Tropical Krichever construction for the non-periodic box and ball system

A solution for an initial value problem of the box and ball system is constructed from a solution of the periodic box and ball system. The construction is done through a specific limiting process based on the theory of tropical geometry. This method gives a tropical analogue of the Krichever construction, which is an algebro-geometric method to construct exact solutions to integrable systems, for the non-periodic system.Comment: 13 pages, 1 figur

Studies of Contact Hypersensitivity Induction in Mice with Optimal Sensitizing Doses of Hapten

To avoid unsuspected and unwanted consequences of excess hapten during epicutaneous sensitization, optimal sensitizing doses of dinitrofluorobenzene (DNFB) were determined for several ultraviolet B radiation (UVB)–resistant and UVB- susceptible strains of mice. Using these doses of hapten applied epicutaneously or injected intracutaneously into normal or UVB-exposed body wall skin, it was determined that four consecutive daily exposures to UVB prevented contact hypersensitivity induction in all mice when optimal sensitizing doses of DNFB were applied epicutaneously. By contrast, UVB-resistant, but not UVB-susceptible, mice developed contact hypersensitivity when an optimal sensitizing dose of DNFB was injected intracutaneously into UVB-irradiated skin. Moreover, whereas UVB-susceptible mice failed to develop contact hypersensitivity when an optimal sensitizing dose of DNFB was painted on skin exposed to a single dose of UVB, UVB-resistant mice did develop contact hypersensitivity under similar circumstances. Based on these results, it is concluded that 1) conventional doses of epicutaneously applied haptens induce contact hypersensitivity with the aid of antigen-presenting cells derived from both the epidermis and the dermis, 2) the phenomenon of UVB susceptibility is mediated by cells and molecules within the dermis when conventional doses of hapten and UVB radiation are employed, and 3) UVB susceptibility is mediated by cells and molecules within the epidermis when optimal sensitizing doses of hapten and a single exposure to UVB are employed

Ultradiscretization of the solution of periodic Toda equation

A periodic box-ball system (pBBS) is obtained by ultradiscretizing the periodic discrete Toda equation (pd Toda eq.). We show the relation between a Young diagram of the pBBS and a spectral curve of the pd Toda eq.. The formula for the fundamental cycle of the pBBS is obtained as a colloraly.Comment: 41 pages; 7 figure

A Substance p Agonist Acts as an Adjuvant to Promote Hapten-Specific Skin Immunity

Because substance p (SP) has been reported to be released from cutaneous sensory nerve endings after hapten application, we determined whether SP participates in contact hypersensitivity (CH) induction by using a SP agonist, GR73632 or δ-Aminovaleryl [Pro9, N-Me-Leu10[-substance P7–11 and a SP antagonist, spantide I. When injected intradermally, SP agonist enhanced CH induced by conventional, but not optimal, sensitizing doses of hapten. By contrast, SP antagonist inhibited the induction of CH by optimal sensitizing doses of hapten. Moreover, SP agonist promoted CH induction and prevented tolerance when hapten was painted on skin exposed to acute, low-dose ultraviolet-B radiation. Intradermally injected SP agonist altered neither the density nor the morphology of epidermal Langerhans cells, implying that SP agonist enhanced the generation of hapten-specific immunogenic signals from the dermis. It is proposed that SP is a natural “adjuvant” that promotes the induction of CH within normal skin. Although exogenous SP agonist can prevent impaired CH and tolerance after ultraviolet-B radiation, the susceptibility of native SP to local neuropeptidases renders the neuropeptide unable to prevent the deleterious effects of ultraviolet-B radiation on cutaneous immunity

Solution of the genaralized periodic discrete Toda equation

A box-ball system with more than one kind of balls is obtained by the generalized periodic discrete Toda equation (pd Toda eq.). We study the pd Toda equation in view of algebraic geometry. The time evolution of pd Toda eq. is linearized on an algebraic variety, and theta function solutions are obtained.Comment: 18pages, 1figur

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

The Coupled Modified Korteweg-de Vries Equations

Generalization of the modified KdV equation to a multi-component system, that is expressed by $(\partial u_i)/(\partial t) + 6 (\sum_{j,k=0}^{M-1} C_{jk} u_j u_k) (\partial u_i)/(\partial x) + (\partial^3 u_{i})/(\partial x^3) = 0, i=0, 1, ..., M-1$, is studied. We apply a new extended version of the inverse scattering method to this system. It is shown that this system has an infinite number of conservation laws and multi-soliton solutions. Further, the initial value problem of the model is solved.Comment: 26 pages, LaTex209 file, uses jpsj.st

Perturbative QCD Forbidden Charmonium Decays and Gluonia

We address the problem of observed charmonium decays which should be forbidden in perturbative QCD. We examine the model in which these decays proceed through a gluonic component of the $J/\Psi$ and the $\eta_c$, arising from a mixing of $(c\bar c)$ and glueball states. We give some bounds on the values of the mixing angles and propose the study of the $p \bar{p} \to \phi \phi$ reaction, at $\sqrt{s} \simeq 3$ GeV, as an independent test of the model.Comment: 8pages, lateX, DFTT 64-9

KLF9 and JNK3 Interact to Suppress Axon Regeneration in the Adult CNS

Neurons in the adult mammalian CNS decrease in intrinsic axon growth capacity during development in concert with changes in Krüppel-like transcription factors (KLFs). KLFs regulate axon growth in CNS neurons including retinal ganglion cells (RGCs). Here, we found that knock-down of KLF9, an axon growth suppressor that is normally upregulated 250-fold in RGC development, promotes long-distance optic nerve regeneration in adult rats of both sexes. We identified a novel binding partner, MAPK10/JNK3 kinase, and found that JNK3 (c-Jun N-terminal kinase 3) is critical for KLF9\u27s axon-growth-suppressive activity. Interfering with a JNK3-binding domain or mutating two newly discovered serine phosphorylation acceptor sites, Ser106 and Ser110, effectively abolished KLF9\u27s neurite growth suppression in vitro and promoted axon regeneration in vivo. These findings demonstrate a novel, physiologic role for the interaction of KLF9 and JNK3 in regenerative failure in the optic nerve and suggest new therapeutic strategies to promote axon regeneration in the adult CNS

Similitude and scale effects of air entrainment in hydraulic jumps

A hydraulic jump is characterised by some strong turbulence and air entrainment in the roller. New measurements were performed in two channels in which similar experiments with identical inflow Froude numbers and relative channel widths were conducted with a geometric scaling ratio of 2:1. Void fraction distributions showed the presence of an advection/diffusion shear layer in which the data followed an analytical solution of the diffusion equation for air bubbles. The data indicated some scale effects in the small channel in terms of void fraction and bubble count rate. Void fraction distributions implied comparatively greater detrainment at low Reynolds numbers yielding to lesser overall aeration of the jump roller. Dimensionless bubble count rates were significantly lower in the smaller channel especially in the mixing layer. The study is believed to be the first systematic investigation of scale effects affecting air entrainment in hydraulic jumps using an accurate air-water measurement technique