g-frames in hilbert spaces are a redundant set of operators which yield a repre-sentation for each vector in the space. in this paper we investigate the connection betweeng-frames, g-orthonormal bases and g-riesz bases. we show that a family of bounded opera-tors is a g-bessel sequences if and only if the gram matrix associated to its denes a boundedoperator.

The randomized result was obtained by viewing random bit sequences as vertices of an expander graph and performing a random walk upon choosing a start vertex uniformly at random, and casting a majority vote. The error (probability of majority vote resulting in error) exponentially decreases with the length of the random walk. We also saw a stronger statement based on Chernoff bounds for random ...

In the moduli space of quadratic differentials over complex structures on a surface, we construct a set of full Hausdorff dimension of points with bounded Teichmüller geodesic trajectories. The main tool is quantitative nondivergence of Teichmüller horocycles, due to Minsky and Weiss. This has an application to billiards in rational polygons.

This paper studies space bounded algorithms, i.e., algorithms that use a constant amount of scratch space, for the k{server problem. The paper rst shows a characterization of the set of space bounded algorithms that are competitive in nite metric spaces. The result yields a method for (1) e ectively deciding if a given space bounded algorithm is competitive in a given nite metric space, and (2)...

A machine solves a problem using space s(·) if, for every input x, the machine outputs the correct answer and uses only the first s(|x|) cells of the tape. For a standard Turing machine, we can’t do better than linear space since x itself must be on the tape. So we will often consider a machine with multiple tapes: a read-only “input” tape, a read/write “work” or “memory” tape, and possibly a w...

Iterative arntys (lAs) are a, parallel computational model with a, sequential processing of the input. They are one-dimensional arrays of interacting identical deterministic finite automata. In this note, realtime-lAs with sublinear space bounds are used to accept formal languages. The existence of a proper hierarchy of space complexity classes between logarithmic anel linear space bounds is pr...