Differential Operators for Edge Detection

We present several results characterizing two differential operators used for edge detection: the Laplacian and the second directional derivative along the gradient. In particular, (a)we give conditions for coincidence of the zeros of the two operators, and (b) we show that the second derivative along the gradient has the same zeros of the normal curvature in the gradient direction. Biological implications are also discussed. An experiment is suggested to test which of the two operators may be used by the human visual system.MIT Artificial Intelligence Laborator

Partial and Complete Observables for Hamiltonian Constrained Systems

We will pick up the concepts of partial and complete observables introduced by Rovelli in order to construct Dirac observables in gauge systems. We will generalize these ideas to an arbitrary number of gauge degrees of freedom. Different methods to calculate such Dirac observables are developed. For background independent field theories we will show that partial and complete observables can be related to Kucha\v{r}'s Bubble Time Formalism. Moreover one can define a non-trivial gauge action on the space of complete observables and also state the Poisson brackets of these functions. Additionally we will investigate, whether it is possible to calculate Dirac observables starting with partially invariant partial observables, for instance functions, which are invariant under the spatial diffeomorphism group.Comment: 38 page

Classification of Generalized Symmetries for the Vacuum Einstein Equations

A generalized symmetry of a system of differential equations is an infinitesimal transformation depending locally upon the fields and their derivatives which carries solutions to solutions. We classify all generalized symmetries of the vacuum Einstein equations in four spacetime dimensions. To begin, we analyze symmetries that can be built from the metric, curvature, and covariant derivatives of the curvature to any order; these are called natural symmetries and are globally defined on any spacetime manifold. We next classify first-order generalized symmetries, that is, symmetries that depend on the metric and its first derivatives. Finally, using results from the classification of natural symmetries, we reduce the classification of all higher-order generalized symmetries to the first-order case. In each case we find that the generalized symmetries are infinitesimal generalized diffeomorphisms and constant metric scalings. There are no non-trivial conservation laws associated with these symmetries. A novel feature of our analysis is the use of a fundamental set of spinorial coordinates on the infinite jet space of Ricci-flat metrics, which are derived from Penrose's ``exact set of fields'' for the vacuum equations.Comment: 57 pages, plain Te

On Unitary Evolution of a Massless Scalar Field In A Schwarzschild Background: Hawking Radiation and the Information Paradox

We develop a Hamiltonian formalism which can be used to discuss the physics of a massless scalar field in a gravitational background of a Schwarzschild black hole. Using this formalism we show that the time evolution of the system is unitary and yet all known results such as the existence of Hawking radiation can be readily understood. We then point out that the Hamiltonian formalism leads to interesting observations about black hole entropy and the information paradox.Comment: 45 pages, revte

Energy helps accuracy: electroweak precision tests at hadron colliders

We show that high energy measurements of Drell-Yan at the LHC can serve as electroweak precision tests. Dimension-6 operators, from the Standard Model Effective Field Theory, modify the high energy behavior of electroweak gauge boson propagators. Existing measurements of the dilepton invariant mass spectrum, from neutral current Drell-Yan at 8 TeV, have comparable sensitivity to LEP. We propose measuring the transverse mass spectrum of charged current Drell-Yan, which can surpass LEP already with 8 TeV data. The 13 TeV LHC will elevate electroweak tests to a new precision frontier.Comment: 8 pages, 5 figures, 2 tables. Added: CEPC reach, projected reach on heavy vector triplet

The large cosmological constant approximation to classical and quantum gravity: model examples

We have recently introduced an approach for studying perturbatively classical and quantum canonical general relativity. The perturbative technique appears to preserve many of the attractive features of the non-perturbative quantization approach based on Ashtekar's new variables and spin networks. With this approach one can find perturbatively classical observables (quantities that have vanishing Poisson brackets with the constraints) and quantum states (states that are annihilated by the quantum constraints). The relative ease with which the technique appears to deal with these traditionally hard problems opens several questions about how relevant the results produced can possibly be. Among the questions is the issue of how useful are results for large values of the cosmological constant and how the approach can deal with several pathologies that are expected to be present in the canonical approach to quantum gravity. With the aim of clarifying these points, and to make our construction as explicit as possible, we study its application in several simple models. We consider Bianchi cosmologies, the asymmetric top, the coupled harmonic oscillators with constant energy density and a simple quantum mechanical system with two Hamiltonian constraints. We find that the technique satisfactorily deals with the pathologies of these models and offers promise for finding (at least some) results even for small values of the cosmological constant. Finally, we briefly sketch how the method would operate in the full four dimensional quantum general relativity case.Comment: 21 pages, RevTex, 2 figures with epsfi

Transcriptomic signatures of neuronal differentiation and their association with risk genes for autism spectrum and related neuropsychiatric disorders.

