Riemannian Optimization via Frank-Wolfe Methods

We study projection-free methods for constrained Riemannian optimization. In particular, we propose the Riemannian Frank-Wolfe (RFW) method. We analyze non-asymptotic convergence rates of RFW to an optimum for (geodesically) convex problems, and to a critical point for nonconvex objectives. We also present a practical setting under which RFW can attain a linear convergence rate. As a concrete example, we specialize Rfw to the manifold of positive definite matrices and apply it to two tasks: (i) computing the matrix geometric mean (Riemannian centroid); and (ii) computing the Bures-Wasserstein barycenter. Both tasks involve geodesically convex interval constraints, for which we show that the Riemannian "linear oracle" required by RFW admits a closed-form solution; this result may be of independent interest. We further specialize RFW to the special orthogonal group and show that here too, the Riemannian "linear oracle" can be solved in closed form. Here, we describe an application to the synchronization of data matrices (Procrustes problem). We complement our theoretical results with an empirical comparison of Rfw against state-of-the-art Riemannian optimization methods and observe that RFW performs competitively on the task of computing Riemannian centroids.Comment: Under Review. Largely revised version, including an extended experimental section and an application to the special orthogonal group and the Procrustes proble

Forman-Ricci flow for change detection in large dynamic data sets

We present a viable solution to the challenging question of change detection in complex networks inferred from large dynamic data sets. Building on Forman's discretization of the classical notion of Ricci curvature, we introduce a novel geometric method to characterize different types of real-world networks with an emphasis on peer-to-peer networks. Furthermore we adapt the classical Ricci flow that already proved to be a powerful tool in image processing and graphics, to the case of undirected and weighted networks. The application of the proposed method on peer-to-peer networks yields insights into topological properties and the structure of their underlying data.Comment: Conference paper, accepted at ICICS 2016. (Updated version

The Role of Metacognition and Anxiety in College Students’ Performance on a General-Knowledge Test

This study was interested in the role of metacognition, confidence, and question type in student’s likelihoods of changing responses to general-knowledge questions. Participants were given two tasks, a general-knowledge multiple-choice test that contained both tricky and non-tricky questions accompanied by confidence judgments and indications for why they chose their answers and a second task which consisted of a test review packet for an opportunity to change and re-assess confidence in questions. Students opted to change very few answers when given the opportunity to do so and when they changed they were more likely to change tricky questions than non-tricky questions. Students were significantly more confident in answers for non-tricky questions and the younger a student was corresponded with higher ratings of confidence. Overall, results suggest that future research should force participants to change answers and to analyze shifts in confidence and reasons for changing answers for both initial and changed responses

Sturzfrei dank Pilates? : Auswirkungen von Pilatesübungen auf das Sturzrisiko geriatrischer Patienten/Patientinnen gemessen am Timed up and go Test

Darstellung des Themas: Die Gesundheitskosten weltweit steigen durch Sturzverletzungen der älter werdenden Gesellschaft kontinuierlich an. Es zeigt sich eine Notwendigkeit diese Kosten durch gezielte Sturzprophylaxen zu senken. Pilates eignet sich durch die sanften, präzisen Übungen besonders gut für ältere Erwachsene. Die Kräftigung der tiefliegenden Muskulatur steht im Zusammenhang mit Gleichgewicht und Stürzen bei Senioren/Seniorinnen. Ziel: Anhand dieser Arbeit sollen die Auswirkungen von Pilatesübungen auf das Sturzrisiko geriatrischer Patienten/Patientinnen anhand des Timed up and go Test geprüft werden. Methode: Mit vorab definierten Ein- und Ausschlusskriterien wurden sechs Studien zum Thema Pilates und Timed up and go Test mittels einer systematischen Literaturrecherche auf Medline, Pedro und Amed erworben. Mit Hilfe des AICA-Formulars und der Pedro-Skala wurde eine Bewertung der Studien vorgenommen. Relevante Ergebnisse: Signifikante TUG-Ergebnisse nach einer sechs- bis zwölfwöchigen Pilatesintervention zeigten sich bei vier von sechs Studien. Schlussfolgerung: Ein regelmässiges Pilatestraining hat tendenziell einen positiven Effekt auf das Sturzrisiko geriatrischer Patienten/Patientinnen. Es zeigte sich jedoch, dass Pilates kein geschützter Begriff ist und die unterrichteten Übungen von klassischen Pilatesübungen oftmals abweichen. Beeinflussende Faktoren für den Trainingserfolg sind insbesondere das Alter der Probanden/Probandinnen und deren Allgemeinzustand.Background: Throughout the world health costs are increasing steadily due to fall injuries of an ageing society. There is a need to reduce these costs with targeted prevention of falls. Pilates in particular qualifies through its gentle and precise motions as an ideal exercise for older adults. The strengthening of the low lying muscle parts stands in relation to balance and the falling of the elderly. Purpose: In this study the effects of pilates exercises will be examined on geriatric patients’ fall risk with the aid of the Timed up and go Test (TUG). Methods: With a systematic research of literature on platforms such as Medline, Pedro and Amed, six studies on the subject of pilates and the Timed up and go Test were selected on the basis of predefined criteria of inclusion and exclusion. With the aid of the AICA-form and the Pedro-scale, an analysis of the studies was performed. Results: After a six to twelve week pilates intervention, four out of six studies showed significant results. Conclusion: Consistent pilates training tends to have a positive effect on the fall risk of geriatric patients. However, it appears that pilates is not a protected term and the taught exercises often deviate from classical pilates exercises. Influencing factors for training success are the study participants’ age and general condition

