Telecommunications Network Case Study: Selecting a Data Network Architecture

This paper documents a model that was pivotal in deciding which of two architectures should be selected for a frame relay data communications network. The choices are either to continue using the current architecture, or to make a large incremental investment in new equipment which reduces the number of high speed inter-office trunks required to interconnect the switches. The analysis requires optimizing the mix of two types of customer port cards to determine the maximum customer port capacity of a switch. Simple approximations are used to estimate the number of inter-office trunks and trunk cards required. Based in large part on the costs computed by this model, an executive level decision was made to move to the new architecture.     

Influence of baseline hematocrit and hemodilution on BOLD fMRI activation.

Current understanding of blood oxygenation level dependent (BOLD) fMRI physiology predicts a close relationship between BOLD signal and blood hematocrit level. However, neither this relationship nor its effect on BOLD percent activation (BPA) has been empirically examined in man. To that end, BPA in primary visual cortex in response to photic stimulation was determined in a group of 24 normal subjects. A positive linear relationship between BPA and hematocrit was seen, particularly in men. To evaluate the effect of change in hematocrit on BPA, 9 men were studied before and following isotonic saline hemodilution, resulting in an average 6% reduction in hematocrit and an 8-31% reduction in BPA. No significant change in the number of activated pixels was seen. A model of predicted BPA as a function of hematocrit and vessel size was developed, and results from this model closely mirrored the empiric data. These results suggest that hematocrit significantly influences the magnitude of BPA and that such baseline factors should be accounted for when comparing BOLD data across groups of subjects, particularly in the many instances in which hematocrit may vary systematically. Such instances include several disease states as well as studies involving sex differences, drug administration, stress and other factors. Finally, the robust agreement between predicted and empiric data serves to validate a semiquantitative approach to the analysis of BOLD fMRI data.     

Half-space theorems for mean curvature one surfaces in hyperbolic space

We give conditions which oblige properly embedded constant mean curvature one surfaces in hyperbolic 3-space to intersect. Our results are inspired by the theorem that two disjoint properly immersed minimal surfaces in must be planes.

     

The Mean and Variance of the Numbers of r-Pronged Nodes and r-Caterpillars in Yule-Generated Genealogical Trees

The Yule model is a frequently-used evolutionary model that can be utilized to generate random genealogical trees. Under this model, using a backwards counting method differing from the approach previously employed by Heard (Evolution 46: 1818–1826), for a genealogical tree of n lineages, the mean number of nodes with exactly r descendants is computed (2 ≤ r ≤ n − 1). The variance of the number of r-pronged nodes is also obtained, as are the mean and variance of the number of r-caterpillars. These results generalize computations of McKenzie and Steel for the case of r = 2 (Math. Biosci. 164: 81–92, 2000). For a given n, the two means are largest at r = 2, equaling 2n/3 for n ≥ 5. However, for n ≥ 9, the variances are largest at r = 3, equaling 23n/420 for n ≥ 7. As n→∞, the fraction of internal nodes that are r-caterpillars for some r approaches (e² − 5)/4≈ 0.59726. Received August 23, 2004     

Two-dimensional Yukawa liquids: correlation and dynamics

A combined theoretical and molecular dynamics (MD) simulation study of the collective modes and their dispersion in a two-dimensional Yukawa system in the strongly coupled liquid state is presented. The theoretical analysis relies upon the quasilocalized charge approximation; the MD simulation generates static pair correlation functions and dynamical current-current correlation spectra.     

Application of FT-based MMSE deconvolution method for cerebral blood flow measurement in patients with leukoaraiosis

Introduction

The bolus-tracking (BT) technique is the most popular perfusion-weighted (PW) dynamic susceptibility contrast MRI method used for estimating cerebral blood flow (CBF), cerebral blood volume and mean transit time. The BT technique uses a convolution model that establishes the input–output relationship between blood flow and the vascular tracer concentration. Singular value decomposition (SVD)- and Fourier transform (FT)-based deconvolution methods are popular and widely used for estimating PW MRI parameters. However, from the published literature, it appears that SVD is more widely accepted than other methods. In a previous article, an FT-based minimum mean-squared error (MMSE) technique was proposed and simulation experiments were performed to compare it with the well-established circular SVD (oSVD) method. In this study, the FT-based MMSE method has been used to estimate relative CBF (rCBF) in 13 patients with white matter lesions (WMLs) (leukoaraiosis), and results are compared with the widely used oSVD method.

