Nature of the glassy phase of RNA secondary structure

We characterize the low temperature phase of a simple model for RNA secondary structures by determining the typical energy scale E(l) of excitations involving l bases. At zero temperature, we find a scaling law E(l) \sim l^\theta with \theta \approx 0.23, and this same scaling holds at low enough temperatures. Above a critical temperature, there is a different phase characterized by a relatively flat free energy landscape resembling that of a homopolymer with a scaling exponent \theta=1. These results strengthen the evidence in favour of the existence of a glass phase at low temperatures.Comment: 7 pages, 1 figur

I Canna Lo\u27e Him Less

My cheek is unco pale, Mither,My heart is unco chill;For sorrow wi\u27 its icy breathChecks ilka happy thrill:And tho\u27 in grief and wae Mither,His name I ever blessFor tho\u27 he\u27s broken plight and vowI canna lo\u27e him less,For tho\u27 he\u27s broken plight and vowI canna lo\u27e him less. The trysting tree is green, Mither,Where we sae aften met,It should hae wither\u27d lang agoWhen he could first forgetThe bonny dell is bright, MitherWi\u27 summer\u27s gaudy dress;While ilka blossom speaks o\u27 himI canna lo\u27e him less,While ilka blossom speaks o\u27 himI canna lo\u27e him less. The ha\u27thorn scents the breeze, Mither,Along the riverside,And far across the waters brightI see his swift boat glideBut it comes not now to me, MitherHis whisper and caressIs gien unto anither,Yet I canna lo\u27e him less, Is gien unto anither,Yet I canna lo\u27e him less. Then tell him when I die, Mither,That wi\u27 my latest breath,I prayed for the fause cruel heart,That gave my ain to death:Tell him the lips then cold, Mither,Ne\u27er murmured but to bless;And tho\u27 he\u27s wrought me wae and ill,I canna lo\u27e him less, And tho\u27 he\u27s wrought me wae and ill,I canna lo\u27e him less

Exact Asymptotic Results for a Model of Sequence Alignment

Finding analytically the statistics of the longest common subsequence (LCS) of a pair of random sequences drawn from c alphabets is a challenging problem in computational evolutionary biology. We present exact asymptotic results for the distribution of the LCS in a simpler, yet nontrivial, variant of the original model called the Bernoulli matching (BM) model which reduces to the original model in the large c limit. We show that in the BM model, for all c, the distribution of the asymptotic length of the LCS, suitably scaled, is identical to the Tracy-Widom distribution of the largest eigenvalue of a random matrix whose entries are drawn from a Gaussian unitary ensemble. In particular, in the large c limit, this provides an exact expression for the asymptotic length distribution in the original LCS problem.Comment: 4 pages Revtex, 2 .eps figures include

Genetic Correlations in Mutation Processes

We study the role of phylogenetic trees on correlations in mutation processes. Generally, correlations decay exponentially with the generation number. We find that two distinct regimes of behavior exist. For mutation rates smaller than a critical rate, the underlying tree morphology is almost irrelevant, while mutation rates higher than this critical rate lead to strong tree-dependent correlations. We show analytically that identical critical behavior underlies all multiple point correlations. This behavior generally characterizes branching processes undergoing mutation.Comment: revtex, 8 pages, 2 fig

Let me Google that for you:a time series analysis of seasonality in internet search trends for terms related to foot and ankle pain

