The Ursinus Weekly, March 18, 1940

Board elects Nicholas T. Barry new Ursinus Weekly editor • Weiland to edit 1941 Ruby ; Dubuque is business manager • Law and morals Goodrich\u27s subject • Candidates listed for April elections • C.A. Kulp talks on old-age security • Jr. ticket committee explains special price • Snyder sets April 2 for spring Lantern issue • Members of faculty quizzed in poll express sentiments on third term • 21-year voting age favored by students • Party is planned for conference week-end • I.R.C. quizzed on current events; will admit members • Committee heads are selected for women\u27s May Day pageant • Hal Moyer chosen honorary basketball captain for season • Ursinus players on all-star quintets • Infield and outfield candidates report • Dorm battlers vie Wednesday in gym • Frosh won five of twelve games • John DeBold wins conference trophy • Undefeated Temple beaten by co-eds • Conference committee secures two speakers • Vespers speaker points way to achieve true personality • Temple professor to address pre-medical society Tuesdayhttps://digitalcommons.ursinus.edu/weekly/1838/thumbnail.jp

The Ursinus Weekly, December 11, 1939

Communion and party in gym will feature Christmas week • Snyder plans new Lantern make-up • Messiah pleases capacity audience • Wood to head interfraternity-sorority dance on January 13 • McClures to entertain women tonight and tomorrow evening • 13 members added to Weekly staff • Sr. play portrays conflicts of Irish Catholicism • Senior ball draws 140 couples to dance to Gordon\u27s orchestra • Russo-Finnish conflict to be discussed by Herber at IRC • Pres. McClure will speak to Brotherhood at meeting Tuesday • Students reveal opinion on editorial comments • First I.R.C. Quarterly under Yoh released • Student poll describes ideal Ursinus professor • Veteran five ready to open season against Rutgers at New Brunswick Saturday; Chern, Keehn will swap posts • Co-ed basketeers down Rosemont in exhibition • The fall seasons in review: football and soccer • Frosh court candidates begin practice tonight • Collection of Madonnas is exhibited in libraryhttps://digitalcommons.ursinus.edu/weekly/1830/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>

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