The central distributions of gustatory and non-gustatory branches of cranial nerves V, VII, IX, and X were examined after application of horseradish peroxidase to the cut nerve. The nerves conveying gustatory information, chorda tympani (CT), greater superficial petrosal (GSP), lingual-tonsilar branch of IX (LT-IX), superior laryngeal branch of X (SL), distributed primarily to the lateral division of the nucleus of the solitary tract (NST) from its rostral pole to the obex. The CT and GSP distributions were coextensive and terminated most densely in the rostral pole of NST. The LT-IX distribution concentrated between this major CT/GSP distribution and the area postrema with a caudal extension into the interstitial nucleus of NST. This nerve also had a substantial projection, not found in other gustatory nerves, into the dorsolateral aspect of the medial NST. The SL distribution overlapped LT-IX in the caudal medulla. The lingual and inferior alveolar nerves, two oral trigeminal branches, projected to regions of NST innervated by the gustatory nerves. The cervical vagus nerve distributed primarily to the medial NST in the caudal half of the nucleus and exhibited only minimal overlap with gustatory nerve distributions. The nucleus of the solitary tract appears to have two major functional divisions--an anterior-lateral oral-gustatory half, and a posterior-medial visceral afferent half.

Over much of the past 25 years, the cycles of house price and consumption growth have been closely synchronised. Three main hypotheses for this co-movement have been proposed in the literature. First, that an increase in house prices raises households' wealth, particularly for those in a position to trade down the housing ladder, which increases their desired level of expenditure. Second, that house price growth increases the collateral available to homeowners, reducing credit constraints and thereby facilitating higher consumption. And third, that house prices and consumption have tended to be influenced by common factors. This paper finds that the relationship between house prices and consumption is stronger for younger than older households, which appears to contradict the wealth channel. These findings therefore suggest that common causality has been the most important factor behind the link between house price and consumption.

The efferent projections of the parvicellular division of the ventroposteromedial nucleus of the thalamus (VMPpc; thalamic taste area) were traced to cortex in Macaca fascicularis by using tritiated amino acid autoradiography. Labeled fascicles could be traced from VPMpc to two discrete regions of cortex. The primary efferent projection was located on ipsilateral insular-opercular cortex adjacent to the superior limiting sulcus and extended as far rostrally as the posterior lateral orbitofrontal cortex. An additional projection was located within primary somatosensory (SI) cortex subjacent to the anterior subcentral sulcus. Following autoradiographic injections in VPM, the trigeminal somatosensory relay, a dense terminal plexus was labeled on SI cortex of both pre- and postcentral gyri, but not within insular-opercular cortex. The autoradiographic data were verified by injecting each cortical projection area with horseradish peroxidase (HRP) and observing the pattern of retrogradely labeled somata within the thalamus. Injections in the precentral gyrus near the anterior subcentral sulcus retrogradely labeled neurons within VPMpc, whereas injections further caudally near the floor of the central sulcus labeled neurons within VPM. Injections of HRP within opercular, insular, or posterior lateral orbitofrontal cortex retrogradely labeled neurons within VPMpc.

We study the regularity of the free boundary for solutions of the porous medium equation u t = Δ u m u_{t}=\Delta u^{m} , m > 1 m >1 , on R 2 × [ 0 , T ] {\mathcal {R}}^{2} \times [0,T] , with initial data u 0 = u ( x , 0 ) u^{0}=u(x,0) nonnegative and compactly supported. We show that, under certain assumptions on the initial data u 0 u^{0} , the pressure f = m u m − 1 f=m\, u^{m-1} will be smooth up to the interface Γ = ∂ { u > 0 } \Gamma = \partial \{ u >0 \} , when 0 > t ≤ T 0>t\leq T , for some T > 0 T >0 . As a consequence, the free-boundary Γ \Gamma is smooth.

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