Projections onto translation—Invariant subspaces of L1(G)

AbstractLet G be a locally compact abelian group. A translation-invariant subspace in L1(G) may or may not be complemented depending on the structure of its hull in Ĝ. Techniques for deciding this complementation problem in a variety of situations are developed and illustrated with examples. A complete characterization is obtained for those ideals with a discrete hull

Embedding Four-directional Paths on Convex Point Sets

A directed path whose edges are assigned labels "up", "down", "right", or "left" is called \emph{four-directional}, and \emph{three-directional} if at most three out of the four labels are used. A \emph{direction-consistent embedding} of an \mbox{$n$-vertex} four-directional path $P$ on a set $S$ of $n$ points in the plane is a straight-line drawing of $P$ where each vertex of $P$ is mapped to a distinct point of $S$ and every edge points to the direction specified by its label. We study planar direction-consistent embeddings of three- and four-directional paths and provide a complete picture of the problem for convex point sets.Comment: 11 pages, full conference version including all proof

GP-SUM. Gaussian Processes Filtering of non-Gaussian Beliefs

This work studies the problem of stochastic dynamic filtering and state propagation with complex beliefs. The main contribution is GP-SUM, a filtering algorithm tailored to dynamic systems and observation models expressed as Gaussian Processes (GP), and to states represented as a weighted sum of Gaussians. The key attribute of GP-SUM is that it does not rely on linearizations of the dynamic or observation models, or on unimodal Gaussian approximations of the belief, hence enables tracking complex state distributions. The algorithm can be seen as a combination of a sampling-based filter with a probabilistic Bayes filter. On the one hand, GP-SUM operates by sampling the state distribution and propagating each sample through the dynamic system and observation models. On the other hand, it achieves effective sampling and accurate probabilistic propagation by relying on the GP form of the system, and the sum-of-Gaussian form of the belief. We show that GP-SUM outperforms several GP-Bayes and Particle Filters on a standard benchmark. We also demonstrate its use in a pushing task, predicting with experimental accuracy the naturally occurring non-Gaussian distributions.Comment: WAFR 2018, 16 pages, 7 figure

Automating the Calibration of a Neonatal Condition Monitoring System

Abstract. Condition monitoring of premature babies in intensive care can be carried out using a Factorial Switching Linear Dynamical System (FSLDS) [15]. A crucial part of training the FSLDS is the manual calibration stage, where an interval of normality must be identified for each baby that is monitored. In this paper we replace this manual step by using a classifier to predict whether an interval is normal or not. We show that the monitoring results obtained using automated calibration are almost as good as those using manual calibration

Ursinus College Alumni Journal, Winter 1947

An auspicious beginning for a worthwhile project • President\u27s page • Committees plan new position at college • Status of the war memorial campaign • 964 students enrolled at Ursinus • Miss Moll resumes duties at Ursinus • General Arnold Founders\u27 Day speaker • Three faculty promotions, one appointment announced • New gymnasium nearing completion • Questionnaires outstanding from 900 alumni • Sports: football, soccer, hockey • The shape of things to come? • The attack on illiteracy in British Guiana • News around town • News about ourselves • Faculty members complete laboratory manual • Necrologyhttps://digitalcommons.ursinus.edu/alumnijournal/1029/thumbnail.jp

Shift invariant preduals of ℓ₁(ℤ)

The Banach space ℓ<sub>1</sub>(ℤ) admits many non-isomorphic preduals, for example, C(K) for any compact countable space K, along with many more exotic Banach spaces. In this paper, we impose an extra condition: the predual must make the bilateral shift on ℓ<sub>1</sub>(ℤ) weak<sup>*</sup>-continuous. This is equivalent to making the natural convolution multiplication on ℓ<sub>1</sub>(ℤ) separately weak*-continuous and so turning ℓ<sub>1</sub>(ℤ) into a dual Banach algebra. We call such preduals <i>shift-invariant</i>. It is known that the only shift-invariant predual arising from the standard duality between C<sub>0</sub>(K) (for countable locally compact K) and ℓ<sub>1</sub>(ℤ) is c<sub>0</sub>(ℤ). We provide an explicit construction of an uncountable family of distinct preduals which do make the bilateral shift weak<sup>*</sup>-continuous. Using Szlenk index arguments, we show that merely as Banach spaces, these are all isomorphic to c<sub>0</sub>. We then build some theory to study such preduals, showing that they arise from certain semigroup compactifications of ℤ. This allows us to produce a large number of other examples, including non-isometric preduals, and preduals which are not Banach space isomorphic to c<sub>0</sub>

Known Unknowns: Novelty Detection in Condition Monitoring

Abstract. In time-series analysis it is often assumed that observed data can be modelled as being derived from a number of regimes of dynamics, as e.g. in a Switching Kalman Filter (SKF) [8, 2]. However, it may not be possible to model all of the regimes, and in this case it can be useful to represent explicitly a ‘novel ’ regime. We apply this idea to the Factorial Switching Kalman Filter (FSKF) by introducing an extra factor (the ‘Xfactor’) to account for the unmodelled variation. We apply our method to physiological monitoring data from premature infants receiving intensive care, and demonstrate that the model is effective in detecting abnormal sequences of observations that are not modelled by the known regimes.

Stromal senescence establishes an immunosuppressive microenvironment that drives tumorigenesis

Age is a significant risk factor for the development of cancer. However, the mechanisms that drive age-related increases in cancer remain poorly understood. To determine if senescent stromal cells influence tumorigenesis, we develop a mouse model that mimics the aged skin microenvironment. Using this model, here we find that senescent stromal cells are sufficient to drive localized increases in suppressive myeloid cells that contributed to tumour promotion. Further, we find that the stromal-derived senescence-associated secretory phenotype factor interleukin-6 orchestrates both increases in suppressive myeloid cells and their ability to inhibit anti-tumour T-cell responses. Significantly, in aged, cancer-free individuals, we find similar increases in immune cells that also localize near senescent stromal cells. This work provides evidence that the accumulation of senescent stromal cells is sufficient to establish a tumour-permissive, chronic inflammatory microenvironment that can shelter incipient tumour cells, thus allowing them to proliferate and progress unabated by the immune system

A comparison of variational and Markov chain Monte Carlo methods for inference in partially observed stochastic dynamic systems

In recent work we have developed a novel variational inference method for partially observed systems governed by stochastic differential equations. In this paper we provide a comparison of the Variational Gaussian Process Smoother with an exact solution computed using a Hybrid Monte Carlo approach to path sampling, applied to a stochastic double well potential model. It is demonstrated that the variational smoother provides us a very accurate estimate of mean path while conditional variance is slightly underestimated. We conclude with some remarks as to the advantages and disadvantages of the variational smoother. © 2008 Springer Science + Business Media LLC