An invitation to quantum tomography (II)

The quantum state of a light beam can be represented as an infinite dimensional density matrix or equivalently as a density on the plane called the Wigner function. We describe quantum tomography as an inverse statistical problem in which the state is the unknown parameter and the data is given by results of measurements performed on identical quantum systems. We present consistency results for Pattern Function Projection Estimators as well as for Sieve Maximum Likelihood Estimators for both the density matrix of the quantum state and its Wigner function. Finally we illustrate via simulated data the performance of the estimators. An EM algorithm is proposed for practical implementation. There remain many open problems, e.g. rates of convergence, adaptation, studying other estimators, etc., and a main purpose of the paper is to bring these to the attention of the statistical community.Comment: An earlier version of this paper with more mathematical background but less applied statistical content can be found on arXiv as quant-ph/0303020. An electronic version of the paper with high resolution figures (postscript instead of bitmaps) is available from the authors. v2: added cross-validation results, reference

Numerical, analytical, experimental study of fluid dynamic forces in seals

NASA/Lewis Research Center is sponsoring a program for providing computer codes for analyzing and designing turbomachinery seals for future aerospace and engine systems. The program is made up of three principal components: (1) the development of advanced three dimensional (3-D) computational fluid dynamics codes, (2) the production of simpler two dimensional (2-D) industrial codes, and (3) the development of a knowledge based system (KBS) that contains an expert system to assist in seal selection and design. The first task has been to concentrate on cylindrical geometries with straight, tapered, and stepped bores. Improvements have been made by adoption of a colocated grid formulation, incorporation of higher order, time accurate schemes for transient analysis and high order discretization schemes for spatial derivatives. This report describes the mathematical formulations and presents a variety of 2-D results, including labyrinth and brush seal flows. Extensions of 3-D are presently in progress

The cartujano stock of the spanish horse in America

The Cartujano stock of the Spanish horse is eumetric, mesomorphous, constitutionally compact and with subconvex profile. It shows a bright and energic aspect, with appreciable elevations and extensions. Its constitutional type is orthostenic or equanimous, its character is noble and docile. It is very interesting for the breaking in high school. This stock has its origin in the farm created by the Cartujanos monks from Jerez de la Frontera, in 1492. Today it can be find in Colombia on Mr. Francisco León Arboleda’s farm; in Costa Rica included in the farms of Mr. Mariano Guardia and Mr. Jorge Herrera, among others. Also in Cuba bought by Mr. Fidel Castro; in E.E.U.U. included in the farms of Mr. Currier, Mr. Broston, Mr. Parkinson, Mr. Garmendia and Mr. Alcalde, among others. In Mexico the most important breeders are Mr. Miguel Alemán, Mr. Enrique Alvarez and Mr. Plácido Arango. We also find this stock in other countries such as Nicaragua, Perú, Venezuela, etc. All that shows its important genetic contribution to the Spanish Breed horse in America.La estirpe Cartujana del Caballo Español es eumétrica, mesomorfa, constitucionalmente compacta y de perfil subconvexo. Esto le da un aspecto elegante y enérgico, con una apreciable elevación y extensión. Su tipo constitucional es ortosténico ó equilibrado, su carácter es noble y dócil. Es muy adecuada para la doma de Alta Escuela. Tiene su origen en la ganadería creada por los monjes Cartujanos de Jerez de la Frontera, en 1492. Se emplea aun como mejorante del caballo de raza española en Colombia (ganadería de D. Francisco León Arboleda) y en Costa Rica en las ganaderías del Sr. Mariano Guardia, D. Jorge Herrera y otras. También en Cuba fue comprada por el Sr. Fidel Castro; en USA se encuentra en las ganaderías de los sres. Currier, Broston, Parkinson, Garmendia, Alcalde, y otros. En México los ganaderos más importantes son D. Miguel Alemán, D. Enrique Alvarez y D. Plácido Arango. También está presente en Nicaragua, Perú, Venezuela, etc. Lo que demuestra su importante aportación genética al caballo Español en América

