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Consider a data set of vector-valued observations that consists of noisy inliers, which are explained well by a low-dimensional subspace, along with some number of outliers. This work describes a convex optimization problem, called reaper, that can reliably fit a low-dimensional model to this type of data. This approach parameterizes linear subspaces using orthogonal projectors and uses a relaxation of the set of orthogonal projectors to reach the convex formulation. The paper provides an efficient algorithm for solving the reaper problem, and it documents numerical experiments that confirm that reaper can dependably find linear structure in synthetic and natural data. In addition, when the inliers lie near a low-dimensional subspace, there is a rigorous theory that describes when reaper can approximate this subspace., Author(s): Gilad Lerman[sup.1] , Michael B. McCoy[sup.2] , Joel A. Tropp[sup.3] , Teng Zhang[sup.4] Author Affiliations: (1) Department of Mathematics, University of Minnesota, 127 Vincent Hall, 206 Church St SE, [...]

Demixing refers to the challenge of identifying two structured signals given only the sum of the two signals and prior information about their structures. Examples include the problem of separating a signal that is sparse with respect to one basis from a signal that is sparse with respect to a second basis, and the problem of decomposing an observed matrix into a low-rank matrix plus a sparse matrix. This paper describes and analyzes a framework, based on convex optimization, for solving these demixing problems, and many others. This work introduces a randomized signal model that ensures that the two structures are incoherent, i.e., generically oriented. For an observation from this model, this approach identifies a summary statistic that reflects the complexity of a particular signal. The difficulty of separating two structured, incoherent signals depends only on the total complexity of the two structures. Some applications include (1) demixing two signals that are sparse in mutually incoherent bases, (2) decoding spread-spectrum transmissions in the presence of impulsive errors, and (3) removing sparse corruptions from a low-rank matrix. In each case, the theoretical analysis of the convex demixing method closely matches its empirical behavior. Keywords Demixing * Sparsity * Integral geometry * Convex optimization Mathematical Subject Classification 60D05 * 52B55 * 52A22 (primary) * 94B75 (secondary), 1 Introduction In modern data-intensive science, it is common to observe a superposition of multiple information-bearing signals. Demixing refers to the challenge of separating out the constituent signals from the [...]

Recent research indicates that many convex optimization problems with random constraints exhibit a phase transition as the number of constraints increases. For example, this phenomenon emerges in the ℓ1 minimization method for identifying a sparse vector from random linear measurements. Indeed, the ℓ1 approach succeeds with high probability when the number of measurements exceeds a threshold that depends on the sparsity level; otherwise, it fails with high probability. This paper provides the first rigorous analysis that explains why phase transitions are ubiquitous in random convex optimization problems. It also describes tools for making reliable predictions about the quantitative aspects of the transition, including the location and the width of the transition region. These techniques apply to regularized linear inverse problems with random measurements, to demixing problems under a random incoherence model, and also to cone programs with random affine constraints. The applied results depend on foundational research in conic geometry. This paper introduces a summary parameter, called the statistical dimension, that canonically extends the dimension of a linear subspace to the class of convex cones. The main technical result demonstrates that the sequence of intrinsic volumes of a convex cone concentrates sharply around the statistical dimension. This fact leads to accurate bounds on the probability that a randomly rotated cone shares a ray with a fixed cone. [ABSTRACT FROM AUTHOR]

An essay is presented regarding the development of the abolition of slavery in Cumberland County, Pennsylvania between 1780 and 1838. Particular focus is given to the social conflict between whites and blacks during the emancipation of slaves, as well as questions related to the voting and citizenship rights of freed slaves.

