Dictionary Learning under Symmetries via Group Representations

The dictionary learning problem can be viewed as a data-driven process to learn a suitable transformation so that data is sparsely represented directly from example data. In this paper, we examine the problem of learning a dictionary that is invariant under a pre-specified group of transformations. Natural settings include Cryo-EM, multi-object tracking, synchronization, pose estimation, etc. We specifically study this problem under the lens of mathematical representation theory. Leveraging the power of non-abelian Fourier analysis for functions over compact groups, we prescribe an algorithmic recipe for learning dictionaries that obey such invariances. We relate the dictionary learning problem in the physical domain, which is naturally modelled as being infinite dimensional, with the associated computational problem, which is necessarily finite dimensional. We establish that the dictionary learning problem can be effectively understood as an optimization instance over certain matrix orbitopes having a particular block-diagonal structure governed by the irreducible representations of the group of symmetries. This perspective enables us to introduce a band-limiting procedure which obtains dimensionality reduction in applications. We provide guarantees for our computational ansatz to provide a desirable dictionary learning outcome. We apply our paradigm to investigate the dictionary learning problem for the groups SO(2) and SO(3). While the SO(2)-orbitope admits an exact spectrahedral description, substantially less is understood about the SO(3)-orbitope. We describe a tractable spectrahedral outer approximation of the SO(3)-orbitope, and contribute an alternating minimization paradigm to perform optimization in this setting. We provide numerical experiments to highlight the efficacy of our approach in learning SO(3)-invariant dictionaries, both on synthetic and on real world data.Comment: 29 pages, 2 figure

Civil society leadership in the struggle for AIDS treatment in South Africa and Uganda

Includes abstract.Includes bibliographical references.This thesis is an attempt to theorise and operationalise empirically the notion of ‘civil society leadership’ in Sub-Saharan Africa. ‘AIDS leadership,’ which is associated with the intergovernmental institutions charged with coordinating the global response to HIV/AIDS, is both under-theorised and highly context-specific. In this study I therefore opt for an inclusive framework that draws on a range of approaches, including the literature on ‘leadership’, institutions, social movements and the ‘network’ perspective on civil society mobilisation. This framework is employed in rich and detailed empirical descriptions (‘thick description’) of civil society mobilisation around AIDS, including contentious AIDS activism, in the key case studies of South Africa and Uganda. South Africa and Uganda are widely considered key examples of poor and good leadership (from national political leaders) respectively, while the Treatment Action Campaign (TAC) and The AIDS Support Organisation (TASO) are both seen as highly effective civil society movements. These descriptions emphasise ‘transnational networks of influence’ in which civil society leaders participated (and at times actively constructed) in order to mobilise both symbolic and material resources aimed at exerting influence at the transnational, national and local levels

Search for excited leptons in pp collisions at √s=7 TeV

This is the pre-print version of the final published paper that is available from the link belowResults are presented of a search for compositeness in electrons and muons using a data sample of pp collisions at a center-of-mass energy √s=7 TeV collected with the CMS detector at the LHC and corresponding to an integrated luminosity of 5.0 fb−15.0 fb−1. Excited leptons (ℓ⁎) are assumed to be produced via contact interactions in conjunction with a standard model lepton and to decay via ℓ⁎→ℓγ, yielding a final state with two energetic leptons and a photon. The number of events observed in data is consistent with that expected from the standard model. The 95% confidence upper limits for the cross section for the production and decay of excited electrons (muons), with masses ranging from 0.6 to 2 TeV, are 1.48 to 1.24 fb (1.31 to 1.11 fb). Excited leptons with masses below 1.9 TeV are excluded for the case where the contact interaction scale equals the excited lepton mass. The limits on the cross sections are the most stringent ones published to date

Molecular mechanisms of cell death: recommendations of the Nomenclature Committee on Cell Death 2018.

Over the past decade, the Nomenclature Committee on Cell Death (NCCD) has formulated guidelines for the definition and interpretation of cell death from morphological, biochemical, and functional perspectives. Since the field continues to expand and novel mechanisms that orchestrate multiple cell death pathways are unveiled, we propose an updated classification of cell death subroutines focusing on mechanistic and essential (as opposed to correlative and dispensable) aspects of the process. As we provide molecularly oriented definitions of terms including intrinsic apoptosis, extrinsic apoptosis, mitochondrial permeability transition (MPT)-driven necrosis, necroptosis, ferroptosis, pyroptosis, parthanatos, entotic cell death, NETotic cell death, lysosome-dependent cell death, autophagy-dependent cell death, immunogenic cell death, cellular senescence, and mitotic catastrophe, we discuss the utility of neologisms that refer to highly specialized instances of these processes. The mission of the NCCD is to provide a widely accepted nomenclature on cell death in support of the continued development of the field

Global, regional, and national incidence, prevalence, and years lived with disability for 328 diseases and injuries for 195 countries, 1990–2016: a systematic analysis for the Global Burden of Disease Study 2016

As mortality rates decline, life expectancy increases, and populations age, non-fatal outcomes of diseases and injuries are becoming a larger component of the global burden of disease. The Global Burden of Diseases, Injuries, and Risk Factors Study 2016 (GBD 2016) provides a comprehensive assessment of prevalence, incidence, and years lived with disability (YLDs) for 328 causes in 195 countries and territories from 1990 to 2016