Peter Scott

Least area incompressible surfaces in 3-manifolds

Let M be a Riemannian manifold and let F be a closed surface. A map f: F---,M is called least area if the area of f is less than the area of any homotopic map from F to M. Note that least area maps are always minimal surfaces, but that in general minimal surfaces are not least area as they represent only local stationary points for the area function. The existence of least area immersions in a homotopy class of maps has been established when the homotopy class satisfies certain injectivity conditions on the fundamental group [18, 17]. In this paper we shall consider the possible singularities of such immersions. Our results show that the general philosophy is that least area surfaces intersect least, meaning that the intersections and self-intersections of least area immersions are as small as their homotopy classes allow, when measured correctly. One should note that evidence supporting this view had been found by Meeks-Yau in their embedding theorems for minimal disks and 2-spheres [13, 143 . Our main result asserts that if a least area immersion is homotopic to an embedding, then it has no self-intersections, which clearly exemplifies the above philosophy. The precise result is the following.

Finite group actions on 3-manifolds

If G is a finite group acting smoothly on a closed surface F, it is well known that G leaves invariant some Riemannian metric of constant curvature on F. Thus any action of G on the 2-sphere S 2 is conjugate in Diff(S 2) to an orthogonal action. If G acts on the torus SX• S 1, there is a G-invariant flat metric on S a • S 1, and if G acts on a surface F with negative Euler number, then F admits a G-invariant hyperbolic metric. Recently Thurston, [Th 1, Th 2, Th 3], has described the eight 3-dimensional geometries which provide geometric structures for closed 3-manifolds in the same way that the 2-sphere S 2, the Euclidean plane E 2 and the hyperbolic plane H 2 provide geometric structures for surfaces. See also the survey article by Scott [Sc4]. Thurston also conjectured that if M is a closed 3-manifold with a geometric structure modelled on one of these eight geometries, say X, then any smooth action of a finite group G on M should leave invariant some metric on M inducing the geometry X. We will say that G preserves the geometric structure on M in this case. It should be noted that the restriction to smooth actions of G on M is essential. For Bing [Bi] showed that there are involutions of S 3 whose fixed set is a wild 2-sphere. However, in dimension two, it was proved by Eilenberg [Ei] that any action of a finite group on a surface is conjugate to a smooth action. In this paper, our main result asserts that Thurstons conjecture holds for five of the eight geometries. The result is the following.

Late-stage [18F]fluorination: new solutions to old problems

The last 2-3 years have seen numerous relationships develop between organometallic chemists, fluorine chemists and PET Centers around the world. These collaborations have led to the development of many new strategies for the late-stage introduction of fluorine-18 into complex bioactive molecules. In this perspective we highlight recent developments and key milestones since 2011.

Engagement of CD14 Mediates the Inflammatory Potential of Monosodium Urate Crystals

Phagocyte ingestion of monosodium urate (MSU) crystals can induce proinflammatory responses and trigger acute gouty inflammation. Alternatively, the uptake of MSU crystals by mature macrophages can be noninflammatory and promote resolution of gouty inflammation. Macrophage activation by extracellular MSU crystals involves apparent recognition and ingestion mediated by TLR2 and TLR4, with subsequent intracellular recognition linked to caspase-1 activation and IL-1β processing driven by the NACHT-LRR-PYD-containing protein-3 inflammasome. In this study, we examined the potential role in gouty inflammation of CD14, a phagocyte-expressed pattern recognition receptor that functionally interacts with both TLR2 and TLR4. MSU crystals, but not latex beads, directly bound recombinant soluble (s) CD14 in vitro. CD14−/− bone marrow-derived macrophages (BMDMs) demonstrated unimpaired phagocytosis of MSU crystals but reduced p38 phosphorylation and ∼90% less IL-1β and CXCL1 release. Attenuated MSU crystal-induced IL-1β release in CD14−/− BMDMs was mediated by decreased pro-IL-1β protein expression and additionally by decreased caspase-1 activation and IL-1β processing consistent with diminished NACHT-LRR-PYD-containing protein-3 inflammasome activation. Coating of MSU crystals with sCD14, but not sTLR2 or sTLR4, restored IL-1β and CXCL1 production in CD14−/− BMDMs in vitro. Gain of function of CD14 directly enhanced TLR4-mediated signaling in response to MSU crystals in transfected Chinese hamster ovary cells in vitro. Last, MSU crystal-induced leukocyte influx at 6 h was reduced by∼75%, and local induction of IL-1β decreased by >80% in CD14−/− mouse s.c. air pouches in vivo. We conclude that engagement of CD14 is a central determinant of the inflammatory potential of MSU crystals.

