Optimal quantum measurements for phase-shift estimation in optical interferometry

Quantum information theory, applied to optical interferometry, yields a 1/n scaling of phase uncertainty Delta phi independent of the applied phase shift phi, where n is the number of photons in the interferometer. This 1/n scaling is achieved provided that the output state is subjected to an optimal phase measurement. We establish this scaling law for both passive (linear) and active (nonlinear) interferometers and identify the coefficient of proportionality. Whereas a highly nonclassical state is required to achieve optimal scaling for passive interferometry, a classical input state yields a 1/n scaling of phase uncertainty for active interferometry.

Screening for serious mental illness in the general population with the K6 screening scale: results from the WHO World Mental Health (WMH) survey initiative

Data are reported on the background and performance of the K6 screening scale for serious mental illness (SMI) in the World Health Organization (WHO) World Mental Health (WMH) surveys. The K6 is a six-item scale developed to provide a brief valid screen for Diagnostic and Statistical Manual of Mental Disorders 4th edition (DSM-IV) SMI based on the criteria in the US ADAMHA Reorganization Act. Although methodological studies have documented good K6 validity in a number of countries, optimal scoring rules have never been proposed. Such rules are presented here based on analysis of K6 data in nationally or regionally representative WMH surveys in 14 countries (combined N = 41,770 respondents). Twelve-month prevalence of DSM-IV SMI was assessed with the fully-structured WHO Composite International Diagnostic Interview. Nested logistic regression analysis was used to generate estimates of the predicted probability of SMI for each respondent from K6 scores, taking into consideration the possibility of variable concordance as a function of respondent age, gender, education, and country. Concordance, assessed by calculating the area under the receiver operating characteristic curve, was generally substantial (median 0.83; range 0.76-0.89; inter-quartile range 0.81-0.85). Based on this result, optimal scaling rules are presented for use by investigators working with the K6 scale in the countries studied. Copyright (c) 2010 John Wiley & Sons, Ltd.

Cambios en calidad de vida en Colombia durante 1997-2003: otra aproximación

Este trabajo analiza, estática y dinámicamente, los cambios en las condiciones de vida de los hogares en Colombia entre los años 1997 y 2003. Se propone un indicador alternativo y se contrasta a nivel nacional, regional y de centro poblacional con el Índice de Calidad de Vida (ICV) convencional. El indicador alterno reconoce la importancia que tienen aspectos de salud y el tiempo gastado en desplazamiento. Estas variables adicionales reducen el impacto de los aspectos concernientes al capital físico y distancian aún más las condiciones de las zonas rurales frente a las urbanas. La importancia de profundizar en las políticas de salud en las zonas rurales y en políticas que permitan disminuir el tiempo gastado en desplazamiento para ambas zonas se torna evidente.

An approximation to the standard of living index: the Colombian case

El documento busca mostrar las principales propiedades de un indicador de estándar de vida dentro del enfoque teórico de Amartya Sen. Establecemos un puente entre conceptos tales como: bienestar económico, bienestar, logro de agencia y estándar de vida. La metodología del Optimal scaling fue usada para probar las propiedades de Monotonicidad, No independencia de alternativas irrelevantes, Concavidad, informatividad y sustituibilidad.

Patterns of Ecstasy Use and Associated Harm: Results of a Brazilian Online Survey

The aim of this study was to gather information about ecstasy users in Brazil, particularly on issues related to risks associated to the use of the drug, so as to offer a basis to prevention projects. A total of 1,140 Brazilian ecstasy users answered an online questionnaire from August 2004 to February 2005. Participants were predominantly young single heterosexual well-educated males from upper economical classes. A categorical regression with optimal scaling (CATREG) was performed to identify the risks associated with ecstasy use. ""Pills taken in life"" had a significant correlation with every investigated risk, particularly ecstasy dependence, unsafe sex, and polydrug use. ""Gender,"" ""sexual orientation,"" and ""socioeconomic class"" were not predictive of risk behavior. The Internet proved to be a useful tool for data collection. Given the recent increase in ecstasy availability in Brazil, a first prevention campaign directed toward the drug is urgent. At least in a preliminary Brazilian intervention, the campaign must be conducted at night leisure places, mainly frequented by youngsters from upper socioeconomic classes. The results do not call for information material with specific targets, such as gender or sexual orientation. The study`s limitations have been noted.

