Algebraic entropy for algebraic maps

We propose an extension of the concept of algebraic entropy, as introduced by Bellon and Viallet for rational maps, to algebraic maps (or correspondences) of a certain kind. The corresponding entropy is an index of the complexity of the map. The definition inherits the basic properties from the definition of entropy for rational maps. We give an example with positive entropy, as well as two examples taken from the theory of Backlund transformations

Methane prediction based on individual or groups of milk fatty acids for dairy cows fed rations with or without linseed

Milk fatty acids (MFA) are a proxy for the prediction of CH4 emission from cows, and prediction differs with diet. Our objectives were (1) to compare the effect of diets on the relation between MFA profile and measured CH4 production, (2) to predict CH4 production based on 6 data sets differing in the number and type of MFA, and (3) to test whether additional inclusion of energy-corrected milk (ECM) yield or dry matter intake (DMI) as explanatory variables improves predictions. Twenty dairy cows were used. Four diets were used based on corn silage (CS) or grass silage (GS) without (L0) or with linseed (LS) supplementation. Ten cows were fed CS-L0 and CS-LS and the other 10 cows were fed GS-L0 and GS-LS in random order. In feeding wk 5 of each diet, CH4 production (L/d) was measured in respiration chambers for 48 h and milk was analyzed for MFA concentrations by gas chromatography. Specific CH4 prediction equations were obtained for L0-, LS-, GS-, and CS-based diets and for all 4 diets collectively and validated by an internal cross-validation. Models were developed containing either 43 identified MFA or a reduced set of 7 groups of biochemically related MFA plus C16:0 and C18:0. The CS and LS diets reduced CH4 production compared with GS and L0 diets, respectively. Methane yield (L/kg of DMI) reduction by LS was higher with CS than GS diets. The concentrations of C18:1 trans and n-3 MFA differed among GS and CS diets. The LS diets resulted in a higher proportion of unsaturated MFA at the expense of saturated MFA. When using the data set of 43 individual MFA to predict CH4 production (L/d), the cross-validation coefficient of determination (R2 CV) ranged from 0.47 to 0.92. When using groups of MFA variables, the R2 CV ranged from 0.31 to 0.84. The fit parameters of the latter models were improved by inclusion of ECM or DMI, but not when added to the data set of 43 MFA for all diets pooled. Models based on GS diets always had a lower prediction potential (R2 CV = 0.31 to 0.71) compared with data from CS diets (R2 CV = 0.56 to 0.92). Models based on LS diets produced lower prediction with data sets with reduced MFA variables (R2 CV = 0.62 to 0.68) compared with L0 diets (R2 CV = 0.67 to 0.80). The MFA C18:1 cis-9 and C24:0 and the monounsaturated FA occurred most often in models. In conclusion, models with a reduced number of MFA variables and ECM or DMI are suitable for CH4 prediction, and CH4 prediction equations based on diets containing linseed resulted in lower prediction accuracy. © 2019 American Dairy Science Associatio

Rare events, escape rates and quasistationarity: some exact formulae

We present a common framework to study decay and exchanges rates in a wide class of dynamical systems. Several applications, ranging form the metric theory of continuons fractions and the Shannon capacity of contrained systems to the decay rate of metastable states, are given

Operator renewal theory and mixing rates for dynamical systems with infinite measure

We develop a theory of operator renewal sequences in the context of infinite ergodic theory. For large classes of dynamical systems preserving an infinite measure, we determine the asymptotic behaviour of iterates $L^n$ of the transfer operator. This was previously an intractable problem. Examples of systems covered by our results include (i) parabolic rational maps of the complex plane and (ii) (not necessarily Markovian) nonuniformly expanding interval maps with indifferent fixed points. In addition, we give a particularly simple proof of pointwise dual ergodicity (asymptotic behaviour of $\sum_{j=1}^nL^j$) for the class of systems under consideration. In certain situations, including Pomeau-Manneville intermittency maps, we obtain higher order expansions for $L^n$ and rates of mixing. Also, we obtain error estimates in the associated Dynkin-Lamperti arcsine laws.Comment: Preprint, August 2010. Revised August 2011. After publication, a minor error was pointed out by Kautzsch et al, arXiv:1404.5857. The updated version includes minor corrections in Sections 10 and 11, and corresponding modifications of certain statements in Section 1. All main results are unaffected. In particular, Sections 2-9 are unchanged from the published versio

Greene SCPrimer: a rapid comprehensive tool for designing degenerate primers from multiple sequence alignments

