Coboundary Lie bialgebras and commutative subalgebras of universal enveloping algebras

We solve a functional version of the problem of twist quantization of a coboundary Lie bialgebra (g,r,Z). We derive from this the following results: (a) the formal Poisson manifolds g^* and G^* are isomorphic; (b) we construct a subalgebra of U(g^*), isomorphic to S(g^*)^g. When g can be quantized, we construct a deformation of the morphism S(g^*)^g subset U(g^*). When g is quasitriangular and nondegenerate, we compare our construction with Semenov-Tian-Shansky's construction of a commutative subalgebra of U(g^*). We also show that the canonical derivation of the function ring of G^* is Hamiltonian

Poisson algebras associated to quasi-Hopf algebras

We define admissible quasi-Hopf quantized universal enveloping (QHQUE) algebras by h-adic valuation conditions. We show that any QHQUE algebra is twist-equivalent to an admissible one. We prove a related statement: any associator is twist-equivalent to a Lie associator. We attach a quantized formal series algebra to each admissible QHQUE algebra and study the resulting Poisson algebras.Comment: We construct a lift for any Lie quasi-bialgebra with zero cobracke

Formality theorems for Hochschild chains in the Lie algebroid setting

In this paper we prove Lie algebroid versions of Tsygan's formality conjecture for Hochschild chains both in the smooth and holomorphic settings. In the holomorphic setting our result implies a version of Tsygan's formality conjecture for Hochschild chains of the structure sheaf of any complex manifold and in the smooth setting this result allows us to describe quantum traces for an arbitrary Poisson Lie algebroid. The proofs are based on the use of Kontsevich's quasi-isomorphism for Hochschild cochains of R[[y_1,...,y_d]], Shoikhet's quasi-isomorphism for Hochschild chains of R[[y_1,...,y_d]], and Fedosov's resolutions of the natural analogues of Hochschild (co)chain complexes associated with a Lie algebroid.Comment: 40 pages, no figure

Differential Regulation of the Period Genes in Striatal Regions following Cocaine Exposure

Several studies have suggested that disruptions in circadian rhythms contribute to the pathophysiology of multiple psychiatric diseases, including drug addiction. In fact, a number of the genes involved in the regulation of circadian rhythms are also involved in modulating the reward value for drugs of abuse, like cocaine. Thus, we wanted to determine the effects of chronic cocaine on the expression of several circadian genes in the Nucleus Accumbens (NAc) and Caudate Putamen (CP), regions of the brain known to be involved in the behavioral responses to drugs of abuse. Moreover, we wanted to explore the mechanism by which these genes are regulated following cocaine exposure. Here we find that after repeated cocaine exposure, expression of the Period (Per) genes and Neuronal PAS Domain Protein 2 (Npas2) are elevated, in a somewhat regionally selective fashion. Moreover, NPAS2 (but not CLOCK (Circadian Locomotor Output Cycles Kaput)) protein binding at Per gene promoters was enhanced following cocaine treatment. Mice lacking a functional Npas2 gene failed to exhibit any induction of Per gene expression after cocaine, suggesting that NPAS2 is necessary for this cocaine-induced regulation. Examination of Per gene and Npas2 expression over twenty-four hours identified changes in diurnal rhythmicity of these genes following chronic cocaine, which were regionally specific. Taken together, these studies point to selective disruptions in Per gene rhythmicity in striatial regions following chronic cocaine treatment, which are mediated primarily by NPAS2. © 2013 Falcon et al

Capacitance free generation and detection of subpicosecond electrical pulses on coplanar transmission lines

Based on a reanalysis of previous work and new experimental measurements, we conclude that the parasitic capacitance at the generation site is negligible for sliding contact excitation of small dimension coplanar transmission lines.Peer reviewedElectrical and Computer Engineerin

Deletion of the GABAA α2-subunit does not alter self dministration of cocaine or reinstatement of cocaine seeking

Rationale GABAA receptors containing α2-subunits are highly represented in brain areas that are involved in motivation and reward, and have been associated with addiction to several drugs, including cocaine. We have shown previously that a deletion of the α2-subunit results in an absence of sensitisation to cocaine. Objective We investigated the reinforcing properties of cocaine in GABAA α2-subunit knockout (KO) mice using an intravenous self-administration procedure. Methods α2-subunit wildtype (WT), heterozygous (HT) and KO mice were trained to lever press for a 30 % condensed milk solution. After implantation with a jugular catheter, mice were trained to lever press for cocaine (0.5 mg/kg/infusion) during ten daily sessions. Responding was extinguished and the mice tested for cue- and cocaine-primed reinstatement. Separate groups of mice were trained to respond for decreasing doses of cocaine (0.25, 0.125, 0.06 and 0.03 mg/kg). Results No differences were found in acquisition of lever pressing for milk. All genotypes acquired self-administration of cocaine and did not differ in rates of self-administration, dose dependency or reinstatement. However, whilst WT and HT mice showed a dose-dependent increase in lever pressing during the cue presentation, KO mice did not. Conclusions Despite a reported absence of sensitisation, motivation to obtain cocaine remains unchanged in KO and HT mice. Reinstatement of cocaine seeking by cocaine and cocaine-paired cues is also unaffected. We postulate that whilst not directly involved in reward perception, the α2-subunit may be involved in modulating the “energising” aspect of cocaine’s effects on reward-seeking