Diffeomorphic Demons using Normalised Mutual Information, Evaluation on Multi-Modal Brain MR Images

The demons algorithm is a fast non-parametric non-rigid registration method. In recent years great efforts have been made to improve the approach; the state of the art version yields symmetric inverse-consistent large-deformation diffeomorphisms. However, only limited work has explored inter-modal similarity metrics, with no practical evaluation on multi-modality data. We present a diffeomorphic demons implementation using the analytical gradient of Normalised Mutual Information (NMI) in a conjugate gradient optimiser. We report the first qualitative and quantitative assessment of the demons for inter-modal registration. Experiments to spatially normalise real MR images, and to recover simulated deformation fields, demonstrate (i) similar accuracy from NMI-demons and classical demons when the latter may be used, and (ii) similar accuracy for NMI-demons on T1w-T1w and T1w-T2w registration, demonstrating its potential in multi-modal scenarios

Diffeomorphic demons using normalized mutual information, evaluation on multimodal brain MR images

The demons algorithm is a fast non-parametric non-rigid registration method. In recent years great efforts have been made to improve the approach; the state of the art version yields symmetric inverse-consistent largedeformation diffeomorphisms. However, only limited work has explored inter-modal similarity metrics, with no practical evaluation on multi-modality data. We present a diffeomorphic demons implementation using the analytical gradient of Normalised Mutual Information (NMI) in a conjugate gradient optimiser. We report the first qualitative and quantitative assessment of the demons for inter-modal registration. Experiments to spatially normalise real MR images, and to recover simulated deformation fields, demonstrate (i) similar accuracy from NMI-demons and classical demons when the latter may be used, and (ii) similar accuracy for NMI-demons on T1w-T1w and T1w-T2w registration, demonstrating its potential in multi-modal scenarios

Renormalization aspects of N=1 Super Yang-Mills theory in the Wess-Zumino gauge

The renormalization of N=1 Super Yang-Mills theory is analysed in the Wess-Zumino gauge, employing the Landau condition. An all orders proof of the renormalizability of the theory is given by means of the Algebraic Renormalization procedure. Only three renormalization constants are needed, which can be identified with the coupling constant, gauge field and gluino renormalization. The non-renormalization theorem of the gluon-ghost-antighost vertex in the Landau gauge is shown to remain valid in N=1 Super Yang-Mills. Moreover, due to the non-linear realization of the supersymmetry in the Wess-Zumino gauge, the renormalization factor of the gauge field turns out to be different from that of the gluino. These features are explicitly checked through a three loop calculation.Comment: 15 pages, minor text improvements, references added. Version accepted for publication in the EPJ

The asymmetry of the dimension 2 gluon condensate: the zero temperature case

We provide an algebraic study of the local composite operators A_\mu A_\nu-\delta_{\mu\nu}/d A^2 and A^2, with d=4 the spacetime dimension. We prove that these are separately renormalizable to all orders in the Landau gauge. This corresponds to a renormalizable decomposition of the operator A_\mu A_\nu into its trace and traceless part. We present explicit results for the relevant renormalization group functions to three loop order, accompanied with various tests of these results. We then develop a formalism to determine the zero temperature effective potential for the corresponding condensates, and recover the already known result for \neq 0, together with <A_\mu A_\nu-\delta_{\mu\nu}/d A^2>=0, a nontrivial check that the approach is consistent with Lorentz symmetry. The formalism is such that it is readily generalizable to the finite temperature case, which shall allow a future analytical study of the electric-magnetic symmetry of the condensate, which received strong evidence from recent lattice simulations by Chernodub and Ilgenfritz, who related their results to 3 regions in the Yang-Mills phase diagram.Comment: 25 page

Forward-Backward Splitting in Deformable Image Registration: A Demons Approach

Efficient non-linear image registration implementations are key for many biomedical imaging applications. By using the classical demons approach, the associated optimization problem is solved by an alternate optimization scheme consisting of a gradient descent step followed by Gaussian smoothing. Despite being simple and powerful, the solution of the underlying relaxed formulation is not guaranteed to minimize the original global energy. Implicitly, however, this second step can be recast as the proximal map of the regularizer. This interpretation introduces a parallel to the more general Forward-Backward Splitting (FBS) scheme consisting of a forward gradient descent and proximal step. By shifting entirely to FBS, we can take advantage of the recent advances in FBS methods and solve the original, non-relaxed deformable registration problem for any type of differentiable similarity measure and convex regularization associated with a tractable proximal operator. Additionally, global convergence to a critical point is guaranteed under weak restrictions. For the first time in the context of image registration, we show that Tikhonov regularization breaks down to the simple use of B-Spline filtering in the proximal step. We demonstrate the versatility of FBS by encoding spatial transformation as displacement fields or free-form B-Spline deformations. We use state-of-the-art FBS solvers and compare their performance against the classical demons, the recently proposed inertial demons and the conjugate gradient optimizer. Numerical experiments performed on both synthetic and clinical data show the advantage of FBS in image registration in terms of both convergence and accuracy

Implementing the Gribov-Zwanziger framework in N=1 Super Yang-Mills in the Landau gauge

The Gribov-Zwanziger framework accounting for the existence of Gribov copies is extended to N=1 Super Yang--Mills theories quantized in the Landau gauge. We show that the restriction of the domain of integration in the Euclidean functional integral to the first Gribov horizon can be implemented in a way to recover non-perturbative features of N=1 Super Yang--Mills theories, namely: the existence of the gluino condensate as well as the vanishing of the vacuum energy.Comment: 19 pages, no figure

Sensitivity of the polar boundary layer to transient phenomena

Numerical weather prediction and climate models encounter challenges in accurately representing flow regimes in the stably stratified atmospheric boundary layer and the transitions between them, leading to an inadequate depiction of regime occupation statistics. As a consequence, existing models exhibit significant biases in near-surface temperatures at high latitudes. To explore inherent uncertainties in modeling regime transitions, the response of the near-surface temperature inversion to transient small-scale phenomena is analyzed based on a stochastic modeling approach. A sensitivity analysis is conducted by augmenting a conceptual model for near-surface temperature inversions with randomizations that account for different types of model uncertainty. The stochastic conceptual model serves as a tool to systematically investigate which types of unsteady flow features may trigger abrupt transitions in the mean boundary layer state. The findings show that the incorporation of enhanced mixing, a common practice in numerical weather prediction models, blurs the two regime characteristic of the stably stratified atmospheric boundary layer. Simulating intermittent turbulence is shown to provide a potential workaround for this issue. Including key uncertainty in models could lead to a better statistical representation of the regimes in long-term climate simulation. This would help to improve our understanding and the forecasting of climate change in high-latitude regions.</p