Gait speed in Parkinson disease correlates with cholinergic degeneration

Objective: We investigated dopaminergic and cholinergic correlates of gait speed in Parkinson disease (PD) and non-PD control subjects to test the hypothesis that gait dysfunction in PD may result from multisystem degeneration. Methods: This was a cross-sectional study. Subjects with PD but without dementia (n = 125, age 65.6 ± 7.3 years) and elderly subjects without PD (n = 32, age 66.0 ± 10.6 years) underwent [11C]dihydrotetrabenazine dopaminergic and [11C]methyl-4-piperidinyl propionate acetylcholinesterase PET imaging, and cognitive and clinical testing, including an 8.5-m walk in the dopaminergic “off” state. The fifth percentile of cortical cholinergic activity in the elderly without PD was used to define normal-range activity in the subjects with PD. Results: Normal-range cortical cholinergic activity was present in 87 subjects with PD (69.6%). Analysis of covariance using gait speed as the dependent variable demonstrated a significant model (F = 6.70, p < 0.0001) with a significant group effect (F = 3.36, p = 0.037) and significant slower gait speed in the low cholinergic PD subgroup (0.97 ± 0.22 m/s) with no significant difference between the normal-range cholinergic PD subgroup (1.12 ± 0.20 m/s) and control subjects (1.17 ± 0.18 m/s). Covariate effects were significant for cognition (F = 6.58, p = 0.011), but not for striatal dopaminergic innervation, sex, or age. Conclusion: Comorbid cortical cholinergic denervation is a more robust marker of slowing of gait in PD than nigrostriatal denervation alone. Gait speed is not significantly slower than normal in subjects with PD with relatively isolated nigrostriatal denervation.

Copper-Catalyzed [18F]Fluorination of (Mesityl)(aryl)iodonium Salts

A practical, rapid, and highly regioselective Cu-catalyzed radiofluorination of (mesityl)(aryl)iodonium salts is described. This protocol utilizes [18F]KF to access 18F-labeled electron-rich, -neutral, and -deficient aryl fluorides under a single set of mild conditions. This methodology is applied to the synthesis of protected versions of two important radiotracers: 4-[18F]fluorophenylalanine and 6-[18F]fluoroDOPA.

Novel Strategies for Fluorine‐18 Radiochemistry

Positron (b) emission tomography (PET) is a powerful, noninvasive tool for the in vivo, three-dimensional imaging of physiological structures and processes. PET imaging involves the incorporation of short-lived radionuclides, particularly carbon-11 and fluorine-18, into biologically active molecules. The resulting radiopharmaceuticals are introduced into human subjects, liberating positrons in the decay process that subsequently annihilate with electrons in adjacent matter. Detection of the g radiation generated during annihilation allows for well-defined images of ongoing bodily processes to be obtained. Understandably, wielding this technology— which requires the manipulation of strong radioemitters, short end-product efficacy timeframes, and rigorous quality control—is not a simple undertaking. In answer to this, and speaking to its clinical value, research pertaining to PET has observed exciting and rapid growth. The prospective applications for PET imaging are innumerable. Exploiting PET to its fullest potential has been limited, however, in large part, by the availability of pertinent radiopharmaceuticals. The identification of a suitable radionuclide for use in labeling is a concern intrinsic to the preparation of radiopharmaceutical agents. Carbon-11 and fluorine-18 are commonly used and each has its own merits. Radiolabeling with C has advantages that include minimal effects on substrate biological activity and ease of incorporation. C-radiolabeling also affords the ability to run multiple scans per day in series. However, C suffers from a rather short half-life (20 min) and susceptibility to environmental C contamination in processing. F finds utility in light of the fact that its incorporation into bioactive species sometimes affects their pharmacological profile. Fluorine-18 offers the benefit of a substantial half-life (about 110 min, allowing for distribution to satellite PET scan facilities), a clean decay process (97% b emission) and limited positron migration (about 1 mm, leading to highly resolved images). Indeed, F is ubiquitous in molecular imaging by positron emission tomography, as is exemplified by the success of [F]2-fluoro2-deoxy-d-glucose (FDG) in oncology research. [F]Fluoride is prepared by the proton bombardment of oxygen-18 enriched water through the nuclear reaction O(p,n)F. Aqueous solutions of F are rendered, from which the ion of interest can be isolated by ion-exchange chromatography. Gaseous [F]F2 is also available through the nuclear reaction Ne(d,a)F. The former facilitates nucleophilic fluorination reactions; the latter, electrophilic fluorination. Both reaction modes have important applications in PET imaging research. This article discusses recent strides in the field of F radiochemistry, categorized by the reaction motif. Gouverneur and co-workers recently disclosed the preparation of [F]Selectfluor bis(triflate) 1 as a means to broaden the scope and utility of electrophilic fluorination for F radiochemistry. Inspired by the mild, commercially available fluorinating agent Selectfluor, 1 was prepared through chloromethylation of diazabicyclo[2.2.2]octane, anion exchange, and subsequent fluorination using high-specific activity [F]F2 (Scheme 1). The resulting bis(triflate) was

