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Medical imaging is spearheading the AI transformation of healthcare. Performance reporting is key to determine which methods should be translated into clinical practice. Frequently, broad conclusions are simply derived from mean performance values. In this paper, we argue that this common practice is often a misleading simplification as it ignores performance variability. Our contribution is threefold. (1) Analyzing all MICCAI segmentation papers (n = 221) published in 2023, we first observe that more than 50% of papers do not assess performance variability at all. Moreover, only one (0.5%) paper reported confidence intervals (CIs) for model performance. (2) To address the reporting bottleneck, we show that the unreported standard deviation (SD) in segmentation papers can be approximated by a second-order polynomial function of the mean Dice similarity coefficient (DSC). Based on external validation data from 56 previous MICCAI challenges, we demonstrate that this approximation can accurately reconstruct the CI of a method using information provided in publications. (3) Finally, we reconstructed 95% CIs around the mean DSC of MICCAI 2023 segmentation papers. The median CI width was 0.03 which is three times larger than the median performance gap between the first and second ranked method. For more than 60% of papers, the mean performance of the second-ranked method was within the CI of the first-ranked method. We conclude that current publications typically do not provide sufficient evidence to support which models could potentially be translated into clinical practice., Comment: Paper accepted at MICCAI 2024 conference

Incomplete Hippocampal Inversion (IHI), sometimes called hippocampal malrotation, is an atypical anatomical pattern of the hippocampus found in about 20% of the general population. IHI can be visually assessed on coronal slices of T1 weighted MR images, using a composite score that combines four anatomical criteria. IHI has been associated with several brain disorders (epilepsy, schizophrenia). However, these studies were based on small samples. Furthermore, the factors (genetic or environmental) that contribute to the genesis of IHI are largely unknown. Large-scale studies are thus needed to further understand IHI and their potential relationships to neurological and psychiatric disorders. However, visual evaluation is long and tedious, justifying the need for an automatic method. In this paper, we propose, for the first time, to automatically rate IHI. We proceed by predicting four anatomical criteria, which are then summed up to form the IHI score, providing the advantage of an interpretable score. We provided an extensive experimental investigation of different machine learning methods and training strategies. We performed automatic rating using a variety of deep learning models (conv5-FC3, ResNet and SECNN) as well as a ridge regression. We studied the generalization of our models using different cohorts and performed multi-cohort learning. We relied on a large population of 2,008 participants from the IMAGEN study, 993 and 403 participants from the QTIM/QTAB studies as well as 985 subjects from the UKBiobank. We showed that deep learning models outperformed a ridge regression. We demonstrated that the performances of the conv5-FC3 network were at least as good as more complex networks while maintaining a low complexity and computation time. We showed that training on a single cohort may lack in variability while training on several cohorts improves generalization., Comment: Accepted for publication at the Journal of Machine Learning for Biomedical Imaging (MELBA) https://melba-journal.org/2024:016

The emergence of clinical data warehouses (CDWs), which contain the medical data of millions of patients, has paved the way for vast data sharing for research. The quality of MRIs gathered in CDWs differs greatly from what is observed in research settings and reflects a certain clinical reality. Consequently, a significant proportion of these images turns out to be unusable due to their poor quality. Given the massive volume of MRIs contained in CDWs, the manual rating of image quality is impossible. Thus, it is necessary to develop an automated solution capable of effectively identifying corrupted images in CDWs. This study presents an innovative transfer learning method for automated quality control of 3D gradient echo T1-weighted brain MRIs within a CDW, leveraging artefact simulation. We first intentionally corrupt images from research datasets by inducing poorer contrast, adding noise and introducing motion artefacts. Subsequently, three artefact-specific models are pre-trained using these corrupted images to detect distinct types of artefacts. Finally, the models are generalised to routine clinical data through a transfer learning technique, utilising 3660 manually annotated images. The overall image quality is inferred from the results of the three models, each designed to detect a specific type of artefact. Our method was validated on an independent test set of 385 3D gradient echo T1-weighted MRIs. Our proposed approach achieved excellent results for the detection of bad quality MRIs, with a balanced accuracy of over 87%, surpassing our previous approach by 3.5 percent points. Additionally, we achieved a satisfactory balanced accuracy of 79% for the detection of moderate quality MRIs, outperforming our previous performance by 5 percent points. Our framework provides a valuable tool for exploiting the potential of MRIs in CDWs., Comment: Accepted for publication at the Journal of Machine Learning for Biomedical Imaging (MELBA) https://melba-journal.org/2024:012

