Likelihood Analysis of Power Spectra and Generalized Moment Problems

We develop an approach to spectral estimation that has been advocated by Ferrante, Masiero and Pavon and, in the context of the scalar-valued covariance extension problem, by Enqvist and Karlsson. The aim is to determine the power spectrum that is consistent with given moments and minimizes the relative entropy between the probability law of the underlying Gaussian stochastic process to that of a prior. The approach is analogous to the framework of earlier work by Byrnes, Georgiou and Lindquist and can also be viewed as a generalization of the classical work by Burg and Jaynes on the maximum entropy method. In the present paper we present a new fast algorithm in the general case (i.e., for general Gaussian priors) and show that for priors with a specific structure the solution can be given in closed form.Comment: 17 pages, 4 figure

Molecular diversity of arbuscular mycorrhizal fungi and patterns of host association over time and space in a tropical forest

We have used molecular techniques to investigate the diversity and distribution of the arbuscular mycorrhizal (AM) fungi colonizing tree seedling roots in the tropical forest on Barro Colorado Island (BCI), Republic of Panama. In the first year, we sampled newly emergent seedlings of the understory treelet Faramea occidentalis and the canopy emergent Tetragastris panamensis, from mixed seedling carpets at each of two sites. The following year we sampled surviving seedlings from these cohorts. The roots of 48 plants were analysed using AM fungal-specific primers to amplify and clone partial small subunit (SSU) ribosomal RNA gene sequences. Over 1300 clones were screened for random fragment length polymorphism (RFLP) variation and 7% of these were sequenced. Compared with AM fungal communities sampled from temperate habitats using the same method, the overall diversity was high, with a total of 30 AM fungal types identified. Seventeen of these types have not been recorded previously, with the remainder being similar to types reported from temperate habitats. The tropical mycorrhizal population showed significant spatial heterogeneity and nonrandom associations with the different hosts. Moreover there was a strong shift in the mycorrhizal communities over time. AM fungal types that were dominant in the newly germinated seedlings were almost entirely replaced by previously rare types in the surviving seedlings the following year. The high diversity and huge variation detected across time points, sites and hosts, implies that the AM fungal types are ecologically distinct and thus may have the potential to influence recruitment and host composition in tropical forests

Arbuscular mycorrhizal community composition associated with two plant species in a grassland ecosystem

Arbuscular mycorrhizal (AM) fungi are biotrophic symbionts colonizing about two-thirds of land plant species and found in all ecosystems. They are of major importance in plant nutrient supply and their diversity is suggested to be an important determinant of plant community composition. The diversity of the AM fungal community composition in the roots of two plant species (Agrostis capillaris and Trifolium repens) that co-occurred in the same grassland ecosystem was characterized using molecular techniques. We analysed the small subunit (SSU) ribosomal RNA gene amplified from a total root DNA extract using AM fungal-specific primers. A total of 2001 cloned fragments from 47 root samples obtained on four dates were analysed by restriction fragment length polymorphism, and 121 of them were sequenced. The diversity found was high: a total of 24 different phylotypes (groups of phylogenetically related sequences) colonized the roots of the two host species. Phylogenetic analyses demonstrate that 19 of these phylotypes belonged to the Glomaceae, three to the Acaulosporaceae and two to the Gigasporaceae. Our study reveals clearly that the AM fungal community colonizing T. repens differed from that colonizing A. capillaris, providing evidence for AM fungal host preference. In addition, our results reveal dynamic changes in the AM fungal community through time

Partial Enumerative Sphere Shaping

The dependency between the Gaussianity of the input distribution for the additive white Gaussian noise (AWGN) channel and the gap-to-capacity is discussed. We show that a set of particular approximations to the Maxwell-Boltzmann (MB) distribution virtually closes most of the shaping gap. We relate these symbol-level distributions to bit-level distributions, and demonstrate that they correspond to keeping some of the amplitude bit-levels uniform and independent of the others. Then we propose partial enumerative sphere shaping (P-ESS) to realize such distributions in the probabilistic amplitude shaping (PAS) framework. Simulations over the AWGN channel exhibit that shaping 2 amplitude bits of 16-ASK have almost the same performance as shaping 3 bits, which is 1.3 dB more power-efficient than uniform signaling at a rate of 3 bit/symbol. In this way, required storage and computational complexity of shaping are reduced by factors of 6 and 3, respectively.Comment: 6 pages, 6 figure

