Finite width model sequence comparison

Abstract

Sequence comparison is a widely used computational technique in modern molecular biology. In spite of the frequent use of sequence comparisons the important problem of assigning statistical significance to a given degree of similarity is still outstanding. Analytical approaches to filling this gap usually make use of an approximation that neglects certain correlations in the disorder underlying the sequence comparison algorithm. Here, we use the longest common subsequence problem, a prototype sequence comparison problem, to analytically establish that this approximation does make a difference to certain sequence comparison statistics. In the course of establishing this difference we develop a method that can systematically deal with these disorder correlations.

Ultrafast Pump-Probe Study of Phase Separation and Competing Orders in the Underdoped(Ba,K)Fe2As2Superconductor

“…The pump-probe setup was described in Ref. 17, where cross-polarized, 800 nm pump and probe pulses, with 40 fs pulse width and 80 MHz repetition rate, were used. The average pump power was 1-2 mW, giving a pump fluence of ∼0.2 µJ/cm 2 .…”

“…A large Fe-isotope effect was seen in BKFA, suggesting the role played by magnetic fluctuations in superconductivity [15]. In all these classes of SCs, how these phases interact with one another, and the role of magnetism, are open questions that might help understand superconductivity in these compounds.In the cuprate HTSCs, femtosecond pump-probe spectroscopy has shown to be a useful tool to discern coexisting/competing phases, such as the pseudogap phase in YBa 2 Cu 2 O 7−x (Y-123) [16], and the suppression of superconductivity by antiferromagnetism in the tri-layered Tl 2 Ba 2 Ca 2 Cu 3 O y [17]. In this Letter, we use the pumpprobe technique to study the BKFA SCs in the undoped, underdoped and optimally-doped regimes.…”

“…In the cuprate HTSCs, femtosecond pump-probe spectroscopy has shown to be a useful tool to discern coexisting/competing phases, such as the pseudogap phase in YBa 2 Cu 2 O 7−x (Y-123) [16], and the suppression of superconductivity by antiferromagnetism in the tri-layered Tl 2 Ba 2 Ca 2 Cu 3 O y [17]. In this Letter, we use the pumpprobe technique to study the BKFA SCs in the undoped, underdoped and optimally-doped regimes.…”

A Practical Approach to Significance Assessment in Alignment with Gaps

“…However, the solutions we can obtain for some few small widths W still skirt far from the limit of infinite W in Eq. (11). As such, Φ(γ; Ω) cannot be straightforwardly approximated from the available Φ W (γ; Ω) with any real accuracy.…”

“…with match probability Pr{η(r, t) = 1} = a=b p 2 a ≡ p and mismatch probability Pr{η(r, t) = −µ} = a =b p a p b = 1 − p. This approximation, also known as the Bernoulli randomness approximation, is known to change characteristic quantities of sequence alignment only slightly [14,15,5,6,9,19,11]. This general property has been confirmed through numerical studies specifically for the quantity of interest here λ [8].…”