We consider the question whether a real threefold X fibred into quadric surfaces over the real projective line is stably rational (over R) if the topological space X(R) is connected. We give a counterexample. When all geometric fibres are irreducible, the question is open. We investigate a family of such fibrations for which the intermediate jacobian technique is not available. We produce two independent methods which in many cases enable one to prove decomposition of the diagonal., Comment: 42 pages, in French language

Over the past years, pseudo-healthy reconstruction for unsupervised anomaly detection has gained in popularity. This approach has the great advantage of not requiring tedious pixel-wise data annotation and offers possibility to generalize to any kind of anomalies, including that corresponding to rare diseases. By training a deep generative model with only images from healthy subjects, the model will learn to reconstruct pseudo-healthy images. This pseudo-healthy reconstruction is then compared to the input to detect and localize anomalies. The evaluation of such methods often relies on a ground truth lesion mask that is available for test data, which may not exist depending on the application. We propose an evaluation procedure based on the simulation of realistic abnormal images to validate pseudo-healthy reconstruction methods when no ground truth is available. This allows us to extensively test generative models on different kinds of anomalies and measuring their performance using the pair of normal and abnormal images corresponding to the same subject. It can be used as a preliminary automatic step to validate the capacity of a generative model to reconstruct pseudo-healthy images, before a more advanced validation step that would require clinician's expertise. We apply this framework to the reconstruction of 3D brain FDG PET using a convolutional variational autoencoder with the aim to detect as early as possible the neurodegeneration markers that are specific to dementia such as Alzheimer's disease., Comment: Accepted for publication at the Journal of Machine Learning for Biomedical Imaging (MELBA) https://melba-journal.org/2024:003

This is an unchanged version of an unpublished, ``state of the art'' survey given at a conference held in Stuttgart in 2001 to celebrate the 100th birthday of Richard Brauer. This text was recently quoted in several papers on the period-index problem for central simple algebras., Comment: The survey is in German

We prove that the i-th unramified cohomology group of the generic diagonal hypersurface in the projective space of dimension n>i is trivial for i=1,2,3., Comment: 12 pages

Medical segmentation models are evaluated empirically. As such an evaluation is based on a limited set of example images, it is unavoidably noisy. Beyond a mean performance measure, reporting confidence intervals is thus crucial. However, this is rarely done in medical image segmentation. The width of the confidence interval depends on the test set size and on the spread of the performance measure (its standard-deviation across of the test set). For classification, many test images are needed to avoid wide confidence intervals. Segmentation, however, has not been studied, and it differs by the amount of information brought by a given test image. In this paper, we study the typical confidence intervals in medical image segmentation. We carry experiments on 3D image segmentation using the standard nnU-net framework, two datasets from the Medical Decathlon challenge and two performance measures: the Dice accuracy and the Hausdorff distance. We show that the parametric confidence intervals are reasonable approximations of the bootstrap estimates for varying test set sizes and spread of the performance metric. Importantly, we show that the test size needed to achieve a given precision is often much lower than for classification tasks. Typically, a 1% wide confidence interval requires about 100-200 test samples when the spread is low (standard-deviation around 3%). More difficult segmentation tasks may lead to higher spreads and require over 1000 samples., Comment: 10 pages

In this chapter, we present the main classic machine learning methods. A large part of the chapter is devoted to supervised learning techniques for classification and regression, including nearest-neighbor methods, linear and logistic regressions, support vector machines and tree-based algorithms. We also describe the problem of overfitting as well as strategies to overcome it. We finally provide a brief overview of unsupervised learning methods, namely for clustering and dimensionality reduction.

