The graded Jacobi algebras and (co)homology

Jacobi algebroids (i.e. `Jacobi versions' of Lie algebroids) are studied in the context of graded Jacobi brackets on graded commutative algebras. This unifies varios concepts of graded Lie structures in geometry and physics. A method of describing such structures by classical Lie algebroids via certain gauging (in the spirit of E.Witten's gauging of exterior derivative) is developed. One constructs a corresponding Cartan differential calculus (graded commutative one) in a natural manner. This, in turn, gives canonical generating operators for triangular Jacobi algebroids. One gets, in particular, the Lichnerowicz-Jacobi homology operators associated with classical Jacobi structures. Courant-Jacobi brackets are obtained in a similar way and use to define an abstract notion of a Courant-Jacobi algebroid and Dirac-Jacobi structure. All this offers a new flavour in understanding the Batalin-Vilkovisky formalism.Comment: 20 pages, a few typos corrected; final version to be published in J. Phys. A: Math. Ge

Jacobi structures revisited

Jacobi algebroids, that is graded Lie brackets on the Grassmann algebra associated with a vector bundle which satisfy a property similar to that of the Jacobi brackets, are introduced. They turn out to be equivalent to generalized Lie algebroids in the sense of Iglesias and Marrero and can be viewed also as odd Jacobi brackets on the supermanifolds associated with the vector bundles. Jacobi bialgebroids are defined in the same manner. A lifting procedure of elements of this Grassmann algebra to multivector fields on the total space of the vector bundle which preserves the corresponding brackets is developed. This gives the possibility of associating canonically a Lie algebroid with any local Lie algebra in the sense of Kirillov.Comment: 20 page

On classical finite and affine W-algebras

This paper is meant to be a short review and summary of recent results on the structure of finite and affine classical W-algebras, and the application of the latter to the theory of generalized Drinfeld-Sokolov hierarchies.Comment: 12 page

Integrable Euler top and nonholonomic Chaplygin ball

We discuss the Poisson structures, Lax matrices, $r$-matrices, bi-hamiltonian structures, the variables of separation and other attributes of the modern theory of dynamical systems in application to the integrable Euler top and to the nonholonomic Chaplygin ball.Comment: 25 pages, LaTeX with AMS fonts, final versio

Natural Diagonal Riemannian Almost Product and Para-Hermitian Cotangent Bundles

We obtain the natural diagonal almost product and locally product structures on the total space of the cotangent bundle of a Riemannian manifold. We find the Riemannian almost product (locally product) and the (almost) para-Hermitian cotangent bundles of natural diagonal lift type. We prove the characterization theorem for the natural diagonal (almost) para-K\"ahlerian structures on the total spaces of the cotangent bundle.Comment: 10 pages, will appear in Czechoslovak Mathematical Journa

Quantum Gravity from Noncommutative Spacetime

We review a novel and authentic way to quantize gravity. This novel approach is based on the fact that Einstein gravity can be formulated in terms of a symplectic geometry rather than a Riemannian geometry in the context of emergent gravity. An essential step for emergent gravity is to realize the equivalence principle, the most important property in the theory of gravity (general relativity), from U(1) gauge theory on a symplectic or Poisson manifold. Through the realization of the equivalence principle, which is an intrinsic property in symplectic geometry known as the Darboux theorem or the Moser lemma, one can understand how diffeomorphism symmetry arises from noncommutative U(1) gauge theory; thus, gravity can emerge from the noncommutative electromagnetism, which is also an interacting theory. As a consequence, a background-independent quantum gravity in which the prior existence of any spacetime structure is not a priori assumed but is defined by using the fundamental ingredients in quantum gravity theory can be formulated. This scheme for quantum gravity can be used to resolve many notorious problems in theoretical physics, such as the cosmological constant problem, to understand the nature of dark energy, and to explain why gravity is so weak compared to other forces. In particular, it leads to a remarkable picture of what matter is. A matter field, such as leptons and quarks, simply arises as a stable localized geometry, which is a topological object in the defining algebra (noncommutative $\star$-algebra) of quantum gravity.Comment: 97 pages, to be published in J. Korean Phys. So

Removal of Misincorporated Ribonucleotides from Prokaryotic Genomes: An Unexpected Role for Nucleotide Excision Repair

