Modeling Spatially Correlated Data in Sensor Networks

Size: px
Start display at page:

Download "Modeling Spatially Correlated Data in Sensor Networks"

Transcription

1 Modeling Spatially Coelated Data in Senso Netwoks Apoova Jindal and Konstantinos Psounis Univesity of Southen Califonia The physical phenomena monitoed by senso netwoks, e.g. foest tempeatue, wate contamination, usually yield sensed data that ae stongly coelated in space. With this in mind, eseaches have designed a lage numbe of senso netwok potocols and algoithms that attempt to exploit such coelations. To caefully study the pefomance of these algoithms, thee is an inceasing need to synthetically geneate lage taces of spatially coelated data epesenting a wide ange of conditions. Futhe, a mathematical model fo geneating synthetic taces would povide guidelines fo designing moe efficient algoithms. These easons motivate us to obtain a simple and accuate model of spatially coelated senso netwok data. The poposed model is Makovian in natue and can captue coelation in data iespective of the node density, the numbe of souce nodes o the topology. We descibe a igoous mathematical pocedue and a simple pactical method to extact the model paametes fom eal taces. We also show how to efficiently geneate synthetic taces on a given topology using these paametes. The coectness of the model is veified by statistically compaing synthetic and eal data. Futhe, the model is validated by compaing the pefomance of algoithms whose behavio depends on the degee of spatial coelation in data, unde eal and synthetic taces. The eal taces ae obtained fom emote sensing data, publicly available senso data, and senso netwoks that we deploy. We show that the poposed model is moe geneal and accuate than the commonly used jointly Gaussian model. Finally, we ceate tools that can be easily used by eseaches to synthetically geneate taces of any size and degee of coelation. Categoies and Subject Desciptos: C.4 [Pefomance of Systems]: Modeling Techniques; I.6.5 [Simulation and Modeling]: Model Development-Modeling Methodologies Geneal Tems: Pefomance Additional Key Wods and Phases: Spatial Coelation, Modeling of Physical Envionment, Wieless Senso Netwoks, Geneating Synthetic Data. INTRODUCTION The wieless senso netwoks of the nea futue ae envisioned to consist of a lage numbe of inexpensive wieless nodes. These nodes will opeate unde significant powe constaints, which pecludes them fom using lage tansmission anges. This, togethe with the low cost of individual sensos, implies that sensos will A peliminay vesion of this pape has appeaed in the Poceedings of the IEEE Intenational Confeence on Senso and Ad hoc Communications and Netwoks (SECON 5), Sep. 25. Autho s Addess: A. Jindal and K. Psounis, Depatment of Electical Engineeing, Univesity of Southen Califonia, Los Angeles, CA 989; apoovaj, kpsounis@usc.edu. Pemission to make digital/had copy of all o pat of this mateial without fee fo pesonal o classoom use povided that the copies ae not made o distibuted fo pofit o commecial advantage, the ACM copyight/seve notice, the title of the publication, and its date appea, and notice is given that copying is by pemission of the ACM, Inc. To copy othewise, to epublish, to post on seves, o to edistibute to lists equies pio specific pemission and/o a fee. c 26 ACM /26/7- $5. ACM Tansactions on Senso Netwoks, Vol. V, No. N, July 26, Pages 35.

