Electronic structure and Fermi surface tolopogy of Nax_xCoO2_2

We construct an effective Hamiltonian for the motion of T2g highly correlated states in NaxCoO2. We solve exactly a multiband model in a CoO6 cluster with electronic occupation corresponding to a nominal Co valence of either +3 or +4. Using the ensuing ground states, we calculate the effective O mediated hopping t=0.10 eV between many-body T2g states, and estimate the direct hopping t'~0.04 eV. The trigonal splitting 3D=0.315 eV is taken from recent quantum chemistry calculations. The resulting effective Hamiltonian is solved using a generalized slave-boson mean-field approximation. The results show a significant band renormalization and a Fermi surface topology that agrees with experiment, in contrast to predictions using the local-density approximation.Comment: 4 pages, 2 figure

The Minimal Length of a Lagrangian Cobordism between Legendrians

To investigate the rigidity and flexibility of Lagrangian cobordisms between Legendrian submanifolds, we investigate the minimal length of such a cobordism, which is a $1$-dimensional measurement of the non-cylindrical portion of the cobordism. Our primary tool is a set of real-valued capacities for a Legendrian submanifold, which are derived from a filtered version of Legendrian Contact Homology. Relationships between capacities of Legendrians at the ends of a Lagrangian cobordism yield lower bounds on the length of the cobordism. We apply the capacities to Lagrangian cobordisms realizing vertical dilations (which may be arbitrarily short) and contractions (whose lengths are bounded below). We also study the interaction between length and the linking of multiple cobordisms as well as the lengths of cobordisms derived from non-trivial loops of Legendrian isotopies.Comment: 33 pages, 9 figures. v2: Minor corrections in response to referee comments. More general statement in Proposition 3.3 and some reorganization at the end of Section

Exact Algorithms for Maximum Independent Set

We show that the maximum independent set problem (MIS) on an $n$-vertex graph can be solved in $1.1996^nn^{O(1)}$ time and polynomial space, which even is faster than Robson's $1.2109^{n}n^{O(1)}$-time exponential-space algorithm published in 1986. We also obtain improved algorithms for MIS in graphs with maximum degree 6 and 7, which run in time of $1.1893^nn^{O(1)}$ and $1.1970^nn^{O(1)}$, respectively. Our algorithms are obtained by using fast algorithms for MIS in low-degree graphs in a hierarchical way and making a careful analyses on the structure of bounded-degree graphs

Highly efficient synthesis of the tricyclic core of Taxol by cascade metathesis

An efficient enantioselective synthesis of the ABC tricyclic core of the anticancer drug Taxol is reported. The key step of this synthesis is a cascade metathesis reaction, which leads in one operation to the required tricycle if appropriate fine-tuning of the dienyne precursor is performed

Discernement, lucidité, conscience et insight en psychopathologie et en pratique expertale

International audienceInsight is a polysemic word coming from the English language. It has been used for a long time by psychoanalysts and from now on in clinical psychiatry. The insight rating scales explore diverse aspects of the awareness of having a mental disorder and the need to be treated. For many decades, meetings and publications on this topic can be found in the (cf. the meeting of March 2002). The new trends try to fragment and quantify the diverse dimensions of consciousness, awareness and insight. To be rigorous insight should be defined by the items, the score, and types of such or such rating scale. French psychiatric experts are required by legal regulations to assess the discernment ("discernement") of indicted persons (offence and crime) (article 122-1 of Code penal). Otherwise insight rating scales are useful for diagnosis, follow up, and to improve therapeutic alliance and compliance

Slippage and boundary layer probed in an almost ideal gas by a nanomechanical oscillator

We have measured the interaction between $^4$He gas at 4.2$~$K and a high-quality nano-electro-mechanical string device for its first 3 symmetric modes (resonating at 2.2$~$MHz, 6.7$~$MHz and 11$~$MHz with quality factor $Q > 0.1$ million) over almost 6 orders of magnitude in pressure. This fluid can be viewed as the best experimental implementation of an almost-ideal monoatomic and inert gas which properties are tabulated. The experiment ranges from high pressure where the flow is of laminar Stokes-type presenting slippage, down to very low pressures where the flow is molecular. In the molecular regime, when the mean-free-path is of the order of the distance between the suspended nano-mechanical probe and the bottom of the trench we resolve for the first time the signature of the boundary (Knudsen) layer onto the measured dissipation. Our results are discussed in the framework of the most recent theories investigating boundary effects in fluids (both analytic approaches and Monte-Carlo DSMC simulations)

Localization Recall Precision (LRP): A New Performance Metric for Object Detection

Average precision (AP), the area under the recall-precision (RP) curve, is the standard performance measure for object detection. Despite its wide acceptance, it has a number of shortcomings, the most important of which are (i) the inability to distinguish very different RP curves, and (ii) the lack of directly measuring bounding box localization accuracy. In this paper, we propose 'Localization Recall Precision (LRP) Error', a new metric which we specifically designed for object detection. LRP Error is composed of three components related to localization, false negative (FN) rate and false positive (FP) rate. Based on LRP, we introduce the 'Optimal LRP', the minimum achievable LRP error representing the best achievable configuration of the detector in terms of recall-precision and the tightness of the boxes. In contrast to AP, which considers precisions over the entire recall domain, Optimal LRP determines the 'best' confidence score threshold for a class, which balances the trade-off between localization and recall-precision. In our experiments, we show that, for state-of-the-art object (SOTA) detectors, Optimal LRP provides richer and more discriminative information than AP. We also demonstrate that the best confidence score thresholds vary significantly among classes and detectors. Moreover, we present LRP results of a simple online video object detector which uses a SOTA still image object detector and show that the class-specific optimized thresholds increase the accuracy against the common approach of using a general threshold for all classes. At https://github.com/cancam/LRP we provide the source code that can compute LRP for the PASCAL VOC and MSCOCO datasets. Our source code can easily be adapted to other datasets as well.Comment: to appear in ECCV 201