Grid cells on steeply sloping terrain: evidence for planar rather than volumetric encoding

Neural encoding of navigable space involves a network of structures centred on the hippocampus, whose neurons –place cells – encode current location. Input to the place cells includes afferents from the entorhinal cortex, which contains grid cells. These are neurons expressing spatially localised activity patches, or firing fields, that are evenly spaced across the floor in a hexagonal close-packed array called a grid. It is thought that grid cell grids function to enable the calculation of distances. The question arises as to whether this odometry process operates in three dimensions, and so we queried whether grids permeate three-dimensional space – that is, form a lattice – or whether they simply follow the environment surface. If grids form a three-dimensional lattice then a tilted floor should transect several layers of this lattice, resulting in interruption of the hexagonal pattern. We model this prediction with simulated grid lattices and show that on a 40-degree slope the firing of a grid cell should cover proportionally less of the surface, with smaller field size and fewer fields and reduced hexagonal symmetry. However, recording of grid cells as animals foraged on a 40-degree-tilted surface found that firing of grid cells was almost indistinguishable, in pattern or rate, from that on the horizontal surface, with if anything increased coverage and field number, and preserved field size. It thus appears unlikely that the sloping surface transected a lattice. However, grid cells on the slope displayed slightly degraded firing patterns, with reduced coherence and slightly reduced symmetry. These findings collectively suggest that the grid cell component of the metric representation of space is not fixed in absolute three-dimensional space but is influenced both by the surface the animal is on and by the relationship of this surface to the horizontal, supporting the hypothesis that the neural map of space is multi-planar rather than fully volumetric

Derivatives of meromorphic functions of finite order

A result is proved concerning meromorphic functions of finite order in the plane such that all but finitely many zeros of the second derivative are zeros of the first derivative

Viral antibody dynamics in a chiropteran host

1. Bats host many viruses that are significant for human and domestic animal health, but the dynamics of these infections in their natural reservoir hosts remain poorly elucidated.<p></p> 2. In these, and other, systems, there is evidence that seasonal life-cycle events drive infection dynamics, directly impacting the risk of exposure to spillover hosts. Understanding these dynamics improves our ability to predict zoonotic spillover from the reservoir hosts.<p></p> 3. To this end, we followed henipavirus antibody levels of >100 individual E. helvum in a closed, captive, breeding population over a 30-month period, using a powerful novel antibody quantitation method.<p></p> 4. We demonstrate the presence of maternal antibodies in this system and accurately determine their longevity. We also present evidence of population-level persistence of viral infection and demonstrate periods of increased horizontal virus transmission associated with the pregnancy/lactation period.<p></p> 5.The novel findings of infection persistence and the effect of pregnancy on viral transmission, as well as an accurate quantitation of chiropteran maternal antiviral antibody half-life, provide fundamental baseline data for the continued study of viral infections in these important reservoir hosts

Magnetic Resonance Imaging Pilot Study of Intravenous Glyburide in Traumatic Brain Injury.

Pre-clinical studies of traumatic brain injury (TBI) show that glyburide reduces edema and hemorrhagic progression of contusions. We conducted a small Phase II, three-institution, randomized placebo-controlled trial of subjects with TBI to assess the safety and efficacy of intravenous (IV) glyburide. Twenty-eight subjects were randomized and underwent a 72-h infusion of IV glyburide or placebo, beginning within 10 h of trauma. Of the 28 subjects, 25 had Glasgow Coma Scale (GCS) scores of 6-10, and 14 had contusions. There were no differences in adverse events (AEs) or severe adverse events (ASEs) between groups. The magnetic resonance imaging (MRI) percent change at 72-168 h from screening/baseline was compared between the glyburide and placebo groups. Analysis of contusions (7 per group) showed that lesion volumes (hemorrhage plus edema) increased 1036% with placebo versus 136% with glyburide (p = 0.15), and that hemorrhage volumes increased 11.6% with placebo but decreased 29.6% with glyburide (p = 0.62). Three diffusion MRI measures of edema were quantified: mean diffusivity (MD), free water (FW), and tissue MD (MDt), corresponding to overall, extracellular, and intracellular water, respectively. The percent change with time for each measure was compared in lesions (n = 14) versus uninjured white matter (n = 24) in subjects receiving placebo (n = 20) or glyburide (n = 18). For placebo, the percent change in lesions for all three measures was significantly different compared with uninjured white matter (analysis of variance [ANOVA], p < 0.02), consistent with worsening of edema in untreated contusions. In contrast, for glyburide, the percent change in lesions for all three measures was not significantly different compared with uninjured white matter. Further study of IV glyburide in contusion TBI is warranted