2 2 A. Jindal and K. Psounis be densely deployed. As a esult, it is expected that a high degee of spatial coelation will exist in the senso netwok data. Many algoithms have been poposed that exploit this coelation. Fo example, spatial coelation has been used in data aggegation and outing algoithms [Goel and Estin 23], [Pattem et al. 24], [Intanagonwiwat et al. 22], [Kishnamachai et al. 22], data stoage and queying [Deshpande et al. 24], [Ganesan et al. 22], [Ganesan et al. 23], [Fauque and Helmy 24], senso selection [L.Dohety and K.Piste 24], [Cistescu and Vetteli 25], MAC potocol design [Vuan and Akyildiz 26], data compession and encoding [Chou et al. 22], and calibation [Whitehouse and Culle 22]. The evaluation of potocols that ae sensitive to the spatial featues of input data equies data epesenting a wide ange of ealistic conditions. Howeve, since vey few eal systems have been deployed, thee is hadly any expeimental data available to test the poposed algoithms. As a esult, senso netwok eseaches make diffeent assumptions when geneating data inputs to evaluate systems; some assume the data to be jointly Gaussian with the coelation being a function of the distance [Deshpande et al. 24], [Cistescu and Vetteli 25], [Vuan and Akyildiz 26], some assume that the data follows the diffusion popety [Fauque and Helmy 24], and some assume a function fo the joint entopy of the data [Pattem et al. 24]. Othe eseaches popose the use of envionmental monitoing data obtained fom emote sensing [Ganesan et al. 22], howeve the ganulaity of these data sets do not match the expected ganulaity of senso netwoks data. Anothe model which can be used to model data dependencies in senso netwoks data is the Makov andom field (MRF) model [Li 2]. MRF s wee poposed in image pocessing to model dependent andom vaiables such as image pixels and coelated featues. But the MRF model equies a desciption of the joint statistics of the data. Using such a model in its geneality is quite cumbesome and, in pactice, vey had to tack analytically. The goal of this pape is to come up with a pasimonious mathematical model that can captue spatial coelation of any degee iespective of the ganulaity, density, numbe of souce nodes o topology. We want the model to be simple than existing complicated models fo two dimensional coelations, like the MRF model, and yet to accuately epesent eality. To keep it simple, we want ou model paametes to depend only on the fist ode statistic and the second ode moments. It should be noted that a jointly Gaussian model is completely defined by the fist and the second ode moments and hence is petty tactable. But, it is not a vey accuate model as shown in [Yu et al. 24]. On the othe hand, we will show that ou model, inspite of being defined by the fist ode statistic and second ode moments, captues the spatial coelation chaacteistics of senso netwok data. Thee ae many benefits fom such a model. Fist, the model will povide a pocedue to synthetically geneate senso netwoks data without having to collect eal taces fist. By vaying the model paametes, one can ceate taces with vaious degees of coelation, thus enabling a meticulous study of the pefomance of poposed algoithms. Second, it will enable diffeent eseaches to evaluate diffeent algoithms using a common tace geneation method, which, in tun, will make compaisons between diffeent algoithms meaningful. In othe wods, the ACM Tansactions on Senso Netwoks, Vol. V, No. N, July 26.

3 Modeling Spatially Coelated Data in Senso Netwoks 3 model can seve as a benchmak. Thid, since the model is analytically tactable, it can be used to analyze and bound the pefomance of algoithms. Thus, it can povide guidelines fo designing optimal algoithms. Fouth, it can be used to geneate lage synthetic taces having the same coelation stuctue as an input eal tace. The model poposed in this pape is a special case of Makov andom fields but is much simple and yet petty accuate. It is simila in flavo to the model poposed in [Psounis et al. 24] (which poposed a model to captue tempoal coelation in web taces). A igoous mathematical pocedue and a simple pactical method to extact the model paametes fom eal taces is povided. A method to efficiently geneate synthetic taces on a given topology using these paametes is also descibed, and publicly available tace geneation tools ae ceated. Futhe, it is shown that the jointly Gaussian model, which is commonly used fo spatially coelated data [Vuan and Akyildiz 26], [Cistescu and Vetteli 25], [Maco et al. 23], [Deshpande et al. 24], is a subcase of ou moe geneal and moe accuate model. The model is veified by compaing the statistics of the eal taces and the coesponding synthetic taces. Since the poposed model will be used to evaluate and compae diffeent algoithms which exploit spatial coelation in data, the model is validated by compaing the pefomance of such algoithms. We use two well known algoithms, DIMENSIONS [Ganesan et al. 22] and CC-MAC [Vuan and Akyildiz 26] fo this pupose. We use publicly available emote sensing taces, publicly available senso netwok taces, and taces collected fom senso netwoks that we deploy. The inte-node distance fo emote sensing data is hunded of metes while fo the taces collected using a senso netwok, this distance is of the ode of a few metes. These taces veify that the poposed model is valid iespective of the ganulaity of data. The pape is oganized as follows. Section 2 intoduces the vaiogam, which is a handy metic to chaacteize spatial coelation in data. Section 2.2 studies the coelation stuctue of a eal tace using vaiogams to come up with an intuition about the stuctue of the model. The model is fomally pesented in Section 3, followed by a mathematically igoous pocedue, and a simple, pactical method to infe the model paametes in Section 4. The coectness of the model is veified by compaing the statistics of the oiginal and synthetic taces in Section 5.2. In Section 5.3, the accuacy of the model is validated by compaing the pefomance of vaious algoithms against eal and the coesponding synthetic taces. Section 6 discusses the elated wok to put ou contibutions in context. In this section, we also show that ou model is moe geneal than the jointly Gaussian model (which is the most popula model in the senso netwok community). In Section 7, we evisit ou chief assumptions in an effot to undestand how geneal is the poposed model. Finally, Section 8 descibes the tace-geneation tools and Section 9 concludes the wok. 2. VARIOGRAM: A STATISTIC TO MEASURE CORRELATION IN DATA A statistic often used to chaacteize spatial coelation in data is the vaiogam [Yu et al. 23], [Rahimi et al. 24], [Kagupta et al. 23]. Given a two dimensional ACM Tansactions on Senso Netwoks, Vol. V, No. N, July 26.