Thalamic cholinergic innervation and postural sensory integration function in Parkinson’s disease

The pathophysiology of postural instability in Parkinsons disease remains poorly understood. Normal postural function depends in part on the ability of the postural control system to integrate visual, proprioceptive, and vestibular sensory information. Degeneration of cholinergic neurons in the brainstem pedunculopontine nucleus complex and their thalamic efferent terminals has been implicated in postural control deficits in Parkinsons disease. Our aim was to investigate the relationship of cholinergic terminal loss in thalamus and cortex, and nigrostriatal dopaminergic denervation, on postural sensory integration function in Parkinsons disease. We studied 124 subjects with Parkinsons disease (32 female/92 male; 65.5 ± 7.4 years old; 6.0 ± 4.2 years motor disease duration; modified Hoehn and Yahr mean stage 2.4 ± 0.5) and 25 control subjects (10 female/15 male, 66.8 ± 10.1 years old). All subjects underwent (11)C-dihydrotetrabenazine vesicular monoaminergic transporter type 2 and (11)C-methylpiperidin-4-yl propionate acetylcholinesterase positron emission tomography and the sensory organization test balance platform protocol. Measures of dopaminergic and cholinergic terminal integrity were obtained, i.e. striatal vesicular monoaminergic transporter type 2 binding (distribution volume ratio) and thalamic and cortical acetylcholinesterase hydrolysis rate per minute (k3), respectively. Total centre of pressure excursion (speed), a measure of total sway, and sway variability were determined for individual sensory organization test conditions. Based on normative data, principal component analysis was performed to reduce postural sensory organization functions to robust factors for regression analysis with the dopaminergic and cholinergic terminal data. Factor analysis demonstrated two factors with eigenvalues >2 that explained 52.2% of the variance, mainly reflecting postural sway during sensory organization test Conditions 1-3 and 5, respectively. Regression analysis of the Conditions 1-3 postural sway-related factor [R(2)adj = 0.123, F(5,109) = 4.2, P = 0.002] showed that decreased thalamic cholinergic innervation was associated with increased centre of pressure sway speed (β = -0.389, t = -3.4, P = 0.001) while controlling for covariate effects of cognitive capacity and parkinsonian motor impairments. There was no significant effect of cortical cholinergic terminal deficits or striatal dopaminergic terminal deficits. This effect could only be found for the subjects with Parkinsons disease. We conclude that postural sensory integration function of subjects with Parkinsons disease is modulated by pedunculopontine nucleus-thalamic but not cortical cholinergic innervation. Impaired integrity of pedunculopontine nucleus cholinergic neurons and their thalamic efferents play a role in postural control in patients with Parkinsons disease, possibly by participating in integration of multimodal sensory input information.

SHORTENING CURVES ON SURFACES

METHODS of shortening a curve in a manifold have been used to establish the existence of closed geodesics, and in particular of simple closed geodesics on 2-spheres. For this purpose, a curve evolution process should (a) not increase the number of self-intersections of a curve, (b) exist for all time or until a curve collapses to a point, (c) shorten curves sufficiently fast so that curves which exist for all time converge to a geodesic, and (d) depend continuously on the choice of initial curve. Birkhoff originated what is now known as the Birkhoff curve shortening process, where midpoints of polygonal approximations to a curve are successively connected by geodesic segments [4]. This type of shortening has the advantage that (b), (c) and (d) are easy to establish, but the disadvantage that (a) seems difficult to arrange. A process of evolving a curve on a surface by its curvature is perhaps the most natural flow. Short term existence is easy to establish for this flow, but long term existence involves deep questions in PDEs and geometry. This flow has recently been studied with considerable success in a series of papers [7,8,9, 11. All four of the desired properties have been shown to hold for the flow by curvature of an embedded curve on a Riemannian surface. For non-embedded curves in Riemannian surfaces, some open questions remain about the types of singularities which may develop in the curvature flow. In particular, it is not known whether arcs of double points can be created. In this paper we introduce a new curve shortening flow. Like the Birkhoff process, this flow involves replacing arcs of a curve with geodesic segments. Unlike the Birkhoff process, it picks out its piecewise-geodesic structure purely from the geometry of the image manifold rather than from a parametrization of the curve. This flow, which we call the disk Jlow, is developed in

Intersections of curves on surfaces

1. In