Iterated harmonic numbers

The harmonic numbers are the sequence 1, 1+1/2, 1+1/2+1/3, ... Their asymptotic difference from the sequence of the natural logarithm of the positive integers is Euler's constant gamma. We define a family of natural generalizations of the harmonic numbers. The jth iterated harmonic numbers are a sequence of rational numbers that nests the previous sequences and relates in a similar way to the sequence of the jth iterate of the natural logarithm of positive integers. The analogues of several well-known properties of the harmonic numbers also hold for the iterated harmonic numbers, including a generalization of Euler's constant. We reproduce the proof that only the first harmonic number is an integer and, providing some numeric evidence for the cases j = 2 and j = 3, conjecture that the same result holds for all iterated harmonic numbers. We also review another proposed generalization of harmonic numbers.Comment: 13 pages, 2 figure

What is the Impact of the Analysis Method Used for Health State Utility Values on QALYs in Oncology? A Simulation Study Comparing Progression-Based and Time-to-Death Approaches

Background: Health state utility values (‘utilities’) are an integral part of health technology assessment. Though traditionally categorised by disease status in oncology (i.e. progression), several recent assessments have adopted values calculated according to the time that measures were recorded before death. We conducted a simulation study to understand the limitations of each approach, with a focus on mismatches between the way utilities are generated, and analysed. Methods: Survival times were simulated based on published literature, with permutations of three utility generation mechanisms (UGMs) and utility analysis methods (UAMs): (1) progression based, (2) time-to-death based, and (3) a ‘combination approach’. For each analysis quality-adjusted life-years (QALYs) were estimated. Goodness of fit was assessed via percentage mean error (%ME) and mean absolute error (%MAE). Scenario analyses were performed varying individual parameters, with complex scenarios mimicking published studies. The statistical code is provided for transparency and to aid future work in the area. Results: %ME and %MAE were lowest when the correct analysis form was specified (i.e. UGM and UAM aligned). Underestimates were produced when a time-to-death element was present in the UGM but not included in the UAM, while the ‘combined’ UAM produced overestimates irrespective of the UGM. Scenario analysis demonstrated the importance of the volume of available data beyond the initial time period, for example follow-up. Conclusions: We show that the use of an incorrectly or over-specified UAM can result in substantial bias in the estimation of utilities. We present a flowchart to highlight the issues that may be faced

POTENTIAL MARKET IMPACTS OF SOYBEAN RUST

Crop Production/Industries,

Post-hospital medical respite care and hospital readmission of homeless persons

Medical respite programs offer medical, nursing, and other care as well as accommodation for homeless persons discharged from acute hospital stays. They represent a community-based adaptation of urban health systems to the specific needs of homeless persons. This article examines whether post-hospital discharge to a homeless medical respite program was associated with a reduced chance of 90-day readmission compared to other disposition options. Adjusting for imbalances in patient characteristics using propensity scores, respite patients were the only group that was significantly less likely to be readmitted within 90 days compared to those released to Own Care. Respite programs merit attention as a potentially efficacious service for homeless persons leaving the hospital

Alluvial fan records from southeast Arabia reveal multiple windows for human dispersal

The dispersal of human populations out of Africa into Arabia was most likely linked to episodes of climatic amelioration, when increased monsoon rainfall led to the activation of drainage systems, improved freshwater availability, and the development of regional vegetation. Here we present the first dated terrestrial record from southeast Arabia that provides evidence for increased rainfall and the expansion of vegetation during both glacial and interglacial periods. Findings from extensive alluvial fan deposits indicate that drainage system activation occurred during Marine Isotope Stage (MIS) 6 (ca. 160–150 ka), MIS 5 (ca. 130–75 ka), and during early MIS 3 (ca. 55 ka). The development of active freshwater systems during these periods corresponds with monsoon intensity increases during insolation maxima, suggesting that humid periods in Arabia were not confined to eccentricity-paced deglaciations, and providing paleoenvironmental support for multiple windows of opportunity for dispersal out of Africa during the late Pleistocene

Quantum properties of classical Fisher information

The Fisher information of a quantum observable is shown to be proportional to both (i) the difference of a quantum and a classical variance, thus providing a measure of nonclassicality; and (ii) the rate of entropy increase under Gaussian diffusion, thus providing a measure of robustness. The joint nonclassicality of position and momentum observables is shown to be complementary to their joint robustness in an exact sense.Comment: 16 page

