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Computer Engineering Commons

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2011

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Articles 481 - 510 of 789

Full-Text Articles in Computer Engineering

Enhancing Simulation Composability And Interoperability Using Conceptual/Semantic/Ontological Models, Andreas Tolk, John A. Miller Jan 2011

Enhancing Simulation Composability And Interoperability Using Conceptual/Semantic/Ontological Models, Andreas Tolk, John A. Miller

Computational Modeling & Simulation Engineering Faculty Publications

(First paragraph) Two emerging trends in Modeling and Simulation (M&S) are beginning to dovetail in a potentially highly productive manner, namely conceptual modeling and semantic modeling. Conceptual modeling has existed for several decades, but its importance has risen to the forefront in the last decade (Taylor and Robinson, 2006; Robinson, 2007). Also, during the last decade, progress on the Semantic Web has begun to influence M&S, with the development of general modeling ontologies (Miller et al, 2004), as well as ontologies for modeling particular domains (Durak, 2006). An ontology, which is a formal specification of a conceptualization (Gruber et al, …


Software Reuse For Modeling And Simulation, Emily Andrew, Charles D. Turnitsa, Andreas Tolk Jan 2011

Software Reuse For Modeling And Simulation, Emily Andrew, Charles D. Turnitsa, Andreas Tolk

Computational Modeling & Simulation Engineering Faculty Publications

In Modeling and Simulation, as a distinct area of software engineering, there is much interest in being able to reuse software components. However, the practice of simulation development and maintenance is different from software engineering because of several factors. In this paper, a brief overview of the foundations of interoperability, and how they apply to the reuse of model based software is explored, as well as examination of current practices to include M&S software repositories. Some recommendations, based on research at the Virginia Modeling Analysis and Simulation Center (VMASC) and practice at the Raytheon Company Network Centric Services, are made.


Executable Architecture Research At Old Dominion University, Andreas Tolk, Johnny J. Garcia, Edwin A. Shuman Jan 2011

Executable Architecture Research At Old Dominion University, Andreas Tolk, Johnny J. Garcia, Edwin A. Shuman

Computational Modeling & Simulation Engineering Faculty Publications

Executable Architectures allow the evaluation of system architectures not only regarding their static, but also their dynamic behavior. However, the systems engineering community do not agree on a common formal specification of executable architectures. To close this gap and identify necessary elements of an executable architecture, a modeling language, and a modeling formalism is topic of ongoing PhD research. In addition, systems are generally defined and applied in an operational context to provide capabilities and enable missions. To maximize the benefits of executable architectures, a second PhD effort introduces the idea of creating an executable context in addition to the …


Data Mining Based Learning Algorithms For Semi-Supervised Object Identification And Tracking, Michael P. Dessauer Jan 2011

Data Mining Based Learning Algorithms For Semi-Supervised Object Identification And Tracking, Michael P. Dessauer

Doctoral Dissertations

Sensor exploitation (SE) is the crucial step in surveillance applications such as airport security and search and rescue operations. It allows localization and identification of movement in urban settings and can significantly boost knowledge gathering, interpretation and action. Data mining techniques offer the promise of precise and accurate knowledge acquisition techniques in high-dimensional data domains (and diminishing the “curse of dimensionality” prevalent in such datasets), coupled by algorithmic design in feature extraction, discriminative ranking, feature fusion and supervised learning (classification). Consequently, data mining techniques and algorithms can be used to refine and process captured data and to detect, recognize, classify, …


Protection Models For Web Applications, Karthick Jayaraman Jan 2011

Protection Models For Web Applications, Karthick Jayaraman

Electrical Engineering and Computer Science - Dissertations

Early web applications were a set of static web pages connected to one another. In contrast, modern applications are full-featured programs that are nearly equivalent to desktop applications in functionality. However, web servers and web browsers, which were initially designed for static web pages, have not updated their protection models to deal with the security consequences of these full-featured programs. This mismatch has been the source of several security problems in web applications.

This dissertation proposes new protection models for web applications. The design and implementation of prototypes of these protection models in a web server and a web browser …


Designing, Understanding, And Analyzing Unconventional Computation: The Important Role Of Logic And Constructive Mathematics, Vladik Kreinovich Jan 2011

Designing, Understanding, And Analyzing Unconventional Computation: The Important Role Of Logic And Constructive Mathematics, Vladik Kreinovich

Departmental Technical Reports (CS)

In this paper, we explain why, in our opinion, logic and constructive mathematics are playing -- and should play -- an important role in the design, understanding, and analysis of unconventional computation.


