A tree-decomposed transfer matrix for computing exact Potts model partition functions for arbitrary graphs, with applications to planar graph colourings

Combining tree decomposition and transfer matrix techniques provides a very general algorithm for computing exact partition functions of statistical models defined on arbitrary graphs. The algorithm is particularly efficient in the case of planar graphs. We illustrate it by computing the Potts model partition functions and chromatic polynomials (the number of proper vertex colourings using Q colours) for large samples of random planar graphs with up to N=100 vertices. In the latter case, our algorithm yields a sub-exponential average running time of ~ exp(1.516 sqrt(N)), a substantial improvement over the exponential running time ~ exp(0.245 N) provided by the hitherto best known algorithm. We study the statistics of chromatic roots of random planar graphs in some detail, comparing the findings with results for finite pieces of a regular lattice.Comment: 5 pages, 3 figures. Version 2 has been substantially expanded. Version 3 shows that the worst-case running time is sub-exponential in the number of vertice

Tigers on trails: occupancy modeling for cluster sampling

Occupancy modeling focuses on inference about the distribution of organisms over space, using temporal or spatial replication to allow inference about the detection process. Inference based on spatial replication strictly requires that replicates be selected randomly and with replacement, but the importance of these design requirements is not well understood. This paper focuses on an increasingly popular sampling design based on spatial replicates that are not selected randomly and that are expected to exhibit Markovian dependence. We develop two new occupancy models for data collected under this sort of design, one based on an underlying Markov model for spatial dependence and the other based on a trap response model with Markovian detections. We then simulated data under the model for Markovian spatial dependence and fit the data to standard occupancy models and to the two new models. Bias of occupancy estimates was substantial for the standard models, smaller for the new trap response model, and negligible for the new spatial process model. We also fit these models to data from a large-scale tiger occupancy survey recently conducted in Karnataka State, southwestern India. In addition to providing evidence of a positive relationship between tiger occupancy and habitat, model selection statistics and estimates strongly supported the use of the model with Markovian spatial dependence. This new model provides another tool for the decomposition of the detection process, which is sometimes needed for proper estimation and which may also permit interesting biological inferences. In addition to designs employing spatial replication, we note the likely existence of temporal Markovian dependence in many designs using temporal replication. The models developed here will be useful either directly, or with minor extensions, for these designs as well. We believe that these new models represent important additions to the suite of modeling tools now available for occupancy estimation in conservation monitoring. More generally, this work represents a contribution to the topic of cluster sampling for situations in which there is a need for specific modeling (e.g., reflecting dependence) for the distribution of the variable(s) of interest among subunits

Systematic review and economic modelling of the relative clinical benefit and cost-effectiveness of laparoscopic surgery and robotic surgery for removal of the prostate in men with localised prostate cancer

PMID: 23127367 [PubMed - indexed for MEDLINE] Free full text Funding for this study was provided by the Health Technology Assessment programme of the National Institute for Health Research.Peer reviewedPublisher PD

Looking for a needle in a haystack: inference about individual fitness components in a heterogeneous population

Studies of wild vertebrates have provided evidence of substantial differences in lifetime reproduction among individuals and the sequences of life history ‘states’ during life (breeding, nonbreeding, etc.). Such differences may reflect ‘fixed’ differences in fitness components among individuals determined before, or at the onset of reproductive life. Many retrospective life history studies have translated this idea by assuming a ‘latent’ unobserved heterogeneity resulting in a fixed hierarchy among individuals in fitness components. Alternatively, fixed differences among individuals are not necessarily needed to account for observed levels of individual heterogeneity in life histories. Individuals with identical fitness traits may stochastically experience different outcomes for breeding and survival through life that lead to a diversity of ‘state’ sequences with some individuals living longer and being more productive than others, by chance alone. The question is whether individuals differ in their underlying fitness components in ways that cannot be explained by observable ‘states’ such as age, previous breeding success, etc. Here, we compare statistical models that represent these opposing hypotheses, and mixtures of them, using data from kittiwakes. We constructed models that accounted for observed covariates, individual random effects (unobserved heterogeneity), first-order Markovian transitions between observed states, or combinations of these features. We show that individual sequences of states are better accounted for by models incorporating unobserved heterogeneity than by models including first-order Markov processes alone, or a combination of both. If we had not considered individual heterogeneity, models including Markovian transitions would have been the best performing ones. We also show that inference about age-related changes in fitness components is sensitive to incorporation of underlying individual heterogeneity in models. Our approach provides insight into the sources of individual heterogeneity in life histories, and can be applied to other data sets to examine the ubiquity of our results across the tree of life

Do female association preferences predict the likelihood of reproduction?

