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

Direct MD simulation of liquid-solid phase equilibria for three-component plasma

The neutron rich isotope 22Ne may be a significant impurity in carbon and oxygen white dwarfs and could impact how the stars freeze. We perform molecular dynamics simulations to determine the influence of 22Ne in carbon-oxygen-neon systems on liquid-solid phase equilibria. Both liquid and solid phases are present simultaneously in our simulation volumes. We identify liquid, solid, and interface regions in our simulations using a bond angle metric. In general we find good agreement for the composition of liquid and solid phases between our MD simulations and the semi analytic model of Medin and Cumming. The trace presence of a third component, neon, does not appear to strongly impact the chemical separation found previously for two component carbon and oxygen systems. This suggests that small amounts of 22Ne may not qualitatively change how the material in white dwarf stars freezes. However, we do find systematically lower melting temperatures (higher Gamma) in our MD simulations compared to the semi analytic model. This difference seems to grow with impurity parameter Q_imp and suggests a problem with simple corrections to the linear mixing rule for the free energy of multicomponent solid mixtures that is used in the semi analytic model.Comment: 11 pages, 6 figures, Phys Rev E in pres

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

3D Tracking via Body Radio Reflections

This paper introduces WiTrack, a system that tracks the 3D motion of a user from the radio signals reflected off her body. It works even if the person is occluded from the WiTrack device or in a different room. WiTrack does not require the user to carry any wireless device, yet its accuracy exceeds current RF localization systems, which require the user to hold a transceiver. Empirical measurements with a WiTrack prototype show that, on average, it localizes the center of a human body to within 10 to 13 cm in the x and y dimensions, and 21 cm in the z dimension. It also provides coarse tracking of body parts, identifying the direction of a pointing hand with a median of 11.2 degrees. WiTrack bridges a gap between RF-based localization systems which locate a user through walls and occlusions, and human-computer interaction systems like WiTrack, which can track a user without instrumenting her body, but require the user to stay within the direct line of sight of the device

Uncertainty in multitask learning: joint representations for probabilistic MR-only radiotherapy planning

Multi-task neural network architectures provide a mechanism that jointly integrates information from distinct sources. It is ideal in the context of MR-only radiotherapy planning as it can jointly regress a synthetic CT (synCT) scan and segment organs-at-risk (OAR) from MRI. We propose a probabilistic multi-task network that estimates: 1) intrinsic uncertainty through a heteroscedastic noise model for spatially-adaptive task loss weighting and 2) parameter uncertainty through approximate Bayesian inference. This allows sampling of multiple segmentations and synCTs that share their network representation. We test our model on prostate cancer scans and show that it produces more accurate and consistent synCTs with a better estimation in the variance of the errors, state of the art results in OAR segmentation and a methodology for quality assurance in radiotherapy treatment planning.Comment: Early-accept at MICCAI 2018, 8 pages, 4 figure

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