The magnitude vector of images

The magnitude of a finite metric space has recently emerged as a novel invariant quantity, allowing to measure the effective size of a metric space. Despite encouraging first results demonstrating the descriptive abilities of the magnitude, such as being able to detect the boundary of a metric space, the potential use cases of magnitude remain under-explored. In this work, we investigate the properties of the magnitude on images, an important data modality in many machine learning applications. By endowing each individual images with its own metric space, we are able to define the concept of magnitude on images and analyse the individual contribution of each pixel with the magnitude vector. In particular, we theoretically show that the previously known properties of boundary detection translate to edge detection abilities in images. Furthermore, we demonstrate practical use cases of magnitude for machine learning applications and propose a novel magnitude model that consists of a computationally efficient magnitude computation and a learnable metric. By doing so, we address the computational hurdle that used to make magnitude impractical for many applications and open the way for the adoption of magnitude in machine learning research

Manifold Filter-Combine Networks

We introduce a large class of manifold neural networks (MNNs) which we call Manifold Filter-Combine Networks. This class includes as special cases, the MNNs considered in previous work by Wang, Ruiz, and Ribeiro, the manifold scattering transform (a wavelet-based model of neural networks), and other interesting examples not previously considered in the literature such as the manifold equivalent of Kipf and Welling's graph convolutional network. We then consider a method, based on building a data-driven graph, for implementing such networks when one does not have global knowledge of the manifold, but merely has access to finitely many sample points. We provide sufficient conditions for the network to provably converge to its continuum limit as the number of sample points tends to infinity. Unlike previous work (which focused on specific MNN architectures and graph constructions), our rate of convergence does not explicitly depend on the number of filters used. Moreover, it exhibits linear dependence on the depth of the network rather than the exponential dependence obtained previously

Topological Graph Neural Networks

Graph neural networks (GNNs) are a powerful architecture for tackling graph learning tasks, yet have been shown to be oblivious to eminent substructures, such as cycles. We present TOGL, a novel layer that incorporates global topological information of a graph using persistent homology. TOGL can be easily integrated into any type of GNN and is strictly more expressive in terms of the Weisfeiler--Lehman test of isomorphism. Augmenting GNNs with our layer leads to beneficial predictive performance for graph and node classification tasks, both on synthetic data sets, which can be classified by humans using their topology but not by ordinary GNNs, and on real-world data

A Heat Diffusion Perspective on Geodesic Preserving Dimensionality Reduction

Diffusion-based manifold learning methods have proven useful in representation learning and dimensionality reduction of modern high dimensional, high throughput, noisy datasets. Such datasets are especially present in fields like biology and physics. While it is thought that these methods preserve underlying manifold structure of data by learning a proxy for geodesic distances, no specific theoretical links have been established. Here, we establish such a link via results in Riemannian geometry explicitly connecting heat diffusion to manifold distances. In this process, we also formulate a more general heat kernel based manifold embedding method that we call heat geodesic embeddings. This novel perspective makes clearer the choices available in manifold learning and denoising. Results show that our method outperforms existing state of the art in preserving ground truth manifold distances, and preserving cluster structure in toy datasets. We also showcase our method on single cell RNA-sequencing datasets with both continuum and cluster structure, where our method enables interpolation of withheld timepoints of data. Finally, we show that parameters of our more general method can be configured to give results similar to PHATE (a state-of-the-art diffusion based manifold learning method) as well as SNE (an attraction/repulsion neighborhood based method that forms the basis of t-SNE).Comment: 31 pages, 13 figures, 10 table

Updated Results of the COVID-19 in MS Global Data Sharing Initiative: Anti-CD20 and Other Risk Factors Associated With COVID-19 Severity

