Stretching an heteropolymer

We study the influence of some quenched disorder in the sequence of monomers on the entropic elasticity of long polymeric chains. Starting from the Kratky-Porod model, we show numerically that some randomness in the favoured angles between successive segments induces a change in the elongation versus force characteristics, and this change can be well described by a simple renormalisation of the elastic constant. The effective coupling constant is computed by an analytic study of the low force regime.Comment: Latex, 7 pages, 3 postscript figur

A variational principle for stationary, axisymmetric solutions of Einstein's equations

Stationary, axisymmetric, vacuum, solutions of Einstein's equations are obtained as critical points of the total mass among all axisymmetric and $(t,\phi)$ symmetric initial data with fixed angular momentum. In this variational principle the mass is written as a positive definite integral over a spacelike hypersurface. It is also proved that if absolute minimum exists then it is equal to the absolute minimum of the mass among all maximal, axisymmetric, vacuum, initial data with fixed angular momentum. Arguments are given to support the conjecture that this minimum exists and is the extreme Kerr initial data.Comment: 21 page

Reachability in Parametric Interval Markov Chains using Constraints

Parametric Interval Markov Chains (pIMCs) are a specification formalism that extend Markov Chains (MCs) and Interval Markov Chains (IMCs) by taking into account imprecision in the transition probability values: transitions in pIMCs are labeled with parametric intervals of probabilities. In this work, we study the difference between pIMCs and other Markov Chain abstractions models and investigate the two usual semantics for IMCs: once-and-for-all and at-every-step. In particular, we prove that both semantics agree on the maximal/minimal reachability probabilities of a given IMC. We then investigate solutions to several parameter synthesis problems in the context of pIMCs -- consistency, qualitative reachability and quantitative reachability -- that rely on constraint encodings. Finally, we propose a prototype implementation of our constraint encodings with promising results

On the existence of initial data containing isolated black holes

We present a general construction of initial data for Einstein's equations containing an arbitrary number of black holes, each of which is instantaneously in equilibrium. Each black hole is taken to be a marginally trapped surface and plays the role of the inner boundary of the Cauchy surface. The black hole is taken to be instantaneously isolated if its outgoing null rays are shear-free. Starting from the choice of a conformal metric and the freely specifiable part of the extrinsic curvature in the bulk, we give a prescription for choosing the shape of the inner boundaries and the boundary conditions that must be imposed there. We show rigorously that with these choices, the resulting non-linear elliptic system always admits solutions.Comment: 11 pages, 2 figures, RevTeX

Anatomic brain asymmetry in vervet monkeys.

Asymmetry is a prominent feature of human brains with important functional consequences. Many asymmetric traits show population bias, but little is known about the genetic and environmental sources contributing to inter-individual variance. Anatomic asymmetry has been observed in Old World monkeys, but the evidence for the direction and extent of asymmetry is equivocal and only one study has estimated the genetic contributions to inter-individual variance. In this study we characterize a range of qualitative and quantitative asymmetry measures in structural brain MRIs acquired from an extended pedigree of Old World vervet monkeys (n = 357), and implement variance component methods to estimate the proportion of trait variance attributable to genetic and environmental sources. Four of six asymmetry measures show pedigree-level bias and one of the traits has a significant heritability estimate of about 30%. We also found that environmental variables more significantly influence the width of the right compared to the left prefrontal lobe

Gating-by-tilt of mechanosensitive membrane channels

We propose an alternative mechanism for the gating of biological membrane channels in response to membrane tension that involves a change in the slope of the membrane near the channel. Under biological membrane tensions we show that the energy difference between the closed (tilted) and open (untilted) states can far exceed kBT and is comparable to what is available under simple ilational gating. Recent experiments demonstrate that membrane leaflet asymmetries (spontaneous curvature) can strong effect the gating of some channels. Such a phenomenon would be more easy to explain under gating-by-tilt, given its novel intrinsic sensitivity to such asymmetry.Comment: 10 pages, 2 figure

