Polymer entanglement loss in extensional flow: Evidence from electrospun short nanofibers

High strain rate extensional flow of a semidilute polymer solution can result in fragmentation caused by polymer entanglement loss, evidenced by appearance of short nanofibers during electrospinning. The typically desired outcome of electrospinning is long continuous fibers or beads, but, under certain material and process conditions, short nanofibers can be obtained, a morphology that has scarcely been studied. Here we study the conditions that lead to the creation of short nanofibers, and find a distinct parametric space in which they are likely to appear, requiring a combination of low entanglement of the polymer chains and high strain rate of the electrospinning jet. Measurements of the length and diameter of short nanofibers, electrospun from PMMA dissolved in a blend of CHCl₃ and DMF, confirm the theoretical prediction that the fragmentation of the jet into short fibers is brought about by elastic stretching and loss of entanglement of the polymer network. The ability to tune nanofiber length, diameter and nanostructure, by modifying variables such as the molar mass, concentration, solvent quality, electric field intensity, and flow rate, can be exploited for improving their mechanical and thermodynamic properties, leading to novel applications in engineering and life sciences. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2013 , 51, 1377–1391     

Graphs of given degree and diameter obtained as abelian lifts of dipoles

We derive an upper bound on the number of vertices in regular graphs of given degree and diameter arising as regular coverings of dipoles over abelian groups.     

Regulation of Stem Cell Differentiation by Control of Retinoic Acid Gradients in Hydrospun 3D Scaffold

Morphogen gradients have been associated with differential gene expression and are implicated in the triggering and regulation of developmental biological processes. This study focused on creating morphogenic gradients through the thickness of hydrospun scaffolds. Specifically, electrospun poly(ε‐caprolactone) fibers were loaded with all‐trans‐retinoic acid (ATRA), and designed to release ATRA at a predetermined rate. Multilayered scaffolds designed to present varied initial ATRA concentrations were then exposed to flow conditions in a bioreactor. Gradient formation was verified by a simple convection‐diffusion mathematical model approving establishment of a continuous solute gradient across the scaffold. The biological value of the designed gradients in scaffolds was evaluated by monitoring the fate of murine embryonal carcinoma cells embedded within the scaffolds. Cell differentiation within the different layers matched the predictions set forth by the theoretical model, in accordance with the ATRA gradient formed across the scaffold. This tool bears powerful potential in establishing in vitro simulation models for better understanding the inner workings of the embryo.

     

Cutoff for the Ising model on the lattice

Introduced in 1963, Glauber dynamics is one of the most practiced and extensively studied methods for sampling the Ising model on lattices. It is well known that at high temperatures, the time it takes this chain to mix in L ¹ on a system of size n is O(logn). Whether in this regime there is cutoff, i.e. a sharp transition in the L ¹-convergence to equilibrium, is a fundamental open problem: If so, as conjectured by Peres, it would imply that mixing occurs abruptly at (c+o(1))logn for some fixed c>0, thus providing a rigorous stopping rule for this MCMC sampler. However, obtaining the precise asymptotics of the mixing and proving cutoff can be extremely challenging even for fairly simple Markov chains. Already for the one-dimensional Ising model, showing cutoff is a longstanding open problem. We settle the above by establishing cutoff and its location at the high temperature regime of the Ising model on the lattice with periodic boundary conditions. Our results hold for any dimension and at any temperature where there is strong spatial mixing: For ?² this carries all the way to the critical temperature. Specifically, for fixed d≥1, the continuous-time Glauber dynamics for the Ising model on (?/n?) ^d with periodic boundary conditions has cutoff at (d/2λ _∞)logn, where λ _∞ is the spectral gap of the dynamics on the infinite-volume lattice. To our knowledge, this is the first time where cutoff is shown for a Markov chain where even understanding its stationary distribution is limited. The proof hinges on a new technique for translating L ¹-mixing to L ²-mixing of projections of the chain, which enables the application of logarithmic-Sobolev inequalities. The technique is general and carries to other monotone and anti-monotone spin-systems, e.g. gas hard-core, Potts, anti-ferromagentic Ising, arbitrary boundary conditions, etc.     

Time-invariant person-specific frequency templates in human brain activity

The various human brain tasks are performed at different locations and time scales. Yet, we discovered the existence of time-invariant (above an essential time scale) partitioning of the brain activity into personal state-specific frequency bands. For that, we perform temporal and ensemble averaging of best wavelet packet bases from multielectrode electroencephalogram recordings. These personal frequency bands provide new templates for quantitative analyses of brain function, e.g., normal versus epileptic activity.     

Photocontrol of tyrosine phosphorylation in mammalian cells via genetic encoding of photocaged tyrosine

We report the first site-specific genetic encoding of photocaged tyrosine into proteins in mammalian cells. By photocaging Tyr701 of STAT1 we demonstrate that it is possible to photocontrol tyrosine phosphorylation and signal transduction in mammalian cells.     

Total variation cutoff in birth-and-death chains

The cutoff phenomenon describes a case where a Markov chain exhibits a sharp transition in its convergence to stationarity. Diaconis [Proc Natl Acad Sci USA 93(4):1659–1664, 1996] surveyed this phenomenon, and asked how one could recognize its occurrence in families of finite ergodic Markov chains. Peres [American Institute of Mathematics (AIM) Research Workshop, Palo Alto. http://www.aimath.org/WWN/mixingtimes, 2004] noted that a necessary condition for cutoff in a family of reversible chains is that the product of the mixing-time and spectral-gap tends to infinity, and conjectured that in many settings, this condition should also be sufficient. Diaconis and Saloff-Coste [Ann Appl Probab 16(4):2098–2122, 2006] verified this conjecture for continuous-time birth-and-death chains, started at an endpoint, with convergence measured in separation. It is natural to ask whether the conjecture holds for these chains in the more widely used total-variation distance. In this work, we confirm the above conjecture for all continuous-time or lazy discrete-time birth-and-death chains, with convergence measured via total-variation distance. Namely, if the product of the mixing-time and spectral-gap tends to infinity, the chains exhibit cutoff at the maximal hitting time of the stationary distribution median, with a window of at most the geometric mean between the relaxation-time and mixing-time. In addition, we show that for any lazy (or continuous-time) birth-and-death chain with stationary distribution π, the separation 1 ? p ^t (x, y)/π(y) is maximized when x, y are the endpoints. Together with the above results, this implies that total-variation cutoff is equivalent to separation cutoff in any family of such chains.