One often lacks sufficient annotated samples for training deep segmentation models. This is in particular the case for less common imaging modalities such as Quantitative Susceptibility Mapping (QSM). It has been shown that deep models tend to fit the target function from low to high frequencies. One may hypothesize that such property can be leveraged for better training of deep learning models. In this paper, we exploit this property to propose a new training method based on frequency-domain disentanglement. It consists of two main steps: i) disentangling the image into high- and low-frequency parts and feature learning; ii) frequency-domain fusion to complete the task. The approach can be used with any backbone segmentation network. We apply the approach to the segmentation of the red and dentate nuclei from QSM data which is particularly relevant for the study of parkinsonian syndromes. We demonstrate that the proposed method provides considerable performance improvements for these tasks. We further applied it to three public datasets from the Medical Segmentation Decathlon (MSD) challenge. For two MSD tasks, it provided smaller but still substantial improvements (up to 7 points of Dice), especially under small training set situations., Comment: 10 pages

This is a structured compilation of some of my favourite open problems., Comment: In French. This text will appear in the book Mathematics Going Forward, Collected Mathematical Brushstrokes, LNM 2313, Springer (2023)

For specific classes of smooth, projective varieties $X$ over a field $k$, we compare two cycle maps on the torsion subgroup $CH^2(X)_{\text{tors} }$ of the second Chow group. The first one goes back to work of S. Bloch (1981), the second one is Jannsen's cycle map into continuous $\ell$-adic cohomology, whose injectivity properties have attracted attention in two recent papers. On the one hand, the comparison gives sufficient hypotheses to guarantee injectivity of Jannsen's cycle map sending $CH^2(X)$ to $H^4_{cont}(X, Z_{\ell}(2))$ on $\ell$-primary torsion. On the other hand, using counterexamples to injectivity of the first map due to Sansuc and the first author (1983), we give examples of smooth, projective, geometrically rational surfaces over a rational function field in one variable over a totally imaginary number field for which Jannsen's map for $\ell=2$ is not injective on $2$-torsion. This answers questions raised in a recent paper., Comment: 25 pages, in French; added one missing hypothesis in condition (H4) in section 3

Early and accurate diagnosis of parkinsonian syndromes is critical to provide appropriate care to patients and for inclusion in therapeutic trials. The red nucleus is a structure of the midbrain that plays an important role in these disorders. It can be visualized using iron-sensitive magnetic resonance imaging (MRI) sequences. Different iron-sensitive contrasts can be produced with MRI. Combining such multimodal data has the potential to improve segmentation of the red nucleus. Current multimodal segmentation algorithms are computationally consuming, cannot deal with missing modalities and need annotations for all modalities. In this paper, we propose a new model that integrates prior knowledge from different contrasts for red nucleus segmentation. The method consists of three main stages. First, it disentangles the image into high-level information representing the brain structure, and low-frequency information representing the contrast. The high-frequency information is then fed into a network to learn anatomical features, while the list of multimodal low-frequency information is processed by another module. Finally, feature fusion is performed to complete the segmentation task. The proposed method was used with several iron-sensitive contrasts (iMag, QSM, R2*, SWI). Experiments demonstrate that our proposed model substantially outperforms a baseline UNet model when the training set size is very small.

An important issue in medical image processing is to be able to estimate not only the performances of algorithms but also the precision of the estimation of these performances. Reporting precision typically amounts to reporting standard-error of the mean (SEM) or equivalently confidence intervals. However, this is rarely done in medical image segmentation studies. In this paper, we aim to estimate what is the typical confidence that can be expected in such studies. To that end, we first perform experiments for Dice metric estimation using a standard deep learning model (U-net) and a classical task from the Medical Segmentation Decathlon. We extensively study precision estimation using both Gaussian assumption and bootstrapping (which does not require any assumption on the distribution). We then perform simulations for other test set sizes and performance spreads. Overall, our work shows that small test sets lead to wide confidence intervals (e.g. $\sim$8 points of Dice for 20 samples with $\sigma \simeq 10$).

Reproducibility is a cornerstone of science, as the replication of findings is the process through which they become knowledge. It is widely considered that many fields of science are undergoing a reproducibility crisis. This has led to the publications of various guidelines in order to improve research reproducibility. This didactic chapter intends at being an introduction to reproducibility for researchers in the field of machine learning for medical imaging. We first distinguish between different types of reproducibility. For each of them, we aim at defining it, at describing the requirements to achieve it and at discussing its utility. The chapter ends with a discussion on the benefits of reproducibility and with a plea for a non-dogmatic approach to this concept and its implementation in research practice.

