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

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

Backlund transformations for difference Hirota equation and supersymmetric Bethe ansatz

We consider GL(K|M)-invariant integrable supersymmetric spin chains with twisted boundary conditions and elucidate the role of Backlund transformations in solving the difference Hirota equation for eigenvalues of their transfer matrices. The nested Bethe ansatz technique is shown to be equivalent to a chain of successive Backlund transformations "undressing" the original problem to a trivial one.Comment: 22 pages, 2 figures, based on the talk given at the Workshop "Classical and Quantum Integrable Systems", Dubna, January 200

A Symmetric Generalization of Linear B\"acklund Transformation associated with the Hirota Bilinear Difference Equation

The Hirota bilinear difference equation is generalized to discrete space of arbitrary dimension. Solutions to the nonlinear difference equations can be obtained via B\"acklund transformation of the corresponding linear problems.Comment: Latex, 12 pages, 1 figur

T-systems and Y-systems in integrable systems

The T and Y-systems are ubiquitous structures in classical and quantum integrable systems. They are difference equations having a variety of aspects related to commuting transfer matrices in solvable lattice models, q-characters of Kirillov-Reshetikhin modules of quantum affine algebras, cluster algebras with coefficients, periodicity conjectures of Zamolodchikov and others, dilogarithm identities in conformal field theory, difference analogue of L-operators in KP hierarchy, Stokes phenomena in 1d Schr\"odinger problem, AdS/CFT correspondence, Toda field equations on discrete space-time, Laplace sequence in discrete geometry, Fermionic character formulas and combinatorial completeness of Bethe ansatz, Q-system and ideal gas with exclusion statistics, analytic and thermodynamic Bethe ans\"atze, quantum transfer matrix method and so forth. This review article is a collection of short reviews on these topics which can be read more or less independently.Comment: 156 pages. Minor corrections including the last paragraph of sec.3.5, eqs.(4.1), (5.28), (9.37) and (13.54). The published version (JPA topical review) also needs these correction

Legionella Metaeffector Exploits Host Proteasome to Temporally Regulate Cognate Effector

Pathogen-associated secretion systems translocate numerous effector proteins into eukaryotic host cells to coordinate cellular processes important for infection. Spatiotemporal regulation is therefore important for modulating distinct activities of effectors at different stages of infection. Here we provide the first evidence of “metaeffector,” a designation for an effector protein that regulates the function of another effector within the host cell. Legionella LubX protein functions as an E3 ubiquitin ligase that hijacks the host proteasome to specifically target the bacterial effector protein SidH for degradation. Delayed delivery of LubX to the host cytoplasm leads to the shutdown of SidH within the host cells at later stages of infection. This demonstrates a sophisticated level of coevolution between eukaryotic cells and L. pneumophila involving an effector that functions as a key regulator to temporally coordinate the function of a cognate effector protein

From nothing to something: discrete integrable systems

Chinese ancient sage Laozi said that everything comes from `nothing'. Einstein believes the principle of nature is simple. Quantum physics proves that the world is discrete. And computer science takes continuous systems as discrete ones. This report is devoted to deriving a number of discrete models, including well-known integrable systems such as the KdV, KP, Toda, BKP, CKP, and special Viallet equations, from `nothing' via simple principles. It is conjectured that the discrete models generated from nothing may be integrable because they are identities of simple algebra, model-independent nonlinear superpositions of a trivial integrable system (Riccati equation), index homogeneous decompositions of the simplest geometric theorem (the angle bisector theorem), as well as the M\"obious transformation invariants.Comment: 11 pages, side 10 repor

Protein Crosslinking by Transglutaminase Controls Cuticle Morphogenesis in Drosophila

Transglutaminase (TG) plays important and diverse roles in mammals, such as blood coagulation and formation of the skin barrier, by catalyzing protein crosslinking. In invertebrates, TG is known to be involved in immobilization of invading pathogens at sites of injury. Here we demonstrate that Drosophila TG is an important enzyme for cuticle morphogenesis. Although TG activity was undetectable before the second instar larval stage, it dramatically increased in the third instar larval stage. RNA interference (RNAi) of the TG gene caused a pupal semi-lethal phenotype and abnormal morphology. Furthermore, TG-RNAi flies showed a significantly shorter life span than their counterparts, and approximately 90% of flies died within 30 days after eclosion. Stage-specific TG-RNAi before the third instar larval stage resulted in cuticle abnormality, but the TG-RNAi after the late pupal stage did not, indicating that TG plays a key role at or before the early pupal stage. Immediately following eclosion, acid-extractable protein from wild-type wings was nearly all converted to non-extractable protein due to wing maturation, whereas several proteins remained acid-extractable in the mature wings of TG-RNAi flies. We identified four proteins—two cuticular chitin-binding proteins, larval serum protein 2, and a putative C-type lectin—as TG substrates. RNAi of their corresponding genes caused a lethal phenotype or cuticle abnormality. Our results indicate that TG-dependent protein crosslinking in Drosophila plays a key role in cuticle morphogenesis and sclerotization

Genetic Ablation of PLA2G6 in Mice Leads to Cerebellar Atrophy Characterized by Purkinje Cell Loss and Glial Cell Activation

Infantile neuroaxonal dystrophy (INAD) is a progressive, autosomal recessive neurodegenerative disease characterized by axonal dystrophy, abnormal iron deposition and cerebellar atrophy. This disease was recently mapped to PLA2G6, which encodes group VI Ca2+-independent phospholipase A2 (iPLA2 or iPLA2β). Here we show that genetic ablation of PLA2G6 in mice (iPLA2β-/-) leads to the development of cerebellar atrophy by the age of 13 months. Atrophied cerebella exhibited significant loss of Purkinje cells, as well as reactive astrogliosis, the activation of microglial cells, and the pronounced up-regulation of the pro-inflammatory cytokines tumor necrosis factor-α (TNF-α) and interleukin-1β (IL-1β). Moreover, glial cell activation and the elevation in TNF-α and IL-1β expression occurred before apparent cerebellar atrophy. Our findings indicate that the absence of PLA2G6 causes neuroinflammation and Purkinje cell loss and ultimately leads to cerebellar atrophy. Our study suggests that iPLA2β-/- mice are a valuable model for cerebellar atrophy in INAD and that early anti-inflammatory therapy may help slow the progression of cerebellar atrophy in this deadly neurodegenerative disease