Linear resolutions of powers and products

The goal of this paper is to present examples of families of homogeneous ideals in the polynomial ring over a field that satisfy the following condition: every product of ideals of the family has a linear free resolution. As we will see, this condition is strongly correlated to good primary decompositions of the products and good homological and arithmetical properties of the associated multi-Rees algebras. The following families will be discussed in detail: polymatroidal ideals, ideals generated by linear forms and Borel fixed ideals of maximal minors. The main tools are Gr\"obner bases and Sagbi deformation

Effects of Cocaine-Kindling on the Expression of NMDA Receptors and Glutamate Levels in Mouse Brain

In the present study we examined the effects of cocaine seizure kindling on the expression of NMDA receptors and levels of extracellular glutamate in mouse brain. Quantitative autoradiography did not reveal any changes in binding of [3H] MK-801 to NMDA receptors in several brain regions. Likewise, in situ hybridization and Western blotting revealed no alteration in expression of the NMDA receptor subunits, NR1 and NR2B. Basal overflow of glutamate in the ventral hippocampus determined by microdialysis in freely moving animals also did not differ between cocaine-kindled and control groups. Perfusion with the selective excitatory amino acid transporter inhibitor, pyrrolidine-2,4-dicarboxylic acid (tPDC, 0.6 mM), increased glutamate overflow confirming transport inhibition. Importantly, KCl-evoked glutamate overflow under tPDC perfusion was significantly higher in cocaine-kindled mice than in control mice. These data suggest that enhancement of depolarization stimulated glutamate release may be one of the mechanisms underlying the development of increased seizure susceptibility after cocaine kindling

Kappa opioid receptor agonists suppress absence seizures in WAG/Rij rats

Contains fulltext : 28023.pdf (publisher's version ) (Open Access)Involvement of the kappa opioid receptor in the regulation of epileptic activity was studied in WAG/Rij rats, a genetic model of absence epilepsy. I.c.v. administration of the kappa agonists U50,488H (trans-3,4-dichloro-N-methyl-N-[2-(1-pyrrolidinyl)-cyclohexyl]- benzeneacetamide), U69,593 (5 alpha, 7 alpha, 8 beta)-(-)-N-methyl-(1-pyrrolidinyl)-1- oxaspiro(4,5)dec-8-yl)benzeneacetamide) or PD117,302 ((+/-)-trans-N-methyl-N-[2-(1-pyrrolidinyl)- cyclohexyl]benzo[b]thiophene-4-acetamide), 50 and 150 micrograms/5 microliter each, dose-dependently decreased the number and mean duration of spike wave discharges (SWD). Peripheral administration of U50,488H (10 and 30 mg/kg s.c.) also attenuated the seizure activity in this model. The specific kappa opioid receptor antagonist nor-binaltorphimine (Nor-BNI, 10 micrograms/5 microliters i.c.v., 18 h before EEG registration) moderately increased the number of SWD, which suggests that endogenous opioids acting through kappa receptors may tonically inhibit the seizure activity in these rats. In addition, the enhancement of an absence-like seizure activity induced by the specific mu opioid receptor agonist D-Ala2-N-methyl-Phe4-Gly5-ol-enkephalin (DAMGO, 0.7 microgram/5 microliters i.c.v.) was also attenuated in rats pretreated with U50,488H, U69,593 or PD117,302. These data indicate that activation of the kappa opioid receptor exerts an inhibitory effect on absence-like seizure activity in WAG/Rij rats