Criticality in quark-gluon systems far beyond thermal and chemical equilibrium

Experimental evidence and theoretical arguments for the existence of self-organized criticality in systems of gluons and quarks are presented. It is observed that the existing data for high-transverse-momentum jet-production exhibit striking regularities; and it is shown that, together with first-principle considerations, such regularities can be used, not only to probe the possible compositness of quarks, but also to obtain {\em direct evidence} for, or against, the existence of critical temperature and/or critical chemical potential in quark-gluon systems when hadrons are squeezed together.Comment: 13 pages, including 1 figure and 1 tabl

Formation of color-singlet gluon-clusters and inelastic diffractive scattering

This is the extensive follow-up report of a recent Letter in which the existence of self-organized criticality (SOC) in systems of interacting soft gluons is proposed, and its consequences for inelastic diffractive scattering processes are discussed. It is pointed out, that color-singlet gluon-clusters can be formed in hadrons as a consequence of SOC in systems of interacting soft gluons, and that the properties of such spatiotemporal complexities can be probed experimentally by examing inelastic diffractive scattering. Theoretical arguments and experimental evidences supporting the proposed picture are presented --- together with the result of a systematic analysis of the existing data for inelastic diffractive scattering processes performed at different incident energies, and/or by using different beam-particles. It is shown in particular that the size- and the lifetime-distributions of such gluon-clusters can be directly extracted from the data, and the obtained results exhibit universal power-law behaviors --- in accordance with the expected SOC-fingerprints. As further consequences of SOC in systems of interacting soft gluons, the $t$-dependence and the $(M_x^2/s)$-dependence of the double differential cross-sections for inelastic diffractive scattering off proton-target are discussed. Here $t$ stands for the four-momentum-transfer squared, $M_x$ for the missing mass, and $\sqrt{s}$ for the total c.m.s. energy. It is shown, that the space-time properties of the color-singlet gluon-clusters due to SOC, discussed above, lead to simple analytical formulae for $d^2\sigma/dt d(M_x^2/s)$ and for $d\sigma/dt$, and that the obtained results are in good agreement with the existing data. Further experiments are suggested.Comment: 67 pages, including 11 figure

Axisymmetric diffusion kurtosis imaging with Rician bias correction: A simulation study

Purpose: To compare the estimation accuracy of axisymmetric diffusion kurtosis imaging (DKI) and standard DKI in combination with Rician bias correction (RBC).Methods: Axisymmetric DKI is more robust against noise-induced variation in the measured signal than standard DKI because of its reduced parameter space. However, its susceptibility to Rician noise bias at low signal-to-noise ratios (SNR) is unknown. Here, we investigate two main questions: first, does RBC improve estimation accuracy of axisymmetric DKI?; second, is estimation accuracy of axisymmetric DKI increased compared to standard DKI? Estimation accuracy was investigated on the five axisymmetric DKI tensor metrics (AxTM): the parallel and perpendicular diffusivity and kurtosis and mean of the kurtosis tensor, using a noise simulation study based on synthetic data of tissues with varying fiber alignment and in-vivo data focusing on white matter.Results: RBC mainly increased accuracy for the parallel AxTM in tissues with highly to moderately aligned fibers. For the perpendicular AxTM, axisymmetric DKI without RBC performed slightly better than with RBC. However, the combination of axisymmetric DKI with RBC was the overall best performing algorithm across all five AxTM in white matter and axisymmetric DKI itself substantially improved accuracy in axisymmetric tissues with low fiber alignment.Conclusion: Combining axisymmetric DKI with RBC facilitates accurate DKI parameter estimation at unprecedented low SNRs ( ≈15) in white matter, possibly making it a valuable tool for neuroscience and clinical research studies where scan time is a limited resource. The tools used here are available in the open-source ACID toolbox for SPM

Automatic, fast and robust characterization of noise distributions for diffusion MRI

Knowledge of the noise distribution in magnitude diffusion MRI images is the centerpiece to quantify uncertainties arising from the acquisition process. The use of parallel imaging methods, the number of receiver coils and imaging filters applied by the scanner, amongst other factors, dictate the resulting signal distribution. Accurate estimation beyond textbook Rician or noncentral chi distributions often requires information about the acquisition process (e.g. coils sensitivity maps or reconstruction coefficients), which is not usually available. We introduce a new method where a change of variable naturally gives rise to a particular form of the gamma distribution for background signals. The first moments and maximum likelihood estimators of this gamma distribution explicitly depend on the number of coils, making it possible to estimate all unknown parameters using only the magnitude data. A rejection step is used to make the method automatic and robust to artifacts. Experiments on synthetic datasets show that the proposed method can reliably estimate both the degrees of freedom and the standard deviation. The worst case errors range from below 2% (spatially uniform noise) to approximately 10% (spatially variable noise). Repeated acquisitions of in vivo datasets show that the estimated parameters are stable and have lower variances than compared methods.Comment: v2: added publisher DOI statement, fixed text typo in appendix A

Error quantification in multi-parameter mapping facilitates robust estimation and enhanced group level sensitivity

Multi-Parameter Mapping (MPM) is a comprehensive quantitative neuroimaging protocol that enables estimation of four physical parameters (longitudinal and effective transverse relaxation rates and , proton density , and magnetization transfer saturation ) that are sensitive to microstructural tissue properties such as iron and myelin content. Their capability to reveal microstructural brain differences, however, is tightly bound to controlling random noise and artefacts (e.g. caused by head motion) in the signal. Here, we introduced a method to estimate the local error of , and maps that captures both noise and artefacts on a routine basis without requiring additional data. To investigate the method's sensitivity to random noise, we calculated the model-based signal-to-noise ratio (mSNR) and showed in measurements and simulations that it correlated linearly with an experimental raw-image-based SNR map. We found that the mSNR varied with MPM protocols, magnetic field strength (3T vs. 7T) and MPM parameters: it halved from to and decreased from to by a factor of 3-4. Exploring the artefact-sensitivity of the error maps, we generated robust MPM parameters using two successive acquisitions of each contrast and the acquisition-specific errors to down-weight erroneous regions. The resulting robust MPM parameters showed reduced variability at the group level as compared to their single-repeat or averaged counterparts. The error and mSNR maps may better inform power-calculations by accounting for local data quality variations across measurements. Code to compute the mSNR maps and robustly combined MPM maps is available in the open-source hMRI toolbox