Zero-Delay Rate Distortion via Filtering for Vector-Valued Gaussian Sources

We deal with zero-delay source coding of a vector-valued Gauss-Markov source subject to a mean-squared error (MSE) fidelity criterion characterized by the operational zero-delay vector-valued Gaussian rate distortion function (RDF). We address this problem by considering the nonanticipative RDF (NRDF) which is a lower bound to the causal optimal performance theoretically attainable (OPTA) function and operational zero-delay RDF. We recall the realization that corresponds to the optimal "test-channel" of the Gaussian NRDF, when considering a vector Gauss-Markov source subject to a MSE distortion in the finite time horizon. Then, we introduce sufficient conditions to show existence of solution for this problem in the infinite time horizon. For the asymptotic regime, we use the asymptotic characterization of the Gaussian NRDF to provide a new equivalent realization scheme with feedback which is characterized by a resource allocation (reverse-waterfilling) problem across the dimension of the vector source. We leverage the new realization to derive a predictive coding scheme via lattice quantization with subtractive dither and joint memoryless entropy coding. This coding scheme offers an upper bound to the operational zero-delay vector-valued Gaussian RDF. When we use scalar quantization, then for "r" active dimensions of the vector Gauss-Markov source the gap between the obtained lower and theoretical upper bounds is less than or equal to 0.254r + 1 bits/vector. We further show that it is possible when we use vector quantization, and assume infinite dimensional Gauss-Markov sources to make the previous gap to be negligible, i.e., Gaussian NRDF approximates the operational zero-delay Gaussian RDF. We also extend our results to vector-valued Gaussian sources of any finite memory under mild conditions. Our theoretical framework is demonstrated with illustrative numerical experiments.Comment: 32 pages, 9 figures, published in IEEE Journal of Selected Topics in Signal Processin

Design and Implementation of an RNS-based 2D DWT Processor

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Database Search Strategies for Proteomic Data Sets Generated by Electron Capture Dissociation Mass Spectrometry

Large data sets of electron capture dissociation (ECD) mass spectra from proteomic experiments are rich in information; however, extracting that information in an optimal manner is not straightforward. Protein database search engines currently available are designed for low resolution CID data, from which Fourier transform ion cyclotron resonance (FT-ICR) ECD data differs significantly. ECD mass spectra contain both z-prime and z-dot fragment ions (and c-prime and c-dot); ECD mass spectra contain abundant peaks derived from neutral losses from charge-reduced precursor ions; FT-ICR ECD spectra are acquired with a larger precursor m/z isolation window than their low-resolution CID counterparts. Here, we consider three distinct stages of postacquisition analysis: (1) processing of ECD mass spectra prior to the database search; (2) the database search step itself and (3) postsearch processing of results. We demonstrate that each of these steps has an effect on the number of peptides identified, with the postsearch processing of results having the largest effect. We compare two commonly used search engines: Mascot and OMSSA. Using an ECD data set of modest size (3341 mass spectra) from a complex sample (mouse whole cell lysate), we demonstrate that search results can be improved from 630 identifications (19% identification success rate) to 1643 identifications (49% identification success rate). We focus in particular on improving identification rates for doubly charged precursors, which are typically low for ECD fragmentation. We compare our presearch processing algorithm with a similar algorithm recently developed for electron transfer dissociation (ETD) data

Streaming Similarity Self-Join

We introduce and study the problem of computing the similarity self-join in a streaming context (SSSJ), where the input is an unbounded stream of items arriving continuously. The goal is to find all pairs of items in the stream whose similarity is greater than a given threshold. The simplest formulation of the problem requires unbounded memory, and thus, it is intractable. To make the problem feasible, we introduce the notion of time-dependent similarity: the similarity of two items decreases with the difference in their arrival time. By leveraging the properties of this time-dependent similarity function, we design two algorithmic frameworks to solve the sssj problem. The first one, MiniBatch (MB), uses existing index-based filtering techniques for the static version of the problem, and combines them in a pipeline. The second framework, Streaming (STR), adds time filtering to the existing indexes, and integrates new time-based bounds deeply in the working of the algorithms. We also introduce a new indexing technique (L2), which is based on an existing state-of-the-art indexing technique (L2AP), but is optimized for the streaming case. Extensive experiments show that the STR algorithm, when instantiated with the L2 index, is the most scalable option across a wide array of datasets and parameters