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

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

Landscape of target: Guide homology effects on Cas9-mediated cleavage

To study target sequence specificity, selectivity, and reaction kinetics of Streptococcus pyogenes Cas9 activity, we challenged libraries of random variant targets with purified Cas9::guide RNA complexes in vitro. Cleavage kinetics were nonlinear, with a burst of initial activity followed by slower sustained cleav-age. Consistent with other recent analyses of Cas9 sequence specificity, we observe considerable (al-beit incomplete) impairment of cleavage for targets mutated in the PAM sequence or in ‘seed ’ sequences matching the proximal 8 bp of the guide. A second target region requiring close homology was located at the other end of the guide::target duplex (posi-tions 13–18 relative to the PAM). Sequences flanking the guide+PAM region had measurable (albeit mod-est) effects on cleavage. In addition, the first-base Guanine constraint commonly imposed by gRNA ex-pression systems has little effect on overall cleavage efficiency. Taken together, these studies provide an in vitro understanding of the complexities of Cas9– gRNA interaction and cleavage beyond the general paradigm of site determination based on the ‘seed’ sequence and PAM

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

Using PrISMa to reveal the interactome of the human claudins family

Here, we provide a protocol for the systematic screening of protein-protein interactions mediated by short linear motifs using the Protein Interaction Screen on a peptide Matrix (PrISMa) technique. We describe how to pull down interacting proteins in a parallelized manner and identify them by mass spectrometry. Finally, we describe a bioinformatic workflow necessary to identify highly probable interaction partners in the large-scale dataset. We describe the application of this method for the transient interactome of the claudin protein family

Optimal estimation of qubit states with continuous time measurements

We propose an adaptive, two steps strategy, for the estimation of mixed qubit states. We show that the strategy is optimal in a local minimax sense for the trace norm distance as well as other locally quadratic figures of merit. Local minimax optimality means that given $n$ identical qubits, there exists no estimator which can perform better than the proposed estimator on a neighborhood of size $n^{-1/2}$ of an arbitrary state. In particular, it is asymptotically Bayesian optimal for a large class of prior distributions. We present a physical implementation of the optimal estimation strategy based on continuous time measurements in a field that couples with the qubits. The crucial ingredient of the result is the concept of local asymptotic normality (or LAN) for qubits. This means that, for large $n$, the statistical model described by $n$ identically prepared qubits is locally equivalent to a model with only a classical Gaussian distribution and a Gaussian state of a quantum harmonic oscillator. The term `local' refers to a shrinking neighborhood around a fixed state $\rho_{0}$. An essential result is that the neighborhood radius can be chosen arbitrarily close to $n^{-1/4}$. This allows us to use a two steps procedure by which we first localize the state within a smaller neighborhood of radius $n^{-1/2+\epsilon}$, and then use LAN to perform optimal estimation.Comment: 32 pages, 3 figures, to appear in Commun. Math. Phy

BÚSQUEDA DE PRINCIPIOS ACTIVOS ANTIPARASITARIOS EN PLANTAS DE USO TRADICIONAL DE LA AMAZONIA PERUANA. ESPECIAL ENFASIS EN ALCALOIDES INDOLICOS

A fin de evaluar el potencial antimalárico de remedios tradicionales utilizadas en el Perú por las poblaciones indígenas y mestizas del río Nanay en Loreto, fueron entrevistados sobre el uso medicina tradicional para el tratamiento de la malaria. La encuesta se llevó a cabo en seis pueblos y llevaron a la recolección de 59 plantas. 35 extracciones hidro-alcohólico se realizaron en las 21 plantas más citadas. A continuación se ensayaron los extractos para la actividad antiplasmodial in vitro sobre cepa resistente a la cloroquina de Plasmodium falciparum (FCR-3), y también se realizó la prueba de inhibición de ferriprotoporfirina con el fin de asumir propiedades farmacológicas. Los extractos de 9 plantas, en veintiún evaluados, mostraron una actividad antiplasmodial interesante (IC50 <10 µg/ml) y 16 extractos resultaron activos en la prueba de inhibición de la ferriprotoporfirina. Cinco alcaloides oxindólicos y dos alcaloides de tipo plumerano subtipo haplophitina, fueron aislados de plantas medicinales: Aspidosperma rigidum y A. schultesii. Uno de estos compuestos se identificó como un confórmero rotámero transoide de la 18-Oxo-O-metilaspidoalbina que no se describió anteriormente, también fueron determinada la actividad antiparasitaria de los compuestos contra Trypanosoma cruzi y Leishmania infantum

Pan-claudin family interactome analysis reveals shared and specific interactions

Claudins are a family of transmembrane proteins expressed in epithelial tissues and are the major components of tight junctions (TJs), which define barrier properties in epithelia and maintain cell polarity. How claudins regulate the formation of TJs and which functions they exert outside of them is not entirely understood. Although the long and unstructured C-terminal tail is essential for regulation, it is unclear how it is involved in these functions beyond interacting with TJ-associated proteins such as TJ protein ZO-1 (TJP1). Here, we present an interactome study of the pan-claudin family in Madin-Darby canine kidney (MDCK)-C7 cells by combining two complementary mass spectrometry-based pull-down techniques creating an interaction landscape of the entire claudin family. The interaction partners of the claudins' C termini reveal their possible implications in localized biological processes in epithelial cells and their regulation by post-translational modifications (PTMs)

Comparing inequalities in the labour market from a segmentation perspective

Production of INCASI Project H2020-MSCA-RISE-2015 GA 691004The purpose of this chapter is to carry out a comparative analysis of labour markets in Europe and Latin America from the perspective of segmentation in order to explain the processes of social inequality that arise in the workplace, in light of recent trends in global socio-economic changes. The chapter proposes two main objectives. The first is to perform a comparative descriptive analysis of the main features of labour markets among 60 European and Latin American countries. The second objective is to propose a model of comparative analysis of labour inequality from the theoretical perspective of the segmentation of the labour market and structural heterogeneity. We will focus our analysis by selecting two countries, Spain and Argentina, which both underwent a late development of capitalism. The following general hypothesis is formulated: Spain and Argentina, having clearly differentiated features in economic structure, level of development, institutional frameworks and socio-historical processes, show common dynamics in the structuring of the capitalist labour market between a primary and secondary segment. Using equivalent databases on the workforce a typology of segmentation of employment is constructed that show, in addition to the specificities of each country, the similarities in the structuring of the labour market