Genes for autism spectrum disorders (ASDs) are also implicated in fragile X syndrome (FXS), intellectual disabilities (ID) or schizophrenia (SCZ), and converge on neuronal function and differentiation. The SH-SY5Y neuroblastoma cell line, the most widely used system to study neurodevelopment, is currently discussed for its applicability to model cortical development. We implemented an optimal neuronal differentiation protocol of this system and evaluated neurodevelopment at the transcriptomic level using the CoNTeXT framework, a machine-learning algorithm based on human post-mortem brain data estimating developmental stage and regional identity of transcriptomic signatures. Our improved model in contrast to currently used SH-SY5Y models does capture early neurodevelopmental processes with high fidelity. We applied regression modelling, dynamic time warping analysis, parallel independent component analysis and weighted gene co-expression network analysis to identify activated gene sets and networks. Finally, we tested and compared these sets for enrichment of risk genes for neuropsychiatric disorders. We confirm a significant overlap of genes implicated in ASD with FXS, ID and SCZ. However, counterintuitive to this observation, we report that risk genes affect pathways specific for each disorder during early neurodevelopment. Genes implicated in ASD, ID, FXS and SCZ were enriched among the positive regulators, but only ID-implicated genes were also negative regulators of neuronal differentiation. ASD and ID genes were involved in dendritic branching modules, but only ASD risk genes were implicated in histone modification or axonal guidance. Only ID genes were over-represented among cell cycle modules. We conclude that the underlying signatures are disorder-specific and that the shared genetic architecture results in overlaps across disorders such as ID in ASD. Thus, adding developmental network context to genetic analyses will aid differentiating the pathophysiology of neuropsychiatric disorders

Ehrenfest's Principle and the Problem of Time in Quantum Gravity

We elaborate on a proposal made by Greensite and others to solve the problem of time in quantum gravity. The proposal states that a viable concept of time and a sensible inner product can be found from the demand for the Ehrenfest equations to hold in quantum gravity. We derive and discuss in detail exact consistency conditions from both Ehrenfest equations as well as from the semiclassical approximation. We also discuss consistency conditions arising from the full field theory. We find that only a very restricted class of solutions to the Wheeler-DeWitt equation fulfills all consistency conditions. We conclude that therefore this proposal must either be abandoned as a means to solve the problem of time or, alternatively, be used as an additional boundary condition to select physical solutions from the Wheeler-DeWitt equation.Comment: 20 pages, LATE

Complete quantization of a diffeomorphism invariant field theory

In order to test the canonical quantization programme for general relativity we introduce a reduced model for a real sector of complexified Ashtekar gravity which captures important properties of the full theory. While it does not correspond to a subset of Einstein's gravity it has the advantage that the programme of canonical quantization can be carried out completely and explicitly, both, via the reduced phase space approach or along the lines of the algebraic quantization programme. This model stands in close correspondence to the frequently treated cylindrically symmetric waves. In contrast to other models that have been looked at up to now in terms of the new variables the reduced phase space is infinite dimensional while the scalar constraint is genuinely bilinear in the momenta. The infinite number of Dirac observables can be expressed in compact and explicit form in terms of the original phase space variables. They turn out, as expected, to be non-local and form naturally a set of countable cardinality.Comment: 32p, LATE

Slow dynamics in a turbulent von K\'arm\'an swirling flow

We present an experimental study of a turbulent von K\'arm\'an flow produced in a cylindrical container using two propellers. The mean flow is stationary up to $Re = 10^4$, where a bifurcation takes place. The new regime breaks some symmetries of the problem, and is time-dependent. The axisymmetry is broken by the presence of equatorial vortices with a precession movement, being the velocity of the vortices proportional to the Reynolds number. The reflection symmetry through the equatorial plane is broken, and the shear layer of the mean flow appears displaced from the equator. These two facts appear simultaneously. In the exact counterrotating case, a bistable regime appears between both mirrored solutions and spontaneous reversals of the azimuthal velocity are registered. This evolution can be explained using a three-well potential model with additive noise. A regime of forced periodic response is observed when a very weak input signal is applied.Comment: Improved model, additional results and figures, accepted in PR