Knowledge of ecological impacts of exotic beach almond (Terminalia catappa) in the central Pacific of Costa Rica are little known, but studies have found this species to be a potentially important food source for endangered scarlet macaws (Ara macao). In this study, reproductive phenology and seed predation by variegated squirrels (Sciurus variegatoides) and scarlet macaws were measured during March and April 2011 on beaches of central Pacific coastal Costa Rica. Seed productivity and predation levels were quantified on a weekly basis for 111 beach almond trees to assess the importance of beach almond as a food source for scarlet macaws and the extent of resource partitioning between seed predators. Seed production of the trees was great (about 194 272 seeds) and approximately 67% of seeds were predated by seed predators. Macaws consumed an estimated 49% of seeds while squirrels consumed 18%. Additionally, evidence of resource partitioning between squirrels and macaws was found. Scarlet macaws preferred to feed on the northern side and edge of the canopy while squirrels preferred to feed on the southern and inside parts of the canopy. Both species ate most seeds on the ocean side of the tree. Despite the status of this tree as an exotic species, the beach almond appears to be an important resource for scarlet macaw population recovery. The resource produced by this tree should be taken into account as reforestation efforts continue in Costa Rica.

Cacao (Theobroma cacao) is an important cash crop in tropical climates such as that of Latin America. Over the past several decades, the infection of cultivated cacao by Moniliophthllora roreri, known commonly as "monilia", has significantly hindered cacao production in Latin America. Studies have proposed the use of Trichoderma sp. fungi in biocontrol treatments to prevent and reduce monilia infection, yet tests of Trichoderma-containing spray treatments on cacao agroforests have produced mixed results. Researchers and agricultural workers have suggested that addition of soil, fly ash, or other carbon sources to a Trichoderma spray may improve its efficacy in fighting monilia. To test these suggestions, we designed a series of spray mixtures including Thichoderma cultures, soil, and all necessary controls. We applied the spray mixtures to 80 cacao trees (20 trees for each of four resistant-selected clones to monilia) at the FINMAC organic cacao plantation in Pueblo Nuevo de Guacimo, Limón Province, in northeastern Costa Rica in March-April 2013. Five treatments were applied (control, water, water plus sterilized soil, water plus Trichoderma, and water plus sterilized soil plus Trichoderma). Each treatment was applied to four trees of each clone. We monitored the incidence of monilia infection under each spray treatment over the course of 35d. We found that spraying entire cacao trees two times with a mixture containing Trichoderma and sterilized soil significantly reduced the incidence of monilia infection by 11% (p ≤ 0.05) in only 35d, as compared to the control. This reduction in loss of cacao pods translates into an increase of plantation mean productivity of 1,500 kg dried beans/ha by 198 kg/ha up to 1,698 kg/ha or by a total increase over the whole 110 ha plantation by 21,780 kg. We propose that using such an antifungal spray over the whole course of a crop cycle (120 days) would decrease infection incidence even more. Application of this fungal control measure has the potential of revitalizing the production of cacao in the region.

The increase of ecotourism operations within Costa Rica during the last 20 yrs has brought more and more humans into close, direct contact with several wildlife species. One of these species is the white-faced capuchin (Cebus capucinos), highly gregarious, and with exposure over time, willing to come into close vicinity of humans and their developments. Such contact has its advantages and disadvantages for the ecotourism industry. We observed white-faced monkeys in order to assess the impact of human presence and development on monkey behavior, with a focus on aggressive, affiliative, and foraging behaviors in Curú Wildlife Refuge (CWR), located in Puntarenas, Costa Rica, and to ascertain the degree of over-habituation of capuchin popula- tions at CWR. Though there exists no discrete behavioral parameters that measure over-habituation, it can be defined as an extreme state of habituation in which non-human primates not only lose fear of humans, but also actively include humans in social interactions or treat them as a food resource. We used instantaneous focal animal and group scan sampling during 8 wks in March and April 2012. Two groups (approximately 20-30 individuals each) of capuchins were observed; the first near the tourist development at the Southwestern area of CWR, representing a habituated population that regularly foraged, rested, and groomed in the presence of humans. The second, was observed in the Northeastern area of CWR, did not visit the center of human activity and exhibited fear of humans. The habituated group exhibited significantly fewer instances of threatened behavior in response to human presence (p < 0.0001) than the non-habituated group, and spent significantly more time eating and foraging (p < 0.0001). While the habituated monkeys at CWR may not be over-habituated, they could become that way as development, especially ecotourism, increases. Over-habituation is a problem that affects capuchins in certain ecotourism sites in Costa Rica. It is critical that the consequences of habituation be studied more carefully, primarily in areas where ecotourism operations draw visitors to wildlife habitats.