π\piVAE: Encoding stochastic process priors with variational autoencoders

Stochastic processes provide a mathematically elegant way model complex data. In theory, they provide flexible priors over function classes that can encode a wide range of interesting assumptions. In practice, however, efficient inference by optimisation or marginalisation is difficult, a problem further exacerbated with big data and high dimensional input spaces. We propose a novel variational autoencoder (VAE) called the prior encoding variational autoencoder ($\pi$VAE). The $\pi$VAE is finitely exchangeable and Kolmogorov consistent, and thus is a continuous stochastic process. We use $\pi$VAE to learn low dimensional embeddings of function classes. We show that our framework can accurately learn expressive function classes such as Gaussian processes, but also properties of functions to enable statistical inference (such as the integral of a log Gaussian process). For popular tasks, such as spatial interpolation, $\pi$VAE achieves state-of-the-art performance both in terms of accuracy and computational efficiency. Perhaps most usefully, we demonstrate that the low dimensional independently distributed latent space representation learnt provides an elegant and scalable means of performing Bayesian inference for stochastic processes within probabilistic programming languages such as Stan

Non-abelian extensions of Rota-Baxter Lie algebras and inducibility of automorphisms

A Rota-Baxter Lie algebra $\mathfrak{g}_T$ is a Lie algebra $\mathfrak{g}$ equipped with a Rota-Baxter operator $T : \mathfrak{g} \rightarrow \mathfrak{g}$. In this paper, we consider non-abelian extensions of a Rota-Baxter Lie algebra $\mathfrak{g}_T$ by another Rota-Baxter Lie algebra $\mathfrak{h}_S.$ We define the non-abelian cohomology $H^2_{nab} (\mathfrak{g}_T, \mathfrak{h}_S)$ which classifies {equivalence classes of} such extensions. Given a non-abelian extension $$0 \rightarrow \mathfrak{h}_S \xrightarrow{i} \mathfrak{e}_U \xrightarrow{p} \mathfrak{g}_T \rightarrow 0$$ of Rota-Baxter Lie algebras, we also show that the obstruction for a pair of Rota-Baxter automorphisms in $\mathrm{Aut}(\mathfrak{h}_S ) \times \mathrm{Aut}(\mathfrak{g}_T)$ to be induced by an automorphism in $\mathrm{Aut}(\mathfrak{e}_U)$ lies in the cohomology group $H^2_{{nab}} (\mathfrak{g}_T, \mathfrak{h}_S)$. As a byproduct, we obtain the Wells short-exact sequence in the context of Rota-Baxter Lie algebras.Comment: Any comments/suggestions are welcom

DEFAULT SELECTIVE MULTICAST ROUTE TO HANDLE HETEROGENEOUS NETWORK DESIGN

Techniques are described for a solution to traffic loss caused by heterogeneous network design with Ethernet Virtual Private Network (EVPN) multicast deployments. The techniques include detecting the presence of a multicast router behind a Bridge Domain and creating a default route to receive traffic from a remote source based on the detection

INTERNET GROUP MANAGEMENT PROTOCOL GENERAL QUERY MECHANISM EXTENSION TO SUPPORT MASS WITHDRAW CASE WITH ETHERNET VIRTUAL PRIVATE NETWORK ALL-ACTIVE MULTI-HOMING

Techniques are described herein for providing an Internet Group Management Protocol (IGMP) general query via an Ethernet Virtual Private Network (EVPN) router irrespective of the IGMP querier role in order to prevent multicast service outage. This may provide an all-active multi-home deployment to minimize service impact in case of network failure. Procedures defined herein achieve this for multicast traffic

Primary squamous cell carcinoma of the sigmoid colon

Primary squamous cell carcinoma (SCC) of the colon and rectum is a rare malignancy. Overall there are less than 150 cases which have been reported and the first was case was reported in 1919. We report a case of pure SCC involving the sigmoid colon. A 55 year old woman presented with chief complaints of bleeding per rectum for 5 months, anorexia and abdominal pain. Histological diagnosis of SCC was made by colonoscopy biopsy. Later it was confirmed by immunohistochemistry (IHC). Any other possible primary sites of malignancy were excluded. Complete surgical resection was performed. The prognosis of this disease seems to be worse than that of adenocarcinoma

PriorVAE: Encoding spatial priors with VAEs for small-area estimation

Gaussian processes (GPs), implemented through multivariate Gaussian distributions for a finite collection of data, are the most popular approach in small-area spatial statistical modelling. In this context they are used to encode correlation structures over space and can generalise well in interpolation tasks. Despite their flexibility, off-the-shelf GPs present serious computational challenges which limit their scalability and practical usefulness in applied settings. Here, we propose a novel, deep generative modelling approach to tackle this challenge, termed PriorVAE: for a particular spatial setting, we approximate a class of GP priors through prior sampling and subsequent fitting of a variational autoencoder (VAE). Given a trained VAE, the resultant decoder allows spatial inference to become incredibly efficient due to the low dimensional, independently distributed latent Gaussian space representation of the VAE. Once trained, inference using the VAE decoder replaces the GP within a Bayesian sampling framework. This approach provides tractable and easy-to-implement means of approximately encoding spatial priors and facilitates efficient statistical inference. We demonstrate the utility of our VAE two stage approach on Bayesian, small-area estimation tasks

Mission Concept for Demonstrating Small-Spacecraft True Anomaly Estimation Using Millisecond X-Ray Pulsars

Navigation based on X-ray pulsars was first suggested in 1981 for deep space navigation as an alternative to the conventional Deep Space Network (DSN) which is inaccurate at large distances from the Earth. This idea was recently demonstrated using the NICER/SEXTANT instrument onboard the ISS. X-ray pulsar-based navigation is of of great interest as it eliminates the reliance on Earth-based systems, and is yet to be implemented as an autonomous navigation system for deep space missions. For the purpose of navigation, X-ray millisecond pulsars are the most appropriate celestial sources. They emit unique, stable and periodic radiation that exhibits high timing stability comparable to atomic clocks, thus making them suitable as navigational beacons. The phase difference between the pulsar’s pulse profile obtained at the satellite and a reference profile is tied to the position of the satellite with respect to the chosen reference location, typically considered to be the Solar System Barycenter (SSB). Measurements from at least four pulsars are required to estimate the 3D position, velocity, and time of the satellite. This article describes a small satellite mission concept being developed at the Small-spacecraft Systems and PAyload CEntre (SSPACE) at the Indian Institute of Space Science and Technology (IIST) that aims to demonstrate navigation in space using X-ray millisecond pulsars. The satellite contains a miniaturized X-ray timing detector payload, which extracts accurate pulse profiles from detected pulsar signals. A mission-specific algorithm is developed that uses measurements from a single pulsar to estimate only the true anomaly of the satellite, since given the orbital insertion, the other orbital elements are assumed to be stationary. Additionally, the process of pulsar selection is presented, where pulsars are ranked according to the weighted parameters of stable time periods, visibility from the chosen orbital configuration, and high signal-to-noise ratio with respect to the diffuse X-ray background. This is followed by details of the instrument design and concept of operations of this technology demonstration mission. The article concludes with an overview of the systems architecture of the small-satellite, which has a standard 6U CubeSat form factor and details regarding the various subsystems including the On Board Computer, Electrical Power System, Communication system, and Attitude Determination and Control System are discussed. A successful demonstration of this mission will pave the way for future small-satellite missions, where 3D position estimation can be carried out using multiple X-ray pulsar detectors