COVID-19; Severe acute respiratory syndrome; Data setCOVID-19; Síndrome respiratorio agudo severo; Conjunto de datosCOVID-19; Síndrome respiratòria aguda severa; Conjunt de dadesBackground and Objectives Certain demographic and clinical characteristics, including the use of some disease-modifying therapies (DMTs), are associated with severe acute respiratory syndrome coronavirus 2 infection severity in people with multiple sclerosis (MS). Comprehensive exploration of these relationships in large international samples is needed. Methods Clinician-reported demographic/clinical data from 27 countries were aggregated into a data set of 5,648 patients with suspected/confirmed coronavirus disease 2019 (COVID-19). COVID-19 severity outcomes (hospitalization, admission to intensive care unit [ICU], requiring artificial ventilation, and death) were assessed using multilevel mixed-effects ordered probit and logistic regression, adjusted for age, sex, disability, and MS phenotype. DMTs were individually compared with glatiramer acetate, and anti-CD20 DMTs with pooled other DMTs and with natalizumab. Results Of 5,648 patients, 922 (16.6%) with suspected and 4,646 (83.4%) with confirmed COVID-19 were included. Male sex, older age, progressive MS, and higher disability were associated with more severe COVID-19. Compared with glatiramer acetate, ocrelizumab and rituximab were associated with higher probabilities of hospitalization (4% [95% CI 1–7] and 7% [95% CI 4–11]), ICU/artificial ventilation (2% [95% CI 0–4] and 4% [95% CI 2–6]), and death (1% [95% CI 0–2] and 2% [95% CI 1–4]) (predicted marginal effects). Untreated patients had 5% (95% CI 2–8), 3% (95% CI 1–5), and 1% (95% CI 0–3) higher probabilities of the 3 respective levels of COVID-19 severity than glatiramer acetate. Compared with pooled other DMTs and with natalizumab, the associations of ocrelizumab and rituximab with COVID-19 severity were also more pronounced. All associations persisted/enhanced on restriction to confirmed COVID-19. Discussion Analyzing the largest international real-world data set of people with MS with suspected/confirmed COVID-19 confirms that the use of anti-CD20 medication (both ocrelizumab and rituximab), as well as male sex, older age, progressive MS, and higher disability are associated with more severe course of COVID-19.The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: the operational costs linked to this study are funded by the Multiple Sclerosis International Federation (MSIF) and the Multiple Sclerosis Data Alliance (MSDA), acting under the umbrella of the European Charcot Foundation (ECF). The MSDA receives income from a range of corporate sponsors, recently including Biogen, Bristol-Myers Squibb (formerly Celgene), Canopy Growth Corporation, Genzyme, Icometrix, Merck, Mylan, Novartis, QMENTA, Quanterix, and Roche. MSIF receives income from a range of corporate sponsors, recently including Biogen, Bristol-Myers Squibb (formerly Celgene), Genzyme, Med-Day, Merck, Mylan, Novartis, and Roche. This work was supported by the Flemish Government under the Onderzoeksprogramma Artificiële Intelligentie (AI) Vlaanderen programme and the Research Foundation Fladers (FWO) for ELIXIR Belgium—Flanders (FWO) for ELIXIR Belgium. The central platform was provided by QMENTA, and the computational resources used in this work were provided by Amazon. The statistical analysis was carried out at CORe, The University of Melbourne, with support from NHMRC (1129189 and 1140766)

Associations of Disease-Modifying Therapies With COVID-19 Severity in Multiple Sclerosis

Coronavirus SARS-CoV-2; COVID-19; 2019-nCoV; Esclerosi múltipleCoronavirus SARS-CoV-2; COVID-19; 2019-nCoV; Esclerosis múltipleCoronavirus SARS-CoV-2; COVID-19; 2019-nCoV; Multiple SclerosisBackground and Objectives People with multiple sclerosis (MS) are a vulnerable group for severe coronavirus disease 2019 (COVID-19), particularly those taking immunosuppressive disease-modifying therapies (DMTs). We examined the characteristics of COVID-19 severity in an international sample of people with MS. Methods Data from 12 data sources in 28 countries were aggregated (sources could include patients from 1–12 countries). Demographic (age, sex), clinical (MS phenotype, disability), and DMT (untreated, alemtuzumab, cladribine, dimethyl fumarate, glatiramer acetate, interferon, natalizumab, ocrelizumab, rituximab, siponimod, other DMTs) covariates were queried, along with COVID-19 severity outcomes, hospitalization, intensive care unit (ICU) admission, need for artificial ventilation, and death. Characteristics of outcomes were assessed in patients with suspected/confirmed COVID-19 using multilevel mixed-effects logistic regression adjusted for age, sex, MS phenotype, and Expanded Disability Status Scale (EDSS) score. Results Six hundred fifty-seven (28.1%) with suspected and 1,683 (61.9%) with confirmed COVID-19 were analyzed. Among suspected plus confirmed and confirmed-only COVID-19, 20.9% and 26.9% were hospitalized, 5.4% and 7.2% were admitted to ICU, 4.1% and 5.4% required artificial ventilation, and 3.2% and 3.9% died. Older age, progressive MS phenotype, and higher disability were associated with worse COVID-19 outcomes. Compared to dimethyl fumarate, ocrelizumab and rituximab were associated with hospitalization (adjusted odds ratio [aOR] 1.56, 95% confidence interval [CI] 1.01–2.41; aOR 2.43, 95% CI 1.48–4.02) and ICU admission (aOR 2.30, 95% CI 0.98–5.39; aOR 3.93, 95% CI 1.56–9.89), although only rituximab was associated with higher risk of artificial ventilation (aOR 4.00, 95% CI 1.54–10.39). Compared to pooled other DMTs, ocrelizumab and rituximab were associated with hospitalization (aOR 1.75, 95% CI 1.29–2.38; aOR 2.76, 95% CI 1.87–4.07) and ICU admission (aOR 2.55, 95% CI 1.49–4.36; aOR 4.32, 95% CI 2.27–8.23), but only rituximab was associated with artificial ventilation (aOR 6.15, 95% CI 3.09–12.27). Compared to natalizumab, ocrelizumab and rituximab were associated with hospitalization (aOR 1.86, 95% CI 1.13–3.07; aOR 2.88, 95% CI 1.68–4.92) and ICU admission (aOR 2.13, 95% CI 0.85–5.35; aOR 3.23, 95% CI 1.17–8.91), but only rituximab was associated with ventilation (aOR 5.52, 95% CI 1.71–17.84). Associations persisted on restriction to confirmed COVID-19 cases. No associations were observed between DMTs and death. Stratification by age, MS phenotype, and EDSS score found no indications that DMT associations with COVID-19 severity reflected differential DMT allocation by underlying COVID-19 severity. Discussion Using the largest cohort of people with MS and COVID-19 available, we demonstrated consistent associations of rituximab with increased risk of hospitalization, ICU admission, and need for artificial ventilation and of ocrelizumab with hospitalization and ICU admission. Despite the cross-sectional design of the study, the internal and external consistency of these results with prior studies suggests that rituximab/ocrelizumab use may be a risk factor for more severe COVID-19.The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article. The operational costs linked to this study are funded by the Multiple Sclerosis International Federation (MSIF) and the Multiple Sclerosis Data Alliance (MSDA), acting under the umbrella of the European Charcot Foundation. The MSDA receives income from a range of corporate sponsors, recently including Biogen, Bristol-Myers Squibb (formerly Celgene), Canopy Growth Corp, Genzyme, Icometrix, Merck, Mylan, Novartis, QMENTA, Quanterix, and Roche. MSIF receives income from a range of corporate sponsors, recently including Biogen, Bristol-Myers Squibb (formerly Celgene), Genzyme, Med-Day, Merck, Mylan, Novartis, and Roche. This work was supported by the Flemish government under the Onderzoeksprogramma Artificiële Intelligentie Vlaanderen programme and the Research Foundation Fladers (FWO) for ELIXIR Belgium–Flanders (FWO) for ELIXIR Belgium. The central platform was provided by QMENTA, and the computational resources used in this work were provided by Amazon. The statistical analysis was carried out at CORe, The University of Melbourne, with support from the National Health and Medical Research Council (NHMRC; 1129189 and 1140766)