Projection-free nonconvex stochastic optimization on Riemannian manifolds

We study stochastic projection-free methods for constrained optimization of smooth functions on Riemannian manifolds, i.e., with additional constraints beyond the parameter domain being a manifold. Specifically, we introduce stochastic Riemannian Frank-Wolfe methods for nonconvex and geodesically convex problems. We present algorithms for both purely stochastic optimization and finite-sum problems. For the latter, we develop variance-reduced methods, including a Riemannian adaptation of the recently proposed Spider technique. For all settings, we recover convergence rates that are comparable to the best-known rates for their Euclidean counterparts. Finally, we discuss applications to two classic tasks: The computation of the Karcher mean of positive definite matrices and Wasserstein barycenters for multivariate normal distributions. For both tasks, stochastic Fw methods yield state-of-the-art empirical performance.Comment: Under Revie

Mitigating Over-Smoothing and Over-Squashing using Augmentations of Forman-Ricci Curvature

While Graph Neural Networks (GNNs) have been successfully leveraged for learning on graph-structured data across domains, several potential pitfalls have been described recently. Those include the inability to accurately leverage information encoded in long-range connections (over-squashing), as well as difficulties distinguishing the learned representations of nearby nodes with growing network depth (over-smoothing). An effective way to characterize both effects is discrete curvature: Long-range connections that underlie over-squashing effects have low curvature, whereas edges that contribute to over-smoothing have high curvature. This observation has given rise to rewiring techniques, which add or remove edges to mitigate over-smoothing and over-squashing. Several rewiring approaches utilizing graph characteristics, such as curvature or the spectrum of the graph Laplacian, have been proposed. However, existing methods, especially those based on curvature, often require expensive subroutines and careful hyperparameter tuning, which limits their applicability to large-scale graphs. Here we propose a rewiring technique based on Augmented Forman-Ricci curvature (AFRC), a scalable curvature notation, which can be computed in linear time. We prove that AFRC effectively characterizes over-smoothing and over-squashing effects in message-passing GNNs. We complement our theoretical results with experiments, which demonstrate that the proposed approach achieves state-of-the-art performance while significantly reducing the computational cost in comparison with other methods. Utilizing fundamental properties of discrete curvature, we propose effective heuristics for hyperparameters in curvature-based rewiring, which avoids expensive hyperparameter searches, further improving the scalability of the proposed approach

Queer international relations

Queer International Relations (IR) is not a new field. For more than 20 years, Queer IR scholarship has focused on how normativities and/or non-normativities associated with categories of sex, gender, and sexuality sustain and contest international formations of power in relation to institutions like heteronormativity, homonormativity, and cisnormativity as well as through queer logics of statecraft. Recently, Queer IR has gained unprecedented traction in IR, as IR scholars have come to recognize how Queer IR theory, methods, and research further IR’s core agenda of analyzing and informing the policies and politics around state and nation formation, war and peace, and international political economy. Specific Queer IR research contributions include work on sovereignty, intervention, security and securitization, torture, terrorism and counter-insurgency, militaries and militarism, human rights and LGBT activism, immigration, regional and international integration, global health, transphobia, homophobia, development and International Financial Institutions, financial crises, homocolonialism, settler colonialism and anti-Blackness, homocapitalism, political/cultural formations, norms diffusion, political protest, and time and temporalitie