Vandermonde and resultant matrices: An abstract approach

We propose an abstract approach to the problems of common divisors and common multiples of rational matrix functions which (in the case of matrix polynomials) have been studied before using Vandermonde and resultant matrices.Supported in part by the Office of Naval Research, Air Force Office of Scientific Research, and the National Science Foundation.The work of this author was partially supported by an NSF grant and was carried out while visiting the University of California, San Diego.     

Pole shifting for matrices over real algebras

Pole shifting of multivariable control system over finite dimensional real algebras is studied. The main results are expressed in terms of the minimal polynomial of A + BF, where F is a feedback.     

Vandermonde and resultant matrices: An abstract approach

Vandermonde and resultant matrices: An abstract approach     

Coaxial Alginate Hydrogels: From Self-Assembled 3D Cellular Constructs to Long-Term Storage

Alginate as a versatile naturally occurring biomaterial has found widespread use in the biomedical field due to its unique features such as biocompatibility and biodegradability. The ability of its semipermeable hydrogels to provide a favourable microenvironment for clinically relevant cells made alginate encapsulation a leading technology for immunoisolation, 3D culture, cryopreservation as well as cell and drug delivery. The aim of this work is the evaluation of structural properties and swelling behaviour of the core-shell capsules for the encapsulation of multipotent stromal cells (MSCs), their 3D culture and cryopreservation using slow freezing. The cells were encapsulated in core-shell capsules using coaxial electrospraying, cultured for 35 days and cryopreserved. Cell viability, metabolic activity and cell–cell interactions were analysed. Cryopreservation of MSCs-laden core-shell capsules was performed according to parameters pre-selected on cell-free capsules. The results suggest that core-shell capsules produced from the low viscosity high-G alginate are superior to high-M ones in terms of stability during in vitro culture, as well as to solid beads in terms of promoting formation of viable self-assembled cellular structures and maintenance of MSCs functionality on a long-term basis. The application of 0.3 M sucrose demonstrated a beneficial effect on the integrity of capsules and viability of formed 3D cell assemblies, as compared to 10% dimethyl sulfoxide (DMSO) alone. The proposed workflow from the preparation of core-shell capsules with self-assembled cellular structures to the cryopreservation appears to be a promising strategy for their off-the-shelf availability.     

Kinetics of the hydroformylation of soybean oil by ligand-modified homogeneous rhodium catalysis

The kinetics and mechanism of the hydroformylation of soybean oil by homogeneous ligand-modified rhodium catalysts were investigated at 70–130°C and 4000–11,000 kPa. The effects of reaction rates on systematic variations in reaction parameters were evaluated in order to develop an industrial process to convert vegetable oils to polyaldehydes. The activation energies in the presence of triphenylphosphine (Ph₃P) (61.1±0.8 kJ/mol) (mean±SD) and triphenyl phosphite [(PhO)₃P] (77.4±5.0 kJ/mol) were determined. The catalyst was deactivated at temperatures higher than 100°C. An evaluation of the effects of the reaction parameters on initial rates yielded the rate laws for Ph₃P {rate=k [olefin][Rh(CO)₂Acac]^1.1 [Ph₃P]^−0.5 (pH₂+pCO)^1.4, where Rh(CO)₂Acac is (acetylacetonato)dicarbonylrhodium (I)} and (PhO)₃P {rate=[olefin] [Rh(CO)₂Acac]^1.2 [(PhO)₃P]^−0.8 (pH₂+pCO)^0.9 at total pressures lower than 7000 kPa, and rate =[olefin] [Rh(CO)₂Acac]^1.2 [(PhO)₃P]^−0.8(pH₂+pCO)^1.7 at total pressures higher than 7000 kPa}.     

Particle Swarm Optimization for Sorted Adapted Gaussian Mixture Models

Recently, we introduced the sorted Gaussian mixture models (SGMMs) algorithm providing the means to tradeoff performance for operational speed and thus permitting the speed-up of GMM-based classification schemes. The performance of the SGMM algorithm depends on the proper choice of the sorting function, and the proper adjustment of its parameters. In the present work, we employ particle swarm optimization (PSO) and an appropriate fitness function to find the most advantageous parameters of the sorting function. We evaluate the practical significance of our approach on the text-independent speaker verification task utilizing the NIST 2002 speaker recognition evaluation (SRE) database while following the NIST SRE experimental protocol. The experimental results demonstrate a superior performance of the SGMM algorithm using PSO when compared to the original SGMM. For comprehensiveness we also compared these results with those from a baseline Gaussian mixture model-universal background model (GMM-UBM) system. The experimental results suggest that the performance loss due to speed-up is partially mitigated using PSO-derived weights in a sorted GMM-based scheme.     

Nondestructive and noncontact method for determining the spring constant of rectangular cantilevers

We present here an experimental setup and suggest an extension to the long existing added-mass method for the calibration of the spring constant of atomic force microscope cantilevers. Instead of measuring the resonance frequency shift that results from attaching particles of known masses to the end of cantilevers, we load them with water microdrops generated by a commercial inkjet dispenser. Such a device is capable of generating drops, and thus masses, of extremely reproducible size. This makes it an ideal tool for calibration tasks. Moreover, the major advantage of water microdrops is that they allow for a nearly contactless calibration: no mechanical micromanipulation of particles on cantilevers is required, neither for their deposition nor for removal. After some seconds the water drop is completely evaporated, and no residues are left on the cantilever surface or tip. We present two variants: we vary the size of the drops and deposit them at the free end of the cantilever, or we keep the size of the drops constant and vary their position along the cantilever. For the second variant, we implemented also numerical simulations. Spring constants measured by this method are comparable to results obtained by the thermal noise method, as we demonstrate for six different cantilevers.