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

Requirements Analysis for an Integrated OCL Development Environment

An Integrated OCL Development Environment (IDE4OCL) can significantly improve the pragmatics and praxis of OCL. We present the domain concepts, toolâlevel interactions with OCL and the use cases we identified in a systematic analysis of requirements for an IDE4OCL. The domain concepts is an important contribution of our work as it attempts to clarify inconsistencies in the relevant specifications. Because OCL is not a standâalone language, the OCL landscape includes several interacting tools including an IDE4OCL. The use cases describe our vision of the desired functionality unique to an IDE4OCL. The results of our analysis and the long term vision of our work should be relevant to developers of OCL tools as well as to the OMG Request for Information regarding the UML Futures1. Our work is relevant to the UML Futures Roadmap because providing OCL for the constraints in the UML specification has been a longstanding problem at the OMG

Cost uncertainty for different levels of technology maturity

It is difficult at best to apply a single methodology for estimating cost uncertainties related to technologies of differing maturity. While highly mature technologies may have significant performance and manufacturing cost data available, less well developed technologies may be defined in only conceptual terms. Regardless of the degree of technical maturity, often a cost estimate relating to application of the technology may be required to justify continued funding for development. Yet, a cost estimate without its associated uncertainty lacks the information required to assess the economic risk. For this reason, it is important for the developer to provide some type of uncertainty along with a cost estimate. This study demonstrates how different methodologies for estimating uncertainties can be applied to cost estimates for technologies of different maturities. For a less well developed technology an uncertainty analysis of the cost estimate can be based on a sensitivity analysis; whereas, an uncertainty analysis of the cost estimate for a well developed technology can be based on an error propagation technique from classical statistics. It was decided to demonstrate these uncertainty estimation techniques with (1) an investigation of the additional cost of remediation due to beyond baseline, nearly complete, waste heel retrieval from underground storage tanks (USTs) at Hanford; and (2) the cost related to the use of crystalline silico-titanate (CST) rather than the baseline CS100 ion exchange resin for cesium separation from UST waste at Hanford

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

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

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

Quantum light transport in phase-separated Anderson localization fiber

Anderson localization, a strong localization effect that prevents wave diffusion, is fundamentally important in manipulating wave propagation in a disordered medium. This work uses a phase separated glass Anderson localization optical fiber and demonstrates quantum light transport, which shows the potential for transmission of high dimensional quantum information, thereby enabling quantum imaging and quantum communication applications.Propagation of light by Anderson localization has been demonstrated in micro-nano-structured fibers. In this work, we introduce a phase separated glass Anderson localization optical fiber for quantum applications. By using a spontaneous parametric down-conversion source, multi-photon detection with a single-photon avalanche diode array camera, and signal post-processing techniques, we demonstrate quantum light transport, where spatial correlations between photon pairs are preserved after propagation. In order to better understand and improve light transport, we study light localization, observing a dependence on wavelength. Our results indicate that the proposed phase separated fiber may become an effective platform for quantum imaging and communication

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