Weighted geometric mean of large-scale matrices: numerical analysis and algorithms

Computing the weighted geometric mean of large sparse matrices is an operation that tends to become rapidly intractable, when the size of the matrices involved grows. However, if we are not interested in the computation of the matrix function itself, but just in that of its product times a vector, the problem turns simpler and there is a chance to solve it even when the matrix mean would actually be impossible to compute. Our interest is motivated by the fact that this calculation has some practical applications, related to the preconditioning of some operators arising in domain decomposition of elliptic problems. In this thesis, we explore how such a computation can be efficiently performed. First, we exploit the properties of the weighted geometric mean and find several equivalent ways to express it through real powers of a matrix. Hence, we focus our attention on matrix powers and examine how well-known techniques can be adapted to the solution of the problem at hand. In particular, we consider two broad families of approaches for the computation of f(A) v, namely quadrature formulae and Krylov subspace methods, and generalize them to the pencil case f(A\B) v. Finally, we provide an extensive experimental evaluation of the proposed algorithms and also try to assess how convergence speed and execution time are influenced by some characteristics of the input matrices. Our results suggest that a few elements have some bearing on the performance and that, although there is no best choice in general, knowing the conditioning and the sparsity of the arguments beforehand can considerably help in choosing the best strategy to tackle the problem.

A Flow Trace Generator using Graph-based Traffic Classification Techniques

We propose a novel methodology to generate realistic network flow traces to enable systematic evaluation of network monitoring systems in various traffic conditions. Our technique uses a graph-based approach to model the communication structure observed in real-world traces and to extract traffic templates. By combining extracted and user-defined traffic templates, realistic network flow traces that comprise normal traffic and customized conditions are generated in a scalable manner. A proof-of-concept implementation demonstrates the utility and simplicity of our method to produce a variety of evaluation scenarios. We show that the extraction of templates from real-world traffic leads to a manageable number of templates that still enable accurate re-creation of the original communication properties on the network flow level.

Improved column-based radiochemical processing of the generator produced 68Ga

An improved chemical strategy for processing of the generator produced 68Ga was developed based on processing of the original 68Ge/68Ga generator eluate on a micro-column. Direct pre-concentration and purification of the eluted 68Ga is performed on a cation-exchange resin in hydrochloric acid/acetone media. A supplementary step based on a second micro-column filled with a second resin allows direct re-adsorption of 68Ga eluted from the cation exchanger. 68Ga is finally striped from the second resin with a small volume of pure water. For this purpose a strong anion exchanger and a novel extraction chromatographic resin based on tetraalkyldiglycolamides are characterized. The strategy allows online pre-concentration and purification of 68Ga from the original generator eluate. The supplementary column allows transferring 68Ga with high radionuclide and chemical quality in the aqueous solution with small volume and low acidity useful for direct radiolabeling reactions.

Mapping the Operation of the Miniature Combustion Aerosol Standard (Mini-CAST) Soot Generator

The Jing Ltd. miniature combustion aerosol standard (Mini-CAST) soot generator is a portable, commercially available burner that is widely used for laboratory measurements of soot processes. While many studies have used the Mini-CAST to generate soot with known size, concentration, and organic carbon fraction under a single or few conditions, there has been no systematic study of the burner operation over a wide range of operating conditions. Here, we present a comprehensive characterization of the microphysical, chemical, morphological, and hygroscopic properties of Mini-CAST soot over the full range of oxidation air and mixing N-2 flow rates. Very fuel-rich and fuel-lean flame conditions are found to produce organic-dominated soot with mode diameters of 10-60nm, and the highest particle number concentrations are produced under fuel-rich conditions. The lowest organic fraction and largest diameter soot (70-130nm) occur under slightly fuel-lean conditions. Moving from fuel-rich to fuel-lean conditions also increases the O:C ratio of the soot coatings from similar to 0.05 to similar to 0.25, which causes a small fraction of the particles to act as cloud condensation nuclei near the Kelvin limit (kappa similar to 0-10(-3)). Comparison of these property ranges to those reported in the literature for aircraft and diesel engine soots indicates that the Mini-CAST soot is similar to real-world primary soot particles, which lends itself to a variety of process-based soot studies. The trends in soot properties uncovered here will guide selection of burner operating conditions to achieve optimum soot properties that are most relevant to such studies.

Anisotropically oriented electrospun matrices with an imprinted periodic micropattern: a new scaffold for engineered muscle constructs

Engineered muscle constructs provide a promising perspective on the regeneration or substitution of irreversibly damaged skeletal muscle. However, the highly ordered structure of native muscle tissue necessitates special consideration during scaffold development. Multiple approaches to the design of anisotropically structured substrates with grooved micropatterns or parallel-aligned fibres have previously been undertaken. In this study we report the guidance effect of a scaffold that combines both approaches, oriented fibres and a grooved topography. By electrospinning onto a topographically structured collector, matrices of parallel-oriented poly(ε-caprolactone) fibres with an imprinted wavy topography of 90 µm periodicity were produced. Matrices of randomly oriented fibres or parallel-oriented fibres without micropatterns served as controls. As previously shown, un-patterned, parallel-oriented substrates induced myotube orientation that is parallel to fibre direction. Interestingly, pattern addition induced an orientation of myotubes at an angle of 24° (statistical median) relative to fibre orientation. Myotube length was significantly increased on aligned micropatterned substrates in comparison to that on aligned substrates without pattern (436 ± 245 µm versus 365 ± 212 µm; p < 0.05). We report an innovative, yet simple, design to produce micropatterned electrospun scaffolds that induce an unexpected myotube orientation and an increase in myotube length.

