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Register a new userA New Approach to the Small Phylogeny Problem
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In the small phylogeny problem we, are given a phylogenetic tree and gene orders of the extant species and our goal is to reconstruct all of the ancestral genomes so that the number of evolutionary operations is minimized. Algorithms for reconstructing evolutionary history from gene orders are usually based on repeatedly computing medians of genomes at neighbouring vertices of the tree. We propose a new, more general approach, based on an iterative local optimization procedure. In each step, we propose candidates for ancestral genomes and choose the best ones by dynamic programming. We have implemented our method and used it to reconstruct evolutionary history of 16 yeast mtDNAs and 13 Campanulaceae cpDNAs.
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Optimally selecting a subset of targets from a larger catalog is a common problem in astronomy and cosmology. A specific example is the selection of targets from an imaging survey for multi-object spectrographic follow-up. We present a new heuristic algorithm, HYBRID, for this purpose and undertake detailed studies of its performance. HYBRID combines elements of the simulated annealing, MCMC and particle-swarm methods and is particularly successful in cases where the survey landscape has multiple curvature or clustering scales. HYBRID consistently outperforms the other methods, especially in high-dimensionality spaces with many extrema. This means many fewer simulations must be run to reach a given performance confidence level and implies very significant advantages in solving complex or computationally expensive optimisation problems.
We address the Merton problem of maximizing the expected utility of terminal wealth using techniques from variational analysis. Under a general continuous semimartingale market model with stochastic parameters, we obtain a characterization of the optimal portfolio for general utility functions in terms of a forward-backward stochastic differential equation (FBSDE) and derive solutions for a number of well-known utility functions. Our results complement a previous studies conducted on optimal strategies in markets driven by Brownian noise with random drift and volatility parameters.
A great variety of complex physical, natural and artificial systems are governed by statistical distributions, which often follow a standard exponential function in the bulk, while their tail obeys the Pareto power law. The recently introduced $kappa$-statistics framework predicts distribution functions with this feature. A growing number of applications in different fields of investigation are beginning to prove the relevance and effectiveness of $kappa$-statistics in fitting empirical data. In this paper, we use $kappa$-statistics to formulate a statistical approach for epidemiological analysis. We validate the theoretical results by fitting the derived $kappa$-Weibull distributions with data from the plague pandemic of 1417 in Florence as well as data from the COVID-19 pandemic in China over the entire cycle that concludes in April 16, 2020. As further validation of the proposed approach we present a more systematic analysis of COVID-19 data from countries such as Germany, Italy, Spain and United Kingdom, obtaining very good agreement between theoretical predictions and empirical observations. For these countries we also study the entire first cycle of the pandemic which extends until the end of July 2020. The fact that both the data of the Florence plague and those of the Covid-19 pandemic are successfully described by the same theoretical model, even though the two events are caused by different diseases and they are separated by more than 600 years, is evidence that the $kappa$-Weibull model has universal features.
We point out that in theories where the gravitino mass, $M_{3/2}$, is in the range (10-50)TeV, with soft-breaking scalar masses and trilinear couplings of the same order, there exists a robust region of parameter space where the conditions for electroweak symmetry breaking (EWSB) are satisfied without large imposed cancellations. Compactified string/M-theory with stabilized moduli that satisfy cosmological constraints generically require a gravitino mass greater than about 30 TeV and provide the natural explanation for this phenomenon. We find that even though scalar masses and trilinear couplings (and the soft-breaking $B$ parameter) are of order (10-50)TeV, the Higgs vev takes its expected value and the $mu$ parameter is naturally of order a TeV. The mechanism provides a natural solution to the cosmological moduli and gravitino problems with EWSB.
Given the Thomas-Fermi equation sqrt(x)phi=phi*(3/2), this paper changes first the dependent variable by defining y(x)=sqrt(x phi(x)). The boundary conditions require that y(x) must vanish at the origin as sqrt(x), whereas it has a fall-off behaviour at infinity proportional to the power (1/2)(1-chi) of the independent variable x, chi being a positive number. Such boundary conditions lead to a 1-parameter family of approximate solutions in the form sqrt(x) times a ratio of finite linear combinations of integer and half-odd powers of x. If chi is set equal to 3, in order to agree exactly with the asymptotic solution of Sommerfeld, explicit forms of the approximate solution are obtained for all values of x. They agree exactly with the Majorana solution at small x, and remain very close to the numerical solution for all values of x. Remarkably, without making any use of series, our approximate solutions achieve a smooth transition from small-x to large-x behaviour. Eventually, the generalized Thomas-Fermi equation that includes relativistic, non-extensive and thermal effects is studied, finding approximate solutions at small and large x for small or finite values of the physical parameters in this equation.
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