Sexual selection acting on male traits through female mate choice is commonly inferred from female association preferences in dichotomous mate choice experiments. However, there are surprisingly few empirical demonstrations that such association preferences predict the likelihood of females reproducing with a particular male. This information is essential to confirm association preferences as good predictors of mate choice. We used green swordtails (<i>Xiphophorus helleri</i>) to test whether association preferences predict the likelihood of a female reproducing with a male. Females were tested for a preference for long- or short-sworded males in a standard dichotomous choice experiment and then allowed free access to either their preferred or non-preferred male. If females subsequently failed to produce fry, they were provided a second unfamiliar male with similar sword length to the first male. Females were more likely to reproduce with preferred than non-preferred males, but for those that reproduced, neither the status (preferred/non-preferred) nor the sword length (long/short) of the male had an effect on brood size or relative investment in growth by the female. There was no overall preference based on sword length in this study, but male sword length did affect likelihood of reproduction, with females more likely to reproduce with long- than short-sworded males (independent of preference for such males in earlier choice tests). These results suggest that female association preferences are good indicators of female mate choice but that ornament characteristics of the male are also important

Length of carotid stenosis predicts peri-procedural stroke or death and restenosis in patients randomized to endovascular treatment or endarterectomy.

BACKGROUND: The anatomy of carotid stenosis may influence the outcome of endovascular treatment or carotid endarterectomy. Whether anatomy favors one treatment over the other in terms of safety or efficacy has not been investigated in randomized trials. METHODS: In 414 patients with mostly symptomatic carotid stenosis randomized to endovascular treatment (angioplasty or stenting; n = 213) or carotid endarterectomy (n = 211) in the Carotid and Vertebral Artery Transluminal Angioplasty Study (CAVATAS), the degree and length of stenosis and plaque surface irregularity were assessed on baseline intraarterial angiography. Outcome measures were stroke or death occurring between randomization and 30 days after treatment, and ipsilateral stroke and restenosis ≥50% during follow-up. RESULTS: Carotid stenosis longer than 0.65 times the common carotid artery diameter was associated with increased risk of peri-procedural stroke or death after both endovascular treatment [odds ratio 2.79 (1.17-6.65), P = 0.02] and carotid endarterectomy [2.43 (1.03-5.73), P = 0.04], and with increased long-term risk of restenosis in endovascular treatment [hazard ratio 1.68 (1.12-2.53), P = 0.01]. The excess in restenosis after endovascular treatment compared with carotid endarterectomy was significantly greater in patients with long stenosis than with short stenosis at baseline (interaction P = 0.003). Results remained significant after multivariate adjustment. No associations were found for degree of stenosis and plaque surface. CONCLUSIONS: Increasing stenosis length is an independent risk factor for peri-procedural stroke or death in endovascular treatment and carotid endarterectomy, without favoring one treatment over the other. However, the excess restenosis rate after endovascular treatment compared with carotid endarterectomy increases with longer stenosis at baseline. Stenosis length merits further investigation in carotid revascularisation trials

The impact of proton LET/RBE modeling and robustness analysis on base-of-skull and pediatric craniopharyngioma proton plans relative to VMAT

