Minimax and adaptive estimation of the Wigner function in quantum homodyne tomography with noisy data

We estimate the quantum state of a light beam from results of quantum homodyne measurements performed on identically prepared quantum systems. The state is represented through the Wigner function, a generalized probability density on $\mathbb{R}^2$ which may take negative values and must respect intrinsic positivity constraints imposed by quantum physics. The effect of the losses due to detection inefficiencies, which are always present in a real experiment, is the addition to the tomographic data of independent Gaussian noise. We construct a kernel estimator for the Wigner function, prove that it is minimax efficient for the pointwise risk over a class of infinitely differentiable functions, and implement it for numerical results. We construct adaptive estimators, that is, which do not depend on the smoothness parameters, and prove that in some setups they attain the minimax rates for the corresponding smoothness class.Comment: Published at http://dx.doi.org/10.1214/009053606000001488 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Apuntes teóricos sobre los conceptos de ideología y discurso político

Leopoldo Artiles (biografía). Sociólogo dominicano. Estudió en la Universidad Pedro Henríquez Ureña (UNPHU). Luego hizo una maestría en la Facultad Latinoamericana de Ciencias Sociales, en México, y posteriormente realizó sus estudios de doctorado en la Universidad de Minnesota. Es profesor de sociología en la Universidad Autónoma de Santo Domingo desde 1978, y ha sido docente invitado en la Pontificia Universidad Católica Madre y Maestra (PUCMM), Instituto Tecnológico de Santo Domingo (INTEC), Universidad Central del Este y la Universidad APEC. Se ha desempeñado como especialista sectorial de la Unidad Asesora de Análisis Económico y Social del Ministerio de Economía, Planificación y Desarrollo y como coordinador de la Unidad de Políticas Públicas del Observatorio Político Dominicano. Algunas de sus publicaciones son: Movimientos sociales dominicanos: identidad y dilemas (en coautoría con César Pérez), El nuevo rol de la ciudadanía, Actitudes hacia el trabajo en la República Dominicana: reflexión sobre las percepciones y orientaciones en el mundo laboral (en coautoría con Carlos Dore Cabral, Francisco Cáceres y Pedro Ortega), El sistema tributario dominicano: propuesta de reforma (en coautoría con César Pérez), Análisis del discurso: introducción a su teoría y práctica.¿Cuál es la relación entre realidad, ideología y discurso? Si, como se interpreta sobre todo a partir de Marx, la ideología es "el reflejo correcto de una realidad falsa", y si —como afirmara Valentín N. Voloshmoz— la ideología se inscribe ante todo en el lenguaje, esto es, en la realidad sígnica que representa, figura y simboliza lo que está fuera de ella, cabe preguntarse: ¿hay posibilidad de un discurso libre de ideología, es decir, de un discurso que dé acceso de modo directo a la verdadera realidad? ¿Y es, en caso de que la respuesta sea negativa, del todo negativa la ideología? Como fenómeno humano inevitable, la ideología constituiría un sistema de sentido construido por el hombre para "ordenar" una realidad que en esencia desconoce. En tal virtud, sería una herramienta defectuosa, pero necesaria, para la edificación del mundo humano. Por ello sería el símbolo más manifiesto de que el hombre ha sido expulsado de aquel mundo adámico en el que la palabra y la cosa se corresponden de manera perfecta

Addressing Community Issues Through Alternative Funding Practice

The mission of United Way of Broome County is “To drive change that will have positive impact on the critical needs of our community by strategically leveraging the collective resources of community partners” United Way of Broome County is interested in improving the quality of services available to the residents of the Village of Endicott by seeking funding partners doing work in the area. This project will explore what some of the issues facing this community is and how United Way can aid helping bring more programs to the area.https://orb.binghamton.edu/mpa_capstone/1001/thumbnail.jp

The Minimal Denominator Function and Geometric Generalizations

We provide a geometric interpretation for a normalized version of the minimal denominator function, $$q_{\min}(x,\delta)=\min\left\{q\in \mathbb{N}: \text{ there exists } p\in\mathbb{Z} \text{ such that } \frac{p}{q}\in (x-\delta,x+\delta)\right\},$$ introduced by Chen and Haynes. We use this interpretation to compute the limiting distribution of a suitably normalized version of $q_{\min}(x,\delta)$ as a function of $x$, and give generalizations of the idea of minimal denominators to higher-dimensional unimodular lattices, linear forms, and translation surfaces. The key idea is to turn this circle of problems into equidistribution problems for translates of unipotent orbits of a Lie group action on an appropriate moduli space.Comment: 16 pages, 6 figure

Multinucleon Short-range Correlation Model for Nuclear Spectral Functions

The main goal of the research presented in my dissertation was to develop a theoretical model for relativistic nuclear spectral functions at high missing momenta and removal energies based on the multi-nucleon short-range correlation (SRC) model. The nuclear spectral functions are necessary for the description of high energy nuclear processes currently being studied at different labs such as JLAB, LHC and FNAL. The model followed the effective Feynman diagrammatic approach in order to ac-count for the relativistic effects important in the SRC domain. In addition to the two-nucleon (2N) SRC with center of mass motion contribution, the contribution of the three-nucleon SRCs to the spectral functions was also derived. The latter was modeled based on the assumption that the 3N SRCs are a product of two sequential short range nucleon-nucleon (NN) interactions. The nuclear spectral functions models were derived from two theoretical frameworks for evaluating covariant Feynman diagrams: In the first, referred to as the virtual nucleon approximation, the Feynman diagrams were reduced to the time ordered non-covariant diagrams by evaluating the nucleon spectators in the SRC at their positive energy poles, neglecting explicitly the contribution from vacuum diagrams. In the second approach, referred to as the light-front approximation, the boost invariant nuclear spectral function was formulated in the light-front reference frame in which case the vacuum diagrams are kinematically suppressed and the bound nucleon is described by its light-front variables such as momentum fraction, transverse momentum and invariant mass. On the basis of the derived nuclear spectral functions, the corresponding computational models were developed from which the numerical estimates of the SRC spectral functions, the SRC momentum distributions, and the SRC density matrices were obtained

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

Tibetan Refugees\u27 Rights and Services in India

The Chinese invasion of Tibet, and the Dalai Lama’s subsequent decision to flee in 1959, resulted in the mass influx of Tibetan refugees into India that continues today. It has become clear to the Indian government, as well as to the Tibetan community in exile, that repatriation is unlikely in the near future. Consequently, an evaluation of India’s protection of, and assistance for Tibetan refugees is necessary to ensure their treatment is in accordance with international standards. Unfortunately, such an assessment shows that there is a lack of proper protections and services; this ought to be of particular concern to the international community as India has served on the Executive Committee of the United Nations High Commissioner for Refugees (UNHCR) since 1995. How can a country be trusted to lead an international organization dedicated to the protection of refugees when it has such unstable and inadequate refugee policies itself