Arnold Polanski

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We explore mathematical properties of models of cancer chemotherapy including cell-cycle dependence. Using the mathematical methods of control theory, we demonstrate two assertions of interest for the biomedical community: 1 Periodic chemotherapy protocols are close to the optimum for a wide class of models and have additional favourable properties. 2 Two(More)
Expressions for marginal distributions of times in the time-varying coalescence process are derived. The proposed method allows also for computation of joint probability distribution for pairs, triples, etc. of coalescence times. The expressions derived are useful for (1) extending several statistics from time constant to time-varying case, (2) increasing(More)
We present new methodology for calculating sampling distributions of single-nucleotide polymorphism (SNP) frequencies in populations with time-varying size. Our approach is based on deriving analytical expressions for frequencies of SNPs. Analytical expressions allow for computations that are faster and more accurate than Monte Carlo simulations. In(More)
Distribution of pairwise differences of nucleotides from data on a sample of DNA sequences from a given segment of the genome has been used in the past to draw inferences about the past history of population size changes. However, all earlier methods assume a given model of population size changes (such as sudden expansion), parameters of which (e.g., time(More)
Myotonic dystrophy (DM), an autosomal dominant neurological disorder, is caused by CTG-repeat expansions at the DMPK locus, with affected individuals having > or = 50 repeats of this trinucleotide. Reduced reproductive fitness of affected individuals and decreased viability of congenital DM have been noted. Expanded CTG-repeat alleles are highly unstable,(More)
We revisit the classical result that financing a pure public good through taxation of private consumption is inefficient. To this standard setup we add a consumption contest in which consumers can win a prize. We show that an appropriately chosen contest—which we call a ‘tax lottery’—can correct the distortion in private consumption while, at the same time,(More)
We propose two simple evaluation methods for time varying density forecasts of continuous higher dimensional random variables. Both methods are based on the probability integral transformation for unidimensional forecasts. The first method tests multinormal densities and relies on the rotation of the coordinate system. The advantage of the second method is(More)