Hilbert's "Verunglueckter Beweis," the first epsilon theorem, and consistency proofs

In the 1920s, Ackermann and von Neumann, in pursuit of Hilbert's Programme, were working on consistency proofs for arithmetical systems. One proposed method of giving such proofs is Hilbert's epsilon-substitution method. There was, however, a second approach which was not reflected in the publications of the Hilbert school in the 1920s, and which is a direct precursor of Hilbert's first epsilon theorem and a certain 'general consistency result' due to Bernays. An analysis of the form of this so-called 'failed proof' sheds further light on an interpretation of Hilbert's Programme as an instrumentalist enterprise with the aim of showing that whenever a `real' proposition can be proved by 'ideal' means, it can also be proved by 'real', finitary means.Comment: 18 pages, final versio

POSE: Pseudo Object Space Error for Initialization-Free Bundle Adjustment

Bundle adjustment is a nonlinear refinement method for camera poses and 3D structure requiring sufficiently good initialization. In recent years, it was experimentally observed that useful minima can be reached even from arbitrary initialization for affine bundle adjustment problems (and fixed-rank matrix factorization instances in general). The key success factor lies in the use of the variable projection (VarPro) method, which is known to have a wide basin of convergence for such problems. In this paper, we propose the Pseudo Object Space Error (pOSE), which is an objective with cameras represented as a hybrid between the affine and projective models. This formulation allows us to obtain 3D reconstructions that are close to the true projective reconstructions while retaining a bilinear problem structure suitable for the VarPro method. Experimental results show that using pOSE has a high success rate to yield faithful 3D reconstructions from random initializations, taking one step towards initialization-free structure from motion

Adversarial Background-Aware Loss for Weakly-supervised Temporal Activity Localization

Temporally localizing activities within untrimmed videos has been extensively studied in recent years. Despite recent advances, existing methods for weakly-supervised temporal activity localization struggle to recognize when an activity is not occurring. To address this issue, we propose a novel method named A2CL-PT. Two triplets of the feature space are considered in our approach: one triplet is used to learn discriminative features for each activity class, and the other one is used to distinguish the features where no activity occurs (i.e. background features) from activity-related features for each video. To further improve the performance, we build our network using two parallel branches which operate in an adversarial way: the first branch localizes the most salient activities of a video and the second one finds other supplementary activities from non-localized parts of the video. Extensive experiments performed on THUMOS14 and ActivityNet datasets demonstrate that our proposed method is effective. Specifically, the average mAP of IoU thresholds from 0.1 to 0.9 on the THUMOS14 dataset is significantly improved from 27.9% to 30.0%.Comment: ECCV 2020 camera ready (Supplementary material: on ECVA soon

Health Status and Access to Care among Maine’s Low-Income Childless Adults: Implications for State Medicaid Expansion

The Affordable Care Act allows states to expand Medicaid coverage to low-income childless adults with income at or below 138 percent of the federal poverty level. Following a 2017 statewide referendum, Maine began enrolling eligible residents in expanded Medicaid in January 2019. While prior research suggests that Maine’s low-income childless adults may face health problems and barriers to accessing services, their health status has not been well documented. The rollout and ongoing implementation of Maine’s Medicaid expansion may be hampered by incomplete information on the characteristics and health status of the low-income childless adult population. This study examines demographic characteristics, health status, and access to care among Maine’s low-income childless adults and offers recommendations to policymakers, providers, and other stakeholders working to implement Medicaid expansion and address the health needs of this vulnerable population

Model Atmospheres for X-ray Bursting Neutron Stars

The hydrogen and helium accreted by X-ray bursting neutron stars is periodically consumed in runaway thermonuclear reactions that cause the entire surface to glow brightly in X-rays for a few seconds. With models of the emission, the mass and radius of the neutron star can be inferred from the observations. By simultaneously probing neutron star masses and radii, X-ray bursts are one of the strongest diagnostics of the nature of matter at extremely high densities. Accurate determinations of these parameters are difficult, however, due to the highly non-ideal nature of the atmospheres where X-ray bursts occur. Observations from X-ray telescopes such as RXTE and NuStar can potentially place strong constraints on nuclear matter once uncertainties in atmosphere models have been reduced. Here we discuss current progress on modeling atmospheres of X-ray bursting neutron stars and some of the challenges still to be overcome.Comment: 25 pages, 14 figure

Projective Bundle Adjustment from Arbitrary Initialization Using the Variable Projection Method

Bundle adjustment is used in structure-from-motion pipelines as final refinement stage requiring a sufficiently good initialization to reach a useful local mininum. Starting from an arbitrary initialization almost always gets trapped in a poor minimum. In this work we aim to obtain an initialization-free approach which returns global minima from a large proportion of purely random starting points. Our key inspiration lies in the success of the Variable Projection (VarPro) method for affine factorization problems, which have close to 100% chance of reaching a global minimum from random initialization. We find empirically that this desirable behaviour does not directly carry over to the projective case, and we consequently design and evaluate strategies to overcome this limitation. Also, by unifying the affine and the projective camera settings, we obtain numerically better conditioned reformulations of original bundle adjustment algorithms

Projective Bundle Adjustment from Arbitrary Initialization Using the Variable Projection Method

Bundle adjustment is used in structure-from-motion pipelines as final refinement stage requiring a sufficiently good initialization to reach a useful local mininum. Starting from an arbitrary initialization almost always gets trapped in a poor minimum. In this work we aim to obtain an initialization-free approach which returns global minima from a large proportion of purely random starting points. Our key inspiration lies in the success of the Variable Projection (VarPro) method for affine factorization problems, which have close to 100% chance of reaching a global minimum from random initialization. We find empirically that this desirable behaviour does not directly carry over to the projective case, and we consequently design and evaluate strategies to overcome this limitation. Also, by unifying the affine and the projective camera settings, we obtain numerically better conditioned reformulations of original bundle adjustment algorithms