Hadamard states from null infinity

Free field theories on a four dimensional, globally hyperbolic spacetime, whose dynamics is ruled by a Green hyperbolic partial differential operator, can be quantized following the algebraic approach. It consists of a two-step procedure: In the first part one identifies the observables of the underlying physical system collecting them in a *-algebra which encodes their relational and structural properties. In the second step one must identify a quantum state, that is a positive, normalized linear functional on the *-algebra out of which one recovers the interpretation proper of quantum mechanical theories via the so-called Gelfand-Naimark-Segal theorem. In between the plethora of possible states, only few of them are considered physically acceptable and they are all characterized by the so-called Hadamard condition, a constraint on the singular structure of the associated two-point function. Goal of this paper is to outline a construction scheme for these states which can be applied whenever the underlying background possesses a null (conformal) boundary. We discuss in particular the examples of a real, massless conformally coupled scalar field and of linearized gravity on a globally hyperbolic and asymptotically flat spacetime.Comment: 23 pages, submitted to the Proceedings of the conference "Quantum Mathematical Physics", held in Regensburg from the 29th of September to the 02nd of October 201

An analogue of the Coleman-Mandula theorem for quantum field theory in curved spacetimes

The Coleman-Mandula (CM) theorem states that the Poincaré and internal symmetries of a Minkowski spacetime quantum field theory cannot combine nontrivially in an extended symmetry group. We establish an analogous result for quantum field theory in curved spacetimes, assuming local covariance, the timeslice property, a local dynamical form of Lorentz invariance, and additivity. Unlike the CM theorem, our result is valid in dimensions n≥2 and for free or interacting theories. It is formulated for theories defined on a category of all globally hyperbolic spacetimes equipped with a global coframe, on which the restricted Lorentz group acts, and makes use of a general analysis of symmetries induced by the action of a group G on the category of spacetimes. Such symmetries are shown to be canonically associated with a cohomology class in the second degree nonabelian cohomology of G with coefficients in the global gauge group of the theory. Our main result proves that the cohomology class is trivial if G is the universal cover S of the restricted Lorentz group. Among other consequences, it follows that the extended symmetry group is a direct product of the global gauge group and S, all fields transform in multiplets of S, fields of different spin do not mix under the extended group, and the occurrence of noninteger spin is controlled by the centre of the global gauge group. The general analysis is also applied to rigid scale covariance

Signal detection in animal psychoacoustics: analysis and simulation of sensory and decision-related influences

Signal detection theory (SDT) provides a framework for interpreting psychophysical experiments, separating the putative internal sensory representation and the decision process. SDT was used to analyse ferret behavioural responses in a (yes–no) tone-in-noise detection task. Instead of measuring the receiver-operating characteristic (ROC), we tested SDT by comparing responses collected using two common psychophysical data collection methods. These (Constant Stimuli, Limits) differ in the set of signal levels presented within and across behavioural sessions. The results support the use of SDT as a method of analysis: SDT sensory component was unchanged between the two methods, even though decisions depended on the stimuli presented within a behavioural session. Decision criterion varied trial-by-trial: a ‘yes’ response was more likely after a correct rejection trial than a hit trial. Simulation using an SDT model with several decision components reproduced the experimental observations accurately, leaving only ∼10% of the variance unaccounted for. The model also showed that trial-by-trial dependencies were unlikely to influence measured psychometric functions or thresholds. An additional model component suggested that inattention did not contribute substantially. Further analysis showed that ferrets were changing their decision criteria, almost optimally, to maximise the reward obtained in a session. The data suggest trial-by-trial reward-driven optimization of the decision process. Understanding the factors determining behavioural responses is important for correlating neural activity and behaviour. SDT provides a good account of animal psychoacoustics, and can be validated using standard psychophysical methods and computer simulations, without recourse to ROC measurements

Landslide susceptibility assessment using logistic regression and its comparison with a rock mass classification system, along a road section in the northern Himalayas (India)

Landslide studies are commonly guided by ground knowledge and field measurements of rock strength and slope failure criteria. With increasing sophistication of GIS-based statistical methods, however, landslide susceptibility studies benefit from the integration of data collected from various sources and methods at different scales. This study presents a logistic regression method for landslide susceptibility mapping and verifies the result by comparing it with the geotechnical-based slope stability probability classification (SSPC) methodology. The study was carried out in a landslide-prone national highway road section in the northern Himalayas, India. Logistic regression model performance was assessed by the receiver operator characteristics (ROC) curve, showing an area under the curve equal to 0.83. Field validation of the SSPC results showed a correspondence of 72% between the high and very high susceptibility classes with present landslide occurrences. A spatial comparison of the two susceptibility maps revealed the significance of the geotechnical-based SSPC method as 90% of the area classified as high and very high susceptible zones by the logistic regression method corresponds to the high and very high class in the SSPC method. On the other hand, only 34% of the area classified as high and very high by the SSPC method falls in the high and very high classes of the logistic regression method. The underestimation by the logistic regression method can be attributed to the generalisation made by the statistical methods, so that a number of slopes existing in critical equilibrium condition might not be classified as high or very high susceptible zones

Cysteine-Altering NOTCH3 Variants Are a Risk Factor for Stroke in the Elderly Population

Background and Purpose:Cysteine altering NOTCH3 variants, which have previously been exclusively associated with the rare hereditary small vessel disease cerebral autosomal dominant arteriopathy with subcortical infarcts and leukoencephalopathy, have a population frequency of 1:300 worldwide. Using a large population database, and taking genotype as a starting point, we aimed to determine whether individuals harboring a NOTCH3 cysteine altering variant have a higher load of small vessel disease markers on brain magnetic resonance imaging than controls, as well as a higher risk of stroke and cognitive impairment.Methods:A cross-sectional study using integrated clinical, neuroimaging, and whole-exome sequencing data of 92 456 participants from the Geisinger DiscovEHR initiative cohort. The case group consisted of individuals harboring a NOTCH3 cysteine altering variant (n=118). The control group consisted of randomly selected age- and sex-matched individuals who did not have any nonsynonymous variants in NOTCH3 (n=184). Medical records including brain magnetic resonance imagings were evaluated for clinical and neuroimaging findings associated with small vessel disease. Group comparisons were done using Fisher exact test and ordinal logistic regression models. Risk of stroke was assessed using Cox regression.Results:Of the 118 cases, 39.0% were men, mean age 58.1 +/- 16.9 years; 12.6% had a history of stroke, compared with 4.9% of controls. The risk of stroke was significantly increased after age 65 years (hazard ratio, 6.0 [95% CI, 1.4-26.3]). Dementia, mild cognitive impairment, migraine with aura and depression were equally prevalent in cases and controls. Twenty-nine cases (25%) and 45 controls (24%) had an available brain magnetic resonance imaging. After age 65 years, cases had a higher white matter lesion burden and more lacunes. A severe small vessel disease phenotype compatible with cerebral autosomal dominant arteriopathy with subcortical infarcts and leukoencephalopathy was rarely seen.Conclusions:Cysteine altering NOTCH3 variants are an important contributor to the risk of stroke, lacunes, and white matter hyperintensities in the elderly population.Genetics of disease, diagnosis and treatmen