Energy harvesting from the beating heart by a mass imbalance oscillation generator

Energy-harvesting devices attract wide interest as power supplies of today's medical implants. Their long lifetime will spare patients from repeated surgical interventions. They also offer the opportunity to further miniaturize existing implants such as pacemakers, defibrillators or recorders of bio signals. A mass imbalance oscillation generator, which consists of a clockwork from a commercially available automatic wrist watch, was used as energy harvesting device to convert the kinetic energy from the cardiac wall motion to electrical energy. An MRI-based motion analysis of the left ventricle revealed basal regions to be energetically most favorable for the rotating unbalance of our harvester. A mathematical model was developed as a tool for optimizing the device's configuration. The model was validated by an in vitro experiment where an arm robot accelerated the harvesting device by reproducing the cardiac motion. Furthermore, in an in vivo experiment, the device was affixed onto a sheep heart for 1 h. The generated power in both experiments-in vitro (30 μW) and in vivo (16.7 μW)-is sufficient to power modern pacemakers.

PMMA-CNT matrices for vacuum electronic, biosensing and energy applications

Carbon nanotubes (CNTs) are interesting materials with extraordinary properties for various applications. Here, vertically-aligned multiwalled CNTs (VA-MWCNTs) are grown by our dual radio frequency plasma enhanced chemical vapor deposition (PECVD). After optimizing the synthesis processes, these VA-MWCNTs were fabricated in to a series of devices for applications in vacuum electronics, glucose biosensors, glucose biofuel cells, and supercapacitors In particular, we have created the so-called PMMA-CNT matrices (opened-tip CNTs embedded in poly-methyl methacrylate) that are promising components in a novel energy sensing, generation and storage (SGS) system that integrate glucose biosensors, biofuel cells, and supercapacitors. The content of this thesis work is described as follows: 1. We have first optimized the synthesis of VA-MWCNTs by our PECVD technique. The effects of CH4 flow rate and growth duration on the lengths of these CNTs were studied. 2. We have characterized these VA-MWCNTs for electron field emission. We noticed that as grown CNTs suffers from high emission threshold, poor emission density and poor long-term stability. We attempted a series of experiments to understand ways to overcome these problems. First, we decrease the screening effects on VA-MWCNTs by creating arrays of self-assembled CNT bundles that are catalyst-free and opened tips. These bundles are found to enhance the field emission stability and emission density. Subsequently, we have created PMMA-CNT matrices that are excellent electron field emitters with an emission threshold field of more than two-fold lower than that of the as-grown sample. Furthermore, no significant emission degradation was observed after a continuous emission test of 40 hours (versus much shorter tests in reported literatures). Based on the new understanding we learnt from the PMMA-CNT matrices, we further created PMMA-STO-CNT matrices by embedding opened-tip VA-MWCNTs that are coated with strontium titanate (SrTiO3) with PMMA. We found that the PMMA-STO-CNT matrices have all the desired properties of the PMMA-CNT matrices. Furthermore, PMMA-STO-CNT matrices offer much lower emission threshold field, about five-fold lower than that of as grown VA-MWCNTs. The new understandings we obtained are important for practical application of VA-MWCNTs in field emission devices. 3. Subsequently, we have functionalized PMMA-CNT matrices for glucose biosensing. Our biosensor was developed by immobilized glucose oxidase (GOχ) on the opened-tip CNTs exposed on the matrices. The durability, stability and sensitivity of the biosensor were studied. In order to understand the performance of miniaturized glucose biosensors, we have then investigated the effect of working electrode area on the sensitivity and current level of our biosensors. 4. Next, functionalized PMMA-CNT matrices were utilized for energy generation and storage. We found that PMMA-CNT matrices are promising component in glucose/O2 biofuel cells (BFCs) for energy generation. The construction of these BFCs and the effect of the electrode area on the power density of these BFCs were investigated. Then, we have attempted to use PMMA-CNT matrices as supercapacitors for energy storage devices. The performance of these supercapacitors and ways to enhance their performance are discussed. 5. Finally, we further evaluated the concept of energy SGS system that integrated glucose biosensors, biofuel cells, and supercapacitors. This SGS system may be implantable to monitor and control the blood glucose level in our body.

