Topological quantum field theory and four-manifolds

I review some recent results on four-manifold invariants which have been obtained in the context of topological quantum field theory. I focus on three different aspects: (a) the computation of correlation functions, which give explicit results for the Donaldson invariants of non-simply connected manifolds, and for generalizations of these invariants to the gauge group SU(N); (b) compactifications to lower dimensions, and relations with three-manifold topology and with intersection theory on the moduli space of flat connections on Riemann surfaces; (c) four-dimensional theories with critical behavior, which give some remarkable constraints on Seiberg-Witten invariants and new results on the geography of four-manifolds.Comment: 10 pages, LaTeX. Talk given at the 3rd ECM, Barcelona, July 2000; references adde

Petrogenetic significance of chromian spinels from the Sudbury Igneous Complex, Ontario, Canada

Chromian spinels occur in mafic-ultramafic inclusions in the Sublayer of the Sudbury Igneous Complex (SIC) as well as in mafic-ultramafic rocks in the immediate footwall of the Sublayer. The host rocks are pyroxenite and melanorite with minor dunite, harzburgite, and melatroctolite. As common accessory phases in these rocks, the chromian spinels display euhedral or subhedral forms and are included in olivine and orthopyroxene. Chromian spinel grains generally have ilmenite lamellae and contain abundant inclusions (zircon, olivine, diopside, plagioclase, biotite, and sulfide). All the chromian spinels have similar trace element abundances and are rich in TiO2 (0.5-15 wt.%). They have constant Cr# (100Cr/(Cr + Al)) (55-70) and exhibit a continuum in composition that traverses the normal fields of spinels in a Al-(Fe3+ + 2Ti)-Cr triangular diagram. This continuum extends to that of the composition of chromian magnetite in the host norite matrix to the mafic -ultramafic inclusions. This continuum in composition of the spinels suggests that the noritic matrix to the Sublayer formed from the same magma as the inclusions. A positive correlation between the Cr and Al contents of the spinels was probably produced by dilution of these elements by Fe3+ contributed, perhaps, by a plagioclase-saturated melt. Zircon inclusions in a chromian spinel grain reflect incorporation of crustal, felsic materials into the magma before crystallization of chromian spinel. The chemical characteristics and mineral inclusions of the spinels suggest that the Sublayer formed in response to magma mixing. It is suggested that subsequent to the formation of the crustal melt, mantle-derived high-Mg magmas mixed vigourously with this and generated the magmatic sulfides that eventually formed the Ni - Cu - platinum-group elements sulfide ore deposits. Some of the early crystallization products of the high-Mg magma settled to the chamber floor, where they partially mixed with the crustal melt and formed the mafic - ultramafic inclusions and footwall complexes.published_or_final_versio

Constraints on chiral operators in N=2 SCFTs

Open Access, © The Authors. Article funded by SCOAP3. This article is distributed under the terms of the Creative Commons Attribution License ( CC-BY 4.0 ), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited

The growth hormone receptor gene deleted for exon three (GHRd3) polymorphism is associated with birth and placental weight.

Human growth hormone receptor (GHR) transcripts have two isoforms, full-length (GHRfl) or exon 3 deleted (GHRd3). An association of these isoforms has been found with small for gestational age (SGA) infants but does not influence adult height. The role of this polymorphism in the birth size spectrum in the general population is unclear

