Analysis of a Class of Symmetric Equilibrium Configurations for a Territorial Model

<正>Motivated by an animal territoriality model,we consider a centroidal Voronoi tessellation algorithm from a dynamical systems perspective.In doing so,we discuss the stability of an aligned equilibrium configuration for a rectangular domain that exhibits interesting symmetry properties.We also demonstrate the procedure for performing a center manifold reduction on the system to extract a set of coordinates which capture the long term dynamics when the system is close to a bifurcation.Bifurcations of the system restricted to the center manifold are then classified and compared to numerical results.Although we analyze a specific set-up,these methods can in principle be applied to any bifurcation point of any equilibrium for any domain.     

On the Choice of Nugget in Kriging Modeling for Deterministic Computer Experiments

Kriging is commonly used for developing emulators as surrogates for computationally intensive simulations. One difficulty with kriging is the potential numerical instability in the computation of the inverse of the covariance matrix, which can lead to large variability and poor performance of the kriging predictor. First, we study some causes of ill-conditioning in kriging. We then study the use of nugget in kriging to overcome the numerical instability. Some asymptotic results on its interpolation bias and mean squared prediction errors are presented. Finally, we study the choice of the nugget parameter based on some algebraic lower bounds and use of a regularizing trace. A simulation study is performed to show the differences between kriging with and without nugget and to demonstrate the advantages of the former. This article has supplementary materials online.     

Realization of Metric Spaces as Inverse Limits, and Bilipschitz Embedding in L 1

We give sufficient conditions for a metric space to bilipschitz embed in L ₁. In particular, if X is a length space and there is a Lipschitz map ${u: X \rightarrow \mathbb R}$ such that for every interval ${I \subset \mathbb R}$ , the connected components of u ^?1(I) have diameter ${\leq {\rm const} \cdot {\rm diam}(I)}$ , then X admits a bilipschitz embedding in L ₁. As a corollary, the Laakso examples, (Geom Funct Anal 10(1):111–123, 2000), bilipschitz embed in L ₁, though they do not embed in any any Banach space with the Radon–Nikodym property (e.g. the space ? ₁ of summable sequences). The spaces appearing the statement of the bilipschitz embedding theorem have an alternate characterization as inverse limits of systems of metric graphs satisfying certain additional conditions. This representation, which may be of independent interest, is the initial part of the proof of the bilipschitz embedding theorem. The rest of the proof uses the combinatorial structure of the inverse system of graphs and a diffusion construction, to produce the embedding in L ₁.     

Integrated optoelectronic circuit forecast

A market research study was conducted, leading to a 10-year forecast of worldwide integrated optoelectronic circuit (IOEC) market and application trends. Four IOEC categories were considered: lightwave, imaging array, digital IC interface optical bus, and other devices. It was concluded that worldwide IOEC production will reach $1.71 billion by 1997. It was also concluded that lightwave IOECs will be the leading device category, with commercial communication the leading application.     

Towards a new framework for evaluating systemic problem structuring methods

Operational researchers and social scientists often make significant claims for the value of systemic problem structuring and other participative methods. However, when they present evidence to support these claims, it is usually based on single case studies of intervention. There have been very few attempts at evaluating across methods and across interventions undertaken by different people. This is because, in any local intervention, contextual factors, the skills of the researcher and the purposes being pursued by stakeholders affect the perceived success or failure of a method. The use of standard criteria for comparing methods is therefore made problematic by the need to consider what is unique in each intervention. So, is it possible to develop a single evaluation approach that can support both locally meaningful evaluations and longer-term comparisons between methods? This paper outlines a methodological framework for the evaluation of systemic problem structuring methods that seeks to do just this.     

Nanohoop Rotaxanes from Active Metal Template Syntheses and Their Potential in Sensing Applications

The unique optoelectronic properties and smooth, rigid pores of macrocycles with radially oriented π systems render them fascinating candidates for the design of novel mechanically interlocked molecules with new properties. Two high‐yielding strategies are used to prepare nanohoop [2]rotaxanes, which owing to the π‐rich macrocycle are highly emissive. Then, metal coordination, an intrinsic property afforded by the resulting mechanical bond, can lead to molecular shuttling as well as modulate the observed fluorescence in both organic and aqueous conditions. Inspired by these findings, a self‐immolative [2]rotaxane was then designed that self‐destructs in the presence of an analyte, eliciting a strong fluorescent turn‐on response, serving as proof‐of‐concept for a new type of molecular sensing material. More broadly, this work highlights the conceptual advantages of combining compact π‐rich macrocyclic frameworks with mechanical bonds formed via active‐template syntheses.     

Carbon Dots as a New Class of Diamagnetic Chemical Exchange Saturation Transfer (diaCEST) MRI Contrast Agents

While carbon dots (C‐dots) have been extensively investigated pertaining to their fluorescent, phosphorescent, electrochemiluminescent, optoelectronic, and catalytic features, their inherent chemical exchange saturation transfer magnetic resonance imaging (CEST MRI) properties are unknown. By virtue of their hydrophilicity and abundant exchangeable protons of hydroxyl, amine, and amide anchored on the surface, we report here that C‐dots can be adapted as effective diamagnetic CEST (diaCEST) MRI contrast agents. As a proof‐of‐concept demonstration, human glioma cells were labeled with liposomes with or without encapsulated C‐dots and implanted in mouse brain. In vivo CEST MRI was able to clearly differentiate labeled cells from non‐labeled cells. The present findings may encourage new applications of C‐dots for in vivo imaging in deep tissues, which is currently not possible using conventional fluorescent (near‐infrared) C‐dots.     

Development of Zinc‐Specific iCEST MRI as an Imaging Biomarker for Prostate Cancer

The healthy prostate contains the highest concentration of mobile zinc in the body. As this level decreases dramatically during the initial development of prostate cancer, in vivo detection of prostate zinc content may be applied for diagnosis of prostate cancer. Using ¹⁹F ion chemical exchange saturation transfer magnetic resonance imaging (iCEST MRI) and TF‐BAPTA as a fluorinated Zn‐binding probe with micromolar sensitivity, we show that iCEST MRI is able to differentiate between normal and malignant prostate cells with a 10‐fold difference in contrast following glucose‐stimulated zinc secretion in vitro. The iCEST signal decreased in normal prostate cells upon downregulation of the ZIP1 zinc transporter. In vivo, using an orthotopic prostate cancer mouse model and a transgenic adenocarcinoma of the mouse prostate (TRAMP) model, a gradual decrease of >300 % in iCEST contrast following the transition of normal prostate epithelial cells to cancer cells was detected.