Almost periodic solution in distribution for stochastic differential equations with Stepanov almost periodic coefficients

This paper deals with the existence and uniqueness of ($\mu$-pseudo) almost periodic mild solution to some evolution equations with Stepanov ($\mu$-pseudo) almost periodic coefficients, in both determinist and stochastic cases. After revisiting some known concepts and properties of Stepanov ($\mu$-pseudo) almost periodicity in complete metric space, we consider a semilinear stochastic evolution equation on a Hilbert separable space with Stepanov ($\mu$-pseudo) almost periodic coefficients. We show existence and uniqueness of the mild solution which is ($\mu$-pseudo) almost periodic in 2-distribution. We also generalize a result by Andres and Pennequin, according to which there is no purely Stepanov almost periodic solutions to differential equations with Stepanov almost periodic coefficients

Pseudoperiodic Words and a Question of Shevelev

We generalize the familiar notion of periodicity in sequences to a new kind of pseudoperiodicity, and we prove some basic results about it. We revisit the results of a 2012 paper of Shevelev and reprove his results in a simpler and more unified manner, and provide a complete answer to one of his previously unresolved questions. We consider finding words with specific pseudoperiod and having the smallest possible critical exponent. Finally, we consider the problem of determining whether a finite word is pseudoperiodic of a given size, and show that it is NP-complete

On Transcendence of Irrationals with Non-eventually Periodic b-adic Expansions

It is known that almost all numbers are transcendental in the sense of Lebesgue measure. However there is no simple rule to separate transcendental numbers from algebraic numbers. Today research in this direction is about establishing new transcendence criteria for new families of transcendental numbers. By applying a recent refinement of Subspace Theorem, Boris Adamczewski and Yann Bugeaud determined new transcendence criteria for real numbers which we shall present in this thesis. Published only three years ago, their articles explore combinatorial, algorithmic and dynamic approaches in discussing the notion of complexity of both continued fraction and b-adic expansions of a certain class of real numbers. The condition on the expansions are those of being stammering and non-eventually periodic. Taking together these articles give a well-structured picture of the interrelationships between sequence characteristics of expansion (i.e. complexity, periodicity, type of generator) and algebraic characteristics of number itself (i.e. class, transcendency)

Patterns of nucleotides that flank substitutions in human orthologous genes

<p>Abstract</p> <p>Background</p> <p>Sequence context is an important aspect of base mutagenesis, and three-base periodicity is an intrinsic property of coding sequences. However, how three-base periodicity is influenced in the vicinity of substitutions is still unclear. The effect of context on mutagenesis should be revealed in the usage of nucleotides that flank substitutions. Relative entropy (also known as Kullback-Leibler divergence) is useful for finding unusual patterns in biological sequences.</p> <p>Results</p> <p>Using relative entropy, we visualized the periodic patterns in the context of substitutions in human orthologous genes. Neighbouring patterns differed both among substitution categories and within a category that occurred at three codon positions. Transition tended to occur in periodic sequences relative to transversion. Periodic signals were stronger in a set of flanking sequences of substitutions that occurred at the third-codon positions than in those that occurred at the first- or second-codon positions. To determine how the three-base periodicity was affected near the substitution sites, we fitted a sine model to the values of the relative entropy. A sine of period equal to 3 is a good approximation for the three-base periodicity at sites not in close vicinity to some substitutions. These periods were interrupted near the substitution site and then reappeared away from substitutions. A comparative analysis between the native and codon-shuffled datasets suggested that the codon usage frequency was not the sole origin of the three-base periodicity, implying that the native order of codons also played an important role in this periodicity. Synonymous codon shuffling revealed that synonymous codon usage bias was one of the factors responsible for the observed three-base periodicity.</p> <p>Conclusions</p> <p>Our results offer an efficient way to illustrate unusual periodic patterns in the context of substitutions and provide further insight into the origin of three-base periodicity. This periodicity is a result of the native codon order in the reading frame. The length of the period equal to 3 is caused by the usage bias of nucleotides in synonymous codons. The periodic features in nucleotides surrounding substitutions aid in further understanding genetic variation and nucleotide mutagenesis.</p

Almost Automorphic Solutions of Delayed Neutral Dynamic Systems on Hybrid Domains

We study the existence of almost automorphic solutions of the delayed neutral dynamic system on hybrid domains that are additively periodic. We use exponential dichotomy and prove uniqueness of projector of exponential dichotomy to obtain some limit results leading to sufficient conditions for existence of almost automorphic solutions to neutral system. Unlike the existing literature we prove our existence results without assuming boundedness of the coefficient matrices in the system. Hence, we significantly improve the results in the existing literature. Finally, we also provide an existence result for an almost periodic solutions of the system

High recombination rates and hotspots in a Plasmodium falciparum genetic cross

Using the universal P2/P8 primers, we were able to obtain the gene segments of chromo-helicase-DNA binding protein (CHD)-Z and CHD-W from ten species of ardeid birds including Chinese egret (Egretta eulophotes), little egret (E. garzetta), eastern reef egret (E. sacra), great egret (Ardea alba), grey heron (A. cinerea), Chinese pond-heron (Ardeola bacchus), cattle egret (Bubulcus ibis), black-crowned night-heron (Nycticorax nycticorax), cinnamon bittern (Ixobrychus cinnamomeus) and yellow bittern (I. sinensis). Based on conserved regions inside the P2/P8-derived sequences, we designed new PCR primers for sex identification in these ardeid species. Using agarose gel electrophoresis, the PCR products showed two bands for females (140 bp derived from CHD-W and the other 250 bp from CHD-ZW), whereas the males showed only the 250 bp band. The results indicated that our new primers could be used for accurate and convenient sex identification in ardeid species.National Natural Science Foundation of China[30970380, 40876077]; Fujian Natural Science Foundation of China[2008S0007, 2009J01195