Descartes' rule of signs and the identifiability of population demographic models from genomic variation data

The sample frequency spectrum (SFS) is a widely-used summary statistic of genomic variation in a sample of homologous DNA sequences. It provides a highly efficient dimensional reduction of large-scale population genomic data and its mathematical dependence on the underlying population demography is well understood, thus enabling the development of efficient inference algorithms. However, it has been recently shown that very different population demographies can actually generate the same SFS for arbitrarily large sample sizes. Although in principle this nonidentifiability issue poses a thorny challenge to statistical inference, the population size functions involved in the counterexamples are arguably not so biologically realistic. Here, we revisit this problem and examine the identifiability of demographic models under the restriction that the population sizes are piecewise-defined where each piece belongs to some family of biologically-motivated functions. Under this assumption, we prove that the expected SFS of a sample uniquely determines the underlying demographic model, provided that the sample is sufficiently large. We obtain a general bound on the sample size sufficient for identifiability; the bound depends on the number of pieces in the demographic model and also on the type of population size function in each piece. In the cases of piecewise-constant, piecewise-exponential and piecewise-generalized-exponential models, which are often assumed in population genomic inferences, we provide explicit formulas for the bounds as simple functions of the number of pieces. Lastly, we obtain analogous results for the "folded" SFS, which is often used when there is ambiguity as to which allelic type is ancestral. Our results are proved using a generalization of Descartes' rule of signs for polynomials to the Laplace transform of piecewise continuous functions.Comment: Published in at http://dx.doi.org/10.1214/14-AOS1264 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Understanding contextualised rational action - author's response

Understanding contextualised rational action - author's respons

A novel spectral method for inferring general diploid selection from time series genetic data

The increased availability of time series genetic variation data from experimental evolution studies and ancient DNA samples has created new opportunities to identify genomic regions under selective pressure and to estimate their associated fitness parameters. However, it is a challenging problem to compute the likelihood of nonneutral models for the population allele frequency dynamics, given the observed temporal DNA data. Here, we develop a novel spectral algorithm to analytically and efficiently integrate over all possible frequency trajectories between consecutive time points. This advance circumvents the limitations of existing methods which require fine-tuning the discretization of the population allele frequency space when numerically approximating requisite integrals. Furthermore, our method is flexible enough to handle general diploid models of selection where the heterozygote and homozygote fitness parameters can take any values, while previous methods focused on only a few restricted models of selection. We demonstrate the utility of our method on simulated data and also apply it to analyze ancient DNA data from genetic loci associated with coat coloration in horses. In contrast to previous studies, our exploration of the full fitness parameter space reveals that a heterozygote advantage form of balancing selection may have been acting on these loci.Comment: Published in at http://dx.doi.org/10.1214/14-AOAS764 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Market regulation and firm performance: the case of smoking bans in the UK

This paper analyzes the effects of a ban on smoking in public places upon firms and consumers. It presents a theoretical model and tests its predictions using unique data from before and after the introduction of smoking bans in the UK. Cigarette smoke is a public bad, and smokers and non-smokers differ in their valuation of smoke-free amenities. Consumer heterogeneity implies that the market equilibrium may result in too much uniformity, whereas social optimality requires a mix of smoking and non-smoking pubs (which can be operationalized via licensing). If the market equilibrium has almost all pubs permitting smoking (as is the case in the data) then a blanket ban reduces pub sales, profits, and consumer welfare. We collect survey data from public houses and find that the Scottish smoking ban (introduced in March 2006) reduced pub sales and harmed medium run profitability. An event study analysis of the stock market performance of pub-holding companies corroborates the negative effects of the smoking ban on firm performance

Holomorphic Bisectional Curvatures, Supersymmetry Breaking, and Affleck-Dine Baryogenesis

Working in $D=4, N=1$ supergravity, we utilize relations between holomorphic sectional and bisectional curvatures of Kahler manifolds to constrain Affleck-Dine baryogenesis. We show the following No-Go result: Affleck-Dine baryogenesis cannot be performed if the holomorphic sectional curvature at the origin is isotropic in tangent space; as a special case, this rules out spaces of constant holomorphic sectional curvature (defined in the above sense) and in particular maximally symmetric coset spaces. We also investigate scenarios where inflationary supersymmetry breaking is identified with the supersymmetry breaking responsible for mass splitting in the visible sector, using conditions of sequestering to constrain manifolds where inflation can be performed.Comment: 9 page

Multiflow Transmission in Delay Constrained Cooperative Wireless Networks

This paper considers the problem of energy-efficient transmission in multi-flow multihop cooperative wireless networks. Although the performance gains of cooperative approaches are well known, the combinatorial nature of these schemes makes it difficult to design efficient polynomial-time algorithms for joint routing, scheduling and power control. This becomes more so when there is more than one flow in the network. It has been conjectured by many authors, in the literature, that the multiflow problem in cooperative networks is an NP-hard problem. In this paper, we formulate the problem, as a combinatorial optimization problem, for a general setting of $k$-flows, and formally prove that the problem is not only NP-hard but it is $o(n^{1/7-\epsilon})$ inapproxmiable. To our knowledge*, these results provide the first such inapproxmiablity proof in the context of multiflow cooperative wireless networks. We further prove that for a special case of k = 1 the solution is a simple path, and devise a polynomial time algorithm for jointly optimizing routing, scheduling and power control. We then use this algorithm to establish analytical upper and lower bounds for the optimal performance for the general case of $k$ flows. Furthermore, we propose a polynomial time heuristic for calculating the solution for the general case and evaluate the performance of this heuristic under different channel conditions and against the analytical upper and lower bounds.Comment: 9 pages, 5 figure

Transverse Mass Distribution Characteristics of π0\pi^0 Production in 208^{208}Pb-induced Reactions and the Combinational Approach

The nature of invariant cross-sections and multiplicities in some $^{208}Pb$-induced reactions and some important ratio-behaviours of the invariant multiplicities for various centralities of the collision will here be dealt with in the light of a combinational approach which has been built up in the recent past by the present authors. Next, the results would be compared with the outcome of some of the simulation-based standard models for multiple production in nuclear collisions at high energies. Finally, the implications of all this would be discussed.Comment: 14 pages, 14 figures, a few changes have been made in the tex

A Simple Testable Model of Baryon Number Violation: Baryogenesis, Dark Matter, Neutron-Antineutron Oscillation and Collider Signals

We study a simple TeV-scale model of baryon number violation which explains the observed proximity of the dark matter and baryon abundances. The model has constraints arising from both low and high-energy processes, and in particular, predicts a sizable rate for the neutron-antineutron ($n-\bar{n}$) oscillation at low energy and the monojet signal at the LHC. We find an interesting complementarity among the constraints arising from the observed baryon asymmetry, ratio of dark matter and baryon abundances, $n-\bar{n}$ oscillation lifetime and the LHC monojet signal. There are regions in the parameter space where the $n-\bar{n}$ oscillation lifetime is found to be more constraining than the LHC constraints, which illustrates the importance of the next-generation $n-\bar{n}$ oscillation experiments.Comment: 8 pages, 4 figures; minor changes, version to appear in Phys. Lett.