Properties and Applications of the Kirkwood-Dirac Distribution

The most famous quasi-probability distribution, the Wigner function, has played a pivotal role in the development of a continuous-variable quantum theory that has clear analogues of position and momentum. However, the Wigner function is ill-suited for much modern quantum-information research, which is focused on finite-dimensional systems and general observables. Instead, recent years have seen the Kirkwood-Dirac (KD) distribution come to the forefront as a powerful quasi-probability distribution for analysing quantum mechanics. The KD distribution allows tools from statistics and probability theory to be applied to problems in quantum-information processing. A notable difference to the Wigner function is that the KD distribution can represent a quantum state in terms of arbitrary observables. This paper reviews the KD distribution, in three parts. First, we present definitions and basic properties of the KD distribution and its generalisations. Second, we summarise the KD distribution's extensive usage in the study or development of measurement disturbance; quantum metrology; weak values; direct measurements of quantum states; quantum thermodynamics; quantum scrambling and out-of-time-ordered correlators; and the foundations of quantum mechanics, including Leggett-Garg inequalities, the consistent-histories interpretation, and contextuality. We emphasise connections between operational quantum advantages and negative or non-real KD quasi-probabilities. Third, we delve into the KD distribution's mathematical structure. We summarise the current knowledge regarding the geometry of KD-positive states (the states for which the KD distribution is a classical probability distribution), describe how to witness and quantify KD non-positivity, and outline relationships between KD non-positivity and observables' incompatibility.Comment: 37 pages, 13 figure

Transcription, one allele at a time

A recent study presents a technique allowing one to image transcription from a single gene copy in live cells, and highlights the dynamic nature of transcriptional regulation

Rapid Transcriptional Pulsing Dynamics of High Expressing Retroviral Transgenes in Embryonic Stem Cells

Single cell imaging studies suggest that transcription is not continuous and occurs as discrete pulses of gene activity. To study mechanisms by which retroviral transgenes can transcribe to high levels, we used the MS2 system to visualize transcriptional dynamics of high expressing proviral integration sites in embryonic stem (ES) cells. We established two ES cell lines each bearing a single copy, self-inactivating retroviral vector with a strong ubiquitous human EF1α gene promoter directing expression of mRFP fused to an MS2-stem-loop array. Transfection of MS2-EGFP generated EGFP focal dots bound to the mRFP-MS2 stem loop mRNA. These transcription foci colocalized with the transgene integration site detected by immunoFISH. Live tracking of single cells for 20 minutes detected EGFP focal dots that displayed frequent and rapid fluctuations in transcription over periods as short as 25 seconds. Similarly rapid fluctuations were detected from focal doublet signals that colocalized with replicated proviral integration sites by immunoFISH, consistent with transcriptional pulses from sister chromatids. We concluded that retroviral transgenes experience rapid transcriptional pulses in clonal ES cell lines that exhibit high level expression. These events are directed by a constitutive housekeeping gene promoter and may provide precedence for rapid transcriptional pulsing at endogenous genes in mammalian stem cells

Gamma estimator of Jarzynski equality for recovering binding energies from noisy dynamic data sets

A fundamental problem in thermodynamics is the recovery of macroscopic equilibrated interaction energies from experimentally measured single-molecular interactions. The Jarzynski equality forms a theoretical basis in recovering the free energy difference between two states from exponentially averaged work performed to switch the states. In practice, the exponentially averaged work value is estimated as the mean of finite samples. Numerical simulations have shown that samples having thousands of measurements are not large enough for the mean to converge when the fluctuation of external work is above 4 kBT, which is easily observable in biomolecular interactions. We report the first example of a statistical gamma work distribution applied to single molecule pulling experiments. The Gibbs free energy of surface adsorption can be accurately evaluated even for a small sample size. The values obtained are comparable to those derived from multi-parametric surface plasmon resonance measurements and molecular dynamics simulations

Exploring the perspectives and preferences for HTA across German healthcare stakeholders using a multi-criteria assessment of a pulmonary heart sensor as a case study

Background Health technology assessment and healthcare decision-making are based on multiple criteria and evidence, and heterogeneous opinions of participating stakeholders. Multi-criteria decision analysis (MCDA) offers a potential framework to systematize this process and take different perspectives into account. The objectives of this study were to explore perspectives and preferences across German stakeholders when appraising healthcare interventions, using multi-criteria assessment of a heart pulmonary sensor as a case study. Methods An online survey of 100 German healthcare stakeholders was conducted using a comprehensive MCDA framework (EVIDEM V2.2). Participants were asked to provide i) relative weights for each criterion of the framework; ii) performance scores for a health pulmonary sensor, based on available data synthesized for each criterion; and iii) qualitative feedback on the consideration of contextual criteria. Normalized weights and scores were combined using a linear model to calculate a value estimate across different stakeholders. Differences across types of stakeholders were explored. Results The survey was completed by 54 participants. The most important criteria were efficacy, patient reported outcomes, disease severity, safety, and quality of evidence (relative weight >0.075 each). Compared to all participants, policymakers gave more weight to budget impact and quality of evidence. The quantitative appraisal of a pulmonary heart sensor revealed differences in scoring performance of this intervention at the criteria level between stakeholder groups. The highest value estimate of the sensor reached 0.68 (on a scale of 0 to 1, 1 representing maximum value) for industry representatives and the lowest value of 0.40 was reported for policymakers, compared to 0.48 for all participants. Participants indicated that most qualitative criteria should be considered and their impact on the quantitative appraisal was captured transparently. Conclusions The study identified important variations in perspectives across German stakeholders when appraising a healthcare intervention and revealed that MCDA can demonstrate the value of a specified technology for all participating stakeholders. Better understanding of these differences at the criteria level, in particular between policymakers and industry representatives, is important to focus innovation aligned with patient health and healthcare system values and constraints

Being Mum’s Confidant, a Boon or Bane? Examining Gender Differences in the Association of Maternal Disclosure with Adolescents’ Depressive Feelings

This article reports on a longitudinal study investigating gender differences in the association between maternal disclosure and adolescents’ depressive symptoms. Little research has examined the relationship of parental disclosure to adolescents’ depressive symptoms and research on sex differences is particularly lacking. In a sample of 428 families with a mean age of 13.36 (52% female) of the target adolescents, maternal and children’s disclosure and depressive symptoms were assessed twice with an interval of 4 years. Controlling for the quality of the parent–child relationship and levels of maternal depressive symptoms, the analyses revealed an interaction effect for child’s gender, moderating the effect of maternal disclosure on adolescents’ depressive symptoms. Higher levels of maternal disclosure were accompanied by lower levels of depressive symptoms in girls and higher levels of depressive symptoms in boys. Gender differences in socialization, communication, individuation and social networks might explain why daughters and sons are differently affected by maternal disclosure