Morphological filtering on hypergraphs

The focus of this article is to develop computationally efficient mathematical morphology operators on hypergraphs. To this aim we consider lattice structures on hypergraphs on which we build morphological operators. We develop a pair of dual adjunctions between the vertex set and the hyper edge set of a hypergraph H, by defining a vertex-hyperedge correspondence. This allows us to recover the classical notion of a dilation/erosion of a subset of vertices and to extend it to subhypergraphs of H. Afterward, we propose several new openings, closings, granulometries and alternate sequential filters acting (i) on the subsets of the vertex and hyperedge set of H and (ii) on the subhypergraphs of a hypergraph

2,4-Bis(4-eth­oxy­phen­yl)-7-methyl-3-aza­bicyclo­[3.3.1]nonan-9-one

The mol­ecule of the title compound, C25H31NO3, exists in a twin-chair conformation with an equatorial orientation of the 4-eth­oxy­phenyl groups, as observed for its ortho isomer [Parthiban, Ramkumar, Park & Jeong (2011b ▶), Acta Cryst. E67, o1475–o1476]. The methyl and 4-eth­oxy­phenyl groups are also equatorially oriented on the bicycle, as in the ortho analogue. In particular, although the cyclo­hexa­none ring deviates from an ideal chair, the piperidone ring is closer to an ideal chair, whereas in the ortho isomer both rings are significantly puckered and deviate from ideal chairs. The 4-eth­oxy­phenyl groups on both sides of the secondary amine group are oriented at an angle of 26.11 (3)° with respect to each other, but the 2-eth­oxy­phenyl groups in the ortho isomer are oriented by less than half this [12.41 (4)°]. In contrast to the absence of any significant inter­actions in the crystal packing of the ortho isomer, the title compound features N—H⋯O inter­actions, linking the mol­ecules along the b axis

The endocannabinoid/cannabinoid receptor 2 system protects against cisplatin-induced hearing loss

Previous studies have demonstrated the presence of cannabinoid 2 receptor (CB2R) in the rat cochlea which was induced by cisplatin. In an organ of Corti-derived cell culture model, it was also shown that an agonist of the CB2R protected these cells against cisplatin-induced apoptosis. In the current study, we determined the distribution of CB2R in the mouse and rat cochleae and examined whether these receptors provide protection against cisplatin-induced hearing loss. In a knock-in mouse model expressing the CB2R tagged with green fluorescent protein, we show distribution of CB2R in the organ of Corti, stria vascularis, spiral ligament and spiral ganglion cells. A similar distribution of CB2R was observed in the rat cochlea using a polyclonal antibody against CB2R. Trans-tympanic administration of (2-methyl-1-propyl-1H-indol-3-yl)-1-naphthalenylmethanone (JWH015), a selective agonist of the CB2R, protected against cisplatin-induced hearing loss which was reversed by blockade of this receptor with 6-iodo-2-methyl-1-[2-(4-morpholinyl)ethyl]-1H-indol-3-yl](4-methoxyphenyl)methanone (AM630), an antagonist of CB2R. JWH015 also reduced the loss of outer hair cells (OHCs) in the organ of Corti, loss of inner hair cell (IHC) ribbon synapses and loss of Na+/K+-ATPase immunoreactivity in the stria vascularis. Administration of AM630 alone produced significant hearing loss (measured by auditory brainstem responses) which was not associated with loss of OHCs, but led to reductions in the levels of IHC ribbon synapses and strial Na+/K+-ATPase immunoreactivity. Furthermore, knock-down of CB2R by trans-tympanic administration of siRNA sensitized the cochlea to cisplatin-induced hearing loss at the low and middle frequencies. Hearing loss induced by cisplatin and AM630 in the rat was associated with increased expression of genes for oxidative stress and inflammatory proteins in the rat cochlea. In vitro studies indicate that JWH015 did not alter cisplatin-induced killing of cancer cells suggesting this agent could be safely used during cisplatin chemotherapy. These data unmask a protective role of the cochlear endocannabinoid/CB2R system which appears tonically active under normal conditions to preserve normal hearing. However, an exogenous agonist is needed to boost the activity of endocannabinoid/CB2R system for protection against a more traumatic cochlear insult, as observed with cisplatin administration.</p

1-Methyl-2,4-bis­(2-methoxy­phen­yl)-3-aza­bicyclo­[3.3.1]nonan-9-one

The crystal structure of the title compound, C23H27NO3, shows that the compound exists in a chair–chair conformation with an equatorial disposition of 2-methoxy­phenyl groups at an angle of 39.94 (3)° with respect to each other. An inter­molecular N—H⋯π inter­action is observed in the crystal packing

2,4-Bis(2-methyl­phen­yl)-3-aza­bicyclo[3.3.1]nonan-9-one O-methyl­oxime

The mol­ecule of the title compound, C23H28N2O, exists in a twin-chair conformation, with equatorial orientation of the ortho-tolyl groups on both sides of the secondary amino group. The title oxime compound and its ketone precursor 2,4-bis­(2-methyl­phen­yl)-3-aza­bicyclo­[3.3.1]nonan-9-one exhibit similar stereochemistries, with the orientation of the o-tolyl rings almost identical in both compounds. In the title compound, the tolyl rings are at an angle of 23.77 (3)° with respect to one another; the angle in the precursor is 29.4 (1)° [Vijayalakshmi, Parthasarathi, Venkatraj & Jeyaraman (2000 ▶), Acta Cryst. C56, 1240–1241]. The cyclo­hexane ring and the oxime ether are disordered over two alternative orientations, with a refined site-occupancy ratio of 0.813 (2):0.186 (4). The crystal structure of the title compound is stabilized by inter­molecular N—H⋯π inter­actions

2,4-Bis(4-propoxyphen­yl)-3-aza­bicyclo­[3.3.1]nonan-9-one

In the title compound, C26H33NO3, a crystallographic mirror plane bis­ects the mol­ecule (two C atoms, one O atom and one N atom lie on the mirror plane). The mol­ecule exists in a twin-chair conformation with equatorial orientations of the 4-propoxyphenyl groups. The dihedral angle between the 4-propoxyphenyl groups is 31.58 (3)°