On surfaces in P^4 and 3-folds in P^5

This is a survey on the classification of smooth surfaces in P^4 and smooth 3-folds in P^5. We recall the corresponding results arising from adjunction theory and explain how to construct examples via syzygies. We discuss some examples in detail and list all families of smooth non-general type surfaces in P^4 and 3-folds in P^5 known to us.Comment: 24 pages, AMS-TeX 2.

Single-Trial Phase Precession in the Hippocampus

During the crossing of the place field of a pyramidal cell in the rat hippocampus, the firing phase of the cell decreases with respect to the local theta rhythm. This phase precession is usually studied on the basis of data in which many place field traversals are pooled together. Here we study properties of phase precession in single trials. We found that single-trial and pooled-trial phase precession were different with respect to phase-position correlation, phase-time correlation, and phase range. Whereas pooled-trial phase precession may span 360°, the most frequent single-trial phase range was only ∼180°. In pooled trials, the correlation between phase and position (r = −0.58) was stronger than the correlation between phase and time (r = −0.27), whereas in single trials these correlations (r = −0.61 for both) were not significantly different. Next, we demonstrated that phase precession exhibited a large trial-to-trial variability. Overall, only a small fraction of the trial-to-trial variability in measures of phase precession (e.g., slope or offset) could be explained by other single-trial properties (such as running speed or firing rate), whereas the larger part of the variability remains to be explained. Finally, we found that surrogate single trials, created by randomly drawing spikes from the pooled data, are not equivalent to experimental single trials: pooling over trials therefore changes basic measures of phase precession. These findings indicate that single trials may be better suited for encoding temporally structured events than is suggested by the pooled data

Role of hilar mossy cells in the CA3-dentate gyrus network during sharp wave-ripple activity in vitro

Der Gyrus dentatus (DG) des Hippokampus wird als Eingangsstation für Informationen aus dem entorhinalen Kortex betrachtet. In das DG-Netzwerk sind zwei exzitatorische Zelltypen eingebettet: Körnerzellen, die Signale von dem entorhinalen Kortex empfangen, und Hilus-Mooszellen (MCs), die Signale von Körnerzellen als auch von feedback-Projektionen von CA3-Pyramidenzellen (PCs) empfangen. Postsynaptische Ziele von MC-Projektionen umfassen DG Körnerzellen und verschiedene Interneurone in der selben und in der kontralateralen Hemisphäre des Gehirns. Die Rolle von MCs während rhythmischer Populationsaktivität, und insbesondere während Sharp-Wave / Ripple-Komplexen (SWRs), ist bisher weitgehend unerforscht. SWRs sind prominente Ereignisse im Hippocampus während des Tiefschlafs (Slow wave sleep) und des ruhigen Wachzustandes, und sie sind an der Gedächtniskonsolidierung beteiligt. In der vorliegenden Arbeit, untersuchen wir mithilfe eines in-vitro-Modells von SWRs, inwieweit Mooszellen an SWRs in CA3 beteiligt sind. Mit CA3-Feldpotential-Ableitungen und gleichzeitigen ‚cell-attached‘ Messungen von einzelnen MCs konnten wir beobachten, dass ein wesentlicher Anteil von MCs (47%) während der SWRs in das aktive neuronale Netzwerk rekrutiert werden. Darüber hinaus fanden wir in MCs SWR-assoziierte synaptische Aktivität, bei denen sowohl die exzitatorischen als auch die inhibitorischen Komponenten phasenkohärent und verzögert zur Ripple Oszillation in CA3 auftreten. Simultane Patch-clamp Messungen von CA3-Pyramidenzellen und MCs zeigten längere exzitatorische und inhibitorische Latenzzeiten bei MCs, was die Hypothese einer von CA3 ausgehenden Feedback-Rekrutierung unterstützt. Unsere Daten zeigen zusätzlich, dass das Verhältnis exzitatorischer zu inhibitorischer Aktivität in MCs höher ist als in CA3-Pyramidenzellen, wodurch die MCs mit höherer Wahrscheinlichkeit während SWRs überschwellig aktiviert werden. Schließlich zeigen wir, dass ein signifikanter Anteil (66%) der getesteten Körnerzellen SWR-assoziierte exzitatorische Signale erhalten, im Vergleich zu MCs zeitlich verzögert, was auf eine indirekte Aktivierung von Körnerzellen durch CA3 PCs über MCs hinweist. Zusammengefasst zeigen unsere Daten die aktive Beteiligung von Mooszellen an SWRs und deuten auf eine funktionelle Bedeutung als Schaltstelle für das CA3- Gyrus dentatus Netzwerk in diesem wichtigen physiologischen Netzwerkzustand hin.The dentate gyrus (DG) is considered as the hippocampal input gate for the information arriving from the entorhinal cortex. Embedded into the DG network are two excitatory cell types –granule cells (GCs), which receive inputs from the entorhinal cortex, and hilar mossy cells (MCs), which receive input from GCs and feedback projections from CA3 pyramidal cells (PCs). The postsynaptic targets of MC projections are the GCs and hilar interneurons in both ipsilateral and contralateral hemispheres of the brain. The role of MCs during rhythmic population activity, and in particular during sharp-wave/ripple complexes (SWRs), has remained largely unexplored. SWRs are prominent field events in the hippocampus during slow wave sleep and quiet wakefulness, and are involved in memory consolidation and future planning. In this study, we sought to understand whether MCs participate during CA3 SWRs using an in vitro model of SWRs. With simultaneous CA3 field potential– and cell-attached recordings from MCs, we observed that a significant fraction of MCs (47%) are recruited into the active neuronal network during SWRs. Moreover, MCs receive pronounced, compound, ripple-associated synaptic input where both excitatory and inhibitory components are phase-coherent with and delayed to the CA3 ripple. Simultaneous patch recordings from CA3 pyramidal neurons and MCs revealed longer excitatory and inhibitory latencies in MCs, supporting a feedback recruitment from CA3. Our data also show that the excitatory to inhibitory charge transfer (E/I) ratio in MCs is higher than in the CA3 PCs, making the MCs more likely to spike during SWRs. Finally, we demonstrate that a significant fraction (66%) of tested GCs receive SWR-associated excitatory inputs that are delayed compared to MCs, indicating an indirect activation of GCs by CA3 PCs via MCs. Together, our data suggest the involvement of mossy cells during SWRs and their importance as a relay for CA3-dentate gyrus networks in this important physiological network state

