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Search Results: 1 - 10 of 28018 matches for " Robert Patterson "
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Properties of the solutions of delocalised coagulation and inception problems with outflow boundaries
Robert I. A. Patterson
Mathematics , 2015,
Abstract: Well posedness is established for a family of equations modelling particle populations undergoing delocalised coagulation, advection, inflow and outflow in a externally specified velocity field. Very general particle types are allowed while the spatial domain is a bounded region of $d$-dimensional space for which every point lies on exactly one streamline associated with the velocity field. The problem is formulated as a semi-linear ODE in the Banach space of bounded measures on particle position and type space. A local Lipschitz property is established in total variation norm for the propagators (generalised semi-groups) associated with the problem and used to construct a Picard iteration that establishes local existence and global uniqueness for any initial condition. The unique weak solution is shown further to be a differentiable or at least bounded variation strong solution under smoothness assumptions on the parameters of the coagulation interaction. In the case of one spatial dimension strong differentiability is established even for coagulation parameters with a particular bounded variation structure in space. This one dimensional extension establishes the convergence of the simulation processes studied in [Patterson, Stoch. Anal. Appl. 31, 2013] to a unique and differentiable limit.
Chasing a Paper Tiger: Evaluating Buffalo’s Analysis of Impediments to Fair Housing Choice  [PDF]
Robert Mark Silvermam, Kelly L. Patterson, Jade Lewis
Current Urban Studies (CUS) , 2013, DOI: 10.4236/cus.2013.13004
Abstract: This article focuses on a specific component of the US Department of Housing and Urban Development’s (HUD’s) strategy to implement fair housing policy, its requirement for local jurisdictions that receive community development block grant (CDBG) dollars to prepare an analysis of impediments to fair housing choice (AI) report. The article’s analysis is based on an evaluation of the City of Buffalo’s 2004 AI report. The evaluation was conducted by a local fair housing organization in collaboration with university-based researchers. The findings from the evaluation revealed that the City had made little progress in implementing the action plan from its AI report over an eight year period. This was an outgrowth of local funding constraints, limited staff capacity, ambiguous HUD rules for AI reporting, and a lack of political will to pursue fair housing in Buffalo. In light of these findings, we recommend that HUD: mandate timeframes for AI implementation, require AI updates at regular intervals, and more clearly specify the format and content of AI reports. We also recommend that HUD require jurisdictions to include evaluation plans in their AI reports and measure outcomes from the implementation of AI action plans. These reforms will enhance the ability of AI reports to serve as effective planning tools for the affirmative furthering of fair housing policy.
Strong laws of large numbers for arrays of row-wise exchangeable random elements
Robert Lee Taylor,Ronald Frank Patterson
International Journal of Mathematics and Mathematical Sciences , 1985, DOI: 10.1155/s0161171285000126
Abstract: Let {Xnk,1 ¢ ‰ ¤k ¢ ‰ ¤n,n ¢ ‰ ¤1} be a triangular array of row-wise exchangeable random elements in a separable Banach space. The almost sure convergence of n ¢ ’1/p ¢ ‘k=1nXnk,1 ¢ ‰ ¤p<2, is obtained under varying moment and distribution conditions on the random elements. In particular, strong laws of large numbers follow for triangular arrays of random elements in(Rademacher) type p separable Banach spaces. Consistency of the kernel density estimates can be obtained in this setting.
Development of an Anatomically Realistic Forward Solver for Thoracic Electrical Impedance Tomography
Fei Yang,Jie Zhang,Robert Patterson
Journal of Medical Engineering , 2013, DOI: 10.1155/2013/983938
Abstract: Electrical impedance tomography (EIT) has the potential to provide a low cost and safe imaging modality for clinically monitoring patients being treated with mechanical ventilation. Variations in reconstruction algorithms at different clinical settings, however, make interpretation of regional ventilation across institutions difficult, presenting the need for a unified algorithm for thoracic EIT reconstruction. Development of such a consensual reconstruction algorithm necessitates a forward model capable of predicting surface impedance measurements as well as electric fields in the interior of the modeled thoracic volume. In this paper, we present an anatomically realistic forward solver for thoracic EIT that was built based on high resolution MR image data of a representative adult. Accuracy assessment of the developed forward solver in predicting surface impedance measurements by comparing the predicted and observed impedance measurements shows that the relative error is within the order of 5%, demonstrating the ability of the presented forward solver in generating high-fidelity surface thoracic impedance data for thoracic EIT algorithm development and evaluation. 1. Introduction Electrical impedance tomography (EIT) is a medical imaging technique in which an image of the conductivity distribution in a part of the body is inferred from surface electrical potentials resulting from application of a number of current patterns through the body. Because of its noninvasiveness, portability, and low cost, EIT has been actively investigated since the 1970s [1] and finds potential applications in a wide variety of clinical areas including monitoring of lung problems such as pulmonary edema [2] or pneumothorax [3], non-invasive monitoring of heart function and blood flow [4], localization of epileptic foci [5], investigating gastric emptying [6], and measuring local internal temperature increases associated with hyperthermia therapy [7]. Lately, similar technique has also been proposed for stenotic plaque detection [8]. Among those, one of the most promising applications of EIT is continuous regional pulmonary monitoring, especially for monitoring patients being treated with mechanical ventilation. Mechanical ventilation is indicated when the patient’s spontaneous ventilation is inadequate and is one of the most common interventions administered in intensive care. Mechanical ventilation can improve the prognosis for acute phase patients; however, it also often leads to potential complications such as ventilator-associated lung injury (VALI) and
On strong laws of large numbers for arrays of rowwise independent random elements
Abolghassem Bozorgnia,Ronald Frank Patterson,Robert Lee Taylor
International Journal of Mathematics and Mathematical Sciences , 1993, DOI: 10.1155/s0161171293000729
Abstract: Let {Xnk} be an array of rowwise independent random elements in a separable Banach space of type r, 1 ¢ ‰ ¤r ¢ ‰ ¤2. Complete convergence of n1/p ¢ ‘k=1nXnk to 0, 0 ±+1. An application to density estimation is also given.
