In this paper, we are interested in the limit theorem question for sums of indicator functions. We show that in every aperiodic dynamical system, for every increasing sequence (an)n∈N ⊂ R+ such that an ր ∞ and an n → 0 as n → ∞, there exist a measurable set A such that the sequence of the partial sums 1 an ∑n−1 i=0 (1lA−μ(A))◦T i is dense in the set of the probability measures on R. Further, in...

Let X and Y be topological vector spaces, A be a continuous linear map from X to Y , C X, B be a convex set dense in C, and d 2 Y be a data point. Conditions are derived guaranteeing the set B \ A ?1 (d) to be nonempty and dense in C \ A ?1 (d). The paper generalizes earlier results by the authors to the case where Y is innnite dimensional. The theory is illustrated with two examples concerning...

In this paper we study control systems whose input sets are quantized, and in particular nite or countable but nowhere dense. We speci cally focus on problems relating to the structure of the reachable set of such systems, which may turn out to be either dense or discrete. We report results on the rechable set of linear quantized systems, and on a particular but interesting class of nonlinear s...

We investigate the spectral properties of Schrödinger operators in `2(Z) with limit-periodic potentials. The perspective we take was recently proposed by Avila and is based on regarding such potentials as generated by continuous sampling along the orbits of a minimal translation of a Cantor group. This point of view allows one to separate the base dynamics and the sampling function. We show tha...

We propose a method to estimate dense motion vector fields from multi-exposure images. Our approach relies on finding a sparse set of correspondences between features in a single-exposure image and each exposure in a multi-exposure image using a global optimization technique. We iteratively establish such matches, compute a set of locally restricted transformations for the matches, and construc...

We introduce the notion of numerical (strong) peak function and investigate the denseness of the norm and numerical peak functions on complex Banach spaces. Let Ab(BX : X) be the Banach space of all bounded continuous functions f on the unit ball BX of a Banach space X and their restrictions f |B◦ X to the open unit ball are holomorphic. In finite dimensional spaces, we show that the intersecti...

The problem of constructing an optimal rooted phylogenetic network from an arbitrary set of rooted triplets is an NP-hard problem. In this paper, we present a heuristic algorithm called TripNet, which tries to construct a rooted phylogenetic network with the minimum number of reticulation nodes from an arbitrary set of rooted triplets. Despite of current methods that work for dense set of roote...

We continue the study of a lattice-ordered ring G(X), associated with the ring C(X). Following [10], X called RG when G(X) = C(Xδ). An RG-space must have a dense set of very weak P-points. It must have a dense set of almost-P-points if Xδ is Lindelöf, or if the continuum hypothesis holds and C(X) has small cardinality. Space which are RG must have finite Krull dimension when taken with respect ...

1 . Introduction . The following question was posed by D . Maharam : Can one divide the unit square into two or more measurable sets each of which has a non-null intersection with every product set A XB of positive measure, where A and B are subsets of the unit interval? In this paper we construct a class of such partitions of the plane, including some that retain the property under various tra...

We present a new feature based algorithm for stereo correspondence. Most of the previous feature based methods match sparse features like edge pixels, producing only sparse disparity maps. Our algorithm detects and matches dense features between the left and right images of a stereo pair, producing a semi-dense disparity map. Our dense feature is defined with respect to both images of a stereo ...