The Einstein constraints: uniqueness and non-uniqueness in the conformal thin sandwich approach

We study the appearance of multiple solutions to certain decompositions of Einstein's constraint equations. Pfeiffer and York recently reported the existence of two branches of solutions for identical background data in the extended conformal thin-sandwich decomposition. We show that the Hamiltonian constraint alone, when expressed in a certain way, admits two branches of solutions with properties very similar to those found by Pfeiffer and York. We construct these two branches analytically for a constant-density star in spherical symmetry, but argue that this behavior is more general. In the case of the Hamiltonian constraint this non-uniqueness is well known to be related to the sign of one particular term, and we argue that the extended conformal thin-sandwich equations contain a similar term that causes the breakdown of uniqueness.Comment: 9 pages, 1 figur

Master equation approach to DNA-breathing in heteropolymer DNA

After crossing an initial barrier to break the first base-pair (bp) in double-stranded DNA, the disruption of further bps is characterized by free energies between less than one to a few kT. This causes the opening of intermittent single-stranded bubbles. Their unzipping and zipping dynamics can be monitored by single molecule fluorescence or NMR methods. We here establish a dynamic description of this DNA-breathing in a heteropolymer DNA in terms of a master equation that governs the time evolution of the joint probability distribution for the bubble size and position along the sequence. The transfer coefficients are based on the Poland-Scheraga free energy model. We derive the autocorrelation function for the bubble dynamics and the associated relaxation time spectrum. In particular, we show how one can obtain the probability densities of individual bubble lifetimes and of the waiting times between successive bubble events from the master equation. A comparison to results of a stochastic Gillespie simulation shows excellent agreement.Comment: 12 pages, 8 figure

Inhibition of BACH1 (FANCJ) helicase by backbone discontinuity is overcome by increased motor ATPase or length of loading strand

The BRCA1 associated C-terminal helicase (BACH1) associated with breast cancer has been implicated in double strand break (DSB) repair. More recently, BACH1 (FANCJ) has been genetically linked to the chromosomal instability disorder Fanconi Anemia (FA). Understanding the roles of BACH1 in cellular DNA metabolism and how BACH1 dysfunction leads to tumorigenesis requires a comprehensive investigation of its catalytic mechanism and molecular functions in DNA repair. In this study, we have determined that BACH1 helicase contacts with both the translocating and the non-translocating strands of the duplex are critical for its ability to track along the sugar phosphate backbone and unwind dsDNA. An increased motor ATPase of a BACH1 helicase domain variant (M299I) enabled the helicase to unwind the backbone-modified DNA substrate in a more proficient manner. Alternatively, increasing the length of the 5′ tail of the DNA substrate allowed BACH1 to overcome the backbone discontinuity, suggesting that BACH1 loading mechanism is critical for its ability to unwind damaged DNA molecules

A Titanium Nitride Absorber for Controlling Optical Crosstalk in Horn-Coupled Aluminum LEKID Arrays for Millimeter Wavelengths

We discuss the design and measured performance of a titanium nitride (TiN) mesh absorber we are developing for controlling optical crosstalk in horn-coupled lumped-element kinetic inductance detector arrays for millimeter-wavelengths. This absorber was added to the fused silica anti-reflection coating attached to previously-characterized, 20-element prototype arrays of LEKIDs fabricated from thin-film aluminum on silicon substrates. To test the TiN crosstalk absorber, we compared the measured response and noise properties of LEKID arrays with and without the TiN mesh. For this test, the LEKIDs were illuminated with an adjustable, incoherent electronic millimeter-wave source. Our measurements show that the optical crosstalk in the LEKID array with the TiN absorber is reduced by 66\% on average, so the approach is effective and a viable candidate for future kilo-pixel arrays.Comment: 7 pages, 5 figures, accepted for publication in the Journal of Low Temperature Physic