ANÁLISE DA INFORMALIDADE: uso de crédito e crescimento perante a pesquisa da Ecinf

Este trabalho procura entender um pouco mais e discutir, partindo dos dados disponíveis do Instituto Brasileiro de Geografia e Estatística (IBGE), através de sua pesquisa de economia informal urbana (ECINF) gerada em 2003 (ultima disponível), aspectos ligados à informalidade, crescimento e uso do crédito. Procura explorar, neste contexto, aspectos relevantes ao crescimento e continuidade da micro e pequena empresa. Para atingir este objetivo, procura-se entender inicialmente conceitos sobre estes aspectos (informalidade, crescimento e uso de crédito) e suas características, e através de dados secundários e com o uso de software estatístico, procurar entender as suas relações, através de ANOVA e regressões, bem como optimal scaling contribuindo para o conhecimento deste cenário. Os dados levantandos e comparados com a teoria apontam as relações entre empregador e trabalhador por conta própria indicando dos fatores adotados no estudo quais mais contribuem e os que indicam pouca contribuição dentro deste contexto. Em conclusões acena para uma tendência onde o individamento através do uso de crédito tende a gerar um maior crescimento até um determinado ponto e a partir desta inflecção tende a dificultar a atividade bem como acena dificultar a formalização.(AU)

Aplicação da análise multivariada na caracterização das empresas de caprinos da raça Serpentina

O trabalho pretende analisar as características das empresas e produtores de caprinos da raça Serpentina e as razões para a continuidade desta atividade, com base num inquérito realizado em 2014. Recorreu-se ao Escalonamento Ótimo (Optimal Scaling em inglês) englobado no SPSS e à seleção de variáveis observadas (package subselect do programa estatístico R) para caracterizar as explorações.

Optimal input states and feedback for interferometric phase estimation

We derive optimal N-photon two-mode input states for interferometric phase measurements. Under canonical measurements the phase variance scales as N-2 for these states, as compared to N-1 or N-1/2 for states considered bq previous authors. We prove, that it is not possible to realize the canonical measurement by counting photons in the outputs of the interferometer, even if an adjustable auxiliary phase shift is allowed in the interferometer. However. we introduce a feedback algorithm based on Bayesian inference to control this auxiliary phase shift. This makes the measurement close to a canonical one, with a phase variance scaling slightly above N-2. With no feedback, the best result (given that the phase to be measured is completely unknown) is a scaling of N-1. For optimal input states having up to four photons, our feedback scheme is the best possible one, but for higher photon numbers more complicated schemes perform marginally better.

Load-unload response ratio and accelerating moment/energy release critical region scaling and earthquake prediction

The main idea of the Load-Unload Response Ratio (LURR) is that when a system is stable, its response to loading corresponds to its response to unloading, whereas when the system is approaching an unstable state, the response to loading and unloading becomes quite different. High LURR values and observations of Accelerating Moment/Energy Release (AMR/AER) prior to large earthquakes have led different research groups to suggest intermediate-term earthquake prediction is possible and imply that the LURR and AMR/AER observations may have a similar physical origin. To study this possibility, we conducted a retrospective examination of several Australian and Chinese earthquakes with magnitudes ranging from 5.0 to 7.9, including Australia's deadly Newcastle earthquake and the devastating Tangshan earthquake. Both LURR values and best-fit power-law time-to-failure functions were computed using data within a range of distances from the epicenter. Like the best-fit power-law fits in AMR/AER, the LURR value was optimal using data within a certain epicentral distance implying a critical region for LURR. Furthermore, LURR critical region size scales with mainshock magnitude and is similar to the AMR/AER critical region size. These results suggest a common physical origin for both the AMR/AER and LURR observations. Further research may provide clues that yield an understanding of this mechanism and help lead to a solid foundation for intermediate-term earthquake prediction.