A Candidate Sub-Parsec Supermassive Binary Black Hole System

We identify SDSS J153636.22+044127.0, a QSO discovered in the Sloan Digital Sky Survey, as a promising candidate for a binary black hole system. This QSO has two broad-line emission systems separated by 3500 km/sec. The redder system at z=0.3889 also has a typical set of narrow forbidden lines. The bluer system (z=0.3727) shows only broad Balmer lines and UV Fe II emission, making it highly unusual in its lack of narrow lines. A third system, which includes only unresolved absorption lines, is seen at a redshift, z=0.3878, intermediate between the two emission-line systems. While the observational signatures of binary nuclear black holes remain unclear, J1536+0441 is unique among all QSOs known in having two broad-line regions, indicative of two separate black holes presently accreting gas. The interpretation of this as a bound binary system of two black holes having masses of 10^8.9 and 10^7.3 solar masses, yields a separation of ~ 0.1 parsec and an orbital period of ~100 years. The separation implies that the two black holes are orbiting within a single narrow-line region, consistent with the characteristics of the spectrum. This object was identified as an extreme outlier of a Karhunen-Loeve Transform of 17,500 z < 0.7 QSO spectra from the SDSS. The probability of the spectrum resulting from a chance superposition of two QSOs with similar redshifts is estimated at 2X10^-7, leading to the expectation of 0.003 such objects in the sample studied; however, even in this case, the spectrum of the lower redshift QSO remains highly unusual.Comment: 8 pages, 2 figures, Nature in pres

Geo-environmental mapping using physiographic analysis: constraints on the evaluation of land instability and groundwater pollution hazards in the Metropolitan District of Campinas, Brazil

Geo-environmental terrain assessments and territorial zoning are useful tools for the formulation and implementation of environmental management instruments (including policy-making, planning, and enforcement of statutory regulations). They usually involve a set of procedures and techniques for delimitation, characterisation and classification of terrain units. However, terrain assessments and zoning exercises are often costly and time-consuming, particularly when encompassing large areas, which in many cases prevent local agencies in developing countries from properly benefiting from such assessments. In the present paper, a low-cost technique based on the analysis of texture of satellite imagery was used for delimitation of terrain units. The delimited units were further analysed in two test areas situated in Southeast Brazil to provide estimates of land instability and the vulnerability of groundwater to pollution hazards. The implementation incorporated procedures for inferring the influences and potential implications of tectonic fractures and other discontinuities on ground behaviour and local groundwater flow. Terrain attributes such as degree of fracturing, bedrock lithology and weathered materials were explored as indicators of ground properties. The paper also discusses constraints on- and limitations of- the approaches taken

Accuracy of diabetes screening methods used for people with tuberculosis, Indonesia, Peru, Romania, South Africa

Objective To evaluate the performance of diagnostic tools for diabetes mellitus, including laboratory methods and clinical risk scores, in newly-diagnosed pulmonary tuberculosis patients from four middle-income countries. Methods In a multicentre, prospective study, we recruited 2185 patients with pulmonary tuberculosis from sites in Indonesia, Peru, Romania and South Africa from January 2014 to September 2016. Using laboratory-measured glycated haemoglobin (HbA1c) as the gold standard, we measured the diagnostic accuracy of random plasma glucose, point-of-care HbA1c, fasting blood glucose, urine dipstick, published and newly derived diabetes mellitus risk scores and anthropometric measurements. We also analysed combinations of tests, including a two-step test using point-of-care HbA1cwhen initial random plasma glucose was ≥ 6.1 mmol/L. Findings The overall crude prevalence of diabetes mellitus among newly diagnosed tuberculosis patients was 283/2185 (13.0%; 95% confidence interval, CI: 11.6–14.4). The marker with the best diagnostic accuracy was point-of-care HbA1c (area under receiver operating characteristic curve: 0.81; 95% CI: 0.75–0.86). A risk score derived using age, point-of-care HbA1c and random plasma glucose had the best overall diagnostic accuracy (area under curve: 0.85; 95% CI: 0.81–0.90). There was substantial heterogeneity between sites for all markers, but the two-step combination test performed well in Indonesia and Peru. Conclusion Random plasma glucose followed by point-of-care HbA1c testing can accurately diagnose diabetes in tuberculosis patients, particularly those with substantial hyperglycaemia, while reducing the need for more expensive point-of-care HbA1c testing. Risk scores with or without biochemical data may be useful but require validation

Submucosal diclofenac for acute postoperative pain in third molar surgery: A randomized, controlled clinical trial