Towards A General Description Of Translation-Invariant And Translation-Covariant Linear Transformations: A Natural Justification Of Fourier Transforms And Fuzzy Transforms, Irina Perfilieva, Vladik Kreinovich Jan 2011

Simulation, Application, And Resilience Of An Organic Neuromorphic Architecture, Made With Organic Bistable Devices And Organic Field Effect Transistors, Robert A. Nawrocki Jan 2011

Simulation, Application, And Resilience Of An Organic Neuromorphic Architecture, Made With Organic Bistable Devices And Organic Field Effect Transistors, Robert A. Nawrocki

Electronic Theses and Dissertations

This thesis presents work done simulating a type of organic neuromorphic architecture, modeled after Artificial Neural Network, and termed Synthetic Neural Network, or SNN. The first major contribution of this thesis is development of a single-transistor-single-organic-bistable-device-per-input circuit that approximates behavior of an artificial neuron. The efficacy of this design is validated by comparing the behavior of a single synthetic neuron to that of an artificial neuron as well as two examples involving a network of synthetic neurons. The analysis utilizes electrical characteristics of polymer electronic elements, namely Organic Bistable Device and Organic Field Effect Transistor, created in the laboratory at …


Video Stabilization Using Sift Features, Fuzzy Clustering, And Kalman Filtering, Kevin Veon Jan 2011

Video Stabilization Using Sift Features, Fuzzy Clustering, And Kalman Filtering, Kevin Veon

Electronic Theses and Dissertations

Video stabilization removes unwanted motion from video sequences, often caused by vibrations or other instabilities. This improves video viewability and can aid in detection and tracking in computer vision algorithms. We have developed a digital video stabilization process using scale-invariant feature transform (SIFT) features for tracking motion between frames. These features provide information about location and orientation in each frame. The orientation information is generally not available with other features, so we employ this knowledge directly in motion estimation. We use a fuzzy clustering scheme to separate the SIFT features representing camera motion from those representing the motion of moving …


Reference Set Metrics For Multi-Objective Algorithms, Chilukuri K. Mohan, Kishan Mehrotra Jan 2011

Reference Set Metrics For Multi-Objective Algorithms, Chilukuri K. Mohan, Kishan Mehrotra

Electrical Engineering and Computer Science - All Scholarship

Several metrics and indicators have been suggested in the past to evaluate multi-objective evolutionary and non-evolutionary algo- rithms. However, these metrics are known to have many problems that make their application sometimes unsound, and sometimes infeasible. This paper proposes a new approach, in which metrics are parameter- ized with respect to a reference set, on which depend the properties of any metric.


Ua3/9/2 I.T. Division Annual Report + Tactical Plan, Wku Information Technology Jan 2011

Ua3/9/2 I.T. Division Annual Report + Tactical Plan, Wku Information Technology

WKU Administration Documents

Annual report of WKU Information Technology Division submitted to WKU President Gary Ransdell. Report is housed in UA3/9/2 Subject Files.


Furthering The Growth Of Cloud Computing By Providing Privacy As A Service, David S. Allison, Miriam Am Capretz Jan 2011

Furthering The Growth Of Cloud Computing By Providing Privacy As A Service, David S. Allison, Miriam Am Capretz

Electrical and Computer Engineering Publications

The evolution of Cloud Computing as a viable business solution for providing hardware and software has created many security concerns. Among these security concerns, privacy is often overlooked. If Cloud Computing is to continue its growth, this privacy concern will need to be addressed. In this work we discuss the current growth of Cloud Computing and the impact the public sector and privacy can have in furthering this growth. To begin to provide privacy protection for Cloud Computing, we introduce privacy constraints that outline privacy preferences. We propose the expansion of Cloud Service Level Agreements (SLAs) to include these privacy …


An Empirical Study Of Open Source Software Usability: The Industrial Perspective, Arif Raza, Luiz Fernando Capretz, Faheem Ahmed Jan 2011

An Empirical Study Of Open Source Software Usability: The Industrial Perspective, Arif Raza, Luiz Fernando Capretz, Faheem Ahmed

