Abstract: A system and method are provided for summarizing dynamic data from distributed sources through the use of histograms. In particular, the method comprises receiving a first data signal at a first location, determining a first array sketch of the first data signal, and constructing a first output histogram from the first array sketch and a first robust histogram via a first hybrid histogram. Array sketches of a number of data signals may be calculated, and added to yield a single vector sum. The histogram is constructed from the vector sum. In that way, the vector sum may be analyzed without revealing the individual data signals that form the basis of the sum.

Abstract: A system and method are provided for summarizing dynamic data from distributed sources through the use of wavelets. The method comprises receiving a first data signal at a first location, where the first data signal is dynamic, determining a first array sketch of the first data signal and constructing a first wavelet representation by manipulating the first array sketch with a B-term wavelet expansion to produce a first representation. The method further comprises receiving a second data signal at a second location, where the second data signal is dynamic and where the second location is distinct from the first location, determining a second array sketch of the second data signal, and constructing a second wavelet representation by manipulating the second array sketch with a B-term wavelet expansion to produce a second representation.

Abstract: Certain exemplary embodiments provide a method comprising a plurality of activities, comprising: automatically: receiving a signal; and via a plurality of iterations, determining, for the received signal, a provable near-optimal B-term representation formed from a linear combination of a plurality of elements selected from a predetermined redundant ?-coherent dictionary, said determined near-optimal B-term representation corresponding to an error that is a minimum of a set of errors corresponding to all possible B-term representations associated with the predetermined redundant ?-coherent dictionary.

Abstract: A system and method are provided for summarizing dynamic data from distributed sources through the use of histograms. In particular, the method comprises receiving a first data signal at a first location, determining a first array sketch of the first data signal, and constructing a first output histogram from the first array sketch and a first robust histogram via a first hybrid histogram. Array sketches of a number of data signals may be calculated, and added to yield a single vector sum. The histogram is constructed from the vector sum. In that way, the vector sum may be analyzed without revealing the individual data signals that form the basis of the sum.

Abstract: A system and method are provided for summarizing dynamic data from distributed sources through the use of wavelets. The method comprises receiving a first data signal at a first location, where the first data signal is dynamic, determining a first array sketch of the first data signal and constructing a first wavelet representation by manipulating the first array sketch with a B-term wavelet expansion to produce a first representation. The method further comprises receiving a second data signal at a second location, where the second data signal is dynamic and where the second location is distinct from the first location, determining a second array sketch of the second data signal, and constructing a second wavelet representation by manipulating the second array sketch with a B-term wavelet expansion to produce a second representation.

Abstract: A system and method are provided for summarizing dynamic data from distributed sources through the use of wavelets. The method comprises receiving a first data signal at a first location, where the first data signal is dynamic, determining a first array sketch of the first data signal and constructing a first wavelet representation by manipulating the first array sketch with a B-term wavelet expansion to produce a first representation. The method further comprises receiving a second data signal at a second location, where the second data signal is dynamic and where the second location is distinct from the first location, determining a second array sketch of the second data signal, and constructing a second wavelet representation by manipulating the second array sketch with a B-term wavelet expansion to produce a second representation.

Abstract: A system and method are provided for monitoring dynamic data from distributed sources through the use of histograms. In the method, an array sketch of the digital signal is determined, a robust histogram is constructed from the array sketch, and an output histogram is constructed from the array sketch and the robust histogram via a hybrid histogram. Dyadic intervals of a representation of the array sketch are used in constructing the robust histogram.

Abstract: Certain exemplary embodiments provide a method comprising a plurality of activities, comprising: automatically: receiving a signal; and via a plurality of iterations, determining, for the received signal, a provable near-optimal B-term representation formed from a linear combination of a plurality of elements selected from a predetermined redundant &mgr;-coherent dictionary, said determined near-optimal B-term representation corresponding to an error that is a minimum of a set of errors corresponding to all possible B-term representations associated with the predetermined redundant &mgr;-coherent dictionary.