BLIS-Net: Classifying and Analyzing Signals on Graphs

Graph neural networks (GNNs) have emerged as a powerful tool for tasks such as node classification and graph classification. However, much less work has been done on signal classification, where the data consists of many functions (referred to as signals) defined on the vertices of a single graph. These tasks require networks designed differently from those designed for traditional GNN tasks. Indeed, traditional GNNs rely on localized low-pass filters, and signals of interest may have intricate multi-frequency behavior and exhibit long range interactions. This motivates us to introduce the BLIS-Net (Bi-Lipschitz Scattering Net), a novel GNN that builds on the previously introduced geometric scattering transform. Our network is able to capture both local and global signal structure and is able to capture both low-frequency and high-frequency information. We make several crucial changes to the original geometric scattering architecture which we prove increase the ability of our network to capture information about the input signal and show that BLIS-Net achieves superior performance on both synthetic and real-world data sets based on traffic flow and fMRI data

Driving pressure during general anesthesia for open abdominal surgery (DESIGNATION) : study protocol of a randomized clinical trial

Background Intraoperative driving pressure (Delta P) is associated with development of postoperative pulmonary complications (PPC). When tidal volume (V-T) is kept constant, Delta P may change according to positive end-expiratory pressure (PEEP)-induced changes in lung aeration. Delta P may decrease if PEEP leads to a recruitment of collapsed lung tissue but will increase if PEEP mainly causes pulmonary overdistension. This study tests the hypothesis that individualized high PEEP, when compared to fixed low PEEP, protects against PPC in patients undergoing open abdominal surgery. Methods The "Driving prESsure durIng GeNeral AnesThesIa for Open abdomiNal surgery trial" (DESIGNATION) is an international, multicenter, two-group, double-blind randomized clinical superiority trial. A total of 1468 patients will be randomly assigned to one of the two intraoperative ventilation strategies. Investigators screen patients aged >= 18 years and with a body mass index <= 40 kg/m(2), scheduled for open abdominal surgery and at risk for PPC. Patients either receive an intraoperative ventilation strategy with individualized high PEEP with recruitment maneuvers (RM) ("individualized high PEEP") or one in which PEEP of 5 cm H2O without RM is used ("low PEEP"). In the "individualized high PEEP" group, PEEP is set at the level at which Delta P is lowest. In both groups of the trial, V-T is kept at 8 mL/kg predicted body weight. The primary endpoint is the occurrence of PPC, recorded as a collapsed composite of adverse pulmonary events. Discussion DESIGNATION will be the first randomized clinical trial that is adequately powered to compare the effects of individualized high PEEP with RM versus fixed low PEEP without RM on the occurrence of PPC after open abdominal surgery. The results of DESIGNATION will support anesthesiologists in their decisions regarding PEEP settings during open abdominal surgery