Leveraging well-conditioned bases : streaming and distributed summaries in Minkowski p-norms

Work on approximate linear algebra has led to efficient distributed and streaming algorithms for problems such as approximate matrix multiplication, low rank approximation, and regression, primarily for the Euclidean norm ℓ2. We study other ℓp norms, which are more robust for p2. Unlike previous algorithms for such norms, we give algorithms that are (1) deterministic, (2) work simultaneously for every p≥1, including p=∞, and (3) can be implemented in both distributed and streaming environments. We study ℓp-regression, entrywise ℓp-low rank approximation, and versions of approximate matrix multiplication

Subspace exploration : bounds on projected frequency estimation

Given an n×d dimensional dataset A, a projection query specifies a subset C⊆[d] of columns which yields a new n×|C| array. We study the space complexity of computing data analysis functions over such subspaces, including heavy hitters and norms, when the subspaces are revealed only after observing the data. We show that this important class of problems is typically hard: for many problems, we show 2Ω(d) lower bounds. However, we present upper bounds which demonstrate space dependency better than 2d. That is, for c,c′∈(0,1) and a parameter N=2d an Nc-approximation can be obtained in space min(Nc′,n), showing that it is possible to improve on the naïve approach of keeping information for all 2d subsets of d columns. Our results are based on careful constructions of instances using coding theory and novel combinatorial reductions that exhibit such space-approximation tradeoffs

High spectral and spatial resolution X-ray transmission radiography and tomography using a Color X-ray Camera

High resolution X-ray radiography and computed tomography are excellent techniques for non-destructive characterization of an object under investigation at a spatial resolution in the micrometer range. However, as the image contrast depends on both chemical composition and material density, no chemical information is obtained from this data. Furthermore, lab-based measurements are affected by the polychromatic X-ray beam, which results in beam hardening effects. New types of X-ray detectors which provide spectral information on the measured X-ray beam can help to overcome these limitations. In this paper, an energy dispersive CCD detector with high spectral resolution is characterized for use in high resolution radiography and tomography, where a focus is put on the experimental conditions and requirements of both measurement techniques

Deterministic Sampling and Range Counting in Geometric Data Streams

We present memory-efficient deterministic algorithms for constructing epsilon-nets and epsilon-approximations of streams of geometric data. Unlike probabilistic approaches, these deterministic samples provide guaranteed bounds on their approximation factors. We show how our deterministic samples can be used to answer approximate online iceberg geometric queries on data streams. We use these techniques to approximate several robust statistics of geometric data streams, including Tukey depth, simplicial depth, regression depth, the Thiel-Sen estimator, and the least median of squares. Our algorithms use only a polylogarithmic amount of memory, provided the desired approximation factors are inverse-polylogarithmic. We also include a lower bound for non-iceberg geometric queries.Comment: 12 pages, 1 figur

Engineering of lipid-coated PLGA nanoparticles with a tunable payload of diagnostically active nanocrystals for medical imaging

Polylactic-co-glycolic acid (PLGA) based nanoparticles are biocompatible and biodegradable and therefore have been extensively investigated as therapeutic carriers. Here, we engineered diagnostically active PLGA nanoparticles that incorporate high payloads of nanocrystals into their core for tunable bioimaging features. We accomplished this through esterification reactions of PLGA to generate polymers modified with nanocrystals. The PLGA nanoparticles formed from modified PLGA polymers that were functionalized with either gold nanocrystals or quantum dots exhibited favorable features for computed tomography and optical imaging, respectively.National Heart, Lung, and Blood Institute (Programs of Excellence in Nanotechnology (PEN) Award, Contract #HHSN268201000045C))National Institutes of Health (U.S.) (R01 EB009638)National Institutes of Health (U.S.) (R01 CA155432)National Institutes of Health (U.S.) (K99 EB012165)Netherlands Organization for Scientific Research ((NWO) ECHO.06.B.047

Dual-modality, fluorescent, PLGA encapsulated bismuth nanoparticles for molecular and cellular fluorescence imaging and computed tomography

Reports of molecular and cellular imaging using computed tomography (CT) are rapidly increasing. Many of these reports use gold nanoparticles. Bismuth has similar CT contrast properties to gold while being approximately 1000-fold less expensive. Herein we report the design, fabrication, characterization, and CT and fluorescence imaging properties of a novel, dual modality, fluorescent, polymer encapsulated bismuth nanoparticle construct for computed tomography and fluorescence imaging. We also report on cellular internalization and preliminary in vitro and in vivo toxicity effects of these constructs. 40 nm bismuth(0) nanocrystals were synthesized and encapsulated within 120 nm Poly(DL-lactic-co-glycolic acid) (PLGA) nanoparticles by oil-in-water emulsion methodologies. Coumarin-6 was co-encapsulated to impart fluorescence. High encapsulation efficiency was achieved ∼ 70% bismuth w/w. Particles were shown to internalize within cells following incubation in culture. Bismuth nanocrystals and PLGA encapsulated bismuth nanoparticles exhibited >90% and >70% degradation, respectively, within 24 hours in acidic, lysosomal environment mimicking media and both remained nearly 100% stable in cytosolic/extracellular fluid mimicking media. μCT and clinical CT imaging was performed at multiple X-ray tube voltages to measure concentration dependent attenuation rates as well as to establish the ability to detect the nanoparticles in an ex vivo biological sample. Dual fluorescence and CT imaging is demonstrated as well. In vivo toxicity studies in rats revealed neither clinically apparent side effects nor major alterations in serum chemistry and hematology parameters. Calculations on minimal detection requirements for in vivo targeted imaging using these nanoparticles are presented. Indeed, our results indicate that these nanoparticles may serve as a platform for sensitive and specific targeted molecular CT and fluorescence imaging

Topical ferumoxytol nanoparticles disrupt biofilms and prevent tooth decay in vivo via intrinsic catalytic activity

Ferumoxytol is a nanoparticle formulation approved by the U.S. Food and Drug Administration for systemic use to treat iron deficiency. Here, we show that, in addition, ferumoxytol disrupts intractable oral biofilms and prevents tooth decay (dental caries) via intrinsic peroxidase-like activity. Ferumoxytol binds within the biofilm ultrastructure and generates free radicals from hydrogen peroxide (H2O2), causing in situ bacterial death via cell membrane disruption and extracellular polymeric substances matrix degradation. In combination with low concentrations of H2O2, ferumoxytol inhibits biofilm accumulation on natural teeth in a human-derived ex vivo biofilm model, and prevents acid damage of the mineralized tissue. Topical oral treatment with ferumoxytol and H2O2 suppresses the development of dental caries in vivo, preventing the onset of severe tooth decay (cavities) in a rodent model of the disease. Microbiome and histological analyses show no adverse effects on oral microbiota diversity, and gingival and mucosal tissues. Our results reveal a new biomedical application for ferumoxytol as topical treatment of a prevalent and costly biofilm-induced oral disease

Synthesis and in vitro evaluation of a multifunctional and surface-switchable nanoemulsion platform

We present a multifunctional nanoparticle platform that has targeting moieties shielded by a matrix metalloproteinase-2 (MMP2) cleavable PEG coating. Upon incubation with MMP2 this surface-switchable coating is removed and the targeting ligands become available for binding. The concept was evaluated in vitro using biotin and αvβ3-integrin-specific RGD-peptide functionalized nanoparticles.National Heart, Lung, and Blood InstituteNational Institutes of Health (U.S.) (Program of Excellence in Nanotechnology (PEN) Award Contract HHSN268201000045C