On the Hausdorff dimension of ultrametric subsets in R^n

For every e>0, any subset of R^n with Hausdorff dimension larger than (1-e)n must have ultrametric distortion larger than 1/(4e).Comment: 4 pages, improved layou

A node-capacitated Okamura-Seymour theorem

The classical Okamura-Seymour theorem states that for an edge-capacitated, multi-commodity flow instance in which all terminals lie on a single face of a planar graph, there exists a feasible concurrent flow if and only if the cut conditions are satisfied. Simple examples show that a similar theorem is impossible in the node-capacitated setting. Nevertheless, we prove that an approximate flow/cut theorem does hold: For some universal c > 0, if the node cut conditions are satisfied, then one can simultaneously route a c-fraction of all the demands. This answers an open question of Chekuri and Kawarabayashi. More generally, we show that this holds in the setting of multi-commodity polymatroid networks introduced by Chekuri, et. al. Our approach employs a new type of random metric embedding in order to round the convex programs corresponding to these more general flow problems.Comment: 30 pages, 5 figure

South Asian Regional Workshop on Groundwater Farmer-Managed Irrigation Systems and Sustainable Groundwater Management, Dhaka, Bangladesh 18-21 May 1992

Farmer managed irrigation systems, Groundwater management, Sustainability, Bangladesh

Measured descent: A new embedding method for finite metrics

We devise a new embedding technique, which we call measured descent, based on decomposing a metric space locally, at varying speeds, according to the density of some probability measure. This provides a refined and unified framework for the two primary methods of constructing Frechet embeddings for finite metrics, due to [Bourgain, 1985] and [Rao, 1999]. We prove that any n-point metric space (X,d) embeds in Hilbert space with distortion O(sqrt{alpha_X log n}), where alpha_X is a geometric estimate on the decomposability of X. As an immediate corollary, we obtain an O(sqrt{(log lambda_X) \log n}) distortion embedding, where \lambda_X is the doubling constant of X. Since \lambda_X\le n, this result recovers Bourgain's theorem, but when the metric X is, in a sense, ``low-dimensional,'' improved bounds are achieved. Our embeddings are volume-respecting for subsets of arbitrary size. One consequence is the existence of (k, O(log n)) volume-respecting embeddings for all 1 \leq k \leq n, which is the best possible, and answers positively a question posed by U. Feige. Our techniques are also used to answer positively a question of Y. Rabinovich, showing that any weighted n-point planar graph embeds in l_\infty^{O(log n)} with O(1) distortion. The O(log n) bound on the dimension is optimal, and improves upon the previously known bound of O((log n)^2).Comment: 17 pages. No figures. Appeared in FOCS '04. To appeaer in Geometric & Functional Analysis. This version fixes a subtle error in Section 2.

Synthesis And Characterization Of (pyNO−)2GaCl: A Redox-Active Gallium Complex

We report the synthesis of a gallium complex incorporating redox-active pyridyl nitroxide ligands. The (pyNO−)2GaCl complex was prepared in 85% yield via a salt metathesis route and was characterized by 1H and 13C NMR spectroscopies, X-ray diffraction, and theory. UV–Vis absorption spectroscopy and electrochemistry were used to access the optical and electrochemical properties of the complex, respectively. Our discussion focuses primarily on a comparison of the gallium complex to the corresponding aluminum derivative and shows that although the complexes are very similar, small differences in the electronic structure of the complexes can be correlated to the identity of the metal

Multiplierz: An Extensible API Based Desktop Environment for Proteomics Data Analysis