Entire functions with Julia sets of positive measure

Let f be a transcendental entire function for which the set of critical and asymptotic values is bounded. The Denjoy-Carleman-Ahlfors theorem implies that if the set of all z for which |f(z)|>R has N components for some R>0, then the order of f is at least N/2. More precisely, we have log log M(r,f) > (N/2) log r - O(1), where M(r,f) denotes the maximum modulus of f. We show that if f does not grow much faster than this, then the escaping set and the Julia set of f have positive Lebesgue measure. However, as soon as the order of f exceeds N/2, this need not be true. The proof requires a sharpened form of an estimate of Tsuji related to the Denjoy-Carleman-Ahlfors theorem.Comment: 17 page

Assessment of agreement between invasive blood pressure measured centrally and peripherally and the influence of different haemodynamic states in anaesthetised horses

Objective To determine the agreement of invasive blood pressure measured in the facial artery, the metatarsal artery and the carotid. Additionally, to evaluate the effects of two haemodynamic conditions on agreement. Study design Prospective, randomized study. Animals Eight horses aged 7 (4 -23) years with a body weight of 493 ± 33 kg. Methods Horses were anaesthetized and positioned in dorsal recumbency. Invasive blood pressure was measured simultaneously via catheters placed in the facial, metatarsal and carotid artery. Cardiovascular function and agreement between arteries was assessed before and during administration of phenylephrine and sodium nitroprusside. These were administered until carotid mean pressure (MAPc) increased or decreased from baseline (65 ± 5 mmHg) to > 90 mmHg or < 50 mmHg, respectively. Data recorded at each sample time included systolic (SAP), mean (MAP) and diastolic (DAP) for carotid (c), facial (f) and metatarsal (m) artery as well as cardiac output (Q̇t) and systemic vascular resistance (SVR). Bland-Altman analysis was used to assess agreement between peripheral and central sites and regression analysis was used to determine influence of Q̇t and SVR. Results The largest difference was observed in SAPc and SAPm with a bias and limits of agreement (LOA) of 2 (-15 to 19) mmHg. The bias (LOA) for MAPc and MAPf was 2 (-4 to 9) mmHg and for MAPc and MAPm was 5 (-4 to 14) mmHg. The best agreement for DAP was seen between DAPc and DAPf with bias (LOA) of 1 (-3 to 5) mmHg. Regression analysis indicated marginal influence on agreement by Q̇t on MAPc and MAPf. Conclusion and clinical relevance The MAP and DAP of the carotid was generally higher compared to the peripheral arteries, which may lead to overzealous treatment of hypotension, albeit maintaining central pressures. Cardiac output and systemic vascular resistance did not largely influence the difference between sites

Modular Equations and Distortion Functions

Modular equations occur in number theory, but it is less known that such equations also occur in the study of deformation properties of quasiconformal mappings. The authors study two important plane quasiconformal distortion functions, obtaining monotonicity and convexity properties, and finding sharp bounds for them. Applications are provided that relate to the quasiconformal Schwarz Lemma and to Schottky's Theorem. These results also yield new bounds for singular values of complete elliptic integrals.Comment: 23 page