BACKGROUND: The analysis of internet search traffic may present the opportunity to gain insights into general trends and patterns in information seeking behaviour related to medical conditions at a population level. For prevalent and widespread problems such as foot and ankle pain, this information has the potential to improve our understanding of seasonality and trends within these conditions and their treatments, and may act as a useful proxy for their true incidence/prevalence characteristics. This study aimed to explore seasonal effects, general trends and relative popularity of internet search terms related to foot and ankle pain over the past decade. METHODS: We used the Google Trends tool to obtain relative search engine traffic for terms relating to foot and ankle pain and common treatments from Google search and affiliated pages for major northern and southern hemisphere English speaking nations. Analysis of overall trends and seasonality including summer/winter differences was carried out on these terms. RESULTS: Searches relating to general foot pain were on average 3.4 times more common than those relating to ankle pain, and twice as common as searches relating to heel pain. Distinct seasonal effects were seen in the northern hemisphere, with large increases in search volumes in the summer months compared to winter for foot (p = 0.004, 95 % CI [22.2–32.1]), ankle (p = 0.0078, 95 % CI [20.9–35.5]), and heel pain (p = 0.004, 95 % CI [29.1–45.6]). These seasonal effects were reflected by data from Australia, with the exception of ankle pain. Annual seasonal effects for treatment options were limited to terms related to foot surgery and ankle orthoses (p = 0.031, 95 % CI [3.5–20.9]; p = 0.004, 95 % CI [7.6–25.2] respectively), again increasing in the summer months. CONCLUSIONS: A number of general trends and annual seasonal effects were found in time series internet search data for terms relating to foot and ankle pain. This data may provide insights into these conditions at population levels. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s13047-015-0074-9) contains supplementary material, which is available to authorized users

The secret world of shrimps: polarisation vision at its best

Animal vision spans a great range of complexity, with systems evolving to detect variations in optical intensity, distribution, colour, and polarisation. Polarisation vision systems studied to date detect one to four channels of linear polarisation, combining them in opponent pairs to provide intensity-independent operation. Circular polarisation vision has never been seen, and is widely believed to play no part in animal vision. Polarisation is fully measured via Stokes' parameters--obtained by combined linear and circular polarisation measurements. Optimal polarisation vision is the ability to see Stokes' parameters: here we show that the crustacean \emph{Gonodactylus smithii} measures the exact components required. This vision provides optimal contrast-enhancement, and precise determination of polarisation with no confusion-states or neutral-points--significant advantages. We emphasise that linear and circular polarisation vision are not different modalities--both are necessary for optimal polarisation vision, regardless of the presence of strongly linear or circularly polarised features in the animal's environment.Comment: 10 pages, 6 figures, 2 table

Addition-Deletion Networks

We study structural properties of growing networks where both addition and deletion of nodes are possible. Our model network evolves via two independent processes. With rate r, a node is added to the system and this node links to a randomly selected existing node. With rate 1, a randomly selected node is deleted, and its parent node inherits the links of its immediate descendants. We show that the in-component size distribution decays algebraically, c_k ~ k^{-beta}, as k-->infty. The exponent beta=2+1/(r-1) varies continuously with the addition rate r. Structural properties of the network including the height distribution, the diameter of the network, the average distance between two nodes, and the fraction of dangling nodes are also obtained analytically. Interestingly, the deletion process leads to a giant hub, a single node with a macroscopic degree whereas all other nodes have a microscopic degree.Comment: 8 pages, 5 figure

Evolution Equation of Phenotype Distribution: General Formulation and Application to Error Catastrophe

An equation describing the evolution of phenotypic distribution is derived using methods developed in statistical physics. The equation is solved by using the singular perturbation method, and assuming that the number of bases in the genetic sequence is large. Applying the equation to the mutation-selection model by Eigen provides the critical mutation rate for the error catastrophe. Phenotypic fluctuation of clones (individuals sharing the same gene) is introduced into this evolution equation. With this formalism, it is found that the critical mutation rate is sometimes increased by the phenotypic fluctuations, i.e., noise can enhance robustness of a fitted state to mutation. Our formalism is systematic and general, while approximations to derive more tractable evolution equations are also discussed.Comment: 22 pages, 2 figure

Thermodynamics of protein folding: a random matrix formulation

The process of protein folding from an unfolded state to a biologically active, folded conformation is governed by many parameters e.g the sequence of amino acids, intermolecular interactions, the solvent, temperature and chaperon molecules. Our study, based on random matrix modeling of the interactions, shows however that the evolution of the statistical measures e.g Gibbs free energy, heat capacity, entropy is single parametric. The information can explain the selection of specific folding pathways from an infinite number of possible ways as well as other folding characteristics observed in computer simulation studies.Comment: 21 Pages, no figure