Ten Simple Rules for Getting Help from Online Scientific Communities

The increasing complexity of research requires scientists to work at the intersection of multiple fields and to face problems for which their formal education has not prepared them. For example, biologists with no or little background in programming are now often using complex scripts to handle the results from their experiments; vice versa, programmers wishing to enter the world of bioinformatics must know about biochemistry, genetics, and other fields. In this context, communication tools such as mailing lists, web forums, and online communities acquire increasing importance. These tools permit scientists to quickly contact people skilled in a specialized field. A question posed properly to the right online scientific community can help in solving difficult problems, often faster than screening literature or writing to publication authors. The growth of active online scientific communities, such as those listed in Table S1, demonstrates how these tools are becoming an important source of support for an increasing number of researchers. Nevertheless, making proper use of these resources is not easy. Adhering to the social norms of World Wide Web communication—loosely termed “netiquette”—is both important and non-trivial. In this article, we take inspiration from our experience on Internet-shared scientific knowledge, and from similar documents such as “Asking the Questions the Smart Way” and “Getting Answers”, to provide guidelines and suggestions on how to use online communities to solve scientific problems

Toward a wiki guide for obstetrics and gynecology trainees in Ireland.

BACKGROUND: The present paper describes the implementation of a novel, web-based, comprehensive national information hub for trainees in obstetrics and gynecology in Ireland. This was a unique development in the context of an entire medical specialty and was aligned with the communication strategy of the governing professional body. To date, trainee doctors working in Ireland undergo an incoherent and inconsistent new-staff induction and handover. In the healthcare setting, staff integration can have a major impact on the quality of patient care. METHODS: A free wiki software platform (PBworks) was used for the website, and freely available software (Google Analytics) was used to determine user interaction and level of engagement. RESULTS: In the first year, 442 user visits were recorded. The average duration of site visits was 4minutes 39seconds, which compared favorably with the 4-minute duration for visits to Wikipedia. CONCLUSION: The project was successful as a proof concept and in practice. Other medical faculties have expressed an interest in adopting the concept and developing it for their trainees. The concept is widely applicable to other countries, with the negligible cost relevant to resource-poor areas

Recommended practices for computerized clinical decision support and knowledge management in community settings: a qualitative study

<p>Abstract</p> <p>Background</p> <p>The purpose of this study was to identify recommended practices for computerized clinical decision support (CDS) development and implementation and for knowledge management (KM) processes in ambulatory clinics and community hospitals using commercial or locally developed systems in the U.S.</p> <p>Methods</p> <p>Guided by the Multiple Perspectives Framework, the authors conducted ethnographic field studies at two community hospitals and five ambulatory clinic organizations across the U.S. Using a Rapid Assessment Process, a multidisciplinary research team: gathered preliminary assessment data; conducted on-site interviews, observations, and field surveys; analyzed data using both template and grounded methods; and developed universal themes. A panel of experts produced recommended practices.</p> <p>Results</p> <p>The team identified ten themes related to CDS and KM. These include: 1) workflow; 2) knowledge management; 3) data as a foundation for CDS; 4) user computer interaction; 5) measurement and metrics; 6) governance; 7) translation for collaboration; 8) the meaning of CDS; 9) roles of special, essential people; and 10) communication, training, and support. Experts developed recommendations about each theme. The original Multiple Perspectives framework was modified to make explicit a new theoretical construct, that of Translational Interaction.</p> <p>Conclusions</p> <p>These ten themes represent areas that need attention if a clinic or community hospital plans to implement and successfully utilize CDS. In addition, they have implications for workforce education, research, and national-level policy development. The Translational Interaction construct could guide future applied informatics research endeavors.</p

Universal geometric approach to uncertainty, entropy and information

It is shown that for any ensemble, whether classical or quantum, continuous or discrete, there is only one measure of the "volume" of the ensemble that is compatible with several basic geometric postulates. This volume measure is thus a preferred and universal choice for characterising the inherent spread, dispersion, localisation, etc, of the ensemble. Remarkably, this unique "ensemble volume" is a simple function of the ensemble entropy, and hence provides a new geometric characterisation of the latter quantity. Applications include unified, volume-based derivations of the Holevo and Shannon bounds in quantum and classical information theory; a precise geometric interpretation of thermodynamic entropy for equilibrium ensembles; a geometric derivation of semi-classical uncertainty relations; a new means for defining classical and quantum localization for arbitrary evolution processes; a geometric interpretation of relative entropy; and a new proposed definition for the spot-size of an optical beam. Advantages of the ensemble volume over other measures of localization (root-mean-square deviation, Renyi entropies, and inverse participation ratio) are discussed.Comment: Latex, 38 pages + 2 figures; p(\alpha)->1/|T| in Eq. (72) [Eq. (A10) of published version