Microfluidic hydrogen generator : featuring passive on-demand gas generation and self-circulated reactant for integration with micro fuel cell

A microfluidic hydrogen generator is presented in this work. Its fabrication, characterization, and integration with a micro proton exchange membrane (PEM) fuel cell are described. Hydrogen gas is generated by the hydrolysis of aqueous ammonia borane. Gas generation, as well as the circulation of ammonia borane from a rechargeable fuel reservoir, is performed without any power consumption. To achieve this, directional growth and selective venting of hydrogen gas is maintained in the microchannels, which results in the circulation of fresh reactant from the fuel reservoir. In addition to this self-circulation mechanism, the hydrogen generator has been demonstrated to self-regulate gas generation to meet demands of a connected micro fuel cell. All of this is done without parasitic power consumption from the fuel cell. Results show its feasibility in applications of high-impedance systems. Lastly, recommendations for improvements and suggestions for future work are described

Development and characterization of fluorescent pH sensors based on porous silica and hydrogel support matrices

The hydrogen ion activity (pH) is a very important parameter in environment monitoring, biomedical research and other applications. Optical pH sensors have several advantages over traditional potentiometric pH measurement, such as high sensitivity, no need of constant calibration, easy for miniaturization and possibility for remote sensing. Several pH indicators has been successfully immobilized in three different solid porous materials to use as pH sensing probes. The fluorescent pH indicator fluorescein-5-isothiocyanate (FITC) was covalently bound onto the internal surface of porous silica (pore size ~10 nm) and retained its pH sensitivity. The excited state pK* a of FITC in porous silica (5.58) was slightly smaller than in solution (5.68) due to the free silanol groups (Si-OH) on the silica surface. The pH sensitive range for this probe is pH 4.5 - 7.0 with an error less than 0.1 pH units. The probe response was reproducible and stable for at least four month, stored in DI water, but exhibit a long equilibrium of up to 100 minutes. Sol-gel based pH sensors were developed with immobilization of two fluorescent pH indicators fluorescein-5-(and-6)-sulfonic acid, trisodium salt (FS) and 8-hydroxypyrene- 1,3,6-trisulfonic acid (HPTS) through physical entrapment. Prior to immobilization, the indicators were ion-paired with a common surfactant hexadecyltrimethylammonium bromide (CTAB) in order to prevent leaching. The sol-gel films were synthesized through the hydrolysis of two different precursors, ethyltriethoxysilane (ETEOS) and 3- glycidoxypropyltrimethoxysilane (GPTMS) and deposited on a quartz slide through spin coating. The pK a of the indicators immobilized in sol-gel films was much smaller than in solutions due to silanol groups on the inner surface of the sol-gel films and ammonium groups from the surrounding surfactants. Unlike in solution, the apparent pK a of the indicators in sol-gel films increased with increasing ionic strength. The equilibrium time for these sensors was within 5 minutes (with film thickness of ~470 nm). Polyethylene glycol (PEG) hydrogel was of interest for optical pH sensor development because it is highly proton permeable, transparent and easy to synthesize. pH indicators can be immobilized in hydrogel through physical entrapment and copolymerization. FS and HPTS ion-pairs were physically entrapped in hydrogel matrix synthesized via free radical initiation. For covalent immobilization, three indicators, 6,8-dihydroxypyrene-1,3- disulfonic acid (DHPDS), 2,7-dihydroxynaphthalene-3,6-disulfonic acid (DHNDS) and cresol red were first reacted with methacrylic anhydride (MA) to form methacryloylanalogs for copolymerization. These hydrogels were synthesized in aqueous solution with a redox initiation system. The thickness of the hydrogel film is controlled as ~ 0.5 cm and the porosity can be adjusted with the percentage of polyethylene glycol in the precursor solutions. The pK a of the indicators immobilized in the hydrogel both physically and covalently were higher than in solution due to the medium effect. The sensors are stable and reproducible with a short equilibrium time (less than 4 minutes). In addition, the color change of cresol red immobilized hydrogel is vivid from yellow (acidic condition) to purple (basic condition). Due to covalently binding, cresol red was not leaching out from the hydrogel, making it a good candidate of reusable "pH paper".

Engineered fibrin matrices for functional display of cell membrane-bound growth factor-like activities: study of angiogenic signaling by ephrin-B2

With the rapid increase in approaches to pro- or anti-angiogenic therapy, new and effective methodologies for administration of cell-bound growth factors will be required. We sought to develop the natural hydrogel matrix fibrin as platform for extensive interactions and continuous signaling by the vascular morphogen ephrin-B2 that normally resides in the plasma membrane and requires multivalent presentation for ligation and activation of Eph receptors on apposing endothelial cell surfaces. Using fibrin and protein engineering technology to induce multivalent ligand presentation, a recombinant mutant ephrin-B2 receptor binding domain was covalently coupled to fibrin networks at variably high densities. The ability of fibrin-bound ephrin-B2 to act as ligand for endothelial cells was preserved, as demonstrated by a concomitant, dose-dependent increase of endothelial cell binding to engineered ephrin-B2-fibrin substrates in vitro. The therapeutic relevance of ephrin-B2-fibrin implant matrices was demonstrated by a local angiogenic response in the chick embryo chorioallontoic membrane evoked by the local and prolonged presentation of matrix-bound ephrin-B2 to tissue adjacing the implant. This new knowledge on biomimetic fibrin vehicles for precise local delivery of membrane-bound growth factor signals may help to elucidate specific biological growth factor function, and serve as starting point for development of new treatment strategies.