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Contains fulltext : 283300.pdf (Publisher’s version ) (Open Access), Deep-learning-based brain magnetic resonance imaging (MRI) reconstruction methods have the potential to accelerate the MRI acquisition process. Nevertheless, the scientific community lacks appropriate benchmarks to assess the MRI reconstruction quality of high-resolution brain images, and evaluate how these proposed algorithms will behave in the presence of small, but expected data distribution shifts. The multi-coil MRI (MC-MRI) reconstruction challenge provides a benchmark that aims at addressing these issues, using a large dataset of high-resolution, three-dimensional, T1-weighted MRI scans. The challenge has two primary goals: (1) to compare different MRI reconstruction models on this dataset and (2) to assess the generalizability of these models to data acquired with a different number of receiver coils. In this paper, we describe the challenge experimental design and summarize the results of a set of baseline and state-of-the-art brain MRI reconstruction models. We provide relevant comparative information on the current MRI reconstruction state-of-the-art and highlight the challenges of obtaining generalizable models that are required prior to broader clinical adoption. The MC-MRI benchmark data, evaluation code, and current challenge leaderboard are publicly available. They provide an objective performance assessment for future developments in the field of brain MRI reconstruction.

Contains fulltext : 283323.pdf (Publisher’s version ) (Open Access), Automatic breast and fibro-glandular tissue (FGT) segmentation in breast MRI allows for the efficient and accurate calculation of breast density. The U-Net architecture, either 2D or 3D, has already been shown to be effective at addressing the segmentation problem in breast MRI. However, the lack of publicly available datasets for this task has forced several authors to rely on internal datasets composed of either acquisitions without fat suppression (WOFS) or with fat suppression (FS), limiting the generalization of the approach. To solve this problem, we propose a data-centric approach, efficiently using the data available. By collecting a dataset of T1-weighted breast MRI acquisitions acquired with the use of the Dixon method, we train a network on both T1 WOFS and FS acquisitions while utilizing the same ground truth segmentation. Using the "plug-and-play" framework nnUNet, we achieve, on our internal test set, a Dice Similarity Coefficient (DSC) of 0.96 and 0.91 for WOFS breast and FGT segmentation and 0.95 and 0.86 for FS breast and FGT segmentation, respectively. On an external, publicly available dataset, a panel of breast radiologists rated the quality of our automatic segmentation with an average of 3.73 on a four-point scale, with an average percentage agreement of 67.5%.

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We introduce computable actions of computable groups and prove the following versions of effective Birkhoff’s ergodic theorem. Let Γ be a computable amenable group, then there always exists a canonically computable tempered two-sided Følner sequence (Fn)n≥ 1 in Γ. For a computable, measure-preserving, ergodic action of Γ on a Cantor space { 0 , 1 } ℕ endowed with a computable probability measure μ, it is shown that for every bounded lower semicomputable function f on { 0 , 1 } ℕ and for every Martin-Löf random ω∈ { 0 , 1 } ℕ the equalitylimn→∞1|Fn|∑g∈Fnf(g⋅ω)=∫fdμholds, where the averages are taken with respect to a canonically computable tempered two-sided Følner sequence (Fn)n≥ 1. We also prove the same identity for all lower semicomputable f’s in the special case when Γ is a computable group of polynomial growth and Fn := B(n) is the Følner sequence of balls around the neutral Γ., Analysis

Item does not contain fulltext, We re-examine the theory of systems with quasi-discrete spectrum initiated in the 1960's by Abramov, Hahn, and Parry. In the first part, we give a simpler proof of the Hahn Parry theorem stating that each minimal topological system with quasi discrete spectrum is isomorphic to a certain affine automorphism system on some compact Abelian group. Next, we show that a suitable application of Gelfand's theorem renders Abramov's theorem-the analogue of the Hahn-Parry theorem for measure-preserving systems-a straightforward corollary of the Hahn-Parry result. In the second part, independent of the first, we present a shortened proof of the fact that each factor of a totally ergodic system with quasi-discrete spectrum (a "QDS-system") again has quasi-discrete spectrum and that such systems have zero entropy. Moreover, we obtain a complete algebraic classification of the factors of a QDS-system. In the third part, we apply the results of the second to the (still open) question whether a Markov quasi-factor of a QDS-system is already a factor of it. We show that this is true when the system satisfies some algebraic constraint on the group of quasi-eigenvalues, which is satisfied, e.g., in the case of the skew shift.

