Experimental Demonstration of Quantum State Multi-meter and One-qubit Fingerprinting in a Single Quantum Device

We experimentally demonstrate in NMR a quantum interferometric multi-meter for extracting certain properties of unknown quantum states without resource to quantum tomography. It can perform direct state determinations, eigenvalue/eigenvector estimations, purity tests of a quantum system, as well as the overlap of any two unknown quantum states. Using the same device, we also demonstrate one-qubit quantum fingerprinting

Fine-Scale Variations in Eucritic Pyroxene FeO/MnO: Process vs. Provenance.

Most asteroidal igneous rocks are eucrite-like basalts and gabbros, composed mostly of ferroan low- and high-Ca pyroxenes and calcic plagioclase, plus smaller amounts of silica (most commonly tridymite), ilmenite, chromite, troilite, Ca-phosphate, metal and sometimes ferroan olivine. Eucrite-like mafic rocks are fragments of the crusts of differentiated asteroids, and most are likely from 4 Vesta

Magnitude and Sign Correlations in Heartbeat Fluctuations

We propose an approach for analyzing signals with long-range correlations by decomposing the signal increment series into magnitude and sign series and analyzing their scaling properties. We show that signals with identical long-range correlations can exhibit different time organization for the magnitude and sign. We find that the magnitude series relates to the nonlinear properties of the original time series, while the sign series relates to the linear properties. We apply our approach to the heartbeat interval series and find that the magnitude series is long-range correlated, while the sign series is anticorrelated and that both magnitude and sign series may have clinical applications.Comment: 4 pages,late

Enantioselective Total Synthesis of Macfarlandin C, a Spongian Diterpenoid Harboring a Concave-Substituted cis-Dioxabicyclo[3.3.0]octanone Fragment.

The enantioselective total synthesis of the rearranged spongian diterpenoid (-)-macfarlandin C is reported. This is the first synthesis of a rearranged spongian diterpenoid in which the bulky hydrocarbon fragment is joined via a quaternary carbon to the highly hindered concave face of the cis-2,8-dioxabicyclo[3.3.0]octan-3-one moiety. The strategy involves a late-stage fragment coupling between a tertiary carbon radical and an electrophilic butenolide resulting in the stereoselective formation of vicinal quaternary and tertiary stereocenters. A stereoselective Mukaiyama hydration that orients a pendant carboxymethyl side chain cis to the bulky octahydronapthalene substituent was pivotal in fashioning the challenging concave-substituted cis-dioxabicyclo[3.3.0]octanone fragment

The Multicomponent KP Hierarchy: Differential Fay Identities and Lax Equations

In this article, we show that four sets of differential Fay identities of an $N$-component KP hierarchy derived from the bilinear relation satisfied by the tau function of the hierarchy are sufficient to derive the auxiliary linear equations for the wave functions. From this, we derive the Lax representation for the $N$-component KP hierarchy, which are equations satisfied by some pseudodifferential operators with matrix coefficients. Besides the Lax equations with respect to the time variables proposed in \cite{2}, we also obtain a set of equations relating different charge sectors, which can be considered as a generalization of the modified KP hierarchy proposed in \cite{3}.Comment: 19 page

Multiple G-It\^{o} integral in the G-expectation space

In this paper, motivated by mathematic finance we introduce the multiple G-It\^{o} integral in the G-expectation space, then investigate how to calculate. We get the the relationship between Hermite polynomials and multiple G-It\^{o} integrals which is a natural extension of the classical result obtained by It\^{o} in 1951.Comment: 9 page

Erratum : Squeezing and entanglement delay using slow light

An inconsistency was found in the equations used to calculate the variance of the quadrature fluctuations of a field propagating through a medium demonstrating electromagnetically induced transparency (EIT). The decoherence term used in our original paper introduces inconsistency under weak probe approximation. In this erratum we give the Bloch equations with the correct dephasing terms. The conclusions of the original paper remain the same. Both entanglement and squeezing can be delayed and preserved using EIT without adding noise when the decoherence rate is small.Comment: 1 page, no figur

Pupillometry, a bioengineering overview

The pupillary control system is examined using a microprocessor based integrative pupillometer. The real time software functions of the microprocessor include: data collection, stimulus generation and area to diameter conversion. Results of an analysis of linear and nonlinear phenomena are presented

Non-degenerate solutions of universal Whitham hierarchy

The notion of non-degenerate solutions for the dispersionless Toda hierarchy is generalized to the universal Whitham hierarchy of genus zero with $M+1$ marked points. These solutions are characterized by a Riemann-Hilbert problem (generalized string equations) with respect to two-dimensional canonical transformations, and may be thought of as a kind of general solutions of the hierarchy. The Riemann-Hilbert problem contains $M$ arbitrary functions $H_a(z_0,z_a)$, $a = 1,...,M$, which play the role of generating functions of two-dimensional canonical transformations. The solution of the Riemann-Hilbert problem is described by period maps on the space of $(M+1)$-tuples $(z_\alpha(p) : \alpha = 0,1,...,M)$ of conformal maps from $M$ disks of the Riemann sphere and their complements to the Riemann sphere. The period maps are defined by an infinite number of contour integrals that generalize the notion of harmonic moments. The $F$-function (free energy) of these solutions is also shown to have a contour integral representation.Comment: latex2e, using amsmath, amssym and amsthm packages, 32 pages, no figur

Assessing the Formation Scenarios for the Double Nucleus of M31 Using Two-Dimensional Image Decomposition

The double nucleus geometry of M31 is currently best explained by the eccentric disk hypothesis of Tremaine, but whether the eccentric disk resulted from the tidal disruption of an inbounding star cluster by a nuclear black hole, or by an m=1 perturbation of a native nuclear disk, remains debatable. I perform detailed 2-D decomposition of the M31 double nucleus in the Hubble Space Telescope V-band to study the bulge structure and to address competing formation scenarios of the eccentric disk. I deblend the double nucleus (P1 and P2) and the bulge simultaneously using five Sersic and one Nuker components. P1 and P2 appear to be embedded inside an intermediate component (r_e=3.2") that is nearly spherical (q=0.97+/-m0.02), while the main galaxy bulge is more elliptical (q=0.81+/-0.01). The spherical bulge mass of 2.8x10^7 M_sol is comparable to the supermassive black hole mass (3x10^7 M_sol). In the 2-D decomposition, the bulge is consistent with being centered near the UV peak of P2, but the exact position is difficult to pinpoint because of dust in the bulge. P1 and P2 are comparable in mass. Within a radius r=1\arcsec of P2, the relative mass fraction of the nuclear components is M_BH:M_bulge:P1: P2 = 4.3:1.2:1:0.7, assuming the luminous components have a common mass-to-light ratio of 5.7. The eccentric disk as a whole (P1+P2) is massive, M ~ 2.1x10^7 M_sol, comparable to the black hole and the local bulge mass. As such, the eccentric disk could not have been formed entirely out of stars that were stripped from an inbounding star cluster. Hence, the more favored scenario is that of a disk formed in situ by an m=1 perturbation, caused possibly by the passing of a giant molecular cloud, or the passing/accretion of a small globular cluster.Comment: 19 pages, 8 figures. AJ accepted. For the version of this paper with high resolution figures, go to: http://zwicky.as.arizona.edu/~cyp/work/m31.ps.g