We apply recent results on the minimax risk in density esti mation to the related problem of pattern classi cation The notion of loss we seek to minimize is an information theoretic measure of how well we can predict the classi cation of future examples given the classi cation of previously seen examples We give an asymptotic characterization of the minimax risk in terms of the metric entropy p...

We establish criteria for turbulence in certain spaces of C∗-algebra representations and apply this to the problem of nonclassifiability by countable structures for group actions on a standard atomless probability space (X,μ) and on the hyperfinite II1 factor R. We also prove that the conjugacy action on the space of free actions of a countably infinite amenable group on R is turbulent, and tha...

Given a volume-preserving homeomorphism of a smooth manifold of dimension n ≥ 5, we give a necessary and sufficient condition for uniform approximability by (volume-preserving) diffeomorphisms.

With teams’ annual payrolls nearing $100 million and valuations for some teams exceeding $2 billion, the National Basketball Association is big business. That being the case, many pro-basketball general managers are turning to analytics to discover ways to improve organizational performance. The purpose of this paper was to highlight the results of an analytics-based assessment of both player a...

In this note we prove some results concerning volume-preserving Anosov diffeomorphisms on compact manifolds. The main theorem is that if a C, α > 0, volume-preserving diffeomorphism on a compact manifold has a hyperbolic invariant set with positive volume, then the map is Anosov. This is not necessarily true for C maps. The proof uses a special type of measure density points different from the ...

We study a measure entropy for finitely generated free group actions called f-invariant entropy. The f-invariant entropy was developed by L. Bowen and is essentially a special case of his measure entropy theory for actions of sofic groups. In this paper we relate the f-invariant entropy of a finitely generated free group action to the f-invariant entropy of the restricted action of a subgroup. ...

We show that in any invertible, ergodic, measure-preserving system, the two-sided square function obtained by comparing forward averages with their backwards counterparts, will diverge if the (time) length of the averages grows too slowly. This contrasts with the onesided case. We also show that for any sequence of times, certain weighted sums of the forward averages diverge. This contrasts wit...

We establish some criteria for the stability of the essential spectrum for unbounded operators acting in Banach modules. The applications cover operators acting on sections of vector fiber bundles over non-smooth manifolds or locally compact abelian groups, in particular differential operators of any order with complex measurable coefficients on R, singular Dirac operators and Laplace-Beltrami ...

Using a geometric realization of the SU(2)R symmetry and a procedure of factorisation of the gauge and SU(2)R charges, we study the small instanton singularities of the Higgs branch of supersymmetric U(1) gauge theories with eight supercharges. We derive new solutions for the moduli space of vacua preserving manifestly the eight supercharges. In particular, we obtain an extension of the ordinar...

When Library Trends devoted its first issue to preservation (Tauber, 1956), the state-of-the-art term was conservation, and the articles dealt with binding, treatments, stack maintenance, and “discarding” (weeding). The focus was almost entirely on libraries, except for an article by Hummel and Barrow on treatment for library and archival material (Hummel & Barrow, 1956). The next Library Trend...