The Schroedinger Problem, Levy Processes Noise in Relativistic Quantum Mechanics

The main purpose of the paper is an essentially probabilistic analysis of relativistic quantum mechanics. It is based on the assumption that whenever probability distributions arise, there exists a stochastic process that is either responsible for temporal evolution of a given measure or preserves the measure in the stationary case. Our departure point is the so-called Schr\"{o}dinger problem of probabilistic evolution, which provides for a unique Markov stochastic interpolation between any given pair of boundary probability densities for a process covering a fixed, finite duration of time, provided we have decided a priori what kind of primordial dynamical semigroup transition mechanism is involved. In the nonrelativistic theory, including quantum mechanics, Feyman-Kac-like kernels are the building blocks for suitable transition probability densities of the process. In the standard "free" case (Feynman-Kac potential equal to zero) the familiar Wiener noise is recovered. In the framework of the Schr\"{o}dinger problem, the "free noise" can also be extended to any infinitely divisible probability law, as covered by the L\'{e}vy-Khintchine formula. Since the relativistic Hamiltonians $|\nabla |$ and $\sqrt {-\triangle +m^2}-m$ are known to generate such laws, we focus on them for the analysis of probabilistic phenomena, which are shown to be associated with the relativistic wave (D'Alembert) and matter-wave (Klein-Gordon) equations, respectively. We show that such stochastic processes exist and are spatial jump processes. In general, in the presence of external potentials, they do not share the Markov property, except for stationary situations. A concrete example of the pseudodifferential Cauchy-Schr\"{o}dinger evolution is analyzed in detail. The relativistic covariance of related waveComment: Latex fil

Extremal flows in Wasserstein space

We develop an intrinsic geometric approach to the calculus of variations in theWasserstein space. We show that the flows associated with the Schr\ua8odinger bridge with general prior, with optimal mass transport, and with the Madelung fluid can all be characterized as annihilating the first variation of a suitable action. We then discuss the implications of this unified framework for stochastic mechanics: It entails, in particular, a sort of fluid-dynamic reconciliation between Bohm\u2019s and Nelson\u2019s stochastic mechanics

Why Are Outcomes Different for Registry Patients Enrolled Prospectively and Retrospectively? Insights from the Global Anticoagulant Registry in the FIELD-Atrial Fibrillation (GARFIELD-AF).

Background: Retrospective and prospective observational studies are designed to reflect real-world evidence on clinical practice, but can yield conflicting results. The GARFIELD-AF Registry includes both methods of enrolment and allows analysis of differences in patient characteristics and outcomes that may result. Methods and Results: Patients with atrial fibrillation (AF) and ≥1 risk factor for stroke at diagnosis of AF were recruited either retrospectively (n = 5069) or prospectively (n = 5501) from 19 countries and then followed prospectively. The retrospectively enrolled cohort comprised patients with established AF (for a least 6, and up to 24 months before enrolment), who were identified retrospectively (and baseline and partial follow-up data were collected from the emedical records) and then followed prospectively between 0-18 months (such that the total time of follow-up was 24 months; data collection Dec-2009 and Oct-2010). In the prospectively enrolled cohort, patients with newly diagnosed AF (≤6 weeks after diagnosis) were recruited between Mar-2010 and Oct-2011 and were followed for 24 months after enrolment. Differences between the cohorts were observed in clinical characteristics, including type of AF, stroke prevention strategies, and event rates. More patients in the retrospectively identified cohort received vitamin K antagonists (62.1% vs. 53.2%) and fewer received non-vitamin K oral anticoagulants (1.8% vs . 4.2%). All-cause mortality rates per 100 person-years during the prospective follow-up (starting the first study visit up to 1 year) were significantly lower in the retrospective than prospectively identified cohort (3.04 [95% CI 2.51 to 3.67] vs . 4.05 [95% CI 3.53 to 4.63]; p = 0.016). Conclusions: Interpretations of data from registries that aim to evaluate the characteristics and outcomes of patients with AF must take account of differences in registry design and the impact of recall bias and survivorship bias that is incurred with retrospective enrolment. Clinical Trial Registration: - URL: http://www.clinicaltrials.gov . Unique identifier for GARFIELD-AF (NCT01090362)

Improved risk stratification of patients with atrial fibrillation: an integrated GARFIELD-AF tool for the prediction of mortality, stroke and bleed in patients with and without anticoagulation.

