A density of ramified primes

Let $K$ be a cyclic totally real number field of odd degree over $\mathbb{Q}$ with odd class number, such that every totally positive unit is the square of a unit, and such that $2$ is inert in $K/\mathbb{Q}$. We define a family of number fields $\{K(p)\}_p$, depending on $K$ and indexed by the rational primes $p$ that split completely in $K/\mathbb{Q}$, such that $p$ is always ramified in $K(p)$ of degree $2$. Conditional on a standard conjecture on short character sums, the density of such rational primes $p$ that exhibit one of two possible ramified factorizations in $K(p)/\mathbb{Q}$ is strictly between $0$ and $1$ and is given explicitly as a formula in terms of $[K:\mathbb{Q}]$. Our results are unconditional in the cubic case. Our proof relies on a detailed study of the joint distribution of spins of prime ideals

Streaking artifact suppression of quantitative susceptibility mapping reconstructions via L1-norm data fidelity optimization (L1-QSM)

Purpose: The presence of dipole-inconsistent data due to substantial noise or artifacts causes streaking artifacts in quantitative susceptibility mapping (QSM) reconstructions. Often used Bayesian approaches rely on regularizers, which in turn yield reduced sharpness. To overcome this problem, we present a novel L1-norm data fidelity approach that is robust with respect to outliers, and therefore prevents streaking artifacts. Methods: QSM functionals are solved with linear and nonlinear L1-norm data fidelity terms using functional augmentation, and are compared with equivalent L2-norm methods. Algorithms were tested on synthetic data, with phase inconsistencies added to mimic lesions, QSM Challenge 2.0 data, and in vivo brain images with hemorrhages. Results: The nonlinear L1-norm-based approach achieved the best overall error metric scores and better streaking artifact suppression. Notably, L1-norm methods could reconstruct QSM images without using a brain mask, with similar regularization weights for different data fidelity weighting or masking setups. Conclusion: The proposed L1-approach provides a robust method to prevent streaking artifacts generated by dipole-inconsistent data, renders brain mask calculation unessential, and opens novel challenging clinical applications such asassessing brain hemorrhages and cortical layers

A new discrete dipole kernel for quantitative susceptibility mapping

PURPOSE: Most approaches for quantitative susceptibility mapping (QSM) are based on a forward model approximation that employs a continuous Fourier transform operator to solve a differential equation system. Such formulation, however, is prone to high-frequency aliasing. The aim of this study was to reduce such errors using an alternative dipole kernel formulation based on the discrete Fourier transform and discrete operators. METHODS: The impact of such an approach on forward model calculation and susceptibility inversion was evaluated in contrast to the continuous formulation both with synthetic phantoms and in vivo MRI data. RESULTS: The discrete kernel demonstrated systematically better fits to analytic field solutions, and showed less over-oscillations and aliasing artifacts while preserving low- and medium-frequency responses relative to those obtained with the continuous kernel. In the context of QSM estimation, the use of the proposed discrete kernel resulted in error reduction and increased sharpness. CONCLUSION: This proof-of-concept study demonstrated that discretizing the dipole kernel is advantageous for QSM. The impact on small or narrow structures such as the venous vasculature might by particularly relevant to high-resolution QSM applications with ultra-high field MRI - a topic for future investigations. The proposed dipole kernel has a straightforward implementation to existing QSM routines

A robust multi-scale approach to quantitative susceptibility mapping

Quantitative Susceptibility Mapping (QSM), best known as a surrogate for tissue iron content, is becoming a highly relevant MRI contrast for monitoring cellular and vascular status in aging, addiction, traumatic brain injury and, in general, a wide range of neurological disorders. In this study we present a new Bayesian QSM algorithm, named Multi-Scale Dipole Inversion (MSDI), which builds on the nonlinear Morphology-Enabled Dipole Inversion (nMEDI) framework, incorporating three additional features: (i) improved implementation of Laplace's equation to reduce the influence of background fields through variable harmonic filtering and subsequent deconvolution, (ii) improved error control through dynamic phase-reliability compensation across spatial scales, and (iii) scalewise use of the morphological prior. More generally, this new pre-conditioned QSM formalism aims to reduce the impact of dipole-incompatible fields and measurement errors such as flow effects, poor signal-to-noise ratio or other data inconsistencies that can lead to streaking and shadowing artefacts. In terms of performance, MSDI is the first algorithm to rank in the top-10 for all metrics evaluated in the 2016 QSM Reconstruction Challenge. It also demonstrated lower variance than nMEDI and more stable behaviour in scan-rescan reproducibility experiments for different MRI acquisitions at 3 and 7 Tesla. In the present work, we also explored new forms of susceptibility MRI contrast making explicit use of the differential information across spatial scales. Specifically, we show MSDI-derived examples of: (i) enhanced anatomical detail with susceptibility inversions from short-range dipole fields (hereby referred to as High-Pass Susceptibility Mapping or HPSM), (ii) high specificity to venous-blood susceptibilities for highly regularised HPSM (making a case for MSDI-based Venography or VenoMSDI), (iii) improved tissue specificity (and possibly statistical conditioning) for Macroscopic-Vessel Suppressed Susceptibility Mapping (MVSSM), and (iv) high spatial specificity and definition for HPSM-based Susceptibility-Weighted Imaging (HPSM-SWI) and related intensity projections