Predicting optimal lengths of random knots

In a thermally fluctuating long linear polymeric chain in a solution, the ends, from time to time, approach each other. At such an instance, the chain can be regarded as closed and thus will form a knot or rather a virtual knot. Several earlier studies of random knotting demonstrated that simpler knots show a higher occurrence for shorter random walks than do more complex knots. However, up to now there have been no rules that could be used to predict the optimal length of a random walk, i.e. the length for which a given knot reaches its highest occurrence. Using numerical simulations, we show here that a power law accurately describes the relation between the optimal lengths of random walks leading to the formation of different knots and the previously characterized lengths of ideal knots of a corresponding type.

Efficient Characterisation and Optimal Control of Open Quantum Systems - Mathematical Foundations and Physical Applications

Since no physical system can ever be completely isolated from its environment, the study of open quantum systems is pivotal to reliably and accurately control complex quantum systems. In practice, reliability of the control field needs to be confirmed via certification of the target evolution while accuracy requires the derivation of high-fidelity control schemes in the presence of decoherence. In the first part of this thesis an algebraic framework is presented that allows to determine the minimal requirements on the unique characterisation of arbitrary unitary gates in open quantum systems, independent on the particular physical implementation of the employed quantum device. To this end, a set of theorems is devised that can be used to assess whether a given set of input states on a quantum channel is sufficient to judge whether a desired unitary gate is realised. This allows to determine the minimal input for such a task, which proves to be, quite remarkably, independent of system size. These results allow to elucidate the fundamental limits regarding certification and tomography of open quantum systems. The combination of these insights with state-of-the-art Monte Carlo process certification techniques permits a significant improvement of the scaling when certifying arbitrary unitary gates. This improvement is not only restricted to quantum information devices where the basic information carrier is the qubit but it also extends to systems where the fundamental informational entities can be of arbitary dimensionality, the so-called qudits. The second part of this thesis concerns the impact of these findings from the point of view of Optimal Control Theory (OCT). OCT for quantum systems utilises concepts from engineering such as feedback and optimisation to engineer constructive and destructive interferences in order to steer a physical process in a desired direction. It turns out that the aforementioned mathematical findings allow to deduce novel optimisation functionals that significantly reduce not only the required memory for numerical control algorithms but also the total CPU time required to obtain a certain fidelity for the optimised process. The thesis concludes by discussing two problems of fundamental interest in quantum information processing from the point of view of optimal control - the preparation of pure states and the implementation of unitary gates in open quantum systems. For both cases specific physical examples are considered: for the former the vibrational cooling of molecules via optical pumping and for the latter a superconducting phase qudit implementation. In particular, it is illustrated how features of the environment can be exploited to reach the desired targets.

Solving complex optimal control problems at no cost with PSOPT

This paper introduces PSOPT, an open source optimal control solver written in C++. PSOPT uses pseudospectral and local discretizations, sparse nonlinear programming, automatic differentiation, and it incorporates automatic scaling and mesh refinement facilities. The software is able to solve complex optimal control problems including multiple phases, delayed differential equations, nonlinear path constraints, interior point constraints, integral constraints, and free initial and/or final times. The software does not require any non-free platform to run, not even the operating system, as it is able to run under Linux. Additionally, the software generates plots as well as LATEX code so that its results can easily be included in publications. An illustrative example is provided.

