Predicting the outcome of renal transplantation

ObjectiveRenal transplantation has dramatically improved the survival rate of hemodialysis patients. However, with a growing proportion of marginal organs and improved immunosuppression, it is necessary to verify that the established allocation system, mostly based on human leukocyte antigen matching, still meets today's needs. The authors turn to machine-learning techniques to predict, from donor-recipient data, the estimated glomerular filtration rate (eGFR) of the recipient 1 year after transplantation.DesignThe patient's eGFR was predicted using donor-recipient characteristics available at the time of transplantation. Donors' data were obtained from Eurotransplant's database, while recipients' details were retrieved from Charite Campus Virchow-Klinikum's database. A total of 707 renal transplantations from cadaveric donors were included.MeasurementsTwo separate datasets were created, taking features with <10% missing values for one and <50% missing values for the other. Four established regressors were run on both datasets, with and without feature selection.ResultsThe authors obtained a Pearson correlation coefficient between predicted and real eGFR (COR) of 0.48. The best model for the dataset was a Gaussian support vector machine with recursive feature elimination on the more inclusive dataset. All results are available at http://transplant.molgen.mpg.de/.LimitationsFor now, missing values in the data must be predicted and filled in. The performance is not as high as hoped, but the dataset seems to be the main cause.ConclusionsPredicting the outcome is possible with the dataset at hand (COR=0.48). Valuable features include age and creatinine levels of the donor, as well as sex and weight of the recipient

Exploiting symmetries in SDP-relaxations for polynomial optimization

In this paper we study various approaches for exploiting symmetries in polynomial optimization problems within the framework of semi definite programming relaxations. Our special focus is on constrained problems especially when the symmetric group is acting on the variables. In particular, we investigate the concept of block decomposition within the framework of constrained polynomial optimization problems, show how the degree principle for the symmetric group can be computationally exploited and also propose some methods to efficiently compute in the geometric quotient.Comment: (v3) Minor revision. To appear in Math. of Operations Researc

Large Magellanic Cloud Microlensing Optical Depth with Imperfect Event Selection

I present a new analysis of the MACHO Project 5.7 year Large Magellanic Cloud (LMC) microlensing data set that incorporates the effects of contamination of the microlensing event sample by variable stars. Photometric monitoring of MACHO LMC microlensing event candidates by the EROS and OGLE groups has revealed that one of these events is likely to be a variable star, while additional data has confirmed that many of the other events are very likely to be microlensing. This additional data on the nature of the MACHO microlensing candidates is incorporated into a simple likelihood analysis to derive a probability distribution for the number of MACHO microlens candidates that are true microlensing events. This analysis shows that 10-12 of the 13 events that passed the MACHO selection criteria are likely to be microlensing events, with the other 1-3 being variable stars. This likelihood analysis is also used to show that the main conclusions of the MACHO LMC analysis are unchanged by the variable star contamination. The microlensing optical depth toward the LMC is = 1.0 +/- 0.3 * 10^{-7}. If this is due to microlensing by known stellar populations, plus an additional population of lens objects in the Galactic halo, then the new halo population would account for 16% of the mass of a standard Galactic halo. The MACHO detection exceeds the expected background of 2 events expected from ordinary stars in standard models of the Milky Way and LMC at the 99.98% confidence level. The background prediction is increased to 3 events if maximal disk models are assumed for both the MilkyWay and LMC, but this model fails to account for the full signal seen by MACHO at the 99.8% confidence level.Comment: 20 pages, 2 postscript figues, accepted by Ap

A unified approach to computing real and complex zeros of zero-dimensional ideals

In this paper we propose a unified methodology for computing the set $V_K(I)$ of complex ($K = C$) or real ($K = R$) roots of an ideal $I$ in $R[x]$, assuming $V_K(I)$ is finite. We show how moment matrices, defined in terms of a given set of generators of the ideal I, can be used to (numerically) find not only the real variety $V_R(I)$, as shown in the authors’ previous work, but also the complex variety $V_C(I)$, thus leading to a unified treatment of the algebraic and real algebraic problem. In contrast to the real algebraic version of the algorithm, the complex analogue only uses basic numerical linear algebra because it does not require positive semidefiniteness of the moment matrix and so avoids semidefinite programming techniques. The links between these algorithms and other numerical algebraic methods are outlined and their stopping criteria are related