Electrical and Computer Engineering Publications

Recent years have seen a sharp increase in the use of open source projects by common novice users; Open Source Software (OSS) is thus no longer a reserved arena for software developers and computer gurus. Although user-centered designs are gaining popularity in OSS, usability is still not considered as one of the prime objectives in many design scenarios. In this paper, we analyze industry users’ perception of usability factors, including understandability, learnability, operability and attractiveness, on OSS usability. The research model of this empirical study establishes the relationship between the key usability factors and OSS usability from industrial perspective. In …


A Midsummer Night’S Dream (With Flying Robots), Robin Murphy, Dylan Shell, Amy Guerin, Brittany Duncan, Benjamin Fine, Kevin Pratt, Takis Zourntos Jan 2011

A Midsummer Night’S Dream (With Flying Robots), Robin Murphy, Dylan Shell, Amy Guerin, Brittany Duncan, Benjamin Fine, Kevin Pratt, Takis Zourntos

School of Computing: Faculty Publications

Seven flying robot “fairies” joined human actors in the Texas A&M production of William Shakespeare’s A Midsummer Night’s Dream. The production was a collaboration between the departments of Computer Science and Engineering, Electrical and Computer Engineering, and Theater Arts. The collaboration was motivated by two assertions. First, that the performing arts have principles for creating believable agents that will transfer to robots. Second, the theater is a natural testbed for evaluating the response of untrained human groups (both actors and the audience) to robots interacting with humans in shared spaces, i.e., were believable agents created? The production used two types …


Performance Analysis Of Mimo-Sess With Alamouti Scheme Over Rayleigh Fading Channels, Shichuan Ma, Lim Nguyen, Yaoqing Lamar Yang, Won Mee Jang Jan 2011

Performance Analysis Of Mimo-Sess With Alamouti Scheme Over Rayleigh Fading Channels, Shichuan Ma, Lim Nguyen, Yaoqing Lamar Yang, Won Mee Jang

Department of Electrical and Computer Engineering: Faculty Publications

Self-encoded spread spectrum (SESS) is a novel modulation technique that acquires its spreading sequence from the random input data stream rather than through the use of the traditional pseudo-noise code generator. It has been incorporated with multiple-input multiple-output (MIMO) systems as a means to combat fading in wireless channels. In this paper, we present the analytical study of the bit-error rate (BER) performance of MIMO-SESS systems under Rayleigh fading. The BER expressions are derived in closed form, and the veracity of the analysis is confirmed by numerical calculations that demonstrate excellent agreement with simulation results. The performance analysis shows that …


All-Dielectric Invisibility Cloaks Made Of Batio3-Loaded Polyurethane Foam, Di Bao, Khalid Z. Rajab, Yang Hao, Efthymios Kallos, Wenxuan Tang, Christos Argyropoulos, Yongzhe Piao, Shoufeng Yang Jan 2011

All-Dielectric Invisibility Cloaks Made Of Batio3-Loaded Polyurethane Foam, Di Bao, Khalid Z. Rajab, Yang Hao, Efthymios Kallos, Wenxuan Tang, Christos Argyropoulos, Yongzhe Piao, Shoufeng Yang

Department of Electrical and Computer Engineering: Faculty Publications

Transformation optics has led the way in the development of electromagnetic invisibility cloaks from science fiction to engineering practice. Invisibility cloaks have been demonstrated over a wide range of the electromagnetic spectrum, and with a variety of different fabrication techniques. However, all previous schemes have relied on the use of metamaterials consisting of arrays of sub-wavelength inclusions. We report on the first cloaking structure made of a high-k dielectric-loaded foam mixture. A polyurethane foam mixed with different ratios of barium titanate is used to produce the required range of permittivities, and the invisibility cloak is demonstrated to work for all …


Battery Capacity Footprinting And Optimization Analysis For Wireless Multimedia Communication, Jianxin Sun, Dalei Wu, Song Ci Jan 2011

Battery Capacity Footprinting And Optimization Analysis For Wireless Multimedia Communication, Jianxin Sun, Dalei Wu, Song Ci

Department of Electrical and Computer Engineering: Faculty Publications (to 2015)

