Affine and toric hyperplane arrangements

We extend the Billera-Ehrenborg-Readdy map between the intersection lattice and face lattice of a central hyperplane arrangement to affine and toric hyperplane arrangements. For arrangements on the torus, we also generalize Zaslavsky's fundamental results on the number of regions.Comment: 32 pages, 4 figure

Effect of renal center characteristics on mortality and technique failure on peritoneal dialysis

BACKGROUND: Recent studies report decreased mortality in patients on peritoneal dialysis (PD) over time, suggesting that advances in PD have resulted in improved patient outcomes. Our investigation sought to assess the effect of renal center characteristics on mortality and technique failure (TF) rates. METHODS: Covariates of interest included center-specific cumulative number of PD patients treated, percentage of patients who initiated dialysis on PD, and academic status. Using data obtained from the Canadian Organ Replacement Register, the 17,900 patients who received PD during the 1981 to 1997 period were studied. Mortality and TF rate ratios (RR) were estimated using Poisson regression, adjusting for age, gender, race, primary renal diagnosis, province, follow-up time, and type of PD. RESULTS: As the cumulative number of PD patients treated increased, covariate-adjusted mortality significantly decreased (P < 0.05); a weaker yet significant association was observed between number of PD patients treated and TF. As the percentage of patients initiating dialysis on PD increased, TF rates decreased significantly. No association was observed between center academic status and PD mortality or TF rates. CONCLUSIONS: These results imply that a center's experience with and degree of specialization toward PD impact strongly on PD outcomes. One hypothesis is that a center's propensity to exploit technical and non-technical advances in PD increases directly with these variables. It is also possible that, through experience, centers become more adept at identifying appropriate patients to receive PD. More detailed research is required to evaluate these hypotheses

Effect of renal center characteristics on mortality and technique failure on peritoneal dialysis

BACKGROUND: Recent studies report decreased mortality in patients on peritoneal dialysis (PD) over time, suggesting that advances in PD have resulted in improved patient outcomes. Our investigation sought to assess the effect of renal center characteristics on mortality and technique failure (TF) rates. METHODS: Covariates of interest included center-specific cumulative number of PD patients treated, percentage of patients who initiated dialysis on PD, and academic status. Using data obtained from the Canadian Organ Replacement Register, the 17,900 patients who received PD during the 1981 to 1997 period were studied. Mortality and TF rate ratios (RR) were estimated using Poisson regression, adjusting for age, gender, race, primary renal diagnosis, province, follow-up time, and type of PD. RESULTS: As the cumulative number of PD patients treated increased, covariate-adjusted mortality significantly decreased (P < 0.05); a weaker yet significant association was observed between number of PD patients treated and TF. As the percentage of patients initiating dialysis on PD increased, TF rates decreased significantly. No association was observed between center academic status and PD mortality or TF rates. CONCLUSIONS: These results imply that a center's experience with and degree of specialization toward PD impact strongly on PD outcomes. One hypothesis is that a center's propensity to exploit technical and non-technical advances in PD increases directly with these variables. It is also possible that, through experience, centers become more adept at identifying appropriate patients to receive PD. More detailed research is required to evaluate these hypotheses

Damage Spreading During Domain Growth

We study damage spreading in models of two-dimensional systems undergoing first order phase transitions. We consider several models from the same non-conserved order parameter universality class, and find unexpected differences between them. An exact solution of the Ohta-Jasnow-Kawasaki model yields the damage growth law $D \sim t^{\phi}$, where $\phi = t^{d/4}$ in $d$ dimensions. In contrast, time-dependent Ginzburg-Landau simulations and Ising simulations in $d= 2$ using heat-bath dynamics show power-law growth, but with an exponent of approximately $0.36$, independent of the system sizes studied. In marked contrast, Metropolis dynamics shows damage growing via $\phi \sim 1$, although the damage difference grows as $t^{0.4}$. PACS: 64.60.-i, 05.50.+qComment: 4 pags of revtex3 + 3 postscript files appended as a compressed and uuencoded file. UIB940320

