Abstract. We study countable sums of two dimensional modules for the continuous complex functions on a compact metric space and show that it is possible to construct a spectral triple which gives the original metric back. This spectral triple will be finitely summable for any positive parameter. We also construct a sum of two dimensional modules which reflects some aspects of the topological di...

We examine general decision problems with loss functions that are bounded below. We allow the loss function to assume the value ∞. No other assumptions are made about the action space, the types of data available, the types of non-randomized decision rules allowed, or the parameter space. By allowing prior distributions and the randomizations in randomized rules to be finitely-additive, we prov...

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.

|This paper presents a new approach to nite-horizon guaranteed state prediction for discrete-time systems aaected by bounded noise and unknown-but-bounded parameter uncertainty. Our framework handles possibly nonlinear dependence of the state-space matrices on the uncertain parameters. The main result is that a minimal conndence ellipsoid for the state, consistent with the measured output and t...

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 ...