Waiting for regulatory sequences to appear

One possible explanation for the substantial organismal differences between humans and chimpanzees is that there have been changes in gene regulation. Given what is known about transcription factor binding sites, this motivates the following probability question: given a 1000 nucleotide region in our genome, how long does it take for a specified six to nine letter word to appear in that region in some individual? Stone and Wray [Mol. Biol. Evol. 18 (2001) 1764--1770] computed 5,950 years as the answer for six letter words. Here, we will show that for words of length 6, the average waiting time is 100,000 years, while for words of length 8, the waiting time has mean 375,000 years when there is a 7 out of 8 letter match in the population consensus sequence (an event of probability roughly 5/16) and has mean 650 million years when there is not. Fortunately, in biological reality, the match to the target word does not have to be perfect for binding to occur. If we model this by saying that a 7 out of 8 letter match is good enough, the mean reduces to about 60,000 years.Comment: Published at http://dx.doi.org/10.1214/105051606000000619 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Deformation of a quantum many-particle system by a rotating impurity

During the last 70 years, the quantum theory of angular momentum has been successfully applied to describing the properties of nuclei, atoms, and molecules, their interactions with each other as well as with external fields. Due to the properties of quantum rotations, the angular momentum algebra can be of tremendous complexity even for a few interacting particles, such as valence electrons of an atom, not to mention larger many-particle systems. In this work, we study an example of the latter: a rotating quantum impurity coupled to a many-body bosonic bath. In the regime of strong impurity-bath couplings the problem involves addition of an infinite number of angular momenta which renders it intractable using currently available techniques. Here, we introduce a novel canonical transformation which allows to eliminate the complex angular momentum algebra from such a class of many-body problems. In addition, the transformation exposes the problem's constants of motion, and renders it solvable exactly in the limit of a slowly-rotating impurity. We exemplify the technique by showing that there exists a critical rotational speed at which the impurity suddenly acquires one quantum of angular momentum from the many-particle bath. Such an instability is accompanied by the deformation of the phonon density in the frame rotating along with the impurity.Comment: 12 pages, 4 figures; revised version, section on experimental implementation adde

Rotation of quantum impurities in the presence of a many-body environment

We develop a microscopic theory describing a quantum impurity whose rotational degree of freedom is coupled to a many-particle bath. We approach the problem by introducing the concept of an 'angulon' - a quantum rotor dressed by a quantum field - and reveal its quasiparticle properties using a combination of variational and diagrammatic techniques. Our theory predicts renormalisation of the impurity rotational structure, such as observed in experiments with molecules in superfluid helium droplets, in terms of a rotational Lamb shift induced by the many-particle environment. Furthermore, we discover a rich many-body-induced fine structure, emerging in rotational spectra due to a redistribution of angular momentum within the quantum many-body system.Comment: 5 pages, 2 figures; revised version, supplementary adde

Efimov states near a Feshbach resonance and the limits of van der Waals universality at finite background scattering length

We calculate the spectrum of three-body Efimov bound states near a Feshbach resonance within a model which accounts both for the finite range of interactions and the presence of background scattering. The latter may be due to direct interactions in an open channel or a second overlapping Feshbach resonance. It is found that background scattering gives rise to substantial changes in the trimer spectrum as a function of the detuning away from a Feshbach resonance, in particular in the regime where the background channel supports Efimov states on its own. Compared to the situation with negligible background scattering, the regime where van der Waals universality applies is shifted to larger values of the resonance strength if the background scattering length is positive. For negative background scattering lengths, in turn, van der Waals universality extends to even small values of the resonance strength parameter, consistent with experimental results on Efimov states in $^{39}$K. Within a simple model, we show that short-range three-body forces do not affect van der Waals universality significantly. Repulsive three-body forces may, however, explain the observed variation between around $-8$ and $-10$ of the ratio between the scattering length where the first Efimov trimer appears and the van der Waals length.Comment: 17 pages, 13 figures; final version as publishe

Biosynthetic pathway of mitochondrial ATPase subunit 9 in Neurospora crassa

Subunit 9 of mitochondrial ATPase (Su9) is synthesized in reticulocyte lysates programmed with Neurospora poly A-RNA, and in a Neurospora cell free system as a precursor with a higher apparent molecular weight than the mature protein (Mr 16,400 vs. 10,500). The RNA which directs the synthesis of Su9 precursor is associated with free polysomes. The precursor occurs as a high molecular weight aggregate in the postribosomal supernatant of reticulocyte lysates. Transfer in vitro of the precursor into isolated mitochondria is demonstrated. This process includes the correct proteolytic cleavage of the precursor to the mature form. After transfer, the protein acquires the following properties of the assembled subunit: it is resistant to added protease, it is soluble in chloroform/methanol, and it can be immunoprecipitated with antibodies to F1-ATPase. The precursor to Su9 is also detected in intact cells after pulse labeling. Processing in vivo takes place posttranslationally. It is inhibited by the uncoupler carbonylcyanide m- chlorophenylhydrazone (CCCP). A hypothetical mechanism is discussed for the intracellular transfer of Su9. It entails synthesis on free polysomes, release of the precursor into the cytosol, recognition by a receptor on the mitochondrial surface, and transfer into the inner mitochondrial membrane, which is accompanied by proteolytic cleavage and which depends on an electrical potential across the inner mitochondrial membrane

The Centrality of Attention in SLA

Attention is a necessary constuct for understanding virtually every respect of second language acquisition. Both information processing and sociolinguistic accounts of variation assume that variation in use is a consequence of variation in attention. Attention is central to all accounts of the development of fluency. Understanding L2 development also invites the concept of anttention. Even assuming a strong innateness position, at least the triggers of innate knowledge must be attention to, and in cognitive theories, attention to input plays an essential role in storage and hyppothesis formation. Attention also mediates beeteen individual difference factors and SLA in at least three ways: attitudes and motivation make a difference because motivated learners attend more; one dimension of language aptitude is working memory, a construct which implies attention; and learning strategies are either strategies for focusing attention on language or for sustaining attention whith doing something else in addition. Lesrner-external factors such as task requirements, task instructions, and all focus-on-form techniques (including explicit instruction) also afrter what is attended to, thereby causing their effects