Self-Organized Branching Processes: A Mean-Field Theory for Avalanches

We discuss mean-field theories for self-organized criticality and the connection with the general theory of branching processes. We point out that the nature of the self-organization is not addressed properly by the previously proposed mean-field theories. We introduce a new mean-field model that explicitly takes the boundary conditions into account; in this way, the local dynamical rules are coupled to a global equation that drives the control parameter to its critical value. We study the model numerically, and analytically we compute the avalanche distributions.Comment: 4 pages + 4 ps figure

Uniform random generation of large acyclic digraphs

Directed acyclic graphs are the basic representation of the structure underlying Bayesian networks, which represent multivariate probability distributions. In many practical applications, such as the reverse engineering of gene regulatory networks, not only the estimation of model parameters but the reconstruction of the structure itself is of great interest. As well as for the assessment of different structure learning algorithms in simulation studies, a uniform sample from the space of directed acyclic graphs is required to evaluate the prevalence of certain structural features. Here we analyse how to sample acyclic digraphs uniformly at random through recursive enumeration, an approach previously thought too computationally involved. Based on complexity considerations, we discuss in particular how the enumeration directly provides an exact method, which avoids the convergence issues of the alternative Markov chain methods and is actually computationally much faster. The limiting behaviour of the distribution of acyclic digraphs then allows us to sample arbitrarily large graphs. Building on the ideas of recursive enumeration based sampling we also introduce a novel hybrid Markov chain with much faster convergence than current alternatives while still being easy to adapt to various restrictions. Finally we discuss how to include such restrictions in the combinatorial enumeration and the new hybrid Markov chain method for efficient uniform sampling of the corresponding graphs.Comment: 15 pages, 2 figures. To appear in Statistics and Computin

End-stage renal disease in Canada: prevalence projections to 2005

BACKGROUND: The incidence and prevalence of end-stage renal disease (ESRD) have increased greatly in Canada over the last 2 decades. Because of the high cost of therapy, predicting numbers of patients who will require dialysis and transplantation is necessary for nephrologists and health care planners. METHODS: The authors projected ESRD incidence rates and therapy-specific prevalence by province to the year 2005 using 1981-1996 data obtained from the Canadian Organ Replacement Register. The model incorporated Poisson regression to project incidence rates, and a Markov model for patient follow-up. RESULTS: Continued large increases in ESRD incidence and prevalence were projected, particularly among people with diabetes mellitus. As of Dec. 31, 1996, there were 17,807 patients receiving renal replacement therapy in Canada. This number was projected to climb to 32,952 by the end of 2005, for a relative increase of 85% and a mean annual increase of 5.8%. The increased prevalence was projected to be greatest for peritoneal dialysis (6.0% annually), followed by hemodialysis (5.9%) and functioning kidney transplant (5.7%). The projected annual increases in prevalence by province ranged from 4.4%, in Saskatchewan, to 7.5%, in Alberta. INTERPRETATION: The projected increases are plausible when one considers that the incidence of ESRD per million population in the United States and other countries far exceeds that in Canada. The authors predict a continued and increasing short-fall in resources to accommodate the expected increased in ESRD prevalence

Hopf algebras and Markov chains: Two examples and a theory

The operation of squaring (coproduct followed by product) in a combinatorial Hopf algebra is shown to induce a Markov chain in natural bases. Chains constructed in this way include widely studied methods of card shuffling, a natural "rock-breaking" process, and Markov chains on simplicial complexes. Many of these chains can be explictly diagonalized using the primitive elements of the algebra and the combinatorics of the free Lie algebra. For card shuffling, this gives an explicit description of the eigenvectors. For rock-breaking, an explicit description of the quasi-stationary distribution and sharp rates to absorption follow.Comment: 51 pages, 17 figures. (Typographical errors corrected. Further fixes will only appear on the version on Amy Pang's website, the arXiv version will not be updated.

Application of Pauli-Villars regularization and discretized light-cone quantization to a single-fermion truncation of Yukawa theory

We apply Pauli-Villars regularization and discretized light-cone quantization to the nonperturbative solution of (3+1)-dimensional Yukawa theory in a single-fermion truncation. Three heavy scalars, including two with negative norm, are used to regulate the theory. The matrix eigenvalue problem is solved for the lowest-mass state with use of a new, indefinite-metric Lanczos algorithm. Various observables are extracted from the wave functions, including average multiplicities and average momenta of constituents, structure functions, and a form factor slope.Comment: 21 pages, 7 figures, RevTeX; published version: more extensive data in the tables of v