated in luminance polarity or were of a single polarity, and (2) either alternated in local orientation or were of a single orientation. We reasoned that if the TAE was agnostic to luminance polarity and was parts-based, we should obtain large TAEs using alternating-polarity adaptors with single-polarity tests. However we found that (i) TAEs using one-alternating-polarity adaptors with all-white tests were relatively small, increased slightly for two-alternating-polarity adaptors, and were largest with all-white or all-black adaptors. (ii) however TAEs were relatively large when the test was one-alternating polarity, irrespective of the adaptor type. (iii) The results with orientation closely mirrored those obtained with polarity with the difference that the TAE transfer across orthogonal orientations was weak. Taken together, our results demonstrate that the TAE for lines is mediated by a global shape mechanism that integrates the parts of lines into whole prior to the site of orientation adaptation. The asymmetry in the magnitude of TAE depending on whether the alternating-polarity lines was the adaptor or test can be explained by an imbalance in the population of neurons sensitive to 1st-and 2nd-order lines, with the 2nd-order lines being encoded by a subset of the mechanisms sensitive to 1st-order lines