71 research outputs found
Spectral Action for Robertson-Walker metrics
We use the Euler-Maclaurin formula and the Feynman-Kac formula to extend our
previous method of computation of the spectral action based on the Poisson
summation formula. We show how to compute directly the spectral action for the
general case of Robertson-Walker metrics. We check the terms of the expansion
up to a_6 against the known universal formulas of Gilkey and compute the
expansion up to a_{10} using our direct method
Asymptotics of relative heat traces and determinants on open surfaces of finite area
The goal of this paper is to prove that on surfaces with asymptotically cusp
ends the relative determinant of pairs of Laplace operators is well defined. We
consider a surface with cusps (M,g) and a metric h on the surface that is a
conformal transformation of the initial metric g. We prove the existence of the
relative determinant of the pair under suitable
conditions on the conformal factor. The core of the paper is the proof of the
existence of an asymptotic expansion of the relative heat trace for small
times. We find the decay of the conformal factor at infinity for which this
asymptotic expansion exists and the relative determinant is defined. Following
the paper by B. Osgood, R. Phillips and P. Sarnak about extremal of
determinants on compact surfaces, we prove Polyakov's formula for the relative
determinant and discuss the extremal problem inside a conformal class. We
discuss necessary conditions for the existence of a maximizer.Comment: This is the final version of the article before it gets published. 51
page
Collaborative Brain-Computer Interface for Aiding Decision-Making
We look at the possibility of integrating the percepts from multiple non-communicating observers as a means of achieving better joint perception and better group decisions. Our approach involves the combination of a brain-computer interface with human behavioural responses. To test ideas in controlled conditions, we asked observers to perform a simple matching task involving the rapid sequential presentation of pairs of visual patterns and the subsequent decision as whether the two patterns in a pair were the same or different. We recorded the response times of observers as well as a neural feature which predicts incorrect decisions and, thus, indirectly indicates the confidence of the decisions made by the observers. We then built a composite neuro-behavioural feature which optimally combines the two measures. For group decisions, we uses a majority rule and three rules which weigh the decisions of each observer based on response times and our neural and neuro-behavioural features. Results indicate that the integration of behavioural responses and neural features can significantly improve accuracy when compared with the majority rule. An analysis of event-related potentials indicates that substantial differences are present in the proximity of the response for correct and incorrect trials, further corroborating the idea of using hybrids of brain-computer interfaces and traditional strategies for improving decision making
The LUX-ZEPLIN (LZ) Experiment
We describe the design and assembly of the LUX-ZEPLIN experiment, a direct detection search for cosmic WIMP dark matter particles. The centerpiece of the experiment is a large liquid xenon time projection chamber sensitive to low energy nuclear recoils. Rejection of backgrounds is enhanced by a Xe skin veto detector and by a liquid scintillator Outer Detector loaded with gadolinium for efficient neutron capture and tagging. LZ is located in the Davis Cavern at the 4850' level of the Sanford Underground Research Facility in Lead, South Dakota, USA. We describe the major subsystems of the experiment and its key design features and requirements
Universal entanglement and boundary geometry in conformal field theory
Employing a conformal map to hyperbolic space cross a circle, we compute the
universal contribution to the vacuum entanglement entropy (EE) across a sphere
in even-dimensional conformal field theory. Previous attempts to derive the EE
in this way were hindered by a lack of knowledge of the appropriate boundary
terms in the trace anomaly. In this paper we show that the universal part of
the EE can be treated as a purely boundary effect. As a byproduct of our
computation, we derive an explicit form for the A-type anomaly contribution to
the Wess-Zumino term for the trace anomaly, now including boundary terms. In
d=4 and 6, these boundary terms generalize earlier bulk actions derived in the
literature.Comment: 35 pages text plus 17 pages appendices and references, 3 figures; v2
package conflict resolved; v3 refs added, claim regarding newness of boundary
central charge in d=4 removed, factor of 3 typo fixe
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