OBJECTIVES: To provide an accurate, web-based tool for stratifying patients with atrial fibrillation to facilitate decisions on the potential benefits/risks of anticoagulation, based on mortality, stroke and bleeding risks. DESIGN: The new tool was developed, using stepwise regression, for all and then applied to lower risk patients. C-statistics were compared with CHA2DS2-VASc using 30-fold cross-validation to control for overfitting. External validation was undertaken in an independent dataset, Outcome Registry for Better Informed Treatment of Atrial Fibrillation (ORBIT-AF). PARTICIPANTS: Data from 39 898 patients enrolled in the prospective GARFIELD-AF registry provided the basis for deriving and validating an integrated risk tool to predict stroke risk, mortality and bleeding risk. RESULTS: The discriminatory value of the GARFIELD-AF risk model was superior to CHA2DS2-VASc for patients with or without anticoagulation. C-statistics (95% CI) for all-cause mortality, ischaemic stroke/systemic embolism and haemorrhagic stroke/major bleeding (treated patients) were: 0.77 (0.76 to 0.78), 0.69 (0.67 to 0.71) and 0.66 (0.62 to 0.69), respectively, for the GARFIELD-AF risk models, and 0.66 (0.64-0.67), 0.64 (0.61-0.66) and 0.64 (0.61-0.68), respectively, for CHA2DS2-VASc (or HAS-BLED for bleeding). In very low to low risk patients (CHA2DS2-VASc 0 or 1 (men) and 1 or 2 (women)), the CHA2DS2-VASc and HAS-BLED (for bleeding) scores offered weak discriminatory value for mortality, stroke/systemic embolism and major bleeding. C-statistics for the GARFIELD-AF risk tool were 0.69 (0.64 to 0.75), 0.65 (0.56 to 0.73) and 0.60 (0.47 to 0.73) for each end point, respectively, versus 0.50 (0.45 to 0.55), 0.59 (0.50 to 0.67) and 0.55 (0.53 to 0.56) for CHA2DS2-VASc (or HAS-BLED for bleeding). Upon validation in the ORBIT-AF population, C-statistics showed that the GARFIELD-AF risk tool was effective for predicting 1-year all-cause mortality using the full and simplified model for all-cause mortality: C-statistics 0.75 (0.73 to 0.77) and 0.75 (0.73 to 0.77), respectively, and for predicting for any stroke or systemic embolism over 1 year, C-statistics 0.68 (0.62 to 0.74). CONCLUSIONS: Performance of the GARFIELD-AF risk tool was superior to CHA2DS2-VASc in predicting stroke and mortality and superior to HAS-BLED for bleeding, overall and in lower risk patients. The GARFIELD-AF tool has the potential for incorporation in routine electronic systems, and for the first time, permits simultaneous evaluation of ischaemic stroke, mortality and bleeding risks. CLINICAL TRIAL REGISTRATION: URL: http://www.clinicaltrials.gov. Unique identifier for GARFIELD-AF (NCT01090362) and for ORBIT-AF (NCT01165710)

Two-year outcomes of patients with newly diagnosed atrial fibrillation: results from GARFIELD-AF.

AIMS: The relationship between outcomes and time after diagnosis for patients with non-valvular atrial fibrillation (NVAF) is poorly defined, especially beyond the first year. METHODS AND RESULTS: GARFIELD-AF is an ongoing, global observational study of adults with newly diagnosed NVAF. Two-year outcomes of 17 162 patients prospectively enrolled in GARFIELD-AF were analysed in light of baseline characteristics, risk profiles for stroke/systemic embolism (SE), and antithrombotic therapy. The mean (standard deviation) age was 69.8 (11.4) years, 43.8% were women, and the mean CHA2DS2-VASc score was 3.3 (1.6); 60.8% of patients were prescribed anticoagulant therapy with/without antiplatelet (AP) therapy, 27.4% AP monotherapy, and 11.8% no antithrombotic therapy. At 2-year follow-up, all-cause mortality, stroke/SE, and major bleeding had occurred at a rate (95% confidence interval) of 3.83 (3.62; 4.05), 1.25 (1.13; 1.38), and 0.70 (0.62; 0.81) per 100 person-years, respectively. Rates for all three major events were highest during the first 4 months. Congestive heart failure, acute coronary syndromes, sudden/unwitnessed death, malignancy, respiratory failure, and infection/sepsis accounted for 65% of all known causes of death and strokes for <10%. Anticoagulant treatment was associated with a 35% lower risk of death. CONCLUSION: The most frequent of the three major outcome measures was death, whose most common causes are not known to be significantly influenced by anticoagulation. This suggests that a more comprehensive approach to the management of NVAF may be needed to improve outcome. This could include, in addition to anticoagulation, interventions targeting modifiable, cause-specific risk factors for death. CLINICAL TRIAL REGISTRATION: http://www.clinicaltrials.gov. Unique identifier: NCT01090362