Polymerase chain reaction (PCR) is widely applied in clinical and environmental microbiology. Primer design is key to the development of successful assays and is often performed manually by using multiple nucleic acid alignments. Few public software tools exist that allow comprehensive design of degenerate primers for large groups of related targets based on complex multiple sequence alignments. Here we present a method for designing such primers based on tree building followed by application of a set covering algorithm, and demonstrate its utility in compiling Multiplex PCR primer panels for detection and differentiation of viral pathogens

Shared probe design and existing microarray reanalysis using PICKY

<p>Abstract</p> <p>Background</p> <p>Large genomes contain families of highly similar genes that cannot be individually identified by microarray probes. This limitation is due to thermodynamic restrictions and cannot be resolved by any computational method. Since gene annotations are updated more frequently than microarrays, another common issue facing microarray users is that existing microarrays must be routinely reanalyzed to determine probes that are still useful with respect to the updated annotations.</p> <p>Results</p> <p><smcaps>PICKY</smcaps> 2.0 can design shared probes for sets of genes that cannot be individually identified using unique probes. <smcaps>PICKY</smcaps> 2.0 uses novel algorithms to track sharable regions among genes and to strictly distinguish them from other highly similar but nontarget regions during thermodynamic comparisons. Therefore, <smcaps>PICKY</smcaps> does not sacrifice the quality of shared probes when choosing them. The latest <smcaps>PICKY</smcaps> 2.1 includes the new capability to reanalyze existing microarray probes against updated gene sets to determine probes that are still valid to use. In addition, more precise nonlinear salt effect estimates and other improvements are added, making <smcaps>PICKY</smcaps> 2.1 more versatile to microarray users.</p> <p>Conclusions</p> <p>Shared probes allow expressed gene family members to be detected; this capability is generally more desirable than not knowing anything about these genes. Shared probes also enable the design of cross-genome microarrays, which facilitate multiple species identification in environmental samples. The new nonlinear salt effect calculation significantly increases the precision of probes at a lower buffer salt concentration, and the probe reanalysis function improves existing microarray result interpretations.</p

Comparative mapping of expressed sequence tags containing microsatellites in rainbow trout (Oncorhynchus mykiss)

BACKGROUND: Comparative genomics, through the integration of genetic maps from species of interest with whole genome sequences of other species, will facilitate the identification of genes affecting phenotypes of interest. The development of microsatellite markers from expressed sequence tags will serve to increase marker densities on current salmonid genetic maps and initiate in silico comparative maps with species whose genomes have been fully sequenced. RESULTS: Eighty-nine polymorphic microsatellite markers were generated for rainbow trout of which at least 74 amplify in other salmonids. Fifty-five have been associated with functional annotation and 30 were mapped on existing genetic maps. Homologous sequences were identified for 20 of the EST containing microsatellites to identify comparative assignments within the tetraodon, mouse, and/or human genomes. CONCLUSION: The addition of microsatellite markers constructed from expressed sequence tag data will facilitate the development of high-density genetic maps for rainbow trout and comparative maps with other salmonids and better studied species

Genome-Wide Functional Analysis of the Cotton Transcriptome by Creating an Integrated EST Database

A total of 28,432 unique contigs (25,371 in consensus contigs and 3,061 as singletons) were assembled from all 268,786 cotton ESTs currently available. Several in silico approaches [comparative genomics, Blast, Gene Ontology (GO) analysis, and pathway enrichment by Kyoto Encyclopedia of Genes and Genomes (KEGG)] were employed to investigate global functions of the cotton transcriptome. Cotton EST contigs were clustered into 5,461 groups with a maximum cluster size of 196 members. A total of 27,956 indel mutants and 149,616 single nucleotide polymorphisms (SNPs) were identified from consensus contigs. Interestingly, many contigs with significantly high frequencies of indels or SNPs encode transcription factors and protein kinases. In a comparison with six model plant species, cotton ESTs show the highest overall similarity to grape. A total of 87 cotton miRNAs were identified; 59 of these have not been reported previously from experimental or bioinformatics investigations. We also predicted 3,260 genes as miRNAs targets, which are associated with multiple biological functions, including stress response, metabolism, hormone signal transduction and fiber development. We identified 151 and 4,214 EST-simple sequence repeats (SSRs) from contigs and raw ESTs respectively. To make these data widely available, and to facilitate access to EST-related genetic information, we integrated our results into a comprehensive, fully downloadable web-based cotton EST database (www.leonxie.com)