Sharp error terms for return time statistics under mixing conditions

We describe the statistics of repetition times of a string of symbols in a stochastic process. Denote by T(A) the time elapsed until the process spells the finite string A and by S(A) the number of consecutive repetitions of A. We prove that, if the length of the string grows unbondedly, (1) the distribution of T(A), when the process starts with A, is well aproximated by a certain mixture of the point measure at the origin and an exponential law, and (2) S(A) is approximately geometrically distributed. We provide sharp error terms for each of these approximations. The errors we obtain are point-wise and allow to get also approximations for all the moments of T(A) and S(A). To obtain (1) we assume that the process is phi-mixing while to obtain (2) we assume the convergence of certain contidional probabilities

On the entropy production of time series with unidirectional linearity

There are non-Gaussian time series that admit a causal linear autoregressive moving average (ARMA) model when regressing the future on the past, but not when regressing the past on the future. The reason is that, in the latter case, the regression residuals are only uncorrelated but not statistically independent of the future. In previous work, we have experimentally verified that many empirical time series indeed show such a time inversion asymmetry. For various physical systems, it is known that time-inversion asymmetries are linked to the thermodynamic entropy production in non-equilibrium states. Here we show that such a link also exists for the above unidirectional linearity. We study the dynamical evolution of a physical toy system with linear coupling to an infinite environment and show that the linearity of the dynamics is inherited to the forward-time conditional probabilities, but not to the backward-time conditionals. The reason for this asymmetry between past and future is that the environment permanently provides particles that are in a product state before they interact with the system, but show statistical dependencies afterwards. From a coarse-grained perspective, the interaction thus generates entropy. We quantitatively relate the strength of the non-linearity of the backward conditionals to the minimal amount of entropy generation.Comment: 16 page

A strong pair correlation bound implies the CLT for Sinai Billiards

For Dynamical Systems, a strong bound on multiple correlations implies the Central Limit Theorem (CLT) [ChMa]. In Chernov's paper [Ch2], such a bound is derived for dynamically Holder continuous observables of dispersing Billiards. Here we weaken the regularity assumption and subsequently show that the bound on multiple correlations follows directly from the bound on pair correlations. Thus, a strong bound on pair correlations alone implies the CLT, for a wider class of observables. The result is extended to Anosov diffeomorphisms in any dimension.Comment: 13 page

The compound Poisson limit ruling periodic extreme behaviour of non-uniformly hyperbolic dynamics

We prove that the distributional limit of the normalised number of returns to small neighbourhoods of periodic points of non-uniformly hyperbolic dynamical systems is compound Poisson. The returns to small balls around a fixed point in the phase space correspond to the occurrence of rare events, or exceedances of high thresholds, so that there is a connection between the laws of Return Times Statistics and Extreme Value Laws. The fact that the fixed point in the phase space is a repelling periodic point implies that there is a tendency for the exceedances to appear in clusters whose average sizes is given by the Extremal Index, which depends on the expansion of the system at the periodic point. We recall that for generic points, the exceedances, in the limit, are singular and occur at Poisson times. However, around periodic points, the picture is different: the respective point processes of exceedances converge to a compound Poisson process, so instead of single exceedances, we have entire clusters of exceedances occurring at Poisson times with a geometric distribution ruling its multiplicity. The systems to which our results apply include: general piecewise expanding maps of the interval (Rychlik maps), maps with indifferent fixed points (Manneville-Pomeau maps) and Benedicks-Carleson quadratic maps.Comment: To appear in Communications in Mathematical Physic

Congenital syndactyly in cattle: four novel mutations in the low density lipoprotein receptor-related protein 4 gene (LRP4)

BACKGROUND: Isolated syndactyly in cattle, also known as mulefoot, is inherited as an autosomal recessive trait with variable penetrance in different cattle breeds. Recently, two independent mutations in the bovine LRP4 gene have been reported as the primary cause of syndactyly in the Holstein and Angus cattle breeds. RESULTS: We confirmed the previously described LRP4 exon 33 two nucleotide substitution in most of the affected Holstein calves and revealed additional evidence for allelic heterogeneity by the identification of four new LRP4 non-synonymous point mutations co-segregating in Holstein, German Simmental and Simmental-Charolais families. CONCLUSION: We confirmed a significant role of LRP4 mutations in the pathogenesis of congenital syndactyly in cattle. The newly detected missense mutations in the LRP4 gene represent independent mutations affecting different conserved protein domains. However, the four newly described LRP4 mutations do still not explain all analyzed cases of syndactyly

Translation invariant extensions of finite volume measures

We investigate the following questions: Given a measure μΛ on configurations on a subset Λ of a lattice L, where a configuration is an element of ΩΛ for some fixed set Ω, does there exist a measure μ on configurations on all of L, invariant under some specified symme- try group of L, such that μΛ is its marginal on configurations on Λ? When the answer is yes, what are the properties, e.g., the entropies, of such measures? Our primary focus is the case in which L = Zd and the symmetries are the translations. For the case in which Λ is an interval in Z we give a simple necessary and sufficient condition, local translation invariance (LTI), for extendibility. For LTI measures we construct extensions having maximal entropy, which we show are Gibbs measures; this construction extends to the case in which L is the Bethe lattice. On Z we also consider extensions supported on periodic configurations, which are analyzed using de Bruijn graphs and which include the extensions with minimal entropy. When Λ ⊂ Z is not an interval, or when Λ ⊂ Zd with d > 1, the LTI condition is necessary but not sufficient for extendibility. For Zd with d > 1, extendibility is in some sense undecidable

