Spectral action for torsion with and without boundaries

We derive a commutative spectral triple and study the spectral action for a rather general geometric setting which includes the (skew-symmetric) torsion and the chiral bag conditions on the boundary. The spectral action splits into bulk and boundary parts. In the bulk, we clarify certain issues of the previous calculations, show that many terms in fact cancel out, and demonstrate that this cancellation is a result of the chiral symmetry of spectral action. On the boundary, we calculate several leading terms in the expansion of spectral action in four dimensions for vanishing chiral parameter $\theta$ of the boundary conditions, and show that $\theta=0$ is a critical point of the action in any dimension and at all orders of the expansion.Comment: 16 pages, references adde

Asymptotics of the Heat Kernel on Rank 1 Locally Symmetric Spaces

We consider the heat kernel (and the zeta function) associated with Laplace type operators acting on a general irreducible rank 1 locally symmetric space X. The set of Minakshisundaram- Pleijel coefficients {A_k(X)}_{k=0}^{\infty} in the short-time asymptotic expansion of the heat kernel is calculated explicitly.Comment: 11 pages, LaTeX fil

Einstein metrics in projective geometry

It is well known that pseudo-Riemannian metrics in the projective class of a given torsion free affine connection can be obtained from (and are equivalent to) the solutions of a certain overdetermined projectively invariant differential equation. This equation is a special case of a so-called first BGG equation. The general theory of such equations singles out a subclass of so-called normal solutions. We prove that non-degerate normal solutions are equivalent to pseudo-Riemannian Einstein metrics in the projective class and observe that this connects to natural projective extensions of the Einstein condition.Comment: 10 pages. Adapted to published version. In addition corrected a minor sign erro

Heat Kernel Expansion for Semitransparent Boundaries

We study the heat kernel for an operator of Laplace type with a $\delta$-function potential concentrated on a closed surface. We derive the general form of the small $t$ asymptotics and calculate explicitly several first heat kernel coefficients.Comment: 16 page

Detours and Paths: BRST Complexes and Worldline Formalism

We construct detour complexes from the BRST quantization of worldline diffeomorphism invariant systems. This yields a method to efficiently extract physical quantum field theories from particle models with first class constraint algebras. As an example, we show how to obtain the Maxwell detour complex by gauging N=2 supersymmetric quantum mechanics in curved space. Then we concentrate on first class algebras belonging to a class of recently introduced orthosymplectic quantum mechanical models and give generating functions for detour complexes describing higher spins of arbitrary symmetry types. The first quantized approach facilitates quantum calculations and we employ it to compute the number of physical degrees of freedom associated to the second quantized, field theoretical actions.Comment: 1+35 pages, 1 figure; typos corrected and references added, published versio

Worldline approach to quantum field theories on flat manifolds with boundaries

We study a worldline approach to quantum field theories on flat manifolds with boundaries. We consider the concrete case of a scalar field propagating on R_+ x R^{D-1} which leads us to study the associated heat kernel through a one dimensional (worldline) path integral. To calculate the latter we map it onto an auxiliary path integral on the full R^D using an image charge. The main technical difficulty lies in the fact that a smooth potential on R_+ x R^{D-1} extends to a potential which generically fails to be smooth on R^D. This implies that standard perturbative methods fail and must be improved. We propose a method to deal with this situation. As a result we recover the known heat kernel coefficients on a flat manifold with geodesic boundary, and compute two additional ones, A_3 and A_{7/2}. The calculation becomes sensibly harder as the perturbative order increases, and we are able to identify the complete A_{7/2} with the help of a suitable toy model. Our findings show that the worldline approach is viable on manifolds with boundaries. Certainly, it would be desirable to improve our method of implementing the worldline approach to further simplify the perturbative calculations that arise in the presence of non-smooth potentials.Comment: 19 pages, 6 figures. Minor rephrasing of a few sentences, references added. Version accepted by JHE

Rapid Artefact Removal and H&E-Stained Tissue Segmentation

We present an innovative method for rapidly segmenting hematoxylin and eosin (H&E)-stained tissue in whole-slide images (WSIs) that eliminates a wide range of undesirable artefacts such as pen marks and scanning artefacts. Our method involves taking a single-channel representation of a lowmagnification RGB overview of the WSI in which the pixel values are bimodally distributed suchthat H&E-stained tissue is easily distinguished from both background and a wide variety of artefacts. We demonstrate our method on 30 WSIs prepared from a wide range of institutions and WSI digital scanners, each containing substantial artefacts, and compare it to segmentations provided by Otsu thresholding and Histolab tissue segmentation and pen filtering tools. We found that our methodsegmented the tissue and fully removed all artefacts in 29 out of 30 WSIs, whereas Otsu thresholding failed to remove any artefacts, and the Histolab pen filtering tools only partially removed the pen marks. The beauty of our approach lies in its simplicity: manipulating RGB colour space and using Otsu thresholding allows for the segmentation of H&E-stained tissue and the rapid removal ofartefacts without the need for machine learning or parameter tuning

The CMS Event Builder

The data acquisition system of the CMS experiment at the Large Hadron Collider will employ an event builder which will combine data from about 500 data sources into full events at an aggregate throughput of 100 GByte/s. Several architectures and switch technologies have been evaluated for the DAQ Technical Design Report by measurements with test benches and by simulation. This paper describes studies of an EVB test-bench based on 64 PCs acting as data sources and data consumers and employing both Gigabit Ethernet and Myrinet technologies as the interconnect. In the case of Ethernet, protocols based on Layer-2 frames and on TCP/IP are evaluated. Results from ongoing studies, including measurements on throughput and scaling are presented. The architecture of the baseline CMS event builder will be outlined. The event builder is organised into two stages with intelligent buffers in between. The first stage contains 64 switches performing a first level of data concentration by building super-fragments from fragments of 8 data sources. The second stage combines the 64 super-fragments into full events. This architecture allows installation of the second stage of the event builder in steps, with the overall throughput scaling linearly with the number of switches in the second stage. Possible implementations of the components of the event builder are discussed and the expected performance of the full event builder is outlined.Comment: Conference CHEP0

The a3/2a_{3/2} heat kernel coefficient for oblique boundary conditions

We present a method for the calculation of the $a_{3/2}$ heat kernel coefficient of the heat operator trace for a partial differential operator of Laplace type on a compact Riemannian manifold with oblique boundary conditions. Using special case evaluations, restrictions are put on the general form of the coefficients, which, supplemented by conformal transformation techniques, allows the entire smeared coefficient to be determined.Comment: 30 pages, LaTe

The hybrid spectral problem and Robin boundary conditions

The hybrid spectral problem where the field satisfies Dirichlet conditions (D) on part of the boundary of the relevant domain and Neumann (N) on the remainder is discussed in simple terms. A conjecture for the C_1 coefficient is presented and the conformal determinant on a 2-disc, where the D and N regions are semi-circles, is derived. Comments on higher coefficients are made. A hemisphere hybrid problem is introduced that involves Robin boundary conditions and leads to logarithmic terms in the heat--kernel expansion which are evaluated explicitly.Comment: 24 pages. Typos and a few factors corrected. Minor comments added. Substantial Robin additions. Substantial revisio