Global regularity of three-dimensional Ricci limit spaces

In their recent work [ST17], Miles Simon and the second author established a local bi-Hölder correspondence between weakly noncollapsed Ricci limit spaces in three dimensions and smooth manifolds. In particular, any open ball of finite radius in such a limit space must be bi-Hölder homeomorphic to some open subset of a complete smooth Riemannian three-manifold. In this work we build on the technology from [ST16, ST17] to improve this local correspondence to a global-local correspondence. That is, we construct a smooth three-manifold M, and prove that the entire (weakly) noncollapsed three-dimensional Ricci limit space is homeomorphic to M via a globally-defined homeomorphism that is bi-Hölder once restricted to any compact subset. Here the bi-Hölder regularity is with respect to the distance dg on M, where g is any smooth complete metric on M. A key step in our proof is the construction of local pyramid Ricci flows, existing on uniform regions of spacetime, that are inspired by Hochard’s partial Ricci flows [Hoc16]. Suppose (M, g0, x0) is a complete smooth pointed Riemannian three-manifold that is (weakly) noncollapsed and satisfies a lower Ricci bound. Then, given any k ∈ N, we construct a smooth Ricci flow g(t) living on a subset of spacetime that contains, for each j ∈ {1, . . . , k}, a cylinder Bg0 (x0, j) × [0, Tj ], where Tj is dependent only on the Ricci lower bound, the (weakly) noncollapsed volume lower bound and the radius j (in particular independent of k) and with the property that g(0) = g0 throughout Bg0 (x0, k).</p

A High-Order Scheme for Image Segmentation via a modified Level-Set method

In this paper we propose a high-order accurate scheme for image segmentation based on the level-set method. In this approach, the curve evolution is described as the 0-level set of a representation function but we modify the velocity that drives the curve to the boundary of the object in order to obtain a new velocity with additional properties that are extremely useful to develop a more stable high-order approximation with a small additional cost. The approximation scheme proposed here is the first 2D version of an adaptive "filtered" scheme recently introduced and analyzed by the authors in 1D. This approach is interesting since the implementation of the filtered scheme is rather efficient and easy. The scheme combines two building blocks (a monotone scheme and a high-order scheme) via a filter function and smoothness indicators that allow to detect the regularity of the approximate solution adapting the scheme in an automatic way. Some numerical tests on synthetic and real images confirm the accuracy of the proposed method and the advantages given by the new velocity.Comment: Accepted version for publication in SIAM Journal on Imaging Sciences, 86 figure

Population Aging as the Social Body in Representation and Real Life

This article uses three levels of body analysis as presented by Nancy Scheper-Hughes and Margaret Lock to compare old age as a construct in population aging discourse with research on lived experience of people aging in the United States and Ghana. I first describe how demographers construct social bodies as becoming “gray” through population statistics and how policy makers then use dependency ratios to rationalize intervention on behalf of older adults in the body-politic. The construction of old age within this discourse is then compared with ethnographic research that suggests this construct leaves out much of the lived experience familiar to anthropologists of aging. Rather than debunk the old age construct, however, the purpose of this article is to argue for study of population aging discourse as constituting a social body reflecting cultural constructions of nature and society. Moreover, this representation is made real through policy and social intervention work, and with very real effect on people’s lives. As such, an anthropology of aging bodies can include the social life of old age as a social construct

Optimizing Filter Size in Convolutional Neural Networks for Facial Action Unit Recognition

Recognizing facial action units (AUs) during spontaneous facial displays is a challenging problem. Most recently, Convolutional Neural Networks (CNNs) have shown promise for facial AU recognition, where predefined and fixed convolution filter sizes are employed. In order to achieve the best performance, the optimal filter size is often empirically found by conducting extensive experimental validation. Such a training process suffers from expensive training cost, especially as the network becomes deeper. This paper proposes a novel Optimized Filter Size CNN (OFS-CNN), where the filter sizes and weights of all convolutional layers are learned simultaneously from the training data along with learning convolution filters. Specifically, the filter size is defined as a continuous variable, which is optimized by minimizing the training loss. Experimental results on two AU-coded spontaneous databases have shown that the proposed OFS-CNN is capable of estimating optimal filter size for varying image resolution and outperforms traditional CNNs with the best filter size obtained by exhaustive search. The OFS-CNN also beats the CNN using multiple filter sizes and more importantly, is much more efficient during testing with the proposed forward-backward propagation algorithm

Global aging: emerging challenges

This repository item contains a single issue of The Pardee Papers, a series papers that began publishing in 2008 by the Boston University Frederick S. Pardee Center for the Study of the Longer-Range Future. The Pardee Papers series features working papers by Pardee Center Fellows and other invited authors. Papers in this series explore current and future challenges by anticipating the pathways to human progress, human development, and human well-being. This series includes papers on a wide range of topics, with a special emphasis on interdisciplinary perspectives and a development orientation.Aging policy frameworks were devised during a demographic and economic context in which population aging seemed confined to wealthy nations. These countries could afford retirement policies that supported older workers, decreased unemployment among younger workers, and decreased family pressure to provide old age care. This calculation was based in part on failure to anticipate three demographic trends: continual decline in fertility below replacement rate, continual gains in longevity, and the rise of population aging in poor and “under-developed” countries. These three trends now fuel a sense of crisis. In the global North, there is fear that increasing numbers of older adults will deplete state pension and health care systems. In the global South, the fear is that population aging coupled with family breakdown” requires such state intervention. Natural disaster metaphors, such as “agequake” and “age-tsunami,” illustrate fears of a “graying globe” in which population aging implies population decay and economic destruction. Yet, global aging trends develop over decades and are not easily reversed. Longer-range trends can be addressed through revising policy frameworks to incorporate how growing old is moving from global exception to expectation. Alexandra Crampton was a 2008–2009 Postdoctoral Fellow at the Frederick S. Pardee Center for the Study of the Longer-Range Future and is currently Assistant Professor in the Department of Social and Cultural Sciences at Marquette University. Her scholarship and teaching bring an anthropological perspective to theoretical and practical questions on aging, social welfare policy, social work practice, negotiation, and alternative dispute resolution. She has presented her work for the American Anthropological Association, the Gerontological Society of America, the Council on Social Work Education, and the Society for Social Work Research. She holds a joint PhD in Social Work and Anthropology from the University of Michigan