Search results for " Matrix"
showing 10 items of 2053 documents
Random Tensor Theory: Extending Random Matrix Theory to Mixtures of Random Product States
2012
We consider a problem in random matrix theory that is inspired by quantum information theory: determining the largest eigenvalue of a sum of p random product states in $${(\mathbb {C}^d)^{\otimes k}}$$ , where k and p/d k are fixed while d → ∞. When k = 1, the Marcenko-Pastur law determines (up to small corrections) not only the largest eigenvalue ( $${(1+\sqrt{p/d^k})^2}$$ ) but the smallest eigenvalue $${(\min(0,1-\sqrt{p/d^k})^2)}$$ and the spectral density in between. We use the method of moments to show that for k > 1 the largest eigenvalue is still approximately $${(1+\sqrt{p/d^k})^2}$$ and the spectral density approaches that of the Marcenko-Pastur law, generalizing the random matrix…
Adjacency matrices of random digraphs: singularity and anti-concentration
2017
Let ${\mathcal D}_{n,d}$ be the set of all $d$-regular directed graphs on $n$ vertices. Let $G$ be a graph chosen uniformly at random from ${\mathcal D}_{n,d}$ and $M$ be its adjacency matrix. We show that $M$ is invertible with probability at least $1-C\ln^{3} d/\sqrt{d}$ for $C\leq d\leq cn/\ln^2 n$, where $c, C$ are positive absolute constants. To this end, we establish a few properties of $d$-regular directed graphs. One of them, a Littlewood-Offord type anti-concentration property, is of independent interest. Let $J$ be a subset of vertices of $G$ with $|J|\approx n/d$. Let $\delta_i$ be the indicator of the event that the vertex $i$ is connected to $J$ and define $\delta = (\delta_1, …
Systematic and statistical uncertainties of the hilbert-transform based high-precision FID frequency extraction method.
2021
Abstract Pulsed nuclear magnetic resonance (NMR) is widely used in high-precision magnetic field measurements. The absolute value of the magnetic field is determined from the precession frequency of nuclear magnetic moments. The Hilbert transform is one of the methods that have been used to extract the phase function from the observed free induction decay (FID) signal and then its frequency. In this paper, a detailed implementation of a Hilbert-transform based FID frequency extraction method is described, and it is briefly compared with other commonly used frequency extraction methods. How artifacts and noise level in the FID signal affect the extracted phase function are derived analytical…
Quasi-static behaviour and damage assessment of flax/epoxy composites
2015
Experimental investigations were conducted on flax and E-glass fibres reinforced epoxy matrix composites subjected to quasi-static loadings. Flax/epoxy samples having [0]12, [90]12, [0/90]3S and [±45]3S stacking sequences, with a fibre volume fraction of 43% have been tested under tension, compression and in-plane shear loadings. Overall, the compression strength of glass/epoxy was 76% greater than for the flax/epoxy composite. The damage evolution of flax/epoxy of [0/90]3S and [±45]3S samples has been evaluated in terms of transverse crack densities with respect to the load increment. The crack density exhibited a classical “S” shaped pattern for [0/90]3S and linearly for [±45]3S specimens…
Diagrammatic Expansion for Positive Spectral Functions in the Steady-State Limit
2019
Recently, a method was presented for constructing self-energies within many-body perturbation theory that are guaranteed to produce a positive spectral function for equilibrium systems, by representing the self-energy as a product of half-diagrams on the forward and backward branches of the Keldysh contour. We derive an alternative half-diagram representation that is based on products of retarded diagrams. Our approach extends the method to systems out of equilibrium. When a steady-state limit exists, we show that our approach yields a positive definite spectral function in the frequency domain.
Ray optics for absorbing particles with application to ice crystals at near-infrared wavelengths
2018
Abstract Light scattering by particles large compared to the wavelength of incident light is traditionally solved using ray optics which considers absorption inside the particle approximately, along the ray paths. To study the effects rising from this simplification, we have updated the ray-optics code SIRIS to take into account the propagation of light as inhomogeneous plane waves inside an absorbing particle. We investigate the impact of this correction on traditional ray-optics computations in the example case of light scattering by ice crystals through the extended near-infrared (NIR) wavelength regime. In this spectral range, ice changes from nearly transparent to opaque, and therefore…
Line parameters and shapes of high clusters: R-branch of the nu3 band of CH4 in He mixtures
2002
International audience; The IR absorption spectra of CH4 in pure gas and in mixture with helium were studied in the region of nu3 band at higher J line clusters R(17)-R(22). The frequencies and intensities of rotation-vibration lines were estimated from the experimental spectra at Doppler shape conditions. The line frequencies and intensities were calculated and used for the attribution of overlapped lines in clusters. The calculated line intensities are close to the experimental values. The calculated frequency structure of the higher J manifolds are somewhat wider than the observed one. The shapes of helium-broadened line clusters were compared with those calculated accounting for line mi…
Interpreting the Schöningen 13II-4 butchery sequence using the Harris Matrix
2021
Abstract The Schoningen 13II-4 site is well known for the discovery of multiple wooden spears in association with a large assemblage of Middle Pleistocene fauna. Such extraordinary organic preservation also extends to a wide array of bone surface modifications that can be used to reconstruct Middle Pleistocene hominin butchery practices. On bones with few hominin-induced marks, the butchery sequence can be determined quite easily. However, the sequence becomes increasingly more difficult to decipher in bones that include a high number and diversity of biotic and abiotic modifications. To aid in this process, we developed a simple approach for determining the order of bone surface modificati…
Biochemical characterization of the skeletal matrix of the massive coral, Porites australiensis - The saccharide moieties and their localization.
2018
11 pages; International audience; To construct calcium carbonate skeletons of sophisticated architecture, scleractinian corals secrete an extracellular skeletal organic matrix (SOM) from aboral ectodermal cells. The SOM, which is composed of proteins, saccharides, and lipids, performs functions critical for skeleton formation. Even though polysaccharides constitute the major component of the SOM, its contribution to coral skeleton formation is poorly understood. To this end, we analyzed the SOM of the massive colonial coral, Porites australiensis, the skeleton of which has drawn great research interest because it records environmental conditions throughout the life of the colony. The coral …
Characterization of MRNP34, a novel methionine-rich nacre protein from the pearl oysters
2012
9 pages; International audience; Nacre of the Pinctada pearl oyster shells is composed of 98% CaCO(3) and 2% organic matrix. The relationship between the organic matrix and the mechanism of nacre formation currently constitutes the main focus regarding the biomineralization process. In this study, we isolated a new nacre matrix protein in P. margaritifera and P. maxima, we called Pmarg- and Pmax-MRNP34 (methionine-rich nacre protein). MRNP34 is a secreted hydrophobic protein, which is remarkably rich in methionine, and which is specifically localised in mineralizing the epithelium cells of the mantle and in the nacre matrix. The structure of this protein is drastically different from those …