A prolongation-projection algorithm for computing the finite real variety of an ideal

We provide a real algebraic symbolic-numeric algorithm for computing the real variety $V_R(I)$ of an ideal $I$, assuming it is finite while $V_C(I)$ may not be. Our approach uses sets of linear functionals on $R[X]$, vanishing on a given set of polynomials generating $I$ and their prolongations up to a given degree, as well as on polynomials of the real radical ideal of $I$, obtained from the kernel of a suitably defined moment matrix assumed to be positive semidefinite and of maximum rank. We formulate a condition on the dimensions of projections of these sets of linear functionals, which serves as stopping criterion for our algorithm. This algorithm, based on standard numerical linear algebra routines and semidefinite optimization, combines techniques from previous work of the authors together with an existing algorithm for the complex variety. This results in a unified methodology for the real and complex cases.Comment: revised versio

Photometric Confirmation of MACHO Large Magellanic Cloud Microlensing Events

We present previously unpublished photometry of three Large Magellanic Cloud (LMC) microlensing events and show that the new photometry confirms the microlensing interpretation of these events. These events were discovered by the MACHO Project alert system and were also recovered by the analysis of the 5.7 year MACHO data set. This new photometry provides a substantial increase in the signal-to-noise ratio over the previously published photometry and in all three cases, the gravitational microlensing interpretation of these events is strengthened. The new data consist of MACHO-Global Microlensing Alert Network (GMAN) follow-up images from the CTIO 0.9 telescope plus difference imaging photometry of the original MACHO data from the 1.3m "Great Melbourne" telescope at Mt. Stromlo. We also combine microlensing light curve fitting with photometry from high resolution HST images of the source stars to provide further confirmation of these events and to show that the microlensing interpretation of event MACHO-LMC-23 is questionable. Finally, we compare our results with the analysis of Belokurov, Evans & Le Du who have attempted to classify candidate microlensing events with a neural network method, and we find that their results are contradicted by the new data and more powerful light curve fitting analysis for each of the four events considered in this paper. The failure of the Belokurov, Evans & Le Du method is likely to be due to their use of a set of insensitive statistics to feed their neural networks.Comment: 29 pages with 8 included postscript figures, accepted by the Astrophysical Journa

China's Arctic Ambitions and What They Mean for Canada

China’s Arctic Ambitions and What They Mean for Canada is one of the first in-depth studies of China’s increasing interest in the Arctic. It offers a holistic approach to understanding Chinese motivations and the potential impacts of greater Chinese presence in the circumpolar region, exploring resource development, shipping, scientific research, governance, and security. Drawing on extensive research in Chinese government documentation, business and media reports, and current academic literature, this timely volume eschews the traditional assumption that Chinese actions are unified and monolithic in their approach to Arctic affairs. Instead, it offers a careful analysis of the different, and often competing, interests and priorities of Chinese government and industry. Analyzing Chinese interests and activities from a Canadian perspective, the book provides an unparalleled point of reference to discuss the implications for the Canadian and broader circumpolar North

Constraints on Cold H_2 Clouds from Gravitational Microlensing Searches

It has been proposed that the Galaxy might contain a population of cold clouds in numbers sufficient to account for a substantial fraction of the total mass of the Galaxy. These clouds would have masses of the order of 10^{-3} Solar mass and sizes of the order of 10 AU. We consider here the lensing effects of such clouds on the light from background stars. A semianalytical formalism for calculation of the magnification event rate produced by such gaseous lensing is developed, taking into account the spatial distribution of the dark matter in the Galaxy, the velocity distribution of the lensing clouds and source stars, and motion of the observer. Event rates are calculated for the case of gaseous lensing of stars in the Large Magellanic Cloud and results are directly compared with the results of the search for gravitational microlensing events undertaken by the MACHO collaboration. The MACHO experiment strongly constrains the properties of the proposed molecular clouds, but does not completely rule them out. Future monitoring programs will either detect or more strongly constrain this proposed population.Comment: 36 pages, 9 figures, 1 table, typos corrected, minor change