Probabilistic Shaping for Finite Blocklengths: Distribution Matching and Sphere Shaping

In this paper, we provide for the first time a systematic comparison of distribution matching (DM) and sphere shaping (SpSh) algorithms for short blocklength probabilistic amplitude shaping. For asymptotically large blocklengths, constant composition distribution matching (CCDM) is known to generate the target capacity-achieving distribution. As the blocklength decreases, however, the resulting rate loss diminishes the efficiency of CCDM. We claim that for such short blocklengths and over the additive white Gaussian channel (AWGN), the objective of shaping should be reformulated as obtaining the most energy-efficient signal space for a given rate (rather than matching distributions). In light of this interpretation, multiset-partition DM (MPDM), enumerative sphere shaping (ESS) and shell mapping (SM), are reviewed as energy-efficient shaping techniques. Numerical results show that MPDM and SpSh have smaller rate losses than CCDM. SpSh--whose sole objective is to maximize the energy efficiency--is shown to have the minimum rate loss amongst all. We provide simulation results of the end-to-end decoding performance showing that up to 1 dB improvement in power efficiency over uniform signaling can be obtained with MPDM and SpSh at blocklengths around 200. Finally, we present a discussion on the complexity of these algorithms from the perspective of latency, storage and computations.Comment: 18 pages, 10 figure

Predictability of evolutionary trajectories in fitness landscapes

Experimental studies on enzyme evolution show that only a small fraction of all possible mutation trajectories are accessible to evolution. However, these experiments deal with individual enzymes and explore a tiny part of the fitness landscape. We report an exhaustive analysis of fitness landscapes constructed with an off-lattice model of protein folding where fitness is equated with robustness to misfolding. This model mimics the essential features of the interactions between amino acids, is consistent with the key paradigms of protein folding and reproduces the universal distribution of evolutionary rates among orthologous proteins. We introduce mean path divergence as a quantitative measure of the degree to which the starting and ending points determine the path of evolution in fitness landscapes. Global measures of landscape roughness are good predictors of path divergence in all studied landscapes: the mean path divergence is greater in smooth landscapes than in rough ones. The model-derived and experimental landscapes are significantly smoother than random landscapes and resemble additive landscapes perturbed with moderate amounts of noise; thus, these landscapes are substantially robust to mutation. The model landscapes show a deficit of suboptimal peaks even compared with noisy additive landscapes with similar overall roughness. We suggest that smoothness and the substantial deficit of peaks in the fitness landscapes of protein evolution are fundamental consequences of the physics of protein folding.Comment: 14 pages, 7 figure

Majority-efficiency and Competition-efficiency in a Binary Policy Model

We introduce a general framework in which politicians choose a (possibly infinite) sequence of binary policies. The two competing candidates are exogenously committed to particular actions on a subset of these issues, while they can choose any policy for the remaining issues to maximize their winning probability. Citizens have general preferences over policies, and the distribution of preferences may be uncertain. We show that a special case of the model, the weighted-issue model, provides a tractable multidimensional model of candidate competition that can generate (i) policy divergence in pure and mixed strategies, (ii) adoption of minority positions, and (iii) inefficient outcomes.multidimensional policy, voting, citizen-candidate, normative analysis of political competition

Decoding coalescent hidden Markov models in linear time

In many areas of computational biology, hidden Markov models (HMMs) have been used to model local genomic features. In particular, coalescent HMMs have been used to infer ancient population sizes, migration rates, divergence times, and other parameters such as mutation and recombination rates. As more loci, sequences, and hidden states are added to the model, however, the runtime of coalescent HMMs can quickly become prohibitive. Here we present a new algorithm for reducing the runtime of coalescent HMMs from quadratic in the number of hidden time states to linear, without making any additional approximations. Our algorithm can be incorporated into various coalescent HMMs, including the popular method PSMC for inferring variable effective population sizes. Here we implement this algorithm to speed up our demographic inference method diCal, which is equivalent to PSMC when applied to a sample of two haplotypes. We demonstrate that the linear-time method can reconstruct a population size change history more accurately than the quadratic-time method, given similar computation resources. We also apply the method to data from the 1000 Genomes project, inferring a high-resolution history of size changes in the European population.Comment: 18 pages, 5 figures. To appear in the Proceedings of the 18th Annual International Conference on Research in Computational Molecular Biology (RECOMB 2014). The final publication is available at link.springer.co