Caspase-8 binding to cardiolipin in giant unilamellar vesicles provides a functional docking platform for bid

Caspase-8 is involved in death receptor-mediated apoptosis in type II cells, the proapoptotic programme of which is triggered by truncated Bid. Indeed, caspase-8 and Bid are the known intermediates of this signalling pathway. Cardiolipin has been shown to provide an anchor and an essential activating platform for caspase-8 at the mitochondrial membrane surface. Destabilisation of this platform alters receptor-mediated apoptosis in diseases such as Barth Syndrome, which is characterised by the presence of immature cardiolipin which does not allow caspase-8 binding. We used a simplified in vitro system that mimics contact sites and/or cardiolipin-enriched microdomains at the outer mitochondrial surface in which the platform consisting of caspase-8, Bid and cardiolipin was reconstituted in giant unilamellar vesicles. We analysed these vesicles by flow cytometry and confirm previous results that demonstrate the requirement for intact mature cardiolipin for caspase-8 activation and Bid binding and cleavage. We also used confocal microscopy to visualise the rupture of the vesicles and their revesiculation at smaller sizes due to alteration of the curvature following caspase-8 and Bid binding. Biophysical approaches, including Laurdan fluorescence and rupture/tension measurements, were used to determine the ability of these three components (cardiolipin, caspase-8 and Bid) to fulfil the minimal requirements for the formation and function of the platform at the mitochondrial membrane. Our results shed light on the active functional role of cardiolipin, bridging the gap between death receptors and mitochondria

Quantitative susceptibility mapping: Report from the 2016 reconstruction challenge

PURPOSE: The aim of the 2016 quantitative susceptibility mapping (QSM) reconstruction challenge was to test the ability of various QSM algorithms to recover the underlying susceptibility from phase data faithfully. METHODS: Gradient-echo images of a healthy volunteer acquired at 3T in a single orientation with 1.06 mm isotropic resolution. A reference susceptibility map was provided, which was computed using the susceptibility tensor imaging algorithm on data acquired at 12 head orientations. Susceptibility maps calculated from the single orientation data were compared against the reference susceptibility map. Deviations were quantified using the following metrics: root mean squared error (RMSE), structure similarity index (SSIM), high-frequency error norm (HFEN), and the error in selected white and gray matter regions. RESULTS: Twenty-seven submissions were evaluated. Most of the best scoring approaches estimated the spatial frequency content in the ill-conditioned domain of the dipole kernel using compressed sensing strategies. The top 10 maps in each category had similar error metrics but substantially different visual appearance. CONCLUSION: Because QSM algorithms were optimized to minimize error metrics, the resulting susceptibility maps suffered from over-smoothing and conspicuity loss in fine features such as vessels. As such, the challenge highlighted the need for better numerical image quality criteria

FLASH Knockdown Sensitizes Cells To Fas-Mediated Apoptosis via Down-Regulation of the Anti-Apoptotic Proteins, MCL-1 and Cflip Short

FLASH (FLICE-associated huge protein or CASP8AP2) is a large multifunctional protein that is involved in many cellular processes associated with cell death and survival. It has been reported to promote apoptosis, but we show here that depletion of FLASH in HT1080 cells by siRNA interference can also accelerate the process. As shown previously, depletion of FLASH halts growth by down-regulating histone biosynthesis and arrests the cell cycle in S-phase. FLASH knockdown followed by stimulating the cells with Fas ligand or anti-Fas antibodies was found to be associated with a more rapid cleavage of PARP, accelerated activation of caspase-8 and the executioner caspase-3 and rapid progression to cellular disintegration. As is the case for most anti-apoptotic proteins, FLASH was degraded soon after the onset of apoptosis. Depletion of FLASH also resulted in the reduced intracellular levels of the anti-apoptotic proteins, MCL-1 and the short isoform of cFLIP. FLASH knockdown in HT1080 mutant cells defective in p53 did not significantly accelerate Fas mediated apoptosis indicating that the effect was dependent on functional p53. Collectively, these results suggest that under some circumstances, FLASH suppresses apoptosis