Fock factorizations, and decompositions of the L2L^2 spaces over general Levy processes

We explicitly construct and study an isometry between the spaces of square integrable functionals of an arbitrary Levy process and a vector-valued Gaussian white noise. In particular, we obtain explicit formulas for this isometry at the level of multiplicative functionals and at the level of orthogonal decompositions, as well as find its kernel. We consider in detail the central special case: the isometry between the $L^2$ spaces over a Poisson process and the corresponding white noise. The key role in our considerations is played by the notion of measure and Hilbert factorizations and related notions of multiplicative and additive functionals and logarithm. The obtained results allow us to introduce a canonical Fock structure (an analogue of the Wiener--Ito decomposition) in the $L^2$ space over an arbitrary Levy process. An application to the representation theory of current groups is considered. An example of a non-Fock factorization is given.Comment: 35 pages; LaTeX; to appear in Russian Math. Survey

How the instability of ranks under long memory affects large-sample inference

Under long memory, the limit theorems for normalized sums of random variables typically involve a positive integer called "Hermite rank". There is a different limit for each Hermite rank. From a statistical point of view, however, we argue that a rank other than one is unstable, whereas, a rank equal to one is stable. We provide empirical evidence supporting this argument. This has important consequences. Assuming a higher-order rank when it is not really there usually results in underestimating the order of the fluctuations of the statistic of interest. We illustrate this through various examples involving the sample variance, the empirical processes and the Whittle estimator.Accepted manuscrip

Currency Derivatives under a Minimal Market Model with Random Scaling

This paper uses an alternative, parsimonious stochastic volatility model to describe the dynamics of a currency market for the pricing and hedging of derivatives. Time transformed squared Bessel processes are the basic driving factors of the minimal market model. The time transformation is characterized by a random scaling, which provides for realistic exchange rate dynamics. The pricing of standard European options is studied. In particular, it is shown that the model produces implied volatility surfaces that are typically observed in real markets.currency derivatives; stochastic volatility; random scaling; minimal market model

Building Predictive Models in R Using the caret Package

The caret package, short for classification and regression training, contains numerous tools for developing predictive models using the rich set of models available in R. The package focuses on simplifying model training and tuning across a wide variety of modeling techniques. It also includes methods for pre-processing training data, calculating variable importance, and model visualizations. An example from computational chemistry is used to illustrate the functionality on a real data set and to benchmark the benefits of parallel processing with several types of models.

Río de la Plata Grasslands: how did land-cover and ecosystem functioning change in the 21st century?

The Río de la Plata Grasslands region is one of the largest plains in the world, covering a significant portion of the southern Brazilian grasslands. This temperate sub-humid region is also one of the most diverse grassland areas globally. However, in the last decades, important land-use and land-cover changes occurred threatening the natural ecosystem and the provision of essential ecosystem services. In this chapter, we provide an overview of the primary land-use and land-cover changes that have occurred in this region over the last two decades. We also discuss some of the consequences derived from these changes on the ecosystem functioning, the supply of ecosystem services, and the human appropriation of primary production. Finally, we evaluate the observed transition trends among land-use and land-covers and speculate on the most likely changes that may occur in the next few years.Agencia Nacional de Investigación e Innovació

The ecology of palm genomes: repeat-associated genome size expansion is constrained by aridity

Genome size varies 2400-fold across plants, influencing their evolution through changes in cell size and cell division rates which impact plants' environmental stress tolerance. Repetitive element expansion explains much genome size diversity, and the processes structuring repeat "communities" are analogous to those structuring ecological communities. However, which environmental stressors influence repeat community dynamics has not yet been examined from an ecological perspective. We measured genome size and leveraged climatic data for 91% of genera within the ecologically diverse palm family (Arecaceae). We then generated genomic repeat profiles for 141 palm species, and analysed repeats using phylogenetically informed linear models to explore relationships between repeat dynamics and environmental factors. We show that palm genome size and repeat "community" composition are best explained by aridity. Specifically, Ty3-gypsy and TIR elements were more abundant in palm species from wetter environments, which generally had larger genomes, suggesting amplification. By contrast, Ty1-copia and LINE elements were more abundant in drier environments. Our results suggest that water stress inhibits repeat expansion through selection on upper genome size limits. However, elements that may associate with stress-response genes (e.g. Ty1-copia) have amplified in arid-adapted palm species. Overall, we provide novel evidence of climate influencing the assembly of repeat "communities".JP was supported by a Ramón y Cajal Fellowship (RYC-2017-2274) funded by MCIN/AEI/10.13039/501100011033 and by ‘ESF Investing in your future’. SB was funded by a Garfield Weston Foundation postdoctoral fellowship. PN and JM were supported by the ELIXIR CZ Research Infrastructure Project (Czech Ministry of Education, Youth and Sports; grant no. LM2018131).IntroductionMaterials and Methods Plant material collection and genome size measurement Phylogenetic, environmental and genomic data collection Modelling relationships between genome size and environmental variables DNA repeat profiling Assessing repeat dynamics in palm genomesResults Palm genome size variation Aridity preferences of palm species help explain genome size variation Ecological metrics of palm repeat ‘communities’ vary with genome size Repeat abundances correlate with genome size Aridity preferences of palm species explain abundances of certain repeat lineagesDiscussion Palm genome size variation Aridity thresholds best explain palm genome size diversity The ‘community ecology’ of repeats correlates with genome size Repeat dynamics may be modulated by aridityConclusionsAcknowledgementsAuthor contributionsPeer reviewe

Exome resequencing and GWAS for growth, ecophysiology, and chemical and metabolomic composition of wood of Populus trichocarpa.

BackgroundPopulus trichocarpa is an important forest tree species for the generation of lignocellulosic ethanol. Understanding the genomic basis of biomass production and chemical composition of wood is fundamental in supporting genetic improvement programs. Considerable variation has been observed in this species for complex traits related to growth, phenology, ecophysiology and wood chemistry. Those traits are influenced by both polygenic control and environmental effects, and their genome architecture and regulation are only partially understood. Genome wide association studies (GWAS) represent an approach to advance that aim using thousands of single nucleotide polymorphisms (SNPs). Genotyping using exome capture methodologies represent an efficient approach to identify specific functional regions of genomes underlying phenotypic variation.ResultsWe identified 813 K SNPs, which were utilized for genotyping 461 P. trichocarpa clones, representing 101 provenances collected from Oregon and Washington, and established in California. A GWAS performed on 20 traits, considering single SNP-marker tests identified a variable number of significant SNPs (p-value < 6.1479E-8) in association with diameter, height, leaf carbon and nitrogen contents, and δ15N. The number of significant SNPs ranged from 2 to 220 per trait. Additionally, multiple-marker analyses by sliding-windows tests detected between 6 and 192 significant windows for the analyzed traits. The significant SNPs resided within genes that encode proteins belonging to different functional classes as such protein synthesis, energy/metabolism and DNA/RNA metabolism, among others.ConclusionsSNP-markers within genes associated with traits of importance for biomass production were detected. They contribute to characterize the genomic architecture of P. trichocarpa biomass required to support the development and application of marker breeding technologies