BACKGROUND. Efficient analysis of results from mass spectrometry-based proteomics experiments requires access to disparate data types, including native mass spectrometry files, output from algorithms that assign peptide sequence to MS/MS spectra, and annotation for proteins and pathways from various database sources. Moreover, proteomics technologies and experimental methods are not yet standardized; hence a high degree of flexibility is necessary for efficient support of high- and low-throughput data analytic tasks. Development of a desktop environment that is sufficiently robust for deployment in data analytic pipelines, and simultaneously supports customization for programmers and non-programmers alike, has proven to be a significant challenge. RESULTS. We describe multiplierz, a flexible and open-source desktop environment for comprehensive proteomics data analysis. We use this framework to expose a prototype version of our recently proposed common API (mzAPI) designed for direct access to proprietary mass spectrometry files. In addition to routine data analytic tasks, multiplierz supports generation of information rich, portable spreadsheet-based reports. Moreover, multiplierz is designed around a "zero infrastructure" philosophy, meaning that it can be deployed by end users with little or no system administration support. Finally, access to multiplierz functionality is provided via high-level Python scripts, resulting in a fully extensible data analytic environment for rapid development of custom algorithms and deployment of high-throughput data pipelines. CONCLUSION. Collectively, mzAPI and multiplierz facilitate a wide range of data analysis tasks, spanning technology development to biological annotation, for mass spectrometry-based proteomics research.Dana-Farber Cancer Institute; National Human Genome Research Institute (P50HG004233); National Science Foundation Integrative Graduate Education and Research Traineeship grant (DGE-0654108

Interfaces, Confinement, And Resonant Raman Scattering In Ge/si Quantum Wells

We address the question of confinement of the Ge-Ge mode in five-monolayer-Ge single and multiple quantum wells. Using Raman scattering, our data show strong dependence of the interface quality on the number of quantum wells and thereby on the confinement of both the phonons and the electronic states in the Ge wells. The dependence of line shape and peak position of the Ge-Ge Raman line with laser photon energy gives a clear indication of the existence of terraces in the interfaces of the Ge/Si multiple quantum wells. © 1995 The American Physical Society.5124178001780

Internal versus external determinants of Schistosoma japonicum transmission in irrigated agricultural villages

Currently schistosomiasis transmission has been suppressed to low levels in many historically endemic areas of China by widespread use of praziquantel in human and bovine populations and application of niclosamide for snail control. However, re-emergent transmission has signalled the need for sustainable interventions beyond these repeated chemical interventions. To take advantage of ongoing investment in rural infrastructure, an index of schistosomiasis transmission potential is needed to identify villages where environmental modifications would be particularly effective. Based on a retrospective analysis of data from 10 villages in Sichuan Province, an index linked to the basic reproductive number is shown to have promise in meeting this need. However, a lack of methods for estimating the spatial components of the proposed metric and for estimating the import of cercariae and miracidia from neighbouring villages leads to significant uncertainty in its estimation. These findings suggest a priority effort to develop methods for measuring the free-swimming forms of the parasite in surface waters. This need is underscored by the high cost and limited sensitivity of current methods for diagnosing human infection and mounting evidence of the inadequacy of snail surveys to identify environments supporting low levels of transmission

Wave-number locking in spatially forced pattern-forming systems

Abstract -We use the Swift-Hohenberg model and normal-form equations to study wave-number locking in two-dimensional systems as a result of one-dimensional spatially periodic weak forcing. The freedom of the system to respond in a direction transverse to the forcing leads to wavenumber locking in a wide range of forcing wave-numbers, even for weak forcing, unlike the locking in a set of narrow Arnold tongues in one-dimensional systems. Multi-stability ranges of stripe, rectangular, and oblique patterns produce a variety of resonant patterns. The results shed new light on rehabilitation practices of banded vegetation in drylands. Copyright c EPLA, 2008 Frequency locking phenomena in temporally forced oscillators are well understood; a forced oscillator can adjust its frequency of oscillation to a rational fraction of the forcing frequency The spatial counterpart of frequency locking, wavenumber locking, is less well understood. Although much work has been devoted to pattern-forming systems that are subjected to spatially periodic forcing In this letter we analyze wave-number locking phenomena associated with a two-dimensional response to a one-dimensional forcing. We are interested in universal aspects of wave-number locking and therefore base our study on normal-form equations. We derive these equations using a periodically forced Swift-Hohenberg (SH) equation, which helps us motivate the problem and test our analysis using direct numerical solutions. The specific equation we consider is In this equation ε is the distance from the instability point of the unforced zero state to a stationary pattern with a wave-number k 0 ∼ O(1), k f is the forcing wave-number, γ is the intensity of multiplicative forcing and α is the intensity of additive forcing. In the absence of forcing (α = γ = 0) the unstable zero state u = 0 evolves towards a stripe pattern with wavenumber k 0 , the pattern that minimizes the Lyapunov function of the SH equation (se