Micro-electronic industry has been boosting the capability of wireless mobile devices on full-scale. However, battery, as the only power source of most mobile devices, is experiencing a relatively slow development. Therefore, how to optimally utilize the limited battery energy on mobile devices under a predefined performance requirement becomes a critical issue. On the other hand, it is still unclear that how the battery capacity consumption is allocated on different working pattern of a specific video codec under various tempo-spatial scales and parameters, which has posed a design challenge on power management on multimedia communication system. Furthermore, an optimization method is …


Distributed Mimo Technologies In Cooperative Wireless Networks, Shichuan Ma, Yaoqing (Lamar) Yang, Hamid Sharif Jan 2011

Distributed Mimo Technologies In Cooperative Wireless Networks, Shichuan Ma, Yaoqing (Lamar) Yang, Hamid Sharif

Department of Electrical and Computer Engineering: Faculty Publications (to 2015)

Multiple-input multiple-output techniques enhance wireless communications performance by taking advantage of spatial diversity. However, most traditional MIMO systems hardly achieve large spatial diversity because of limited terminal size. In this article, we present recent advances of the distributed MIMO technologies in cooperative wireless networks. We also compare and discuss various relay protocols and cooperative strategies. Our simulation results indicate that distributed MIMO systems can provide larger spatial diversity, and the data rate in cooperative networks can be significantly increased.


Video Surveillance Over Wireless Sensor And Actuator Networks Using Active Cameras, Dalei Wu, Song Ci, Haiyan Luo, Yun Ye, Haohong Wang Jan 2011

Video Surveillance Over Wireless Sensor And Actuator Networks Using Active Cameras, Dalei Wu, Song Ci, Haiyan Luo, Yun Ye, Haohong Wang

Department of Electrical and Computer Engineering: Faculty Publications (to 2015)

Although there has been much work focused on the camera control issue on keeping tracking a target of interest, few has been done on jointly considering the video coding, video transmission, and camera control for effective and efficient video surveillance over wireless sensor and actuator networks (WSAN). In this work, we propose a framework for real-time video surveillance with pan-tilt cameras where the video coding and transmission as well as the automated camera control are jointly optimized by taking into account the surveillance video quality requirement and the resource constraint of WSANs. The main contributions of this work are: i) …


Transparent Interconnections Formed By Rapid Single-Step Fabrication Of Graphene Patterns, J. B. Park, W. Xiong, Z. Q. Xie, Y. Gao, M. Qian, M. Mitchell, M. Mahjouri-Samani, Y. S. Zhou, L. Jiang, Yongfeng Lu Jan 2011

Transparent Interconnections Formed By Rapid Single-Step Fabrication Of Graphene Patterns, J. B. Park, W. Xiong, Z. Q. Xie, Y. Gao, M. Qian, M. Mitchell, M. Mahjouri-Samani, Y. S. Zhou, L. Jiang, Yongfeng Lu

Department of Electrical and Computer Engineering: Faculty Publications

We developed a process to form transparent interconnections using graphene patterns that were synthesized by laser chemical vapor deposition. The number of graphene layers was tightly controlled by laser scan speed. Graphene patterns were fabricated at a high scan speed of up to 200 µm/s with a single-step process. The process time is about a million times faster than the conventional chemical vapor deposition method. The fabricated graphene patterns on nickel foils were directly transferred to desired positions on patterned electrodes. The position-controlled transfer with rapid single-step fabrication of graphene patterns provides an innovative pathway for graphene-based interconnections.


Fast Growth Of Graphene Patterns By Laser Direct Writing, J. B. Park, W. Xiong, Y. Gao, M. Qian, Z. Q. Xie, M. Mitchell, Y. S. Zhou, G. H. Han, L. Jiang, Yongfeng Lu Jan 2011

Fast Growth Of Graphene Patterns By Laser Direct Writing, J. B. Park, W. Xiong, Y. Gao, M. Qian, Z. Q. Xie, M. Mitchell, Y. S. Zhou, G. H. Han, L. Jiang, Yongfeng Lu

Department of Electrical and Computer Engineering: Faculty Publications

Rapid single-step fabrication of graphene patterns was developed using laser-induced chemical vapor deposition (LCVD). A laser beam irradiates a thin nickel foil in a CH4 and H2 environment to induce a local temperature rise, thereby allowing the direct writing of graphene patterns in precisely controlled positions at room temperature. Line patterns can be achieved with a single scan without pre- or post-processes. Surprisingly, the growth rate is several thousand times faster than that of general CVD methods. The discovery and development of the LCVD growth process provide a route for the rapid fabrication of graphene patterns for various …


