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Midbrain dopaminergic (DAergic) regions including ventral tegmental area (VTA) and substantia nigra pars compacta (SNc) are involved in diverse brain functions. Previous studies demonstrated that the VTA/SNc to nucleus accumbens (NAc) pathway is critical in reward and motivation. Moreover, DAergic innervations within the insular cortex (IC) are reported to play important roles in pain regulation. To investigate whether VTA/SNc sends collateral projections to NAc and IC, we injected retrograde tracer Fluoro-Gold (FG) into the NAc and Fluorescent retrograde tracer beads (RetroBeads) into the ipsilateral IC in rats. Then, to detect whether collateral projection neurons participate in neuropathic pain, parts of the rats received the spare nerve injury (SNI) surgery. The immunofluorescence staining results showed that FG, RetroBeads, and FG/RetroBeads double-labeled neurons were distributed in the VTA/SNc bilaterally with an ipsilateral predominance. The proportion of FG/RetroBeads double-labeled neurons to the total number of FG and RetroBeads-labeled neurons was 16.7% and 30.3%, respectively. About 90.3% of FG/RetroBeads double-labeled neurons showed DAergic neuron marker tyrosine hydroxylase (TH)-immunoreactive (IR), whereas, only 7.5% exhibited a subset of GABAergic inhibitory projection neuron marker parvalbumin (PV)-IR. One week after SNI, about 53.1% and 33.6% of FG- and RetroBeads-labeled neurons were FG/Fos- and RetroBeads/Fos-IR neurons, respectively. Finally, about 35.9% of the FG/RetroBeads double-labeled neurons showed Fos-IR. The present study indicates that parts of DAergic and PV-IR GABAergic neurons in the VTA/SNc send collateral projections to both NAc and IC, which are activated under SNI-induced neuropathic pain, and probably contribute to the regulation of nociception. [ABSTRACT FROM AUTHOR]

Directionally solidified single crystal superalloy test bars were prepared by the spiral grain selection method. The microstructural evolution and orientation characteristics of the starter block and spiral part were studied, and the influence of the competitive growth of crystals on the microstructural characteristics was analyzed. The results show that the divergent grain groups, with small size and randomly oriented grains, appear at the bottom of the start block due to the chilling effect, which is an important area for competitive growth. As the height of the starter block increases, the primary dendrite spacing increases, and the grain density decreases; furthermore, the proportion of grains with an orientation deflection angle less than 10° gradually increases. The <001> texture gradually becomes stronger as the height of the starter block increases, which indicates that the competitive growth of crystals gradually weakens. At the initial stage of the crystal selection in the spiral part, the obstacle of adjacent grains and spiral passage is the main working mechanism. The grains located at the inner side of the front edge of the spiral passage have the growth advantage. The single crystal screening process is achieved at about two-thirds of the spiral height, and the single crystal with the orientation deviation angle of 6.7° from the casting axis is prepared. [ABSTRACT FROM AUTHOR]

We describe the relation between quasi-minuscule representations, polytopes and Weyl group orbits in Picard lattices of rational surfaces. As an application, to each quasi-minuscule representation we attach a class of rational surfaces, and realize such a representation as an associated vector bundle of a principal bundle over these surfaces. Moreover, any quasi-minuscule representation can be defined by rational curves, or their disjoint unions in a rational surface, satisfying certain natural numerical conditions. [ABSTRACT FROM AUTHOR]

In this article, we study certain quadratic Diophantine equations in Picard lattices of blow-ups of the complex projective plane, and describe their relations with root systems and Weyl group orbits of quasiminuscule fundamental weights. We apply these to study the geometry of certain rational surfaces. [ABSTRACT FROM AUTHOR]

Given an elliptic curve Σ, flat E-bundles over Σ are in one-to-one correspondence with smooth del Pezzo surfaces of degree 9 − k containing Σ as an anti-canonical curve. This correspondence was generalized to Lie groups of any type. In this article, we show that there is a similar correspondence between del Pezzo surfaces of degree 0 with an A-singularity containing Σ as an anti-canonical curve and Kac-Moody $${\widetilde{E}_{k}}$$-bundles over Σ with k = 8 − d. In the degenerate case where surfaces are rational elliptic surfaces, the corresponding $${\widetilde{E}_k}$$-bundles over Σ can be reduced to E-bundles. [ABSTRACT FROM AUTHOR]

In this paper, for an arbitrary regular biordered setE, by using biorder-isomorphisms between the ?-ideals ofE, we construct a fundamental regular semigroupWE called NH-semigroup ofE, whose idempotent biordered set is isomorphic toE. We prove further thatWE can be used to give a new representation of general regular semigroups in the sense that, for any regular semigroupSwith the idempotent biordered set isomorphic toE, there exists a homomorphism fromStoWE whose kernel is the greatest idempotent-separating congruence onSand the image is a full symmetric subsemigroup ofWE. Moreover, whenEis a biordered set of a semilatticeE0,WE is isomorphic to the Munn-semigroup; and whenEis the biordered set of a bandB,WE is isomorphic to the Hall-semigroupWB. [ABSTRACT FROM AUTHOR]