arXiv subjects

V. V. Anh

Publications and source records attributed to V. V. Anh.

3 recordsLinked to original sources

arXiv2017

Space-time fractional diffusion of Riesz-Bessel type on regular bounded open domains

Fractional (in time and in space) evolution equations defined on Dirichlet regular bounded open domains, driven by fractional integrated in time Gaussian spatiotemporal white noise, are considered here. Sufficient conditions for the definition of a weak-sense Gaussian solution, in the mean-square sense, are derived. The temporal, spatial and spatiotemporal Hölder continuity, in the mean-square sense, of the formulated solution is obtained, under suitable conditions, from the asymptotic properties of the Mittag-Leffler function, and the asymptotic order of the eigenvalues of a fractional polynomial of the Dirichlet negative Laplacian operator on such bounded open domains.

math.DS↗

arXiv2002

Recognition of an organism from fragments of its complete genome

This paper considers the problem of matching fragment to organism using its complete genome. Our method is based on the probability measure representation of a genome. We first demonstrate that these probability measures can be modelled as recurrent iterated function systems (RIFS) consisting of four contractive similarities. Our hypothesis is that the multifractal characteristic of the probability measure of a complete genome, as captured by the RIFS, is preserved in its reasonably long fragments. We compute the RIFS of fragments of various lengths and random starting points, and compare with that of the original sequence for recognition using the Euclidean distance. A demonstration on five randomly selected organisms supports the above hypothesis.

physics.bio-ph↗

arXiv2000

Correlation property of length sequences based on global structure of complete genome

This paper considers three kinds of length sequences of the complete genome. Detrended fluctuation analysis, spectral analysis, and the mean distance spanned within time $L$ are used to discuss the correlation property of these sequences. The values of the exponents from these methods of these three kinds of length sequences of bacteria indicate that the long-range correlations exist in most of these sequences. The correlation have a rich variety of behaviours including the presence of anti-correlations. Further more, using the exponent $γ$, it is found that these correlations are all linear ($γ=1.0\pm 0.03$). It is also found that these sequences exhibit $1/f$ noise in some interval of frequency ($f>1$). The length of this interval of frequency depends on the length of the sequence. The shape of the periodogram in $f>1$ exhibits some periodicity. The period seems to depend on the length and the complexity of the length sequence.

physics.bio-ph↗