Effects of body size on estimation of mammalian area requirements.

Accurately quantifying species' area requirements is a prerequisite for effective area-based conservation. This typically involves collecting tracking data on species of interest and then conducting home range analyses. Problematically, autocorrelation in tracking data can result in space needs being severely underestimated. Based on the previous work, we hypothesized the magnitude of underestimation varies with body mass, a relationship that could have serious conservation implications. To evaluate this hypothesis for terrestrial mammals, we estimated home-range areas with global positioning system (GPS) locations from 757 individuals across 61 globally distributed mammalian species with body masses ranging from 0.4 to 4000 kg. We then applied blockcross validation to quantify bias in empirical home range estimates. Area requirements of mammals 1, meaning the scaling of the relationship changedsubstantially at the upper end of the mass spectrum

A framework for the development of a global standardised marine taxon reference image database (SMarTaR-ID) to support image-based analyses

Video and image data are regularly used in the field of benthic ecology to document biodiversity. However, their use is subject to a number of challenges, principally the identification of taxa within the images without associated physical specimens. The challenge of applying traditional taxonomic keys to the identification of fauna from images has led to the development of personal, group, or institution level reference image catalogues of operational taxonomic units (OTUs) or morphospecies. Lack of standardisation among these reference catalogues has led to problems with observer bias and the inability to combine datasets across studies. In addition, lack of a common reference standard is stifling efforts in the application of artificial intelligence to taxon identification. Using the North Atlantic deep sea as a case study, we propose a database structure to facilitate standardisation of morphospecies image catalogues between research groups and support future use in multiple front-end applications. We also propose a framework for coordination of international efforts to develop reference guides for the identification of marine species from images. The proposed structure maps to the Darwin Core standard to allow integration with existing databases. We suggest a management framework where high-level taxonomic groups are curated by a regional team, consisting of both end users and taxonomic experts. We identify a mechanism by which overall quality of data within a common reference guide could be raised over the next decade. Finally, we discuss the role of a common reference standard in advancing marine ecology and supporting sustainable use of this ecosystem

Man and the Last Great Wilderness: Human Impact on the Deep Sea

The deep sea, the largest ecosystem on Earth and one of the least studied, harbours high biodiversity and provides a wealth of resources. Although humans have used the oceans for millennia, technological developments now allow exploitation of fisheries resources, hydrocarbons and minerals below 2000 m depth. The remoteness of the deep seafloor has promoted the disposal of residues and litter. Ocean acidification and climate change now bring a new dimension of global effects. Thus the challenges facing the deep sea are large and accelerating, providing a new imperative for the science community, industry and national and international organizations to work together to develop successful exploitation management and conservation of the deep-sea ecosystem. This paper provides scientific expert judgement and a semi-quantitative analysis of past, present and future impacts of human-related activities on global deep-sea habitats within three categories: disposal, exploitation and climate change. The analysis is the result of a Census of Marine Life – SYNDEEP workshop (September 2008). A detailed review of known impacts and their effects is provided. The analysis shows how, in recent decades, the most significant anthropogenic activities that affect the deep sea have evolved from mainly disposal (past) to exploitation (present). We predict that from now and into the future, increases in atmospheric CO2 and facets and consequences of climate change will have the most impact on deep-sea habitats and their fauna. Synergies between different anthropogenic pressures and associated effects are discussed, indicating that most synergies are related to increased atmospheric CO2 and climate change effects. We identify deep-sea ecosystems we believe are at higher risk from human impacts in the near future: benthic communities on sedimentary upper slopes, cold-water corals, canyon benthic communities and seamount pelagic and benthic communities. We finalise this review with a short discussion on protection and management methods