A general basis for quarter-power scaling in animals

It has been known for decades that the metabolic rate of animals scales with body mass with an exponent that is almost always <1, >2/3, and often very close to 3/4. The 3/4 exponent emerges naturally from two models of resource distribution networks, radial explosion and hierarchically branched, which incorporate a minimum of specific details. Both models show that the exponent is 2/3 if velocity of flow remains constant, but can attain a maximum value of 3/4 if velocity scales with its maximum exponent, 1/12. Quarterpower scaling can arise even when there is no underlying fractality. The canonical “fourth dimension” in biological scaling relations can result from matching the velocity of flow through the network to the linear dimension of the terminal “service volume” where resources are consumed. These models have broad applicability for the optimal design of biological and engineered systems where energy, materials, or information are distributed from a single source.

A tutorial on pseudospectral methods for computational optimal control

[English] This paper is a tutorial introduction to pseudospectral optimal control. With pseudospectral methods, a function is approximated as a linear combination of smooth basis functions, which are often chosen to be Legendre or Chebyshev polynomials. Collocation of the differential-algebraic equations is performed at orthogonal collocation points, which are selected to yield interpolation of high accuracy. Pseudospectral methods directly discretize the original optimal control problem to recast it into a nonlinear programming format. A numerical optimizer is then employed to find approximate local optimal solutions. The paper also briefly describes the functionality and implementation of PSOPT, an open source software package written in C++ that employs pseudospectral discretization methods to solve multi-phase optimal control problems. The software implements the Legendre and Chebyshev pseudospectral methods, and it has useful features such as automatic differentiation, sparsity detection, and automatic scaling. The use of pseudospectral methods is illustrated in two problems taken from the literature on computational optimal control. [Portuguese] Este artigo e um tutorial introdutorio sobre controle otimo pseudo-espectral. Em metodos pseudo-espectrais, uma funcao e aproximada como uma combinacao linear de funcoes de base suaves, tipicamente escolhidas como polinomios de Legendre ou Chebyshev. A colocacao de equacoes algebrico-diferenciais e realizada em pontos de colocacao ortogonal, que sao selecionados de modo a minimizar o erro de interpolacao. Metodos pseudoespectrais discretizam o problema de controle otimo original de modo a converte-lo em um problema de programa cao nao-linear. Um otimizador numerico e entao empregado para obter solucoes localmente otimas. Este artigo tambem descreve sucintamente a funcionalidade e a implementacao de um pacote computacional de codigo aberto escrito em C++ chamado PSOPT. Tal pacote emprega metodos de discretizacao pseudo-spectrais para resolver problemas de controle otimo com multiplas fase. O PSOPT permite a utilizacao de metodos de Legendre ou Chebyshev, e possui caractersticas uteis tais como diferenciacao automatica, deteccao de esparsidade e escalonamento automatico. O uso de metodos pseudo-espectrais e ilustrado em dois problemas retirados da literatura de controle otimo computacional.

Evidence of a universal scaling relationship for leaf CO2 drawdown along an aridity gradient

The leaf carbon isotope ratio (δ13C) of C3 plants is inversely related to the drawdown of CO2 concentration during photosynthesis, which increases towards drier environments. We aimed to discriminate between the hypothesis of universal scaling, which predicts between-species responses of δ13C to aridity similar to within-species responses, and biotic homoeostasis, which predicts offsets in the δ13C of species occupying adjacent ranges. The Northeast China Transect spans 130–900 mm annual precipitation within a narrow latitude and temperature range. Leaves of 171 species were sampled at 33 sites along the transect (18 at ≥ 5 sites) for dry matter, carbon (C) and nitrogen (N) content, specific leaf area (SLA) and δ13C. The δ13C of species generally followed a common relationship with the climatic moisture index (MI). Offsets between adjacent species were not observed. Trees and forbs diverged slightly at high MI. In C3 plants, δ13C predicted N per unit leaf area (Narea) better than MI. The δ13C of C4 plants was invariant with MI. SLA declined and Narea increased towards low MI in both C3 and C4 plants. The data are consistent with optimal stomatal regulation with respect to atmospheric dryness. They provide evidence for universal scaling of CO2 drawdown with aridity in C3 plants.