Purpose: Pediatric craniopharyngioma, adult base-of-skull sarcoma and chordoma cases are all regarded as priority candidates for proton therapy. In this study, a dosimetric comparison between volumetric modulated arc therapy (VMAT) and intensity modulated proton therapy (IMPT) was first performed. We then investigated the impact of physical and biological uncertainties. We assessed whether IMPT plans remained dosimetrically superior when such uncertainty estimates were considered, especially with regards to sparing organs at risk (OARs). Methodology: We studied 10 cases: four chondrosarcoma, two chordoma and four pediatric craniopharyngioma. VMAT and IMPT plans were created according to modality-specific protocols. For IMPT, we considered (i) variable RBE modeling using the McNamara model for different values of (a/b)x, and (ii) robustness analysis with ±3 mm set-up and 3.5% range uncertainties. Results: When comparing the VMAT and IMPT plans, the dosimetric advantages of IMPT were clear: IMPT led to reduced integral dose and, typically, improved CTV coverage given our OAR constraints. When physical robustness analysis was performed for IMPT, some uncertainty scenarios worsened the CTV coverage but not usually beyond that achieved by VMAT. Certain scenarios caused OAR constraints to be exceeded, particularly for the brainstem and optical chiasm. However, variable RBE modeling predicted even more substantial hotspots, especially for low values of (a/b)x. Variable RBE modeling often prompted dose constraints to be exceeded for critical structures. Conclusion: For base-of-skull and pediatric craniopharyngioma cases, both physical and biological robustness analyses should be considered for IMPT: these analyses can substantially affect the sparing of OARs and comparisons against VMAT. All proton RBE modeling is subject to high levels of uncertainty, but the clinical community should remain cognizant possible RBE effects. Careful clinical and imaging follow-up, plus further research on end-of-range RBE mitigation strategies such as LET optimization, should be prioritized for these cohorts of proton patients

VEMAP Phase 2 Bioclimatic Database. I. Gridded Historical (20th century) Climate for Modeling Ecosystem Dynamics Across the Conterminous USA

Analysis and simulation of biospheric responses to historical forcing require surface climate data that capture those aspects of climate that control ecological processes, including key spatial gradients and modes of temporal variability. We developed a multivariate, gridded historical climate dataset for the conterminous USA as a common input database for the Vegetation/Ecosystem Modeling and Analysis Project (VEMAP), a biogeochemical and dynamic vegetation model intercomparison. The dataset covers the period 1895-1993 on a 0.5° latitude/longitude grid. Climate is represented at both monthly and daily timesteps. Variables are: precipitation, mininimum and maximum temperature, total incident solar radiation, daylight-period irradiance, vapor pressure, and daylight-period relative humidity. The dataset was derived from US Historical Climate Network (HCN), cooperative network, and snowpack telemetry (SNOTEL) monthly precipitation and mean minimum and maximum temperature station data. We employed techniques that rely on geostatistical and physical relationships to create the temporally and spatially complete dataset. We developed a local kriging prediction model to infill discontinuous and limited-length station records based on spatial autocorrelation structure of climate anomalies. A spatial interpolation model (PRISM) that accounts for physiographic controls was used to grid the infilled monthly station data. We implemented a stochastic weather generator (modified WGEN) to disaggregate the gridded monthly series to dailies. Radiation and humidity variables were estimated from the dailies using a physically-based empirical surface climate model (MTCLIM3). Derived datasets include a 100 yr model spin-up climate and a historical Palmer Drought Severity Index (PDSI) dataset. The VEMAP dataset exhibits statistically significant trends in temperature, precipitation, solar radiation, vapor pressure, and PDSI for US National Assessment regions. The historical climate and companion datasets are available online at data archive centers

Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models. V. Further Results for the Square-Lattice Chromatic Polynomial

We derive some new structural results for the transfer matrix of square-lattice Potts models with free and cylindrical boundary conditions. In particular, we obtain explicit closed-form expressions for the dominant (at large |q|) diagonal entry in the transfer matrix, for arbitrary widths m, as the solution of a special one-dimensional polymer model. We also obtain the large-q expansion of the bulk and surface (resp. corner) free energies for the zero-temperature antiferromagnet (= chromatic polynomial) through order q^{-47} (resp. q^{-46}). Finally, we compute chromatic roots for strips of widths 9 <= m <= 12 with free boundary conditions and locate roughly the limiting curves.Comment: 111 pages (LaTeX2e). Includes tex file, three sty files, and 19 Postscript figures. Also included are Mathematica files data_CYL.m and data_FREE.m. Many changes from version 1: new material on series expansions and their analysis, and several proofs of previously conjectured results. Final version to be published in J. Stat. Phy