Lichtenbaum proved that index and period coincide for a curve of genus one over a $p$-adic field. Salberger proved that the Hasse principle holds for a smooth complete intersection of two quadrics $X \subset P^n$ over a number field, if it contains a conic and if $n\geq 5$. Building upon these two results, we extend recent results of Creutz and Viray (2021) on the existence of a quadratic point on intersections of two quadrics over $p$-adic fields and number fields. We then recover Heath-Brown's theorem (2018) that the Hasse principle holds for smooth complete intersections of two quadrics in $P^7$. We also give an alternate proof of a theorem of Iyer and Parimala (2022) on the local-global principle in the case $n=5$., Comment: Paper in French, appendix by A. Kuznetsov in English. Version v2 takes into account the remarks of a referee. Final version, to appear in Journal f\"ur die reine und angewandte Mathematik (Crelle)

Deep learning methods have become very popular for the processing of natural images, and were then successfully adapted to the neuroimaging field. As these methods are non-transparent, interpretability methods are needed to validate them and ensure their reliability. Indeed, it has been shown that deep learning models may obtain high performance even when using irrelevant features, by exploiting biases in the training set. Such undesirable situations can potentially be detected by using interpretability methods. Recently, many methods have been proposed to interpret neural networks. However, this domain is not mature yet. Machine learning users face two major issues when aiming to interpret their models: which method to choose, and how to assess its reliability? Here, we aim at providing answers to these questions by presenting the most common interpretability methods and metrics developed to assess their reliability, as well as their applications and benchmarks in the neuroimaging context. Note that this is not an exhaustive survey: we aimed to focus on the studies which we found to be the most representative and relevant.

Understanding how few distributed areas can steer large-scale brain activity is a fundamental question that has practical implications, which range from inducing specific patterns of behavior to counteracting disease. Recent endeavors based on network controllability provided fresh insights into the potential ability of single regions to influence whole brain dynamics through the underlying structural connectome. However, controlling the entire brain activity is often unfeasible and might not always be necessary. The question whether single areas can control specific target subsystems remains crucial, albeit still poorly explored. Furthermore, the structure of the brain network exhibits progressive changes across the lifespan, but little is known about the possible consequences in the controllability properties. To address these questions, we adopted a novel target controllability approach that quantifies the centrality of brain nodes in controlling specific target anatomo-functional systems. We then studied such target control centrality in human connectomes obtained from healthy individuals aged from 5 to 85. Main results showed that the sensorimotor system has a high influencing capacity, but it is difficult for other areas to influence it. Furthermore, we reported that target control centrality varies with age and that temporal-parietal regions, whose cortical thinning is crucial in dementia-related diseases, exhibit lower values in older people. By simulating targeted attacks, such as those 19 occurring in focal stroke, we showed that the ipsilesional hemisphere is the most affected one regardless of the damaged area. Notably, such degradation in target control centrality was more evident in younger people, thus supporting early-vulnerability hypotheses after stroke.

Choroid plexuses (CP) are structures of the ventricles of the brain which produce most of the cerebrospinal fluid (CSF). Several postmortem and in vivo studies have pointed towards their role in the inflammatory process in multiple sclerosis (MS). Automatic segmentation of CP from MRI thus has high value for studying their characteristics in large cohorts of patients. To the best of our knowledge, the only freely available tool for CP segmentation is FreeSurfer but its accuracy for this specific structure is poor. In this paper, we propose to automatically segment CP from non-contrast enhanced T1-weighted MRI. To that end, we introduce a new model called "Axial-MLP" based on an assembly of Axial multi-layer perceptrons (MLPs). This is inspired by recent works which showed that the self-attention layers of Transformers can be replaced with MLPs. This approach is systematically compared with a standard 3D U-Net, nnU-Net, Freesurfer and FastSurfer. For our experiments, we make use of a dataset of 141 subjects (44 controls and 97 patients with MS). We show that all the tested deep learning (DL) methods outperform FreeSurfer (Dice around 0.7 for DL vs 0.33 for FreeSurfer). Axial-MLP is competitive with U-Nets even though it is slightly less accurate. The conclusions of our paper are two-fold: 1) the studied deep learning methods could be useful tools to study CP in large cohorts of MS patients; 2)~Axial-MLP is a potentially viable alternative to convolutional neural networks for such tasks, although it could benefit from further improvements.

