The Matrix Ansatz, Orthogonal Polynomials, and Permutations

In this paper we outline a Matrix Ansatz approach to some problems of combinatorial enumeration. The idea is that many interesting quantities can be expressed in terms of products of matrices, where the matrices obey certain relations. We illustrate this approach with applications to moments of orthogonal polynomials, permutations, signed permutations, and tableaux.Comment: to appear in Advances in Applied Mathematics, special issue for Dennis Stanto

Data analysis methods for the cosmic microwave background

41 pages, 21 figuresInternational audienceIn this review, we give an overview of some of the major aspects of data reduction and analysis for the cosmic microwave background (CMB). Since its prediction and discovery in the last century, the CMB radiation has proven itself to be one of our most valuable tools for precision cosmology. Recently, and especially when combined with complementary cosmological data, measurements of the CMB anisotropies have provided us with a wealth of quantitive information about the birth, evolution and structure of our Universe. We begin with a simple, general introduction to the physics of the CMB, including a basic overview of the experiments which record CMB data. The focus, however, will be the data analysis treatment of CMB data sets

Improved modelling of liquid GeSe2_2: the impact of the exchange-correlation functional

The structural properties of liquid GeSe$_2$ are studied by using first-principles molecular dynamics in conjuncton with the Becke, Lee, Yang and Parr (BLYP) generalized gradient approximation for the exchange and correlation energy. The results on partial pair correlation functions, coordination numbers, bond angle distributions and partial structure factors are compared with available experimental data and with previous first-principle molecular dynamics results obtained within the Perdew and Wang (PW) generalized gradient approximation for the exchange and correlation energy. We found that the BLYP approach substantially improves upon the PW one in the case of the short-range properties. In particular, the Ge$-$Ge pair correlation function takes a more structured profile that includes a marked first peak due to homopolar bonds, a first maximum exhibiting a clear shoulder and a deep minimum, all these features being absent in the previous PW results. Overall, the amount of tetrahedral order is significantly increased, in spite of a larger number of Ge$-$Ge homopolar connections. Due to the smaller number of miscoordinations, diffusion coefficients obtained by the present BLYP calculation are smaller by at least one order of magnitude than in the PW case.Comment: 6 figure

35.4 T field generated using a layer-wound superconducting coil made of (RE)Ba2Cu3O7-x (RE = Rare Earth) coated conductor

To explore the limits of layer wound (RE)Ba2Cu3O7-x (REBCO, RE = Rare Earth) coils in a high magnetic field environment > 30 T, a series of small insert coils have been built and characterized in background fields. One of the coils repeatedly reached 35.4 T using a single ~100 m length of REBCO tape wet wound with epoxy and nested in a 31 T background magnet. The coil was quenched safely several times without degradation. Contributing to the success of this coil was the introduction of a thin polyester film that surrounded the conductor. This approach introduces a weak circumferential plane in the coil pack that prevents conductor delamination that has caused degradation of several epoxy impregnated coils previously made by this and other groups.Comment: 7 pages, 3 figures, 1 tabl

Developing a Complex Independent Component Analysis (CICA) technique to extract non-stationary patterns from geophysical time series

