Similarity density of the Thue-Morse word with overlap-free infinite binary words

We consider a measure of similarity for infinite words that generalizes the notion of asymptotic or natural density of subsets of natural numbers from number theory. We show that every overlap-free infinite binary word, other than the Thue-Morse word t and its complement t bar, has this measure of similarity with t between 1/4 and 3/4. This is a partial generalization of a classical 1927 result of Mahler.Comment: In Proceedings AFL 2014, arXiv:1405.527

Recent Advances about Local Gene Delivery by Ultrasound

Gene therapy has been widely explored as a pharmacological approach, with a great potential to treat various diseases. Generally, many diseases have definite lesion’s site, especially for tumors. This feature results in a great demand on the delivery of therapeutic gene to the local lesion’s site. Ultrasound combined with microbubbles provides a promising platform to deliver gene in a spatiotemporally controlled way. Ultrasound beam can be positioned and targeted onto the deep-seated lesion’s site of diseases by an external mobile transducer. Microbubbles can serve as vehicles for carrying genetic cargo and can be destructed by ultrasound, resulting in the local release of genetic payload. Meanwhile, sonoporation effect will occur upon which the bubbles are exposed to the appropriate ultrasonic energy, producing the transient small holes on the adjacent cell membrane and thus increasing the vascular and cellular permeability. In this chapter, we will review the recent advances about local gene delivery by ultrasound

Ground-state Properties and Bogoliubov Modes of a Harmonically Trapped One-Dimensional Quantum Droplet

We study the stationary and excitation properties of a one-dimensional quantum droplet in the two-component Bose mixture trapped in a harmonic potential. By constructing the energy functional for the inhomogeneous mixture, we elaborate the extended the Gross-Pitaevskii equation applicable to both symmetric and asymmetric mixtures into a universal form, and the equations in two different dimensionless schemes are in a duality relation, i.e. the unique parameters left are inverse of each other. The Bogoliubov equations for the trapped droplet are obtained by linearizing the small density fluctuation around the ground state and the low-lying excitation modes are calculated numerically.It is found that the confinement trap changes easily the flat-top structure for large droplets and alters the mean square radius and the chemical potential intensively. The breathing mode of the confined droplet connects the self-bound and ideal gas limits, with the excitation in the weakly interacting Bose condensate for large particle numbers lying in between. We explicitly show how the continuum spectrum of the excitation is split into discrete modes, and finally taken over by the harmonic trap. Two critical particle numbers are identified by the minimum size of the trapped droplet and the maximum breathing mode energy, both of which are found to decrease exponentially with the trapping parameter.Comment: 11 pages, 7 figure

Regulation and Function of the Caspase-1 in an Inflammatory Microenvironment.

The inflammasome is a complex of proteins that has a critical role in mounting an inflammatory response in reply to a harmful stimulus that compromises the homeostatic state of the tissue. The NLRP3 inflammasome, which is found in a wound-like environment, is comprised of three components: the NLRP3, the adaptor protein ASC and caspase-1. Interestingly, although ASC levels do not fluctuate, caspase-1 levels are elevated in both physiological and pathological conditions. Despite the observation that merely raising caspase-1 levels is sufficient to induce inflammation, the crucial question regarding the mechanism governing its expression is unexplored. We found that, in an inflammatory microenvironment, caspase-1 is regulated by NF-κB. Consistent with this association, the inhibition of caspase-1 activity parallels the effects on wound healing caused by the abrogation of NF-κB activation. Surprisingly, not only does inhibition of the NF-κB/caspase-1 axis disrupt the inflammatory phase of the wound-healing program, but it also impairs the stimulation of cutaneous epithelial stem cells of the proliferative phase. These data provide a mechanistic basis for the complex interplay between different phases of the wound-healing response in which the downstream signaling activity of immune cells can kindle the amplification of local stem cells to advance tissue repair

Reversible intercalation of methyl viologen as a dicationic charge carrier in aqueous batteries.

The interactions between charge carriers and electrode structures represent one of the most important considerations in the search for new energy storage devices. Currently, ionic bonding dominates the battery chemistry. Here we report the reversible insertion of a large molecular dication, methyl viologen, into the crystal structure of an aromatic solid electrode, 3,4,9,10-perylenetetracarboxylic dianhydride. This is the largest insertion charge carrier when non-solvated ever reported for batteries; surprisingly, the kinetic properties of the (de)insertion of methyl viologen are excellent with 60% of capacity retained when the current rate is increased from 100 mA g-1 to 2000 mA g-1. Characterization reveals that the insertion of methyl viologen causes phase transformation of the organic host, and embodies guest-host chemical bonding. First-principles density functional theory calculations suggest strong guest-host interaction beyond the pure ionic bonding, where a large extent of covalency may exist. This study extends the boundary of battery chemistry to large molecular ions as charge carriers and also highlights the electrochemical assembly of a supramolecular system