We study local-global principles for torsors under reductive linear algebraic groups over semi-global fields; i.e., over one variable function fields over complete discretely valued fields. We provide conditions on the group and the semiglobal field under which the local-global principle holds, and we compute the obstruction to the local-global principle in certain classes of examples. Using our description of the obstruction, we give the first example of a semisimple simply connected group over a semi-global field where the local-global principle fails. Our methods include patching and R-equivalence., Comment: 59 pages. Some improved phrasing to clarify the presentation

We present Clinica (www.clinica.run), an open-source software platform designed to make clinical neuroscience studies easier and more reproducible. Clinica aims for researchers to i) spend less time on data management and processing, ii) perform reproducible evaluations of their methods, and iii) easily share data and results within their institution and with external collaborators. The core of Clinica is a set of automatic pipelines for processing and analysis of multimodal neuroimaging data (currently, T1-weighted MRI, diffusion MRI and PET data), as well as tools for statistics, machine learning and deep learning. It relies on the brain imaging data structure (BIDS) for the organization of raw neuroimaging datasets and on established tools written by the community to build its pipelines. It also provides converters of public neuroimaging datasets to BIDS (currently ADNI, AIBL, OASIS and NIFD). Processed data include image-valued scalar fields (e.g. tissue probability maps), meshes, surface-based scalar fields (e.g. cortical thickness maps) or scalar outputs (e.g. regional averages). These data follow the ClinicA Processed Structure (CAPS) format which shares the same philosophy as BIDS. Consistent organization of raw and processed neuroimaging files facilitates the execution of single pipelines and of sequences of pipelines, as well as the integration of processed data into statistics or machine learning frameworks. The target audience of Clinica is neuroscientists or clinicians conducting clinical neuroscience studies involving multimodal imaging, and researchers developing advanced machine learning algorithms applied to neuroimaging data.

Many studies on machine learning (ML) for computer-aided diagnosis have so far been mostly restricted to high-quality research data. Clinical data warehouses, gathering routine examinations from hospitals, offer great promises for training and validation of ML models in a realistic setting. However, the use of such clinical data warehouses requires quality control (QC) tools. Visual QC by experts is time-consuming and does not scale to large datasets. In this paper, we propose a convolutional neural network (CNN) for the automatic QC of 3D T1-weighted brain MRI for a large heterogeneous clinical data warehouse. To that purpose, we used the data warehouse of the hospitals of the Greater Paris area (Assistance Publique-H\^opitaux de Paris [AP-HP]). Specifically, the objectives were: 1) to identify images which are not proper T1-weighted brain MRIs; 2) to identify acquisitions for which gadolinium was injected; 3) to rate the overall image quality. We used 5000 images for training and validation and a separate set of 500 images for testing. In order to train/validate the CNN, the data were annotated by two trained raters according to a visual QC protocol that we specifically designed for application in the setting of a data warehouse. For objectives 1 and 2, our approach achieved excellent accuracy (balanced accuracy and F1-score \textgreater 90\%), similar to the human raters. For objective 3, the performance was good but substantially lower than that of human raters. Nevertheless, the automatic approach accurately identified (balanced accuracy and F1-score \textgreater 80\%) low quality images, which would typically need to be excluded. Overall, our approach shall be useful for exploiting hospital data warehouses in medical image computing.

In 1974, D. Coray showed that on a smooth cubic surface with a closed point of degree prime to 3 there exists such a point of degree 1, 4 or 10. We first show how a combination of generisation, specialisation, Bertini theorems and large fields avoids considerations of special cases in his argument. For smooth cubic surfaces with a rational point, we show that any zero-cycle of degree at least 10 is rationally equivalent to an effective cycle. We establish analogues of these results for del Pezzo surfaces of degree 2 and of degree 1. For smooth cubic surfaces without a rational point, we relate the question whether there exists a degree 3 point which is not on a line to the question whether rational points are dense on a del Pezzo surface of degree 1. ---- Une surface cubique lisse qui poss\`ede un point ferm\'e de degr\'e premier \`a 3 poss\`ede un tel point de degr\'e 1, 4 ou 10 (Coray, 1974). Un m\'elange de g\'en\'erisation, de sp\'ecialisation, de th\'eor\`emes de Bertini et d'utilisation des corps fertiles donne de la souplesse \`a sa m\'ethode. Pour les surfaces cubiques avec un point rationnel, on montre que tout z\'ero-cycle de degr\'e au moins 10 est rationnellement \'equivalent \`a un z\'ero-cycle effectif. On \'etablit l'analogue de ces r\'esultats pour les surfaces de del Pezzo de degr\'e 2 et de degr\'e 1. On discute l'existence de points ferm\'es de degr\'e 3 non align\'es sur une surface cubique sans point rationnel. On la relie \`a la question de la densit\'e des points rationnels sur une surface de del Pezzo de degr\'e 1., Comment: 27 pages, in French. In Version v3, the introduction has been expanded to put the results into perspective. For arbitrary geometrically rational surfaces, two general effectivity results for zero cycles are now given, with bounds simple functions of the square of the canonical class. To appear in L'Enseignement math\'ematique