Access and analysis of ISTAC data through the use of R and Shiny

[EN] The increasing availability of open data resources provides opportunities for research and data science. It is necessary to develope tools that take advantage of the full potential of new information resources. In this work we developed the package for R istacr that provides a collection of eurostat functions to be able to consult and discard the data that Eurostat, including functions to retrieve, download and manipulate the data set available through the ISTAC BASE API of the Canary Institute of Statistics (ISTAC). In addition, A Shiny app was designed for a responsive visulization of the data. This develope is part of the growing demand for open data and ecosystems dedicated to reproducible research in computational social science and digital humanities. With this interest, this package has been included within rOpenSpain, a project that aims to promote transparent research methods mainly through the use of free software and open data in Spain.González-Martel, C.; Cazorla-Artiles, JM.; Pérez-González, C. (2018). Access and analysis of ISTAC data through the use of R and Shiny. En 2nd International Conference on Advanced Reserach Methods and Analytics (CARMA 2018). Editorial Universitat Politècnica de València. 193-200. https://doi.org/10.4995/CARMA2018.2018.8345OCS19320

Minimax estimation of the Wigner function in quantum homodyne tomography with ideal detectors

We estimate the quantum state of a light beam from results of quantum homodyne measurements performed on identically prepared pulses. The state is represented through the Wigner function, a ``quasi-probability density'' on $\mathbb{R}^{2}$ which may take negative values and must respect intrinsic positivity constraints imposed by quantum physics. The data consists of $n$ i.i.d. observations from a probability density equal to the Radon transform of the Wigner function. We construct an estimator for the Wigner function, and prove that it is minimax efficient for the pointwise risk over a class of infinitely differentiable functions. A similar result was previously derived by Cavalier in the context of positron emission tomography. Our work extends this result to the space of smooth Wigner functions, which is the relevant parameter space for quantum homodyne tomography.Comment: 15 page

A double-layer Boussinesq-type model for highly nonlinear and dispersive waves

28 pages, 5 figures. Soumis à Proceedings of the Royal Society of London A.We derive and analyze in the framework of the mild-slope approximation a new double-layer Boussinesq-type model which is linearly and nonlinearly accurate up to deep water. Assuming the flow to be irrotational, we formulate the problem in terms of the velocity potential thereby lowering the number of unknowns. The model derivation combines two approaches, namely the method proposed by Agnon et al. (Agnon et al. 1999, J. Fluid Mech., 399 pp. 319-333) and enhanced by Madsen et al. (Madsen et al. 2003, Proc. R. Soc. Lond. A, 459 pp. 1075-1104) which consists in constructing infinite-series Taylor solutions to the Laplace equation, to truncate them at a finite order and to use Padé approximants, and the double-layer approach of Lynett & Liu (Lynett & Liu 2004, Proc. R. Soc. Lond. A, 460 pp. 2637-2669) allowing to lower the order of derivatives. We formulate the model in terms of a static Dirichlet-Neumann operator translated from the free surface to the still-water level, and we derive an approximate inverse of this operator that can be built once and for all. The final model consists of only four equations both in one and two horizontal dimensions, and includes only second-order derivatives, which is a major improvement in comparison with so-called high-order Boussinesq models. A linear analysis of the model is performed and its properties are optimized using a free parameter determining the position of the interface between the two layers. Excellent dispersion and shoaling properties are obtained, allowing the model to be applied up to deep water. Finally, numerical simulations are performed to quantify the nonlinear behaviour of the model, and the results exhibit a nonlinear range of validity reaching deep water areas

Robustness of raw quantum tomography

We scrutinize the effects of non-ideal data acquisition on the homodyne tomograms of photon quantum states. The presence of a weight function, schematizing the effects of the finite thickness of the probing beam or equivalently noise, only affects the state reconstruction procedure by a normalization constant. The results are extended to a discrete mesh and show that quantum tomography is robust under incomplete and approximate knowledge of tomograms.Comment: 7 pages, 1 figure, published versio

