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

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

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

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

Limitations of Algebraic Approaches to Graph Isomorphism Testing

We investigate the power of graph isomorphism algorithms based on algebraic reasoning techniques like Gr\"obner basis computation. The idea of these algorithms is to encode two graphs into a system of equations that are satisfiable if and only if if the graphs are isomorphic, and then to (try to) decide satisfiability of the system using, for example, the Gr\"obner basis algorithm. In some cases this can be done in polynomial time, in particular, if the equations admit a bounded degree refutation in an algebraic proof systems such as Nullstellensatz or polynomial calculus. We prove linear lower bounds on the polynomial calculus degree over all fields of characteristic different from 2 and also linear lower bounds for the degree of Positivstellensatz calculus derivations. We compare this approach to recently studied linear and semidefinite programming approaches to isomorphism testing, which are known to be related to the combinatorial Weisfeiler-Lehman algorithm. We exactly characterise the power of the Weisfeiler-Lehman algorithm in terms of an algebraic proof system that lies between degree-k Nullstellensatz and degree-k polynomial calculus

Reionization Constraints on the Contribution of Primordial Compact Objects to Dark Matter

Many lines of evidence suggest that nonbaryonic dark matter constitutes roughly 30% of the critical closure density, but the composition of this dark matter is unknown. One class of candidates for the dark matter is compact objects formed in the early universe, with typical masses M between 0.1 and 1 solar masses to correspond to the mass scale of objects found with microlensing observing projects. Specific candidates of this type include black holes formed at the epoch of the QCD phase transition, quark stars, and boson stars. Here we show that accretion onto these objects produces substantial ionization in the early universe, with an optical depth to Thomson scattering out to z=1100 of approximately tau=2-4 [f_CO\epsilon_{-1}(M/Msun)]^{1/2} (H_0/65)^{-1}, where \epsilon_{-1} is the accretion efficiency \epsilon\equiv L/{\dot M}c^2 divided by 0.1 and f_CO is the fraction of matter in the compact objects. The current upper limit to the scattering optical depth, based on the anisotropy of the microwave background, is approximately 0.4. Therefore, if accretion onto these objects is relatively efficient, they cannot be the main component of nonbaryonic dark matter.Comment: 12 pages including one figure, uses aaspp4, submitted to Ap

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

Depression with atypical features and increase in obesity, body mass index, waist circumference, and fat mass: a prospective, population-based study.

IMPORTANCE: Depression and obesity are 2 prevalent disorders that have been repeatedly shown to be associated. However, the mechanisms and temporal sequence underlying this association are poorly understood. OBJECTIVE: To determine whether the subtypes of major depressive disorder (MDD; melancholic, atypical, combined, or unspecified) are predictive of adiposity in terms of the incidence of obesity and changes in body mass index (calculated as weight in kilograms divided by height in meters squared), waist circumference, and fat mass. DESIGN, SETTING, AND PARTICIPANTS: This prospective population-based cohort study, CoLaus (Cohorte Lausannoise)/PsyCoLaus (Psychiatric arm of the CoLaus Study), with 5.5 years of follow-up included 3054 randomly selected residents (mean age, 49.7 years; 53.1% were women) of the city of Lausanne, Switzerland (according to the civil register), aged 35 to 66 years in 2003, who accepted the physical and psychiatric baseline and physical follow-up evaluations. EXPOSURES: Depression subtypes according to the DSM-IV. Diagnostic criteria at baseline and follow-up, as well as sociodemographic characteristics, lifestyle (alcohol and tobacco use and physical activity), and medication, were elicited using the semistructured Diagnostic Interview for Genetic Studies. MAIN OUTCOMES AND MEASURES: Changes in body mass index, waist circumference, and fat mass during the follow-up period, in percentage of the baseline value, and the incidence of obesity during the follow-up period among nonobese participants at baseline. Weight, height, waist circumference, and body fat (bioimpedance) were measured at baseline and follow-up by trained field interviewers. RESULTS: Only participants with the atypical subtype of MDD at baseline revealed a higher increase in adiposity during follow-up than participants without MDD. The associations between this MDD subtype and body mass index (β = 3.19; 95% CI, 1.50-4.88), incidence of obesity (odds ratio, 3.75; 95% CI, 1.24-11.35), waist circumference in both sexes (β = 2.44; 95% CI, 0.21-4.66), and fat mass in men (β = 16.36; 95% CI, 4.81-27.92) remained significant after adjustments for a wide range of possible cofounding. CONCLUSIONS AND RELEVANCE: The atypical subtype of MDD is a strong predictor of obesity. This emphasizes the need to identify individuals with this subtype of MDD in both clinical and research settings. Therapeutic measures to diminish the consequences of increased appetite during depressive episodes with atypical features are advocated

Approximate volume and integration for basic semi-algebraic sets

Given a basic compact semi-algebraic set \K\subset\R^n, we introduce a methodology that generates a sequence converging to the volume of \K. This sequence is obtained from optimal values of a hierarchy of either semidefinite or linear programs. Not only the volume but also every finite vector of moments of the probability measure that is uniformly distributed on \K can be approximated as closely as desired, and so permits to approximate the integral on \K of any given polynomial; extension to integration against some weight functions is also provided. Finally, some numerical issues associated with the algorithms involved are briefly discussed