In this paper, we introduce a new and highly scalable algorithm, PASTA, for large-scale multiple sequence alignment estimation. PASTA uses a new technique to produce an alignment given a guide tree that enables it to be both highly scalable and very accurate. We present a study on biological and simulated data with up to 200,000 sequences, showing that PASTA produces highly accurate alignments,...

Given an orthogonal polynomial sequence on the real line, another of polynomials can be found by composing them with a Möbius transformation. In this work, we study properties such Möbius-transformed in systematically way. We show that these are given curve complex plane respect to particular kind varying measure, and they enjoy several common line. Moreover, many easier derived from approach, ...

A closed integral expression is derived for Neumann series of Bessel functions — a series of Bessel functions of increasing order — over the set of real numbers.

Let H be a finite dimensional (real or complex) Hilbert space and let {ai}i=1 be a non-increasing sequence of positive numbers. Given a finite sequence of vectors F = {fi}pi=1 in H we find necessary and sufficient conditions for the existence of r ∈ N∪{∞} and a Bessel sequence G = {gi}i=1 in H such that F ∪ G is a tight frame for H and ‖gi‖ = ai for 1 ≤ i ≤ r. Moreover, in this case we compute ...

We report the creation of white-light, achromatic Bessel beams using a spatial light modulator and a prism to compensate for the dispersion. Unlike the Bessel beam created by a refractive axicon, this achromatic beam has a radial wavevector and hence an intensity cross-section which is independent of wavelength. The technique also lends itself to the generation of higher order Bessel beams with...

Recently Pogány and Süli [Proc. Amer. Math. Soc. 137(7) (2009), 2363–2368] derived a closed-form integral expression for Neumann series of Bessel functions of the first kind Jν . In this paper our aim is to establish analogous integral representations for the Neumann-type series of modified Bessel functions of the first kind Iν and for Bessel functions of the second kind Yν , Kν , and to give l...

We establish a simple relative trace formula for GSp(4) and inner forms with respect to Bessel subgroups to obtain a certain Bessel identity. From such an identity, one can hope to prove a formula relating central values of degree four spinor L-functions to squares of Bessel periods as conjectured by Böcherer. Under some local assumptions, we obtain nonvanishing results, i.e., a global Gross–Pr...

A theory of the recently discussed and demonstrated novel phenomenon of self-phase-matching [B.Glushko, B. Kryzhanovsky, and D. Sarkisyan, Phys. Rev. Lett. 71, 243 (1993)j is given by representing the conical beam, produced in the experiments, by a Bessel beam and as a superposition of Bessel beams. The predictions of the theory with the superposition of Bessel beams are in conformity with the ...

We prove a limit relation for the Dunkl–Bessel function of type BN with multiplicity parameters k1 on the roots ±ei and k2 on ±ei ± ej where k1 tends to infinity and the arguments are suitably scaled. It gives a good approximation in terms of the Dunkltype Bessel function of type AN−1 with multiplicity k2. For certain values of k2 an improved estimate is obtained from a corresponding limit rela...

The nitrogen-vacancy center (NVC) in a diamond is promising platform for Floquet engineering. Using the synchronized readout, we investigate NVC's state driven by Carr-Purcell sequence large-amplitude ac magnetic field. We observe dynamics represented as Bessel functions up to 211th order systematic and quantitative agreement with theoretical model. Furthermore, numerical calculations show that...