this paper is an attempt to generalize, simultaneously, the ring of real-valued continuous functions and the ring of real-valued measurable functions.

in this paper we get some results and applications for duals and approximate duals of g-frames in hilbert spaces. in particular, we consider the stability of duals and approximate duals under bounded operators and we study duals and approximate duals of g-frames in the direct sum of hilbert spaces. we also obtain some results for perturbations of approximate duals.

This paper describes our work in learning online models that forecast real-valued variables in a high-dimensional space. A 3GB database was collected by sampling 421 real-valued sensors in a cement manufacturing plant, once every minute, for several months. The goal is to learn models that, every minute, forecast the values of all 421 sensors for the next hour. The underlying process is highly ...

Hilbert frames theory have been extended to frames in Hilbert $C^*$-modules. The paper introduces equivalent $*$-frames and presents ordinary duals of a constructed $*$-frame by an adjointable and invertible operator. Also, some necessary and sufficient conditions are studied such that $*$-frames and ordinary duals or operator duals of another $*$-frames are equivalent under these conditions. W...

In the frame of classical Constraint Satisfaction Problems (CSPs), the backtrack tree search, combined with learning methods, presents a double advantage : for static solving, it improves the search speed by avoiding redundant explorations; for dynamic solving (after a slight change of the problem), it reuses the previous searches to build a new solution quickly. Backtrack reasoning concludes t...

We introduce a class of informationally complete positive-operator-valued measures which are, in analogy with a tight frame, “as close as possible” to orthonormal bases for the space of quantum states. These measures are distinguished by an exceptionally simple state-reconstruction formula which allows “painless” quantum state tomography. Complete sets of mutually unbiased bases and symmetric i...

A system for recognising continuously spoken sentences is presented. The system has a vocabulary of approx. 35 words and a granunar specifying a few thousand sentences. The system operates in three stages. In the frrst stage, cepstrum vectors are computed in real time and used as input to a self organised neural network. The output of the network is mapped to a continuous valued acoustic phonet...

Fundamental discrepancy between first order logic and statistical inference (global versus local properties of universe) is shown to be the obstacle for integration of logic and probability in L.p. logic of Bacchus. To overcome the counterintuitiveness of L.p. behaviour, a 3-valued logic is proposed.

Software model-checking based on the CEGAR framework can be made more precise by separating non-determinism from the lack of information due to abstraction. The two can be modeled individually using four-valued Belnap logic. In addition, this logic allows reasoning about negations effectively and thus enables checking of full CTL. In this paper, we present YASM – a new symbolic software model-c...