Small Molecule Inhibitors Of Staphylococcus Aureus Rnpa Alter Cellular Mrna Turnover, Exhibit Antimicrobial Activity, And Attenuate Pathogenesis, Patrick D. Olson, Lisa J. Kuechenmeister, Kelsi L. Anderson, Sonja Daily, Karen E. Beenken, Christelle M. Roux, Michelle L. Reniere, Tami L. Lewis, William J, Weiss, Mark Pulse, Phung Nguyen, Jerry W. Simecka, John M. Morrison, Khalid Sayood, Oluwatoyin A. Asojo, Mark S. Smeltzer, Eric P. Skaar, Paul M. Dunman Jan 2011

Small Molecule Inhibitors Of Staphylococcus Aureus Rnpa Alter Cellular Mrna Turnover, Exhibit Antimicrobial Activity, And Attenuate Pathogenesis, Patrick D. Olson, Lisa J. Kuechenmeister, Kelsi L. Anderson, Sonja Daily, Karen E. Beenken, Christelle M. Roux, Michelle L. Reniere, Tami L. Lewis, William J, Weiss, Mark Pulse, Phung Nguyen, Jerry W. Simecka, John M. Morrison, Khalid Sayood, Oluwatoyin A. Asojo, Mark S. Smeltzer, Eric P. Skaar, Paul M. Dunman

Department of Electrical and Computer Engineering: Faculty Publications

Methicillin-resistant Staphylococcus aureus is estimated to cause more U.S. deaths annually than HIV/AIDS. The emergence of hypervirulent and multidrug-resistant strains has further amplified public health concern and accentuated the need for new classes of antibiotics. RNA degradation is a required cellular process that could be exploited for novel antimicrobial drug development. However, such discovery efforts have been hindered because components of the Gram-positive RNA turnover machinery are incompletely defined. In the current study we found that the essential S. aureus protein, RnpA, catalyzes rRNA and mRNA digestion in vitro. Exploiting this activity, high through-put and secondary screening assays identified …


A Novel Adaptive Distributed Cooperative Relaying Mac Protocol For Vehicular Networks, Ting Zhou, Hamid Sharif, Michael Hempel, Puttipong Mahasukhon, Wei Wang, Tao Ma Jan 2011

A Novel Adaptive Distributed Cooperative Relaying Mac Protocol For Vehicular Networks, Ting Zhou, Hamid Sharif, Michael Hempel, Puttipong Mahasukhon, Wei Wang, Tao Ma

Department of Electrical and Computer Engineering: Faculty Publications (to 2015)

Explosive growth in Information Technology has enabled many innovative application areas such as large-scale outdoor vehicular networks for vehicle-to-vehicle communications. By providing time-sensitive and location-aware information, vehicular networks can contribute to a safer and more efficient driving experience. However, the performance of vehicular networks requires robust and real-time data communications and is impacted by high mobility, intermittent connectivity, and unreliability of the wireless channel. In this paper, a novel adaptive distributed cooperative medium access control (ADCMAC) protocol is proposed in order to address the inherent problems in the IEEE 802.11 standard when employed in vehicular networks. ADC-MAC exploits spatial diversities …


Quantitative Analysis Of Propagation Characteristics For Mobile Wimax, Pradhumna Shrestha, Puttipong Mahasukhon, Michael Hempel, Tao Ma, Hamid Sharif Jan 2011

Quantitative Analysis Of Propagation Characteristics For Mobile Wimax, Pradhumna Shrestha, Puttipong Mahasukhon, Michael Hempel, Tao Ma, Hamid Sharif

Department of Electrical and Computer Engineering: Faculty Publications (to 2015)

In wireless networks, careful planning and link budget analysis is required for delivering maximum throughput reliably with minimum overhead. The efficiency of planning and eventual network performance is totally dependent upon the accuracy and quality of data used for analysis. In most studies, computer simulations and analytical models are used for generating such data. However these simulations are limited to many assumptions which are different from the actual implemented hardware, therefore, the data generated are not accurate. In this paper, we analyze the performance of Mobile WiMAX utilizing the empirical data measured from leading WiMAX equipment. We believe this data …


Power Controlled Coded-Sequence Self-Encoded Spread Spectrum Communications, Poomathi Duraisamy, Liang Chi, Won Mee Jang, Lim Nguyen Jan 2011

Power Controlled Coded-Sequence Self-Encoded Spread Spectrum Communications, Poomathi Duraisamy, Liang Chi, Won Mee Jang, Lim Nguyen

Department of Electrical and Computer Engineering: Faculty Publications (to 2015)

In this paper, we propose to apply power control to coded-sequence self-encoded spread spectrum (CS-SESS) communications in dynamic fading channels. We determine the statistical characteristics of the power enhancement in the transmitter due to power control and show that the proposed approach improves the power efficiency in mobile cellular systems.