A novel μCT analysis reveals different responses of bioerosion and secondary accretion to environmental variability

Corals build reefs through accretion of calcium carbonate (CaCO3) skeletons, but net reef growth also depends on bioerosion by grazers and borers and on secondary calcification by crustose coralline algae and other calcifying invertebrates. However, traditional field methods for quantifying secondary accretion and bioerosion confound both processes, do not measure them on the same time-scale, or are restricted to 2D methods. In a prior study, we compared multiple environmental drivers of net erosion using pre- and post-deployment micro-computed tomography scans (μCT; calculated as the % change in volume of experimental CaCO3 blocks) and found a shift from net accretion to net erosion with increasing ocean acidity. Here, we present a novel μCT method and detail a procedure that aligns and digitally subtracts pre- and post-deployment μCT scans and measures the simultaneous response of secondary accretion and bioerosion on blocks exposed to the same environmental variation over the same time-scale. We tested our method on a dataset from a prior study and show that it can be used to uncover information previously unattainable using traditional methods. We demonstrated that secondary accretion and bioerosion are driven by different environmental parameters, bioerosion is more sensitive to ocean acidity than secondary accretion, and net erosion is driven more by changes in bioerosion than secondary accretion

I-SceI-Mediated Double-Strand Break Does Not Increase the Frequency of Homologous Recombination at the Dct Locus in Mouse Embryonic Stem Cells

Targeted induction of double-strand breaks (DSBs) at natural endogenous loci was shown to increase the rate of gene replacement by homologous recombination in mouse embryonic stem cells. The gene encoding dopachrome tautomerase (Dct) is specifically expressed in melanocytes and their precursors. To construct a genetic tool allowing the replacement of Dct gene by any gene of interest, we generated an embryonic stem cell line carrying the recognition site for the yeast I-SceI meganuclease embedded in the Dct genomic segment. The embryonic stem cell line was electroporated with an I-SceI expression plasmid, and a template for the DSB-repair process that carried sequence homologies to the Dct target. The I-SceI meganuclease was indeed able to introduce a DSB at the Dct locus in live embryonic stem cells. However, the level of gene targeting was not improved by the DSB induction, indicating a limited capacity of I-SceI to mediate homologous recombination at the Dct locus. These data suggest that homologous recombination by meganuclease-induced DSB may be locus dependent in mammalian cells

Rapid bioerosion in a tropical upwelling coral reef

Coral reefs persist in an accretion-erosion balance, which is critical for understanding the natural variability of sediment production, reef accretion, and their effects on the carbonate budget. Bioerosion (i.e. biodegradation of substrate) and encrustation (i.e. calcified overgrowth on substrate) influence the carbonate budget and the ecological functions of coral reefs, by substrate formation/consolidation/erosion, food availability and nutrient cycling. This study investigates settlement succession and carbonate budget change by bioeroding and encrusting calcifying organisms on experimentally deployed coral substrates (skeletal fragments of Stylophora pistillata branches). The substrates were deployed in a marginal coral reef located in the Gulf of Papagayo (Costa Rica, Eastern Tropical Pacific) for four months during the northern winter upwelling period (December 2013 to March 2014), and consecutively sampled after each month. Due to the upwelling environmental conditions within the Eastern Tropical Pacific, this region serves as a natural laboratory to study ecological processes such as bioerosion, which may reflect climate change scenarios. Time-series analyses showed a rapid settlement of bioeroders, particularly of lithophagine bivalves of the genus Lithophaga/ Leiosolenus (Dillwyn, 1817), within the first two months of exposure. The observed enhanced calcium carbonate loss of coral substrate (>30%) may influence seawater carbon chemistry. This is evident by measurements of an elevated seawater pH (>8.2) and aragonite saturation state (Ωarag >3) at Matapalo Reef during the upwelling period, when compared to a previous upwelling event observed at a nearby site in distance to a coral reef (Marina Papagayo). Due to the resulting local carbonate buffer effect of the seawater, an influx of atmospheric CO2 into reef waters was observed. Substrates showed no secondary cements in thin-section analyses, despite constant seawater carbonate oversaturation (Ωarag >2.8) during the field experiment. Micro Computerized Tomography (μCT) scans and microcast-embeddings of the substrates revealed that the carbonate loss was primarily due to internal macrobioerosion and an increase in microbioerosion. This study emphasizes the interconnected effects of upwelling and carbonate bioerosion on the reef carbonate budget and the ecological turnovers of carbonate producers in tropical coral reefs under environmental change.Sistema Nacional de Áreas de Conservación/[028-2013-SINAC]/SINAC/Costa RicaSistema Nacional de Áreas de Conservación/[72-2013-SINAC]/SINAC/Costa RicaUCR::Vicerrectoría de Investigación::Unidades de Investigación::Ciencias Básicas::Centro de Investigación en Ciencias del Mar y Limnología (CIMAR