8,305 research outputs found
Lattice path counting and the theory of queues
In this paper we will show how recent advances in the combinatorics of lattice paths can be applied to solve interesting and nontrivial problems in the theory of queues. The problems we discuss range from classical ones like M^a/M^b/1 systems to open tandem systems with and without global blocking and to queueing models that are related to random walks in a quarter plane like the Flatto-Hahn model or systems with preemptive priorities. (authorÂŽs abstract)Series: Research Report Series / Department of Statistics and Mathematic
Structure-Aware Sampling: Flexible and Accurate Summarization
In processing large quantities of data, a fundamental problem is to obtain a
summary which supports approximate query answering. Random sampling yields
flexible summaries which naturally support subset-sum queries with unbiased
estimators and well-understood confidence bounds.
Classic sample-based summaries, however, are designed for arbitrary subset
queries and are oblivious to the structure in the set of keys. The particular
structure, such as hierarchy, order, or product space (multi-dimensional),
makes range queries much more relevant for most analysis of the data.
Dedicated summarization algorithms for range-sum queries have also been
extensively studied. They can outperform existing sampling schemes in terms of
accuracy on range queries per summary size. Their accuracy, however, rapidly
degrades when, as is often the case, the query spans multiple ranges. They are
also less flexible - being targeted for range sum queries alone - and are often
quite costly to build and use.
In this paper we propose and evaluate variance optimal sampling schemes that
are structure-aware. These summaries improve over the accuracy of existing
structure-oblivious sampling schemes on range queries while retaining the
benefits of sample-based summaries: flexible summaries, with high accuracy on
both range queries and arbitrary subset queries
Dynamic Range Majority Data Structures
Given a set of coloured points on the real line, we study the problem of
answering range -majority (or "heavy hitter") queries on . More
specifically, for a query range , we want to return each colour that is
assigned to more than an -fraction of the points contained in . We
present a new data structure for answering range -majority queries on a
dynamic set of points, where . Our data structure uses O(n)
space, supports queries in time, and updates in amortized time. If the coordinates of the points are integers,
then the query time can be improved to . For constant values of , this improved query
time matches an existing lower bound, for any data structure with
polylogarithmic update time. We also generalize our data structure to handle
sets of points in d-dimensions, for , as well as dynamic arrays, in
which each entry is a colour.Comment: 16 pages, Preliminary version appeared in ISAAC 201
Multiple Comparative Metagenomics using Multiset k-mer Counting
Background. Large scale metagenomic projects aim to extract biodiversity
knowledge between different environmental conditions. Current methods for
comparing microbial communities face important limitations. Those based on
taxonomical or functional assignation rely on a small subset of the sequences
that can be associated to known organisms. On the other hand, de novo methods,
that compare the whole sets of sequences, either do not scale up on ambitious
metagenomic projects or do not provide precise and exhaustive results.
Methods. These limitations motivated the development of a new de novo
metagenomic comparative method, called Simka. This method computes a large
collection of standard ecological distances by replacing species counts by
k-mer counts. Simka scales-up today's metagenomic projects thanks to a new
parallel k-mer counting strategy on multiple datasets.
Results. Experiments on public Human Microbiome Project datasets demonstrate
that Simka captures the essential underlying biological structure. Simka was
able to compute in a few hours both qualitative and quantitative ecological
distances on hundreds of metagenomic samples (690 samples, 32 billions of
reads). We also demonstrate that analyzing metagenomes at the k-mer level is
highly correlated with extremely precise de novo comparison techniques which
rely on all-versus-all sequences alignment strategy or which are based on
taxonomic profiling
Biologically Inspired Approaches to Automated Feature Extraction and Target Recognition
Ongoing research at Boston University has produced computational models of biological vision and learning that embody a growing corpus of scientific data and predictions. Vision models perform long-range grouping and figure/ground segmentation, and memory models create attentionally controlled recognition codes that intrinsically cornbine botton-up activation and top-down learned expectations. These two streams of research form the foundation of novel dynamically integrated systems for image understanding. Simulations using multispectral images illustrate road completion across occlusions in a cluttered scene and information fusion from incorrect labels that are simultaneously inconsistent and correct. The CNS Vision and Technology Labs (cns.bu.edulvisionlab and cns.bu.edu/techlab) are further integrating science and technology through analysis, testing, and development of cognitive and neural models for large-scale applications, complemented by software specification and code distribution.Air Force Office of Scientific Research (F40620-01-1-0423); National Geographic-Intelligence Agency (NMA 201-001-1-2016); National Science Foundation (SBE-0354378; BCS-0235298); Office of Naval Research (N00014-01-1-0624); National Geospatial-Intelligence Agency and the National Society of Siegfried Martens (NMA 501-03-1-2030, DGE-0221680); Department of Homeland Security graduate fellowshi
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