Materials and Methods

Thirteen patients with leukoaraiosis were imaged on a 1.5-T Siemens whole-body scanner. After acquiring the localizer and structural scans consisting of FLAIR (fluid attenuated with inversion recovery), T₁-weighted and T₂-weighted images, perfusion study was implemented as part of the MRI protocol. For each patient and method, two values were calculated: (a) rCBF for normal white matter (NWM) ROI, obtained by dividing the average CBF value in NWM ROI with average CBF in gray matter (GM) ROI, and (b) rCBF for WML ROI, obtained by dividing the average CBF value in WML ROI with average CBF in GM ROI. Results for the two deconvolution methods were computed.

Results and Discussion

A significant (P<.05) decrease in estimated rCBF was observed in the WML in all the patients using the MMSE method, while for the oSVD method, the decrease was observed in all but one patient. Initial results suggest that the MMSE method is comparable to the oSVD method for estimating rCBF in NMW while it may be better than oSVD for estimating rCBF in lesions of low flow. Studies involving a larger patient population may be required to further validate the findings of this work.     

On solving a primal geometric program by partial dual optimization

The several published methods for mapping a dual solution estimate to a primal solution estimate in posynomial geometric programming provide no criteria for deciding how much deviation from primal feasibility, or discrepancy between the primal and dual objective function values, should be permitted before the primal solution estimate is accepted by the designer. This paper presents a new and simple dual-to-primal conversion method that uses the cost coefficients to provide a sound economic criterion for determining when to accept a primal solution estimate. The primal solution estimate generated is the exact solution to a modified primal obtained from the given primal by modifying the cost coefficients, with the exponent matrix left unchanged. The method is shown to have desirable properties when coupled with a convergent dual algorithm.     

Energy dependence of directed flow over a wide range of pseudorapidity in Au + Au collisions at the BNL Relativistic Heavy Ion Collider

We report on measurements of directed flow as a function of pseudorapidity in Au + Au collisions at energies of square root of SNN = 19.6, 62.4, 130 and 200 GeV as measured by the PHOBOS detector at the BNL Relativistic Heavy Ion Collider. These results are particularly valuable because of the extensive, continuous pseudorapidity coverage of the PHOBOS detector. There is no significant indication of structure near midrapidity and the data surprisingly exhibit extended longitudinal scaling similar to that seen for elliptic flow and charged particle pseudorapidity density.     

Mössbauer spectroscopic investigations of Fe/Mn-Fischer-Tropsch-catalysts

The phase composition of Fe/Mn oxide catalysts of different compositions after 200 h of Fischer-Tropsch synthesis have been investigated by Mößbauer spectroscopy at room temperature, 77 K and 5 K. The final composition of the bulk catalysts depends strongly on the Mn content and the temperature of reduction before the synthesis. Catalytic activity and selectivity are partly correlated to this phase composition.     

The MaxMin value of stochastic games with imperfect monitoring

We study finite zero-sum stochastic games in which players do not observe the actions of their opponent. Rather, at each stage, each player observes a stochastic signal that may depend on the current state and on the pair of actions chosen by the players. We assume that each player observes the state and his/her own action. We prove that the uniform max-min value always exists. Moreover, the uniform max-min value is independent of the information structure of player 2. Symmetric results hold for the uniform min-max value. We deeply thank E. Lehrer, J.-F. Mertens, A. Neyman and S. Sorin. The discussions we had, and the suggestions they provided, were extremely useful. We acknowledge the financial support of the Arc-en-Ciel/Keshet program for 2001/2002. The research of the second author was supported by the Israel Science Foundation (grant No. 69/01-1).