Book Reviews

The Variational Auto-Encoder (VAE) is one of the most used unsupervised machine learning models. But although the default choice of a Gaussian distribution for both the prior and posterior represents a mathematically convenient distribution often leading to competitive results, we show that this parameterization fails to model data with a latent hyperspherical structure. To address this issue we propose using a von Mises-Fisher (vMF) distribution instead, leading to a hyperspherical latent space. Through a series of experiments we show how such a hyperspherical VAE, or $\mathcal{S}$-VAE, is more suitable for capturing data with a hyperspherical latent structure, while outperforming a normal, $\mathcal{N}$-VAE, in low dimensions on other data types.Comment: GitHub repository: http://github.com/nicola-decao/s-vae-tf, Blogpost: https://nicola-decao.github.io/s-va

Increasing Expressivity of a Hyperspherical VAE

Learning suitable latent representations for observed, high-dimensional data is an important research topic underlying many recent advances in machine learning. While traditionally the Gaussian normal distribution has been the go-to latent parameterization, recently a variety of works have successfully proposed the use of manifold-valued latents. In one such work (Davidson et al., 2018), the authors empirically show the potential benefits of using a hyperspherical von Mises-Fisher (vMF) distribution in low dimensionality. However, due to the unique distributional form of the vMF, expressivity in higher dimensional space is limited as a result of its scalar concentration parameter leading to a 'hyperspherical bottleneck'. In this work we propose to extend the usability of hyperspherical parameterizations to higher dimensions using a product-space instead, showing improved results on a selection of image datasets.Comment: NeurIPS 2019, in Workshop on Bayesian Deep Learnin

Minimum charge-recovery time control with parallel connected buck converters

Optimal-time control to minimise a converter’s recovery time has thus far been reported only for single power module converters. This paper adapts the optimal-time control problem and applies it to converters based on multiple power modules. Additionally, a novel minimum charge-recovery time control is also proposed for the multiple power module converter which produces a recovery time shorter than that in the optimal-time control. A 20 W converter is used to demonstrate the improved characteristics under primary regions of operation. Results show that the transient recovery time during a load step change is improved by 75% compared to traditional optimal time control

Energies of S^2-valued harmonic maps on polyhedra with tangent boundary conditions

A unit-vector field n:P \to S^2 on a convex polyhedron P \subset R^3 satisfies tangent boundary conditions if, on each face of P, n takes values tangent to that face. Tangent unit-vector fields are necessarily discontinuous at the vertices of P. We consider fields which are continuous elsewhere. We derive a lower bound E^-_P(h) for the infimum Dirichlet energy E^inf_P(h) for such tangent unit-vector fields of arbitrary homotopy type h. E^-_P(h) is expressed as a weighted sum of minimal connections, one for each sector of a natural partition of S^2 induced by P. For P a rectangular prism, we derive an upper bound for E^inf_P(h) whose ratio to the lower bound may be bounded independently of h. The problem is motivated by models of nematic liquid crystals in polyhedral geometries. Our results improve and extend several previous results.Comment: 42 pages, 2 figure

Mortality and Morbidity Following Endovascular Repair of Abdominal Aortic Aneurysms: Analysis of Two Single Centre Experiences

AbstractObjective to show how differences in anatomical and physiological risk factors can affect the outcome of endovascular repair of AAA by describing the experience of two centres with different selection policies. Methods one hundred and thirty-five patients (group I) were treated at Queen's Medical Centre (Nottingham, U.K.) using 101 in-house made and 34 manufactured stent-grafts. Median diameter, length and angulation of the proximal aneurysm neck were 26 mm, 27 mm, 40°, respectively. Seventy-six patients had ischaemic heart disease, 47 had left ventricular failure, median forced expiratory volume in one second (FEV1) was 83%, median creatinine was 100 μmol/l and median age was 72 years. Fifty patients (group II) were treated at Timone Hospital (Marseilles, France) using seven in-house made and 43 manufactured stent-grafts. Median diameter, length and angulation of the proximal aneurysm neck were 25 mm, 34 mm, 33°, respectively. Thirteen patients had ischaemic heart disease, two had left ventricular failure, median forced expiratory volume in one second was 101%, median creatinine was 108 μmol/l and mean age was 72 years. Results anatomical characteristics of the proximal neck were significantly worse in group I (p=0.02 for the three variables). Cardiac comorbidities were more frequent and mean FEV1 was lower in group I (p<0.0001 and p=0.001, respectively. Median aneurysm diameter was significantly greater in group I (65 mm) than in group II (53 mm) (p<0.001). Postoperative mortality was 9% and 0% in groups I and II respectively (p=0.03). The incidence of technical complications (groin wound complications and side branches endoleaks being excluded) was 20% and 0% in groups I and II, respectively (p=0.0006). Conclusion postoperative mortality and technical complication rates were significantly greater in group I than in group II, readily explained by poorer general condition and worse anatomical characteristics of the proximal neck in group I

Lignins As Stabilizing Agents for Northeastern Iowa Loess

One of the common problems in highway .and airport construction faced by engineers all over the world is the scarcity of suitable materials for base and subbase construction. Lately, there has been such an increase in traffic on highways and airfields that the problem of suitable base and subbase design can no longer be ignored. Engineers have been striving hard to find ways and means to solve this problem. One solution lies in the utilization of locally available materials. Since soil is the most plentiful of available materials, it has been chosen by engineers and scientists to do the job. Unfortunately, not every soil in its original condition can be utilized as an engineering material without modification of its properties. For this reason, emphasis is being placed on finding ways to make suitable construction material out of unsatisfactory soil; the art and science of doing this \u27is called soil stabilization. There are several methods of stabilizing soils. One of such methods is the use of admixtures. Admixtures such as Portland cement, bituminous material, lime-fly ash, lime, and lignins are a few of the possibilities. Since 1947 the Iowa Engineering Experiment Station has been conducting research on soil stabilization. Various kinds of admixtures have been investigated during this period. This report presents the work done to date with lignins as stabilizing agents for northeastern Iowa loess and loess derived soil

Non-stationary Rayleigh-Taylor instability in supernovae ejecta

The Rayleigh-Taylor instability plays an important role in the dynamics of several astronomical objects, in particular, in supernovae (SN) evolution. In this paper we develop an analytical approach to study the stability analysis of spherical expansion of the SN ejecta by using a special transformation in the co-moving coordinate frame. We first study a non-stationary spherical expansion of a gas shell under the pressure of a central source. Then we analyze its stability with respect to a no radial, non spherically symmetric perturbation of the of the shell. We consider the case where the polytropic constant of the SN shell is $\gamma=5/3$ and we examine the evolution of a arbitrary shell perturbation. The dispersion relation is derived. The growth rate of the perturbation is found and its temporal and spatial evolution is discussed. The stability domain depends on the ejecta shell thickness, its acceleration, and the perturbation wavelength.Comment: 16 page