Pulmonary giant cells and their significance for the diagnosis of asphyxiation

This study was performed to prove whether the detection of polynuclear giant cells in lungs is useful for the diagnosis of asphyxiation due to throttling or strangulation. Therefore, lung specimens of 54 individuals with different natural and unnatural causes of death were investigated. In most lungs examined numerous alveolar macrophages with 1-2 nuclei were found. Polynuclear giant cells, which were arbitrarily defined as alveolar macrophages containing 3 or more nuclei, were observed in all groups investigated except in the cases of hypoxia due to covering the head with plastic bags. Apparent differences between the other groups in particular an increased number in cases of throttling or strangulation, could not be observed. Immunohistochemical investigations confirmed the hypothesis that the observed polynuclear giant cells were derived from alveolar macrophages. The immunohistochemical analysis of the proliferation marker antigen Ki 67 revealed no positive reaction in the nuclei of polynuclear giant cells indicating that these cells had not developed shortly before death by endomitosis as an adaptative change following reduction in oxygen supply. The results provide evidence that the detection of pulmonary polynuclear giant cells cannot be used as a practical indicator for death by asphyxiation due to throttling or strangulation

The theory of prime ends and spatial mappings

It is given a canonical representation of prime ends in regular spatial domains and, on this basis, it is studied the boundary behavior of the so-called lower Q-homeomorphisms that are the natural generalization of the quasiconformal mappings. In particular, it is found a series of effective conditions on the function Q(x) for a homeomorphic extension of the given mappings to the boundary by prime ends in domains with regular boundaries. The developed theory is applied, in particular, to mappings of the classes of Sobolev and Orlicz-Sobolev and also to finitely bi-Lipschitz mappings that a far-reaching extension of the well--known classes of isometric and quasiisometric mappings.Comment: 40 pages, we improve modulus estimates and on this basis prove a series of new criteria for homeomorphic extension of spatial mappings to the boundary by prime ends in terms of inner dilatation

A combinatorial Yamabe flow in three dimensions

A combinatorial version of Yamabe flow is presented based on Euclidean triangulations coming from sphere packings. The evolution of curvature is then derived and shown to satisfy a heat equation. The Laplacian in the heat equation is shown to be a geometric analogue of the Laplacian of Riemannian geometry, although the maximum principle need not hold. It is then shown that if the flow is nonsingular, the flow converges to a constant curvature metric.Comment: 20 pages, 5 figures. The paper arxiv:math.MG/0211195 was absorbed into its new version and this pape

A Neural Model of Timed Response Learning in the Cerebellum

A spectral timing model is developed to explain how the cerebellum learns adaptively timed responses during the rabbit's conditioned nictitating membrane response (NMR). The model posits two learning sites that respectively enable conditioned excitation and timed disinhibition of the response. Long-term potentiation of mossy fiber pathways projecting to interpositus nucleus cells allows conditioned excitation of the response's adaptive gain. Long-term depression of parallel fiber- Purkinje cell synapses in the cerebellar cortex allows learning of an adaptively timed reduction in Purkinje cell inhibition of the same nuclear cells. A spectrum of partially timed responses summate to generate an accurately timed population response. In agreement with physiological data, the model Purkinje cell activity decreases in the interval following the onset of the conditioned stimulus, and nuclear cell responses match conditioned response (CR) topography. The model reproduces key behavioral features of the NMR, including the properties that CR peak amplitude occurs at the unconditioned stimulus (US) onset, a discrete CR peak shift occurs with a change in interstimulus interval (ISI) between conditioned stim- ulus (CS) and US, mixed training at two different ISis produces a double-peaked CR, CR acquisition and rate of responding depend unimodally on the lSI, CR onset latency decreases during training, and maladaptively-timed, small-amplitude CRs result from ablation of cerebellar cortex.National Science Foundation (IRI-90-24877); Office of Naval Research (N00014-92-J-1309); Air Force Office of Scientific Research (F49620-92-J-0225