The orientable cover of the moduli space of real genus zero algebraic curves with marked points is a compact aspherical manifold tiled by associahedra, which resolves the singularities of the space of phylogenetic trees. The resolution maps planar metric trees to their underlying abstract representatives, collapsing and folding an explicit geometric decomposition of the moduli space into cubes, endowing the resolving space with an interesting canonical pseudometric. Indeed, the given map can be reinterpreted as relating the real and the tropical versions of the Deligne–Knudsen–Mumford compactification of the moduli space of Riemann spheres.
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The advent of dendritic spines in the aspect of treatment of illnesses see educreations
J Neurosci. 2012 May 16;32(20):6795-807. doi: 10.1523/JNEUROSCI.1017-12.2012.
Maladaptive dendritic spine remodeling contributes to diabetic neuropathic pain.
Tan AM1, Samad OA, Fischer TZ, Zhao P, Persson AK, Waxman SG.
Diabetic neuropathic pain imposes a huge burden on individuals and society, and represents a major public health problem. Despite aggressive efforts, diabetic neuropathic pain is generally refractory to available clinical treatments. A structure-function link between maladaptive dendritic spine plasticity and pain has been demonstrated previously in CNS and PNS injury models of neuropathic pain. Here, we reasoned that if dendritic spine remodeling contributes to diabetic neuropathic pain, then (1) the presence of malformed spines should coincide with the development of pain, and (2) disrupting maladaptive spine structure should reduce chronic pain. To determine whether dendritic spine remodeling contributes to neuropathic pain in streptozotocin (STZ)-induced diabetic rats, we analyzed dendritic spine morphology and electrophysiological and behavioral signs of neuropathic pain. Our results show changes in dendritic spine shape, distribution, and shape on wide-dynamic-range (WDR) neurons within lamina IV-V of the dorsal horn in diabetes. These diabetes-induced changes were accompanied by WDR neuron hyperexcitability and decreased pain thresholds at 4 weeks. Treatment with NSC23766 (N(6)-[2-[[4-(diethylamino)-1-methylbutyl]amino]-6-methyl-4-pyrimidinyl]-2-methyl-4,6-quinolinediamine trihydrochloride), a Rac1-specific inhibitor known to interfere with spine plasticity, decreased the presence of malformed spines in diabetes, attenuated neuronal hyperresponsiveness to peripheral stimuli, reduced spontaneous firing activity from WDR neurons, and improved nociceptive mechanical pain thresholds. At 1 week after STZ injection, animals with hyperglycemia with no evidence of pain had few or no changes in spine morphology. These results demonstrate that diabetes-induced maladaptive dendritic spine remodeling has a mechanistic role in neuropathic pain. Molecular pathways that control spine morphogenesis and plasticity may be promising future targets for treatment.
PMID: 22593049 [PubMed – indexed for MEDLINE] Free full text