BACKGROUND:Automated volumetry software (AVS) has recently become widely available to neuroradiologists. MRI volumetry with AVS may support the diagnosis of dementias by identifying regional atrophy. Moreover, automatic classifiers using machine learning techniques have recently emerged as promising approaches to assist diagnosis. However, the performance of both AVS and automatic classifiers has been evaluated mostly in the artificial setting of research datasets.OBJECTIVE:Our aim was to evaluate the performance of two AVS and an automatic classifier in the clinical routine condition of a memory clinic.METHODS:We studied 239 patients with cognitive troubles from a single memory center cohort. Using clinical routine T1-weighted MRI, we evaluated the classification performance of: 1) univariate volumetry using two AVS (volBrain and Neuroreader$^{TM}$); 2) Support Vector Machine (SVM) automatic classifier, using either the AVS volumes (SVM-AVS), or whole gray matter (SVM-WGM); 3) reading by two neuroradiologists. The performance measure was the balanced diagnostic accuracy. The reference standard was consensus diagnosis by three neurologists using clinical, biological (cerebrospinal fluid) and imaging data and following international criteria.RESULTS:Univariate AVS volumetry provided only moderate accuracies (46% to 71% with hippocampal volume). The accuracy improved when using SVM-AVS classifier (52% to 85%), becoming close to that of SVM-WGM (52 to 90%). Visual classification by neuroradiologists ranged between SVM-AVS and SVM-WGM.CONCLUSION:In the routine practice of a memory clinic, the use of volumetric measures provided by AVS yields only moderate accuracy. Automatic classifiers can improve accuracy and could be a useful tool to assist diagnosis.

Identifying the nodes that have the potential to influence the state of a network is a relevant question for many complex systems. In many applications it is often essential to test the ability of an individual node to control a specific target subset of the network. In biological networks, this might provide precious information on how single genes regulate the expression of specific groups of molecules in the cell. Taking into account these constraints, we propose an optimized heuristic based on the Kalman rank condition to quantify the centrality of a node as the number of target nodes it can control. By introducing a hierarchy among the nodes in the target set, and performing a step-wise research, we ensure for sparse and directed networks the identification of a controllable driver-target configuration in a significantly reduced space and time complexity. We show how the method works for simple network configurations, then we use it to characterize the inflammatory pathways in molecular gene networks associated with macrophage dysfunction in patients with multiple sclerosis. Results indicate that the targeted secreted molecules can in general be controlled by a large number of driver nodes (51%) involved in different cell functions, i.e. sensing, signaling and transcription. However, during the inflammatory response only a moderate fraction of all the possible driver-target pairs are significantly coactivated, as measured by gene expression data obtained from human blood samples. Notably, they differ between multiple sclerosis patients and healthy controls, and we find that this is related to the presence of dysregulated genes along the controllable walks. Our method, that we name step-wise target controllability, represents a practical solution to identify controllable driver-target configurations in directed complex networks and test their relevance from a functional perspective.

Gaussian Graphical Models (GGM) are often used to describe the conditional correlations between the components of a random vector. In this article, we compare two families of GGM inference methods: nodewise edge selection and penalised likelihood maximisation. We demonstrate on synthetic data that, when the sample size is small, the two methods produce graphs with either too few or too many edges when compared to the real one. As a result, we propose a composite procedure that explores a family of graphs with an nodewise numerical scheme and selects a candidate among them with an overall likelihood criterion. We demonstrate that, when the number of observations is small, this selection method yields graphs closer to the truth and corresponding to distributions with better KL divergence with regards to the real distribution than the other two. Finally, we show the interest of our algorithm on two concrete cases: first on brain imaging data, then on biological nephrology data. In both cases our results are more in line with current knowledge in each field.

