Prediction intervals for the realization of a random variable under a general mixed linear model

Let y represent an n x 1 observable random vector and w an unobservable random variable, whose joint distribution is of the multivariate normal form with E(y) = X(beta) and E(w) = (lamda)\u27(beta), where X is a given n x k matrix, (lamda) is a given k x 1 vector and (beta) is a k x 1 vector of unknown parameters. The elements of the variance-covariance matrix of y and w are assumed to be known functions of a q x 1 vector (theta) of unknown parameters;The problem considered is that of constructing an approximate 100(1 - (alpha))% prediction interval for the realized value of w, that is, an interval P(,1)(y),P(,2)(y) such that the probability (with respect to the joint distribution of y and w) of the event P(,1)(y) \u3c w \u3c P(,2)(y) approxi- mates 1 - (alpha), for all (beta) and (theta);There exist functions p(,1)*((.);(alpha),(theta)) and p(,2)*((.);(alpha),(theta)), depending on (alpha) and (theta) such that P P(,1)*(y;(alpha),(theta)) \u3c w \u3c P(,2)*(y;(alpha),(theta)) = 1 - (alpha), for all (theta) and (beta). If (theta) were known, P(,1)*(y;(alpha),(theta)),P(,2)*(y;(alpha),(theta)) would be an exact 100(1 - (alpha))% prediction interval for the realization of w. When (theta) is unknown, an exact 100(1 - (alpha))% prediction interval for the realization of w does not exist (except in relatively simple special cases);Five types of approximate intervals were investigated: (1) naive intervals P(,1)*(y;(alpha),(\u27)(theta)),P(,2)*(y;(alpha),(\u27)(theta)) , where (\u27)(theta) is an even translation-invariant estimator of (theta); (2) modified naive intervals (eta)(,B)(y;(\u27)(theta)) (+OR-) t(,(alpha)/2) (nu)((\u27)(theta)) M*((\u27)(theta)) (\u271/2), where (nu)((.)) is a specified function, t(,(alpha)/2) (nu)((\u27)(theta)) is the upper (alpha)/2 point of the t-distribution with (nu)((\u27)(theta)) degrees of freedom;and where M*((\u27)(theta)) is an approximation to E (eta)(,B)(y;(\u27)(theta))-w (\u272); (3) conserva- tive intervals of the general form;(DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI);where R represents a confidence set for (theta); (4) parametric bootstrap intervals (eta)(,B)(y;(\u27)(theta)(,m)) (+OR-) k(,(alpha)/2)((\u27)(theta)(,m)) M(,m)*((\u27)(theta)(,m)) (\u271/2), where k(,(alpha)/2)((theta)) is the upper (alpha)/2 point of the distribution of (eta)(,B)(y;(\u27)(theta)(,m))-w / M*((\u27)(theta)(,m)) (\u271/2) and (\u27)(theta)(,m) is the maximum likelihood estimator of (theta); (5) Bayesian credibility intervals;Results on the properties of these intervals are given for the general case and for the following two special cases: (1) the comparison of the means of two independent normal populations with unknown and unequal variances (the Behrens-Fisher problem), and (2) the prediction of a group mean in the balanced one-way random model. The modified naive intervals, the conservative intervals and the parametric bootstrap intervals seem to provide satisfactory approximate prediction intervals

Deciphering the Grand Village of the Illinois: A Preliminary Assessment of the Grand Village Research Project