In addition, we propose to mitigate self interference in CSSESS by exploiting the information that the transmitter obtains, through feedback training sequences, about the de-spreading code in the receiver. The results show that the mitigation is significant even with only selective training chips from the de-spreading sequence. Similar improvement can …


A Study On Energy Efficient Multi-Tier Multi-Hop Wireless Sensor Networks For Freight-Train Monitoring, Puttipong Mahasukhon, Hamid Sharif, Michael Hempel, Ting Zhou, Tao Ma, Pradhumna Shrestha Jan 2011

A Study On Energy Efficient Multi-Tier Multi-Hop Wireless Sensor Networks For Freight-Train Monitoring, Puttipong Mahasukhon, Hamid Sharif, Michael Hempel, Ting Zhou, Tao Ma, Pradhumna Shrestha

Department of Electrical and Computer Engineering: Faculty Publications (to 2015)

The North American freight railroad industry is trying to leverage wireless sensor networks (WSN) onboard railcars for advanced monitoring and alerting. In railroad environments, freight train WSNs exhibit a linear chain-like topology of significant length. Thus, existing wireless technologies such as the IEEE 802.15.4 communication protocol, based on a star topology, are unable to provide reliable service. The end-to-end communication between nodes generally relies on individual nodes communicating with their respective neighbors to carry the information over multiple hops and deliver it to the preferred destination. The routing performance and reliability significantly degrades with increasing number of hops. We proposed …


A High-Quality Mach-Zehnder Interferometer Fiber Sensor By Femtosecond Laser One-Step Processing, Longjiang Zhao, Lan Jiang, Sumei Wang, Hai Xiao, Yongfeng Lu, Hai-Lung Tsai Jan 2011

A High-Quality Mach-Zehnder Interferometer Fiber Sensor By Femtosecond Laser One-Step Processing, Longjiang Zhao, Lan Jiang, Sumei Wang, Hai Xiao, Yongfeng Lu, Hai-Lung Tsai

Department of Electrical and Computer Engineering: Faculty Publications

During new fiber sensor development experiments, an easy-to-fabricate simple sensing structure with a trench and partially ablated fiber core is fabricated by using an 800 nm 35 fs 1 kHz laser. It is demonstrated that the structure forms a Mach-Zehnder interferometer (MZI) with the interference between the laser light passing through the air in the trench cavity and that in the remained fiber core. The fringe visibilities are all more than 25 dB. The transmission spectra vary with the femtosecond (fs) laser ablation scanning cycle. The free spectral range (FSR) decreases as the trench length increases. The MZI structure is …


A Web Application For Financial Trading Simulation, Li-Chiou Chen, Lixin Tao, Padma Kadiyala Jan 2011

A Web Application For Financial Trading Simulation, Li-Chiou Chen, Lixin Tao, Padma Kadiyala

Cornerstone 3 Reports : Interdisciplinary Informatics

No abstract provided.


Pwisegen: Generating Test Cases For Pairwise Testing Using Genetic Algorithms, Pedro Flores, Yoonsik Cheon Jan 2011

Towards Optimal Few-Parametric Representation Of Spatial Variation: Geometric Approach And Environmental Applications, Misha Kosheleva, Octavio Lerma, Craig Tweedie Jan 2011

Towards Optimal Few-Parametric Representation Of Spatial Variation: Geometric Approach And Environmental Applications, Misha Kosheleva, Octavio Lerma, Craig Tweedie

Departmental Technical Reports (CS)

In this paper, we use geometric approach to showthat under reasonable assumption, the spatialvariability of a field f(x), i.e., the expectedvalue F(z)=E[(f(x+z)-f(x))2], has the formF(z)=|Σ gij*zi*zj|α.We explain how to find gij and αfrom the observations, and how to optimally place sensorsin view of this spatial variability.