We investigate a strong version of the integral Tate conjecture for 1-cycles on the product of a curve and a surface over a finite field, under the assumption that the surface is geometrically $CH_0$-trivial. By this we mean that over any algebraically closed field extension, the degree map on the zero-dimensional Chow group of the surface is an isomorphism. This applies to Enriques surfaces. When the N\'eron-Severi group has no torsion, we recover earlier results of A. Pirutka. The results rely on a detailed study of the third unramified cohomology group of specific products of varieties., Comment: 33 pages, in French. Title changed (original title : Produit d'une courbe et d'une surface $CH_{0}$-triviale sur un corps fini : cohomologie non ramifi\'ee et cycles de codimension deux). Introduction revised. New Remark 4.6

The use of neural networks for diagnosis classification is becoming more and more prevalent in the medical imaging community. However, deep learning method outputs remain hard to explain. Another difficulty is to choose among the large number of techniques developed to analyze how networks learn, as all present different limitations. In this paper, we extended the framework of Fong and Vedaldi [IEEE International Conference on Computer Vision (ICCV), 2017] to visualize the training of convolutional neural networks (CNNs) on 3D quantitative neuroimaging data. Our application focuses on the detection of Alzheimer's disease with gray matter probability maps extracted from structural MRI. We first assessed the robustness of the visualization method by studying the coherence of the longitudinal patterns and regions identified by the network. We then studied the stability of the CNN training by computing visualization-based similarity indexes between different re-runs of the CNN. We demonstrated that the areas identified by the CNN were consistent with what is known of Alzheimer's disease and that the visualization approach extract coherent longitudinal patterns. We also showed that the CNN training is not stable and that the areas identified mainly depend on the initialization and the training process. This issue may exist in many other medical studies using deep learning methods on datasets in which the number of samples is too small and the data dimension is high. This means that it may not be possible to rely on deep learning to detect stable regions of interest in this field yet.

Students are incomplete note takers who routinely record just one third of a lesson's important information in their notes. This is unfortunate, because the number of lesson points recorded in notes is positively correlated with student achievement. Moreover, both the activity of recording notes and the subsequent review of notes are advantageous. The authors offer instructors a menu of research-based advice for bolstering student note taking: provide complete notes, provide partial notes, provide note-taking cues, re-present the lesson, provide pauses and revision opportunities, control laptop usage, control "cyber slacking," use PowerPoint slides effectively, and teach note-taking skills. They also suggest ways to help students transform their notes during the note-review process and SOAR (select, organize, associate, and regulate) to success.

In this paper we study local-global principles for tori over semi-global fields, which are one variable function fields over complete discretely valued fields. In particular, we show that for principal homogeneous spaces for tori over the underlying discrete valuation ring, the obstruction to a local-global principle with respect to discrete valuations can be computed using methods coming from patching. We give a sufficient condition for the vanishing of the obstruction, as well as examples were the obstruction is nontrivial or even infinite. A major tool is the notion of a flasque resolution of a torus., Comment: 27 pages; final pre-publication version; correction to Theorem 6.5, rewording at Proposition 6.3 and beginning of Section 8.3

Let $k$ be a number field and $U$ a smooth integral $k$-variety. Let $X \to U$ be an abelian scheme. We consider the set $\mathcal{R}$ of rational points $m \in U(k)$ such that the Mordell-Weil rank of the fibre $U_{m}$ is strictly bigger than the Mordell-Weil rank of the generic fibre. We prove the following results. If the $k$-variety $X$ is $k$-unirational, then $\mathcal{R}$ is dense for the Zariski topology on $U$. If $X$ is $k$-rational, then $\mathcal{R}$ is not thin in $U$. This generalizes results of Billard and of Salgado. The main idea goes back to N\'eron's thesis: use the generic point of the generic fibre of the family., Comment: 16 pages, in French; the second version contains an introduction; this version (third version) slightly modified to take referee's comments into account

Over 30 papers have proposed to use convolutional neural network (CNN) for AD classification from anatomical MRI. However, the classification performance is difficult to compare across studies due to variations in components such as participant selection, image preprocessing or validation procedure. Moreover, these studies are hardly reproducible because their frameworks are not publicly accessible and because implementation details are lacking. Lastly, some of these papers may report a biased performance due to inadequate or unclear validation or model selection procedures. In the present work, we aim to address these limitations through three main contributions. First, we performed a systematic literature review and found that more than half of the surveyed papers may have suffered from data leakage. Our second contribution is the extension of our open-source framework for classification of AD using CNN and T1-weighted MRI. Finally, we used this framework to rigorously compare different CNN architectures. The data was split into training/validation/test sets at the very beginning and only the training/validation sets were used for model selection. To avoid any overfitting, the test sets were left untouched until the end of the peer-review process. Overall, the different 3D approaches (3D-subject, 3D-ROI, 3D-patch) achieved similar performances while that of the 2D slice approach was lower. Of note, the different CNN approaches did not perform better than a SVM with voxel-based features. The different approaches generalized well to similar populations but not to datasets with different inclusion criteria or demographical characteristics.