On April 24, 1987, Thomas Emerson at the State Historic Preservation Office received a telephone call from a Chicago lawyer who wanted an answer to a simple question: Are there any laws that protect old Indian villages and graves that are on the National Register? Unfortunately, the answer was a simple “no.” At the time, Emerson did not suspect that this question would initiate a more than four-year struggle to save one of the most important historic sites in the country. The site, known variously as the Zimmerman site, the Grand Village of the Kaskaskia, Old Kaskaskia Village, the Grand Village of the Illinois, or simply llLS13, was purchased by developers who planned to build vacation homes on it. Eventually, after a private and public campaign that reached an international level, Governor James Thompson authorized the Illinois Historic Preservation Agency (IHPA) to seek condemnation of the property to bring it into public ownership. In April 1991, a final settlement was reached and the site was purchased by the state. It is currently under the administration of the IHPA and has been renamed the Grand Village of the Illinois State Historic Site. The Grand Village is the most important surviving village and burial site of the seventeenth-century Illinois Confederacy. In addition, it is the location of the initial French-Illinois contact and of the first Catholic mission in the Illinois Country. The site also contains materials that represent an unbroken sequence of late prehistoric, protohistoric, and Historic Indian cultural development from the ninth to the last quarter of the eighteenth century

Different forms of African cassava mosaic virus capsid protein within plants and virions

One geminiviral gene encodes the capsid protein (CP), which can appear as several bands after electrophoresis depending on virus and plant. African cassava mosaic virus-Nigeria CP in Nicotiana benthamiana, however, yielded one band (~ 30 kDa) in total protein extracts and purified virions, although its expression in yeast yielded two bands (~ 30, 32 kDa). Mass spectrometry of the complete protein and its tryptic fragments from virions is consistent with a cleaved start M1, acetylated S2, and partial phosphorylation at T12, S25 and S62. Mutants for additional potentially modified sites (N223A; C235A) were fully infectious and formed geminiparticles. Separation in triton acetic acid urea gels confirmed charge changes of the CP between plants and yeast indicating differential phosphorylation. If the CP gene alone was expressed in plants, multiple bands were observed like in yeast. A high turnover rate indicates that post-translational modifications promote CP decay probably via the ubiquitin-triggered proteasomal pathway

The potential benefits of low-molecular-weight heparins in cancer patients

Cancer patients are at increased risk of venous thromboembolism due to a range of factors directly related to their disease and its treatment. Given the high incidence of post-surgical venous thromboembolism in cancer patients and the poor outcomes associated with its development, thromboprophylaxis is warranted. A number of evidence-based guidelines delineate anticoagulation regimens for venous thromboembolism treatment, primary and secondary prophylaxis, and long-term anticoagulation in cancer patients. However, many give equal weight to several different drugs and do not make specific recommendations regarding duration of therapy. In terms of their efficacy and safety profiles, practicality of use, and cost-effectiveness the low-molecular-weight heparins are at least comparable to, and offer several advantages over, other available antithrombotics in cancer patients. In addition, data are emerging that the antithrombotics, and particularly low-molecular-weight heparins, may exert an antitumor effect which could contribute to improved survival in cancer patients when given for long-term prophylaxis. Such findings reinforce the importance of thromboprophylaxis with low-molecular-weight heparin in cancer patients

Search for dark matter produced in association with bottom or top quarks in √s = 13 TeV pp collisions with the ATLAS detector

A search for weakly interacting massive particle dark matter produced in association with bottom or top quarks is presented. Final states containing third-generation quarks and miss- ing transverse momentum are considered. The analysis uses 36.1 fb−1 of proton–proton collision data recorded by the ATLAS experiment at √s = 13 TeV in 2015 and 2016. No significant excess of events above the estimated backgrounds is observed. The results are in- terpreted in the framework of simplified models of spin-0 dark-matter mediators. For colour- neutral spin-0 mediators produced in association with top quarks and decaying into a pair of dark-matter particles, mediator masses below 50 GeV are excluded assuming a dark-matter candidate mass of 1 GeV and unitary couplings. For scalar and pseudoscalar mediators produced in association with bottom quarks, the search sets limits on the production cross- section of 300 times the predicted rate for mediators with masses between 10 and 50 GeV and assuming a dark-matter mass of 1 GeV and unitary coupling. Constraints on colour- charged scalar simplified models are also presented. Assuming a dark-matter particle mass of 35 GeV, mediator particles with mass below 1.1 TeV are excluded for couplings yielding a dark-matter relic density consistent with measurements