A note on Verhulst's logistic equation and related logistic maps

We consider the Verhulst logistic equation and a couple of forms of the corresponding logistic maps. For the case of the logistic equation we show that using the general Riccati solution only changes the initial conditions of the equation. Next, we consider two forms of corresponding logistic maps reporting the following results. For the map x_{n+1} = rx_n(1 - x_n) we propose a new way to write the solution for r = -2 which allows better precision of the iterative terms, while for the map x_{n+1}-x_n = rx_n(1 - x_{n+1}) we show that it behaves identically to the logistic equation from the standpoint of the general Riccati solution, which is also provided herein for any value of the parameter r.Comment: 6 pages, 3 figures, 7 references with title

Low-energy electrodynamics of superconducting diamond

Heavily-boron-doped diamond films become superconducting with critical temperatures $T_c$ well above 4 K. Here we first measure the reflectivity of such a film down to 5 cm$^{-1}$, by also using Coherent Synchrotron Radiation. We thus determine the optical gap, the field penetration depth, the range of action of the Ferrell-Glover-Tinkham sum rule, and the electron-phonon spectral function. We conclude that diamond behaves as a dirty BCS superconductor.Comment: 4 pages including 3 figure

Creation of ballot sequences in a periodic cellular automaton

Motivated by an attempt to develop a method for solving initial value problems in a class of one dimensional periodic cellular automata (CA) associated with crystal bases and soliton equations, we consider a generalization of a simple proposition in elementary mathematics. The original proposition says that any sequence of letters 1 and 2, having no less 1's than 2's, can be changed into a ballot sequence via cyclic shifts only. We generalize it to treat sequences of cells of common capacity s > 1, each of them containing consecutive 2's (left) and 1's (right), and show that these sequences can be changed into a ballot sequence via two manipulations, cyclic and "quasi-cyclic" shifts. The latter is a new CA rule and we find that various kink-like structures are traveling along the system like particles under the time evolution of this rule.Comment: 31 pages. Section 1 changed and section 5 adde

Bethe ansatz at q=0 and periodic box-ball systems

A class of periodic soliton cellular automata is introduced associated with crystals of non-exceptional quantum affine algebras. Based on the Bethe ansatz at q=0, we propose explicit formulas for the dynamical period and the size of certain orbits under the time evolution in A^{(1)}_n case.Comment: 12 pages, Introduction expanded, Summary added and minor modifications mad

Factorization, reduction and embedding in integrable cellular automata

Factorized dynamics in soliton cellular automata with quantum group symmetry is identified with a motion of particles and anti-particles exhibiting pair creation and annihilation. An embedding scheme is presented showing that the D^{(1)}_n-automaton contains, as certain subsectors, the box-ball systems and all the other automata associated with the crystal bases of non-exceptional affine Lie algebras. The results extend the earlier ones to higher representations by a certain reduction and to a wider class of boundary conditions.Comment: LaTeX2e, 20 page

Observation of a superconducting gap in boron-doped diamond by laser-excited photoemission spectroscopy

&lt;p&gt;We investigate the temperature (T)-dependent low-energy electronic structure of a boron-doped diamond thin film using ultrahigh resolution laser-excited photoemission spectroscopy. We observe a clear shift of the leading edge below T=11 K, indicative of a superconducting gap opening (Delta~0.78 meV at T=4.5 K). The gap feature is significantly broad and a well-defined quasiparticle peak is lacking even at the lowest temperature of measurement (=4.5 K). We discuss our results in terms of disorder effects on the normal state transport and superconductivity in this system.&lt;/p&gt;</p

Anti-Prion Activity of Brilliant Blue G

BACKGROUND: Prion diseases are fatal neurodegenerative disorders with no effective therapy currently available. Accumulating evidence has implicated over-activation of P2X7 ionotropic purinergic receptor (P2X7R) in the progression of neuronal loss in several neurodegenerative diseases. This has led to the speculation that simultaneous blockade of this receptor and prion replication can be an effective therapeutic strategy for prion diseases. We have focused on Brilliant Blue G (BBG), a well-known P2X7R antagonist, possessing a chemical structure expected to confer anti-prion activity and examined its inhibitory effect on the accumulation of pathogenic isoforms of prion protein (PrPres) in a cellular and a mouse model of prion disease in order to determine its therapeutic potential. PRINCIPAL FINDINGS: BBG prevented PrPres accumulation in infected MG20 microglial and N2a neural cells at 50% inhibitory concentrations of 14.6 and 3.2 µM, respectively. Administration of BBG in vivo also reduced PrPres accumulation in the brains of mice with prion disease. However, it did not appear to alleviate the disease progression compared to the vehicle-treated controls, implying a complex role of P2X7R on the neuronal degeneration in prion diseases. SIGNIFICANCE: These results provide novel insights into the pathophysiology of prion diseases and have important implications for the treatment

Production of scFv-Conjugated Affinity Silk Powder by Transgenic Silkworm Technology

Bombyx mori (silkworm) silk proteins are being utilized as unique biomaterials for medical applications. Chemical modification or post-conjugation of bioactive ligands expand the applicability of silk proteins; however, the processes are elaborate and costly. In this study, we used transgenic silkworm technology to develop single-chain variable fragment (scFv)-conjugated silk fibroin. The cocoons of the transgenic silkworm contain fibroin L-chain linked with scFv as a fusion protein. After dissolving the cocoons in lithium bromide, the silk solution was dialyzed, concentrated, freeze-dried, and crushed into powder. Immunoprecipitation analyses demonstrate that the scFv domain retains its specific binding activity to the target molecule after multiple processing steps. These results strongly suggest the promise of scFv-conjugated silk fibroin as an alternative affinity reagent, which can be manufactured using transgenic silkworm technology at lower cost than traditional affinity carriers