Vertex operator for the non-autonomous ultradiscrete KP equation

We propose an ultradiscrete analogue of the vertex operator in the case of the ultradiscrete KP equation--several other ultradiscrete equations--which maps N-soliton solutions to N+1-soliton ones.Comment: 9 page

PLA2 activity is required for nuclear shrinkage in caspase-independent cell death

Apoptosis is defined on the basis of morphological changes like nuclear fragmentation and chromatin condensation, which are dependent on caspases. Many forms of caspase-independent cell death have been reported, but the mechanisms are still poorly understood. We found that hypoxic cell death was independent of caspases and was associated with significant nuclear shrinkage. Neither Bcl-2 nor Apaf-1 deficiency prevented hypoxic nuclear shrinkage. To understand the molecular mechanism of the nuclear shrinkage, we developed an in vitro system using permeabilized cells, which allowed us to purify a novel member of the phospholipase A2 (PLA2) family that induced nuclear shrinkage. Purified PLA2 induced nuclear shrinkage in our permeabilized cell system. PLA2 inhibitors prevented hypoxic nuclear shrinkage in cells and cell death. Hypoxia caused elevation of PLA2 activity and translocation of intracellular PLA2s to the nucleus. Knockdown of the Ca2+-independent PLA2 delayed nuclear shrinkage and cell death. These results indicate that Ca2+-independent PLA2 is crucial for a caspase-independent cell death signaling pathway leading to nuclear shrinkage

Symmetric Linear Backlund Transformation for Discrete BKP and DKP equation

Proper lattices for the discrete BKP and the discrete DKP equaitons are determined. Linear B\"acklund transformation equations for the discrete BKP and the DKP equations are constructed, which possesses the lattice symmetries and generate auto-B\"acklund transformationsComment: 18 pages,3 figure

Bilinear Equations and B\"acklund Transformation for Generalized Ultradiscrete Soliton Solution

Ultradiscrete soliton equations and B\"acklund transformation for a generalized soliton solution are presented. The equations include the ultradiscrete KdV equation or the ultradiscrete Toda equation in a special case. We also express the solution by the ultradiscrete permanent, which is defined by ultradiscretizing the signature-free determinant, that is, the permanent. Moreover, we discuss a relation between B\"acklund transformations for discrete and ultradiscrete KdV equations.Comment: 11 page