Dynamics and pattern formation in invasive tumor growth

In this work, we study the in-vitro dynamics of the most malignant form of the primary brain tumor: Glioblastoma Multiforme. Typically, the growing tumor consists of the inner dense proliferating zone and the outer less dense invasive region. Experiments with different types of cells show qualitatively different behavior. Wild-type cells invade a spherically symmetric manner, but mutant cells are organized in tenuous branches. We formulate a model for this sort of growth using two coupled reaction-diffusion equations for the cell and nutrient concentrations. When the ratio of the nutrient and cell diffusion coefficients exceeds some critical value, the plane propagating front becomes unstable with respect to transversal perturbations. The instability threshold and the full phase-plane diagram in the parameter space are determined. The results are in a good agreement with experimental findings for the two types of cells.Comment: 4 pages, 4 figure

Singular Modes of the Electromagnetic Field

We show that the mode corresponding to the point of essential spectrum of the electromagnetic scattering operator is a vector-valued distribution representing the square root of the three-dimensional Dirac's delta function. An explicit expression for this singular mode in terms of the Weyl sequence is provided and analyzed. An essential resonance thus leads to a perfect localization (confinement) of the electromagnetic field, which in practice, however, may result in complete absorption.Comment: 14 pages, no figure

Lieb-Thirring Bound for Schr\"odinger Operators with Bernstein Functions of the Laplacian

A Lieb-Thirring bound for Schr\"odinger operators with Bernstein functions of the Laplacian is shown by functional integration techniques. Several specific cases are discussed in detail.Comment: We revised the first versio

Precise design of environmental data warehouses

People use data warehouses to help them make decisions. For example, public policy decision-makers can improve their decisions by using this technology to analyze the environmental effects of human activity. In production systems, data warehouses provide structures for extracting the knowledge required to optimize systems. Designing data warehouses is a complex task; designers need flexible and precise methods to help them create data warehouses and adapt their analysis criteria to developments in the decision-making process. In this paper, we introduce a flexible method based on UML (Unified Modeling Language). We introduce a UML profile for building multi-dimensional models and for choosing different criteria according to analysis requirements. This profile makes it possible to specify integrity constraints in OCL (Object Constraint Language). We apply our method to the construction of an environmental system for analyzing the use of certain agricultural fertilizers. We integrate various data sources into a multi-dimensional model showing several categories of analysis, and the consistency of data can be checked with OCL constraints

Solvent and thermal stability, and pH kinetics, of proline-specific dipeptidyl peptidase IV-like enzyme from bovine serum

Proline-specific dipeptidyl peptidase-like (DPP IV; EC 3.4.14.5) activity in bovine serum has attracted little attention despite its ready availability and the paucity of useful proline-cleaving enzymes. Bovine serum DPP IV-like peptidase is very tolerant of organic solvents, particularly acetonitrile: upon incubation for 1 h at room temperature in 70% acetonitrile, 47% dimethylformamide, 54% DMSO and 33% tetrahydrofuran (v/v concentrations) followed by dilution into the standard assay mixture, the enzyme retained half of its aqueous activity. As for thermal performance in aqueous buffer, its relative activity increased up to 50 ◦C. Upon thermoinactivation at 71 ◦C, pH 8.0 (samples removed periodically, cooled on ice, then assayed under optimal conditions), residual activities over short times fit a first-order decay with a k-value of 0.071±0.0034 min−1. Over longer times, residual activities fit to a double exponential decay with k1 and k2 values of 0.218±0.025 min−1 (46±4% of overall decay) and 0.040±0.002 min−1 (54±4% of overall decay), respectively. The enzyme’s solvent and thermal tolerances suggest that it may have potential for use as a biocatalyst in industry. Kinetic analysis with the fluorogenic substrate Gly-Pro-7-aminomethylcoumarin over a range of pH values indicated two pK values at 6.18±0.07 and at 9.70±0.50. We ascribe the lower value to the active site histidine; the higher may be due to the active site serine or to a free amino group in the substrate

Composite Dissolving Microneedles for Coordinated Control of Antigen and Adjuvant Delivery Kinetics in Transcutaneous Vaccination

Transcutaneous administration has the potential to improve therapeutics delivery, providing an approach that is safer and more convenient than traditional alternatives, while offering the opportunity for improved therapeutic efficacy through sustained/controlled drug release. To this end, a microneedle materials platform is demonstrated for rapid implantation of controlled-release polymer depots into the cutaneous tissue. Arrays of microneedles composed of drug-loaded poly(lactide-co-glycolide) (PLGA) microparticles or solid PLGA tips are prepared with a supporting and rapidly water-soluble poly(acrylic acid) (PAA) matrix. Upon application of microneedle patches to the skin of mice, the microneedles perforate the stratum corneum and epidermis. Penetration of the outer skin layers is followed by rapid dissolution of the PAA binder on contact with the interstitial fluid of the epidermis, implanting the microparticles or solid polymer microneedles in the tissue, which are retained following patch removal. These polymer depots remain in the skin for weeks following application and sustain the release of encapsulated cargos for systemic delivery. To show the utility of this approach the ability of these composite microneedle arrays to deliver a subunit vaccine formulation is demonstrated. In comparison to traditional needle-based vaccination, microneedle delivery gives improved cellular immunity and equivalent generation of serum antibodies, suggesting the potential of this approach for vaccine delivery. However, the flexibility of this system should allow for improved therapeutic delivery in a variety of diverse contexts.Massachusetts Institute of Technology. Ragon Institute of MGH, MIT and HarvardNational Institutes of Health (U.S.) (Award AI095109)United States. Army Research Office (Contract W911NF-07-D-0004

The transport dynamics of zirconium liquid-liquid extraction based on the purex process used for reprocessing spent nuclear reactor fuel

Fundamental diffusion and chemical reaction theory have been used to model the Purex process solvent extraction of zirconium. Statistical methods have been used to select an appropriate mass transfer model which permits estimation of the complexation reaction rate constants. A non-reacting process was studied in order to characterize the mass transfer coefficients for the contacting vessel used to study the zirconium-Purex process. Zirconium-Purex equilibrium data existing in the literature were used to estimate the metal complex distribution coefficient, and complexation equilibrium constant. The complexation reaction rate constants, and metal complex distribution coefficient, can be used to predict zirconium-Purex mass transfer behavior in most any contacting equipment. The Purex process utilizes a nitric acid based aqueous phase and a tri-butyl phosphate (TBP)-dodecane organic phase. TBP is the extracting agent in the dodecane diluent. The practical application lies in reprocessing spent nuclear reactor fuel of which zirconium is a fission product. It is necessary to purify recyclable materials (primarily uranium and plutonium), and isolate the waste (fission products and some actinides). While a good deal of study has been conducted with zirconium in the Purex process since the 1940\u27s, this work and/or (3) consideration of diffusion or chemical reaction, but not both combined. This study indicated diffusion and chemical reaction both significantly affect the overall mass transfer rate of zirconium for the specific process conditions and contacting equipment of the study

Schroedinger operators with singular interactions: a model of tunneling resonances

We discuss a generalized Schr\"odinger operator in $L^2(\mathbb{R}^d), d=2,3$, with an attractive singular interaction supported by a $(d-1)$-dimensional hyperplane and a finite family of points. It can be regarded as a model of a leaky quantum wire and a family of quantum dots if $d=2$, or surface waves in presence of a finite number of impurities if $d=3$. We analyze the discrete spectrum, and furthermore, we show that the resonance problem in this setting can be explicitly solved; by Birman-Schwinger method it is cast into a form similar to the Friedrichs model.Comment: LaTeX2e, 34 page