Strong laws of large numbers for arrays of rowwise conditionally independent random elements
Ronald Frank Patterson,Abolghassem Bozorgnia,Robert Lee Taylor
International Journal of Stochastic Analysis , 1993, DOI: 10.1155/s1048953393000012
Abstract: Let {Xnk} be an array of rowwise conditionally independent random elements in a separable Banach space of type p, 1≤p≤2. Complete convergence of n 1r∑k=1nXnk to 0, 0
A Self-Localization Method for Wireless Sensor Networks
Robert M. Patterson,Dushyanth Krishnamurthy,Randolph L. Moses
EURASIP Journal on Advances in Signal Processing , 2003, DOI: 10.1155/s1687617203212063
Abstract: We consider the problem of locating and orienting a network of unattended sensor nodes that have been deployed in a scene at unknown locations and orientation angles. This self-calibration problem is solved by placing a number of source signals, also with unknown locations, in the scene. Each source in turn emits a calibration signal, and a subset of sensor nodes in the network measures the time of arrival and direction of arrival (with respect to the sensor node's local orientation coordinates) of the signal emitted from that source. From these measurements we compute the sensor node locations and orientations, along with any unknown source locations and emission times. We develop necessary conditions for solving the self-calibration problem and provide a maximum likelihood solution and corresponding location error estimate. We also compute the Cram r-Rao bound of the sensor node location and orientation estimates, which provides a lower bound on calibration accuracy. Results using both synthetic data and field measurements are presented.
Large deviations in relay-augmented wireless networks
Christian Hirsch,Benedikt Jahnel,Paul Keeler,Robert I. A. Patterson
Mathematics , 2015,
Abstract: We analyze a model of relay-augmented cellular wireless networks. The network users, who move according to a general mobility model based on a Poisson point process of continuous trajectories in a bounded domain, try to communicate with a base station located at the origin. Messages can be sent either directly or indirectly by relaying over a second user. We show that in a scenario of an increasing number of users, the probability that an atypically high number of users experiences bad quality of service over a certain amount of time, decays at an exponential speed. This speed is characterized via a constrained entropy minimization problem. Further, we provide simulation results indicating that solutions of this problem are potentially non-unique due to symmetry breaking. Also two general sources for bad quality of service can be detected, which we refer to as isolation and screening.
Large-deviation principles for connectable receivers in wireless networks
Christian Hirsch,Benedikt Jahnel,Paul Keeler,Robert I. A. Patterson
Mathematics , 2015,
Abstract: We study large-deviation principles for a model of wireless networks consisting of Poisson point processes of transmitters and receivers, respectively. To each transmitter we associate a family of connectable receivers whose signal-to-interference-and-noise ratio is larger than a certain connectivity threshold. First, we show a large-deviation principle for the empirical measure of connectable receivers associated with transmitters in large boxes. Second, making use of the observation that the receivers connectable to the origin form a Cox point process, we derive a large-deviation principle for the rescaled process of these receivers as the connection threshold tends to zero. Finally, we show how these results can be used to develop importance-sampling algorithms that substantially reduce the variance for the estimation of probabilities of certain rare events such as users being unable to connect
Effect of Winter Flooding on Weeds, Soybean Yield, Straw Degradation, and Soil Chemical and Biochemical Characteristics  [PDF]
Clifford H. Koger, Robert M. Zablotowicz, Mark A. Weaver, Melanie R. Tucker-Patterson, J. L. Krutz, Timothy W. Walker, Joe E. Street
American Journal of Plant Sciences (AJPS) , 2013, DOI: 10.4236/ajps.2013.47A2002
Abstract: Winter flooding of harvested rice fields attracts migratory waterfowl and may assist in degrading rice straw residue. Field studies were conducted between 2003 and 2005 in Stoneville, MS to evaluate the impacts of winter flooding of harvested rice fields on rice straw degradation, winter weeds, soybean yield, and soil biochemical and chemical properties. The experimental area each year consisted of a harvested rice field that remained no-till after harvest and that was dissected into 7.6- by 15-m bays with constructed levees to accommodate winter flooding treatments. Flooding treatments (10-cm depth) consisted of: 1) flooded from mid-October to early March; 2) flooded mid-October to early January; 3) flooded mid-December to early March; 4) flooded mid-December to mid-January; and 5) no flood. Winter weeds were counted, biomass determined as well as residual rice straw before flooding and in early April of each year. Winter flooding reduced rice straw biomass 32% to 60% compared to 21% to 31% reduction for no winter flood with the longest flood duration resulting in the greatest loss of carbon and nitrogen from straw residues in both years. Winter flooding treatments reduced weed populations and weed biomass from 43% to 99% when compared to no flooding treatment. Soybean yields ranged from 3295 kg.ha-1 with the longest winter flooding regime to 4295 kg.ha-1 with no flooding. Significant reductions in soil nitrate levels were most consistent in the upper 0 to 2.5-cm surface soil. Soil enzymatic activity (dehydrogenase and fluorescein diacetate hydrolysis) was increased by flooding in 2003, while minimal effects were found in the second year consistent with more anaerobic conditions attained in 2003 compared to 2004. Environmental benefits of accelerated straw decomposition and weed control is achieved by winter flooding; however, there are negative consequences of nitrogen losses and reduced soybean yield.
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