In recent decades, decomposition techniques have enabled increasingly more applications for dimension reduction, as well as extraction of additional information from geophysical time series. Traditionally, the principal component analysis (PCA)/empirical orthogonal function (EOF) method and more recently the independent component analysis (ICA) have been applied to extract, statistical orthogonal (uncorrelated), and independent modes that represent the maximum variance of time series, respectively. PCA and ICA can be classified as stationary signal decomposition techniques since they are based on decomposing the autocovariance matrix and diagonalizing higher (than two) order statistical tensors from centered time series, respectively. However, the stationarity assumption in these techniques is not justified for many geophysical and climate variables even after removing cyclic components, e.g., the commonly removed dominant seasonal cycles. In this paper, we present a novel decomposition method, the complex independent component analysis (CICA), which can be applied to extract non-stationary (changing in space and time) patterns from geophysical time series. Here, CICA is derived as an extension of real-valued ICA, where (a) we first define a new complex dataset that contains the observed time series in its real part, and their Hilbert transformed series as its imaginary part, (b) an ICA algorithm based on diagonalization of fourth-order cumulants is then applied to decompose the new complex dataset in (a), and finally, (c) the dominant independent complex modes are extracted and used to represent the dominant space and time amplitudes and associated phase propagation patterns. The performance of CICA is examined by analyzing synthetic data constructed from multiple physically meaningful modes in a simulation framework, with known truth. Next, global terrestrial water storage (TWS) data from the Gravity Recovery And Climate Experiment (GRACE) gravimetry mission (2003–2016), and satellite radiometric sea surface temperature (SST) data (1982–2016) over the Atlantic and Pacific Oceans are used with the aim of demonstrating signal separations of the North Atlantic Oscillation (NAO) from the Atlantic Multi-decadal Oscillation (AMO), and the El Niño Southern Oscillation (ENSO) from the Pacific Decadal Oscillation (PDO). CICA results indicate that ENSO-related patterns can be extracted from the Gravity Recovery And Climate Experiment Terrestrial Water Storage (GRACE TWS) with an accuracy of 0.5–1 cm in terms of equivalent water height (EWH). The magnitude of errors in extracting NAO or AMO from SST data using the complex EOF (CEOF) approach reaches up to ~50% of the signal itself, while it is reduced to ~16% when applying CICA. Larger errors with magnitudes of ~100% and ~30% of the signal itself are found while separating ENSO from PDO using CEOF and CICA, respectively. We thus conclude that the CICA is more effective than CEOF in separating non-stationary patterns

Qubit State Discrimination

We show how one can solve the problem of discriminating between qubit states. We use the quantum state discrimination duality theorem and the Bloch sphere representation of qubits which allows for an easy geometric and analytical representation of the optimal guessing strategies.Comment: 6 pages, 4 figures. v2 has small corrections and changes in reference

Study of additive manufactured microwave cavities for pulsed optically pumped atomic clock applications

Additive manufacturing (AM) of passive microwave components is of high interest for the cost-effective and rapid prototyping or manufacture of devices with complex geometries. Here, we pre-sent an experimental study on the properties of recently demonstrated microwave resonator cavities manufactured by AM, in view of their applications to high-performance compact atomic clocks. The microwave cavities employ a loop-gap geometry using six electrodes. The critical electrode structures were manufactured monolithically using two different approaches: Stereolithography (SLA) of a polymer followed by metal coating and Selective Laser Melting (SLM) of aluminum. The tested microwave cavities show the desired TE011-like resonant mode at the Rb clock frequency of ≈6.835 GHz, with a microwave magnetic field highly parallel to the quantization axis across the vapor cell. When operated in an atomic clock setup, the measured atomic Rabi oscillations are com-parable to those observed for conventionally manufactured cavities and indicate a good uniformity of the field amplitude across the vapor cell. Employing a time-domain Ramsey scheme on one of the SLA cavities, high-contrast (34%) Ramsey fringes are observed for the Rb clock transition, along with a narrow (166 Hz linewidth) central fringe. The measured clock stability of 2.2 × 10-13 τ-1/2 up to the integration time of 30 s is comparable to the current state-of-the-art stabilities of com-pact vapor-cell clocks based on conventional microwave cavities and thus demonstrates the feasibility of the approach

Existence of global strong solutions to a beam-fluid interaction system

We study an unsteady non linear fluid-structure interaction problem which is a simplified model to describe blood flow through viscoleastic arteries. We consider a Newtonian incompressible two-dimensional flow described by the Navier-Stokes equations set in an unknown domain depending on the displacement of a structure, which itself satisfies a linear viscoelastic beam equation. The fluid and the structure are fully coupled via interface conditions prescribing the continuity of the velocities at the fluid-structure interface and the action-reaction principle. We prove that strong solutions to this problem are global-in-time. We obtain in particular that contact between the viscoleastic wall and the bottom of the fluid cavity does not occur in finite time. To our knowledge, this is the first occurrence of a no-contact result, but also of existence of strong solutions globally in time, in the frame of interactions between a viscous fluid and a deformable structure