Supporting Children with Disabilities in Low- and Middle- Income Countries: Promoting Inclusive Practice within Community-Based Childcare Centres in Malawi through a Bioecological Systems Perspective

RLOsGiven the narrow scope and conceptualisation of inclusion for young children with disabilities in research within low- and middle income countries (LMICs) contexts, we draw on a bioecological systems perspective to propose the parameters for a broader unit of analysis. This perspective situates human development within a specific cultural context in which family, peers and schooling are regarded as key in responding to young children with disabilities in a given setting. We outline a new bioecological model to illustrate the proximal and distal factors that can influence inclusive early development for children with disabilities within LMICs. To illustrate the relevance of this model to early child development research, we consider its application, as a conceptual framework, with reference to a research study in Malawi. The study was designed to promote greater inclusive practice for young children with disabilities in Community-Based Childcare Centres (CBCCs) with a particular focus on the role of the CBCC volunteer ‘caregiver’ in rural Malawi. It has significance for educators, service providers and researchers concerned with facilitating inclusive early development across national boundaries and contexts.ESRC-DFI

Extending Graph (Discrete) Derivative Descriptors to N-Tuple Atom-Relations

In the present manuscript, an extension of the previously defined Graph Derivative Indices (GDIs) is discussed. To achieve this objective, the concept of a hypermatrix, conceived from the calculation of the frequencies of triple and quadruple atom relations in a set of connected sub-graphs, is introduced. This set of subgraphs is generated following a predefined criterion, known as the event (S), being in this particular case the connectivity among atoms. The triple and quadruple relations frequency matrices serve as a basis for the computation of triple and quadruple discrete derivative indices, respectively. The GDIs are implemented in a computational program denominated DIVATI (acronym for DIscrete DeriVAtive Type Indices), a module of TOMOCOMD-CARDD program. Shannon‟s entropy-based variability analysis demonstrates that the GDIs show major variability than others indices used in QSAR/QSPR researches. In addition, it can be appreciated when the indices are extended over n-elements from the graph, its quality increases, principally when they are used in a combined way. QSPR modeling of the physicochemical properties Log P and Log K of the 2-furylethylenes derivatives reveals that the GDIs obtained using the tripleand quadruple matrix approaches yield superior performance to the duplex matrix approach. Moreover, the statistical parameters for models obtained with the GDI method are superior to those reported in the literature by using other methods. It can therefore be suggested that the GDI method, seem to be a promissory tool to reckon on in QSAR/QSPR studies, virtual screening of compound datasets and similarity/dissimilarity evaluations

Physico-Chemical and structural interpretation of discrete derivative indices on N-tuples atoms

This report examines the interpretation of the Graph Derivative Indices (GDIs) from three different perspectives (i.e., in structural, steric and electronic terms). It is found that the individual vertex frequencies may be expressed in terms of the geometrical and electronic reactivity of the atoms and bonds, respectively. On the other hand, it is demonstrated that the GDIs are sensitive to progressive structural modifications in terms of: size, ramifications, electronic richness, conjugation effects and molecular symmetry. Moreover, it is observed that the GDIs quantify the interaction capacity among molecules and codify information on the activation entropy. A structure property relationship study reveals that there exists a direct correspondence between the individual frequencies of atoms and Hückel’s Free Valence, as well as between the atomic GDIs and the chemical shift in NMR, which collectively validates the theory that these indices codify steric and electronic information of the atoms in a molecule. Taking in consideration the regularity and coherence found in experiments performed with the GDIs, it is possible to say that GDIs possess plausible interpretation in structural and physicochemical terms. © 2016 by the authors; licensee MDPI, Basel, Switzerland.Pharmaceutical Preparation