Recently, there has been a growing interest in understanding the complexity of common analytic equivalence relations between separable Banach spaces via the notion of Borel reducibility in descriptive set theory (see [Bos] [FG] [FLR] [FR1] [FR2] [Me]). In general, the notion of Borel reducibility yields a hierarchy (though not linear) among equivalence relations in terms of their relative compl...

For real hyperbolic spaces, the dynamics of individual isometries and the geometry of the limit set of nonelementary discrete isometry groups have been studied in great detail. Most of the results were generalised to discrete isometry groups of simply connected Riemannian manifolds of pinched negative curvature. For symmetric spaces of higher rank, which contain isometrically embedded Euclidean...

We consider sub-Riemannian spaces admitting an isometry group that is maximal in the sense any linear of horizontal tangent realized by a global isometry. will show these have canonical partial connection defined on their bundle. However, unlike Riemannian case, such are not uniquely determined curvature and metric cone. Furthermore, number invariants needed to determine model with same cone ge...

For each countable ordinal α, let Sα be the Schreier set of order α and XSα corresponding space α. In this paper, we prove several new properties these spaces. 1. If is nonzero, then XSαpossesses λ-property Aron Lohman a (V)-polyhedral in sense Fonf Vesely. 2. nonzero 1<p<∞, p-convexification p possesses uniform Lohman. 3. ∗ has λ-property. 4. n∈N, if T:XSn→XSnis an onto linear isometry, Tei=±e...

A major enterprise in compressed sensing and sparse approximation is the design and analysis of computationally tractable algorithms for recovering sparse, exact or approximate, solutions of underdetermined linear systems of equations. Many such algorithms have now been proven using the ubiquitous Restricted Isometry Property (RIP) [9] to have optimal-order uniform recovery guarantees. However,...

Online sparse linear regression is an online problem where an algorithm repeatedly chooses a subset of coordinates to observe in an adversarially chosen feature vector, makes a real-valued prediction, receives the true label, and incurs the squared loss. The goal is to design an online learning algorithm with sublinear regret to the best sparse linear predictor in hindsight. Without any assumpt...

In this paper, we consider a model of classical linear logic based on coherence spaces endowed with a notion of totality. If we restrict ourselves to total objects, each coherence space can be regarded as a uniform space and each linear map as a uniformly continuous function. The linear exponential comonad then assigns to each uniform space X the finest uniform space !X compatible with X . By a...

Let X be a polygonal complex with finitely many isometry classes of links. We establish a restriction on the covolumes of uniform lattices acting on X. When all links of X are isometric, and are either a complete bipartite graph or the building for a Chevalley group of rank 2 over a field of prime order, we obtain further restrictions on covolumes. Some of these restrictions are sharp: in [Th] ...

a new definition of boundedness of linear order-homomorphisms (loh)in $l$-topological vector spaces is proposed. the new definition iscompared with the previous one given by fang [the continuity offuzzy linear order-homomorphism, j. fuzzy math. 5 (4) (1997)829$-$838]. in addition, the relationship between boundedness andcontinuity of lohs is discussed. finally, a new uniform boundednessprincipl...