Diffusion MRI is the modality of choice to study alterations of white matter. In past years, various works have used diffusion MRI for automatic classification of AD. However, classification performance obtained with different approaches is difficult to compare and these studies are also difficult to reproduce. In the present paper, we first extend a previously proposed framework to diffusion MRI data for AD classification. Specifically, we add: conversion of diffusion MRI ADNI data into the BIDS standard and pipelines for diffusion MRI preprocessing and feature extraction. We then apply the framework to compare different components. First, FS has a positive impact on classification results: highest balanced accuracy (BA) improved from 0.76 to 0.82 for task CN vs AD. Secondly, voxel-wise features generally gives better performance than regional features. Fractional anisotropy (FA) and mean diffusivity (MD) provided comparable results for voxel-wise features. Moreover, we observe that the poor performance obtained in tasks involving MCI were potentially caused by the small data samples, rather than by the data imbalance. Furthermore, no extensive classification difference exists for different degree of smoothing and registration methods. Besides, we demonstrate that using non-nested validation of FS leads to unreliable and over-optimistic results: 0.05 up to 0.40 relative increase in BA. Lastly, with proper FR and FS, the performance of diffusion MRI features is comparable to that of T1w MRI. All the code of the framework and the experiments are publicly available: general-purpose tools have been integrated into the Clinica software package (www.clinica.run) and the paper-specific code is available at: https://github.com/aramis-lab/AD-ML., Comment: 51 pages, 5 figure and 6 tables

In Alzheimer's disease (AD), the progressive atrophy leads to aberrant network reconfigurations both at structural and functional levels. In such network reorganization, the core and peripheral nodes appear to be crucial for the prediction of clinical outcome due to their ability to influence large-scale functional integration. However, the role of the different types of brain connectivity in such prediction still remains unclear. Using a multiplex network approach we integrated information from DWI, fMRI and MEG brain connectivity to extract an enriched description of the core-periphery structure in a group of AD patients and age-matched controls. Globally, the regional coreness - i.e., the probability of a region to be in the multiplex core - significantly decreased in AD patients as a result of the randomization process initiated by the neurodegeneration. Locally, the most impacted areas were in the core of the network - including temporal, parietal and occipital areas - while we reported compensatory increments for the peripheral regions in the sensorimotor system. Furthermore, these network changes significantly predicted the cognitive and memory impairment of patients. Taken together these results indicate that a more accurate description of neurodegenerative diseases can be obtained from the multimodal integration of neuroimaging-derived network data., Comment: 5 figures, 1 table, 1 supplementary figure, 2 supplementary tables

A large number of papers have introduced novel machine learning and feature extraction methods for automatic classification of AD. However, they are difficult to reproduce because key components of the validation are often not readily available. These components include selected participants and input data, image preprocessing and cross-validation procedures. The performance of the different approaches is also difficult to compare objectively. In particular, it is often difficult to assess which part of the method provides a real improvement, if any. We propose a framework for reproducible and objective classification experiments in AD using three publicly available datasets (ADNI, AIBL and OASIS). The framework comprises: i) automatic conversion of the three datasets into BIDS format, ii) a modular set of preprocessing pipelines, feature extraction and classification methods, together with an evaluation framework, that provide a baseline for benchmarking the different components. We demonstrate the use of the framework for a large-scale evaluation on 1960 participants using T1 MRI and FDG PET data. In this evaluation, we assess the influence of different modalities, preprocessing, feature types, classifiers, training set sizes and datasets. Performances were in line with the state-of-the-art. FDG PET outperformed T1 MRI for all classification tasks. No difference in performance was found for the use of different atlases, image smoothing, partial volume correction of FDG PET images, or feature type. Linear SVM and L2-logistic regression resulted in similar performance and both outperformed random forests. The classification performance increased along with the number of subjects used for training. Classifiers trained on ADNI generalized well to AIBL and OASIS. All the code of the framework and the experiments is publicly available at: https://gitlab.icm-institute.org/aramislab/AD-ML.