Diclofenac sodium is a widely used nonsteroidal anti-inflammatory drug (NSAID) for relief of inflammatory pain. A recent formulation combines this drug with hydroxypropyl-β-cyclodextrin (HPβCD) to improve its solubility and to enable subcutaneous administration. Previous studies confirmed the efficacy of this combination. This study’s aim was to evaluate the efficacy, safety, and local tolerability of diclofenac HPβCD administered as a local submucosal injection prior to lower third molar surgery. We conducted a prospective, randomized, double-blind, placebo-controlled, parallel-group phase II single-center study. Seventy-five patients requiring mandibular third molar surgery were randomized into 1 of 5 groups: 5 mg/1 mL diclofenac HPβCD, 12.5 mg/1 mL diclofenac HPβCD, 25 mg/1 mL diclofenac HPβCD, 50 mg/1 mL diclofenac HPβCD, or 1 mL placebo. The respective study drug was injected into the mucosal tissue surrounding the surgical site prior to surgery following achievement of local anesthesia. The primary outcome measure was the area under the curve (AUC) of cumulative pain scores from end of surgery to 6 h postsurgery. This demonstrated a global treatment effect between the active groups and placebo, hence confirming the study drug’s efficacy (P = 0.0126). Secondary outcome measures included the time until onset of pain and the time until patients required rescue medication, both showing statistical significance of the study drug compared to placebo (P < 0.0161 and P < 0.0001, respectively). The time until rescue medication ranged between 7.8 h (for 25 mg/1 mL diclofenac HPβCD) and 16 h (for 50 mg/1 mL diclofenac HPβCD). Interestingly, the 5-mg/1-mL solution appeared superior to the 12.5-mg/1-mL and 25-mg/1-mL solutions (time until rescue medication = 12.44 h). A total of 14% of patients experienced minor adverse drug reactions (ADRs), of which 2 cases demonstrated flap necrosis. These resolved without further intervention. The study results overall indicate efficacy, safety, and relative tolerability of diclofenac HPβCD used locally as a submucosal injection prior to third molar surgery (ClinicalTrials.gov NCT01706588)

Some Field Theoretic Issues Regarding the Chiral Magnetic Effect

In this paper, we shall address some field theoretic issues regarding the chiral magnetic effect. The general structure of the magnetic current consistent with the electromagnetic gauge invariance is obtained and the impact of the infrared divergence is examined. Some subtleties on the relation between the chiral magnetic effect and the axial anomaly are clarified through a careful examination of the infrared limit of the relevant thermal diagrams.Comment: 19 pages, 4 figures in Latex. Typos fixed, version accepted to be published in JHE

The role of ongoing dendritic oscillations in single-neuron dynamics

The dendritic tree contributes significantly to the elementary computations a neuron performs while converting its synaptic inputs into action potential output. Traditionally, these computations have been characterized as temporally local, near-instantaneous mappings from the current input of the cell to its current output, brought about by somatic summation of dendritic contributions that are generated in spatially localized functional compartments. However, recent evidence about the presence of oscillations in dendrites suggests a qualitatively different mode of operation: the instantaneous phase of such oscillations can depend on a long history of inputs, and under appropriate conditions, even dendritic oscillators that are remote may interact through synchronization. Here, we develop a mathematical framework to analyze the interactions of local dendritic oscillations, and the way these interactions influence single cell computations. Combining weakly coupled oscillator methods with cable theoretic arguments, we derive phase-locking states for multiple oscillating dendritic compartments. We characterize how the phase-locking properties depend on key parameters of the oscillating dendrite: the electrotonic properties of the (active) dendritic segment, and the intrinsic properties of the dendritic oscillators. As a direct consequence, we show how input to the dendrites can modulate phase-locking behavior and hence global dendritic coherence. In turn, dendritic coherence is able to gate the integration and propagation of synaptic signals to the soma, ultimately leading to an effective control of somatic spike generation. Our results suggest that dendritic oscillations enable the dendritic tree to operate on more global temporal and spatial scales than previously thought