Overcoming ambiguities in classical and quantum correlation measures

We identify ambiguities in the available frameworks for defining quantum, classical, and total correlations as measured by discordlike quantifiers. More specifically, we determine situations for which either classical or quantum correlations are not uniquely defined due to degeneracies arising from the optimization procedure over the state space. In order to remove such degeneracies, we introduce a general approach where correlations are independently defined, escaping therefore from a degenerate subspace. As an illustration, we analyze the trace-norm geometric quantum discord for two-qubit Bell-diagonal states.Comment: 5 pages, 2 figures. v2: Minor corrections. Published versio

Geometric classical and total correlations via trace distance

We introduce the concepts of geometric classical and total correlations through Schatten 1-norm (trace norm), which is the only Schatten p-norm able to ensure a well-defined geometric measure of correlations. In particular, we derive the analytical expressions for the case of two-qubit Bell-diagonal states, discussing the superadditivity of geometric correlations. As an illustration, we compare our results with the entropic correlations, discussing both their hierarchy and monotonicity properties. Moreover, we apply the geometric correlations to investigate the ground state of spin chains in the thermodynamic limit. In contrast to the entropic quantifiers, we show that the classical correlation is the only source of 1-norm geometric correlation that is able to signaling an infinite-order quantum phase transition.Comment: v2: published versio

Violence against aged people: a new issue?

O envelhecimento da população mundial é um fato concreto e de conhecimento público. O Brasil inicia seu processo de transição demográfica seguindo o padrão mundial: o aumento do número de idosos com possibilidade de atingir elevadas faixas etárias, o que traz a necessidade de pesquisas nesse campo, devido à demanda apresentada por essa nova parcela da população. A questão da violência doméstica contra idosos tem se ampliado e sugere necessidade de maior campo de investigação nessa área, dado o risco suposto ao qual essa população mais idosa está submetida. O objetivo deste artigo é verificar os estudos relacionados ao tema já realizados no Brasil e em diferentes países, com enfoque epidemiológico. O trabalho apresenta diversos pontos de abordagem da violência contra idosos, considerando questões relacionadas à cultura do envelhecimento, ações de políticas públicas, atuação de equipes de saúde, definição do termo abordado, aspectos legais e éticos da violência contra o idoso. Tal estudo permite ao pesquisador analisar os diferentes aspectos que envolvem a temática, demonstrando a necessidade de pesquisas específicas direcionadas ao tema.The world population is getting older and this is a very well known fact. The demographic transition of the Brazilian population is just beginning, and follows the world pattern: an increase in the number of older persons with an actual chance of reaching higher ages. As a consequence, there is the need of new studies to supply data about this new aspect of the population demands. Household violence against old persons has been growing and this strongly recommends that special research studies should be conducted, in view of the risk to which these individuals are exposed. The objective of this study is to list and analyze Brazilian and international studies related to aged persons, in light of an epidemiological point of view. The article presents many ways of approaching violence against old people, considering the culture of aging, actions of public policies, the practice of health teams, and legal and ethical aspects of violence against aged people. Such a study allows the researcher to analyze different aspects of the theme, showing the need of specific research on the elderly

Modelling menstrual cycle length in athletes using state-space models

The ability to predict an individual’s menstrual cycle length to a high degree of precision could help female athletes to track their period and tailor their training and nutrition correspondingly. Such individualisation is possible and necessary, given the known inter‐individual variation in cycle length. To achieve this, a hybrid predictive model was built using data on 16,524 cycles collected from a sample of 2125 women (mean age 34.38 years, range 18.00–47.10, number of menstrual cycles ranging from 4 to 53). A mixed‐effect state‐space model was fitted to capture the within‐subject temporal correlation, incorporating a Bayesian approach for process forecasting to predict the duration (in days) of the next menstrual cycle. The modelling procedure was split into three steps (1) a time trend component using a random walk with an overdispersion parameter, (2) an autocorrelation component using an autoregressive moving‐average model, and (3) a linear predictor to account for covariates (e.g. injury, stomach cramps, training intensity). The inclusion of an overdispersion parameter suggested that 26.36% [23.68%, 29.17%] of cycles in the sample were overdispersed. The random walk standard deviation for a non‐overdispersed cycle is 27.41 ± 1.05 [1.00, 1.09] days while under an overdispersed cycle, the menstrual cycle variance increase in 4.78 [4.57, 5.00] days. To assess the performance and prediction accuracy of the model, each woman’s last observation was used as test data. The root mean square error (RMSE), concordance correlation coefficient and Pearson correlation coefficient (r) between the observed and predicted values were calculated. The model had an RMSE of 1.6412 days, a precision of 0.7361 and overall accuracy of 0.9871. In conclusion, the hybrid model presented here is a helpful approach for predicting menstrual cycle length, which in turn can be used to support female athlete wellness