Stringent steric exclusion mechanisms limit the misincorporation of ribonucleotides by high-fidelity DNA polymerases into genomic DNA. In contrast, low-fidelity Escherichia coli DNA polymerase V (pol V) has relatively poor sugar discrimination and frequently misincorporates ribonucleotides. Substitution of a steric gate tyrosine residue with alanine (umuC_Y11A) reduces sugar selectivity further and allows pol V to readily misincorporate ribonucleotides as easily as deoxynucleotides, whilst leaving its poor base-substitution fidelity essentially unchanged. However, the mutability of cells expressing the steric gate pol V mutant is very low due to efficient repair mechanisms that are triggered by the misincorporated rNMPs. Comparison of the mutation frequency between strains expressing wild-type and mutant pol V therefore allows us to identify pathways specifically directed at ribonucleotide excision repair (RER). We previously demonstrated that rNMPs incorporated by umuC_Y11A are efficiently removed from DNA in a repair pathway initiated by RNase HII. Using the same approach, we show here that mismatch repair and base excision repair play minimal back-up roles in RER in vivo. In contrast, in the absence of functional RNase HII, umuC_Y11A-dependent mutagenesis increases significantly in ΔuvrA, uvrB5 and ΔuvrC strains, suggesting that rNMPs misincorporated into DNA are actively repaired by nucleotide excision repair (NER) in vivo. Participation of NER in RER was confirmed by reconstituting ribonucleotide-dependent NER in vitro. We show that UvrABC nuclease-catalyzed incisions are readily made on DNA templates containing one, two, or five rNMPs and that the reactions are stimulated by the presence of mispaired bases. Similar to NER of DNA lesions, excision of rNMPs proceeds through dual incisions made at the 8th phosphodiester bond 5′ and 4th-5th phosphodiester bonds 3′ of the ribonucleotide. Ribonucleotides misinserted into DNA can therefore be added to the broad list of helix-distorting modifications that are substrates for NER

Gene-specific repair of Pt/DNA lesions and induction of apoptosis by the oral platinum drug JM216 in three human ovarian carcinoma cell lines sensitive and resistant to cisplatin

JM216, an oral platinum drug entering into phase III clinical trial, exhibited comparable cytotoxicity to cisplatin in three human ovarian carcinoma cell lines: the sensitive (CH1), acquired resistant (CH1cisR) and intrinsically resistant (SKOV-3). Platinum accumulation and binding to DNA were similar in each of the three cell lines at equimolar doses, indicating that the resistant cell lines could tolerate higher intracellular platinum levels and platinum bound to DNA at IC50 concentrations of drug. Comparison with cisplatin demonstrated that intracellular platinum levels were marginally higher with JM216, but that platinum binding to DNA was similar for the two drugs in each of the cell lines. Each of the cell lines exhibited an ability to repair JM216 induced platinum/DNA lesions in the N-ras gene (gene-specific repair) at equitoxic concentrations of drug. However, this occurred to a greater extent in the two resistant cell lines such that by 24 h the CH1cisR and SKOV-3 had removed 72% and 67% respectively compared with approximately 32% for the CH1. Reduced gene-specific repair capacity in CH1 cells was also seen following incubation with 25 μM (or 5 μM – 2 × IC50) cisplatin, whereas the CH1cisR and SKOV-3 cell lines were repair proficient. JM216 induced apoptosis in the three cell lines following a 2h incubation with 2 × the IC50 of drug. Fluorescent microscopy of cells stained with propidium iodide showed that the detached cell population displayed typical apoptotic nuclei. Furthermore, field inversion gel electrophoresis demonstrated the presence of DNA fragments approximately 23–50 kb in size, indicative of apoptosis, in the detached cells. JM216 induced an S phase slow down in each of the three cell lines accompanied by a G2 block in the CH1 pair. Incubation with this concentration of JM216 also resulted in the induction of p53 in the CH1 and CH1cisR. These studies suggest that the relative sensitivity of the CH1 cell line to cisplatin and JM216 is at least partly attributable to a deficiency in gene-specific repair. The oral platinum drug, JM216, exerts its cytotoxic effects through the induction of apoptosis following a slow-down in S phase in both the sensitive and resistant lines. © 1999 Cancer Research Campaig

Quantizing N=2 Multicenter Solutions

N=2 supergravity in four dimensions, or equivalently N=1 supergravity in five dimensions, has an interesting set of BPS solutions that each correspond to a number of charged centers. This set contains black holes, black rings and their bound states, as well as many smooth solutions. Moduli spaces of such solutions carry a natural symplectic form which we determine, and which allows us to study their quantization. By counting the resulting wavefunctions we come to an independent derivation of some of the wall-crossing formulae. Knowledge of the explicit form of these wavefunctions allows us to find quantum resolutions to some apparent classical paradoxes such as solutions with barely bound centers and those with an infinitely deep throat. We show that quantum effects seem to cap off the throat at a finite depth and we give an estimate for the corresponding mass gap in the dual CFT. This is an interesting example of a system where quantum effects cannot be neglected at macroscopic scales even though the curvature is everywhere small.Comment: 49 pages + appendice