Item does not contain fulltext, It was shown by S. Kalikow and B. Weiss that, given a measure-preserving action of Zd on a probability space X and a nonnegative measurable function f on X, the probability that the sequence of ergodic averages 1/(2k+1)(d) Sigma(g subset of[k1. . . , k]d) f(g.x) has at least n fluctuations across an interval (alpha, beta) can be bounded from above by c(1)c(2)(n) for some universal constants c(1) is an element of R and c(2) is an element of (0,1), which depend only on d,alpha,beta. The purpose of this article is to generalize this result to measure -preserving actions of groups of polynomial growth. As the main tool we develop a generalization of the effective Vitali covering theorem to groups of polynomial growth.

We re-examine the theory of systems with quasi-discrete spectrum initiated in the 1960's by Abramov, Hahn, and Parry. In the first part, we give a simpler proof of the Hahn-Parry theorem stating that each minimal topological system with quasidiscrete spectrum is isomorphic to a certain affine automorphism system on some compact Abelian group. Next, we show that a suitable application of Gelfand's theorem renders Abramov's theorem-the analogue of the Hahn-Parry theorem for measure-preserving systems-a straightforward corollary of the Hahn-Parry result. In the second part, independent of the first, we present a shortened proof of the fact that each factor of a totally ergodic system with quasi-discrete spectrum (a "QDS-system") again has quasi-discrete spectrum and that such systems have zero entropy. Moreover, we obtain a complete algebraic classification of the factors of a QDS-system. In the third part, we apply the results of the second to the (still open) question whether a Markov quasi-factor of a QDS-system is already a factor of it. We show that this is true when the system satisfies some algebraic constraint on the group of quasi-eigenvalues, which is satisfied, e.g., in the case of the skew shift., Analysis

This thesis is dedicated to studying the theory of entropy and its relation to the Kolmogorov complexity. Originating in physics, the notion of entropy was introduced to mathematics by C. E. Shannon as a way of measuring the rate at which information is coming from a data source. There are, however, a few different ways of telling how much information there is: an alternative approach to quantifying the amount of information is the Kolmogorov complexity, which was proposed by A. N. Kolmogorov. The Shannon entropy is the key ingredient in the definition of the Kolmogorov-Sinai entropy of a measure-preserving systems. Roughly speaking, the Kolmogorov-Sinai entropy is the expected amount of information in `Shannon sense' that one obtains per unit of time by observing the evolution of a measure-preserving system. In topological dynamics, the topological entropy takes place of the Kolmogorov-Sinai entropy. For metrizable systems, the topological entropy measures the exponential growth rate of the number of distinguishable partial orbits of length n as n tends to infinity. Originally defined for Z-actions, the 'classical' theories of entropy were later extended to actions of amenable groups. We provide a necessary background on amenable groups, topological/measurepreserving dynamics and the entropy theory in Chapters 1, 2, 3 and 5. The main focus of this thesis is extending the following results. First of all, a common generalization of the topological and the Kolmogorov-Sinai entropy theories for Z-systems was suggested by G. Palm. We provide an abstract generalization of the work of Palm for actions of discrete amenable groups in the language of measurement functors in Chapter 6. Secondly, we investigate the connection of entropy and Kolmogorov complexity. Originally, the equality between the topological entropy and a certain quantity measuring maximal asymptotic Kolmogorov complexity of the trajectories was established by A. A. Brudno for subshifts over, Analysis