4 4 A. Jindal and K. Psounis stationay pocess V (x, y), the vaiogam (also called semivaiance) is defined as γ(, 2 )= 2 E[(V (x, y) V (x +,y+ 2 )) 2 ]. () Fo isotopic andom pocesses [Olea 999] the vaiogam depends only on the distance = between two nodes (as opposed to anisotopic pocesses in which the vaiogam depends on both distance and diection). In this case, if (x,y ) denotes a point which is distance away fom (x, y), γ() = 2 E[(V (x, y) V (x,y )) 2 ], (2) whee (x x ) 2 +(y y ) 2 = 2. Fo a set of samples v(x i,y i ) i =, 2,... on a egula gid, γ() can be estimated as follows: γ () = m() [v(x i,y i ) v(x j,y j )] 2, (3) 2m() whee m() is the numbe of points at a distance within each othe, i.e. the sum is ove all points fo which (x i x j ) 2 +(y i y j ) 2 = 2. A staightfowad method to estimate the vaiogam fo a set of samples on an iegula gid consists of the following steps: (i) fo evey pai of samples, compute the distance between them and the squaed diffeence between thei data values, (ii) make a scatte plot of the vaiogam values against the distance, and (iii) cuve fit the scatte plot to obtain an estimate of the vaiogam. A moe statistically obust method, taditionally used in Geostatistics [Olea 999], [Goovaets 997], [Cessie 993] consists of the following steps: (i) as befoe, fo evey pai of samples compute the distance between them and the squaed diffeence between thei data values, (ii) divide the entie ange of distance into discete intevals with an inteval size being equal to the aveage distance to the neaest neighbo, (iii) assign each of the pai of samples to one of the distance intevals and compute the aveage vaiance in each inteval by dividing the sum of the squaed-diffeences between data-values by the total numbe of pais lying in that distance inteval, and (iv) assign the aveage vaiance to the mid point of each inteval and cuve fit these points to one of the standad vaiogam models used in Geostatistics. 2 In this pape, we will use the second method to estimate the vaiogam fom the expeimental taces. 2. Relationship between the vaiogam and the covaiance Anothe vey commonly used statistic to measue coelation in data is the covaiance [Cistescu and Vetteli 25], [Maco et al. 23], [Cistescu et al. 24]. Fo a two dimensional isotopic stationay pocess V (x, y), the covaiance is defined as C() =E [(V (x, y) µ)(v (x,y ) µ)], Unless othewise stated, we will use the Euclidean distance to measue distances between two points. 2 Appendix A.2 pesents the commonly used standad vaiogam models. ACM Tansactions on Senso Netwoks, Vol. V, No. N, July 26.

5 Modeling Spatially Coelated Data in Senso Netwoks 5 whee (x,y ) is denotes a point distance away fom (x, y) andµ = E[V (x, y)]. Since both the vaiogam and the covaiance ae measues of coelation in data, we deive the elationship between them and veify that both of them can be used intechangeably. Fom Equation (2), γ() = [ 2 E (V (x, y) V (x,y )) 2] = [ 2 E ((V (x, y) µ) (V (x,y ) µ)) 2] γ() =σv 2 C(), (4) whee σv 2 = E [ (V (x, y) µ) 2] is the vaiance of the pocess V (x, y). Equation (4) implies that a lowe (highe) value of the vaiogam implies a highe (lowe) value of the covaiance and coelation. Figue plots the vaiogam and the covaiance fo a tace geneated by assuming a jointly Gaussian model fo the spatial data covaiance vaiogam Fig.. Vaiogam and Covaiance plots fo a tace geneated by assuming jointly Gaussian model fo the spatial data. A chaacteistic of the vaiogam which can be infeed fom the plot is that it levels off (becomes paallel to the x-axis) at a distance beyond which the covaiance o the coelation between the samples go to zeo. Futhe, the constant value to which the vaiogam satuates is equal to the vaiance of the pocess. Since both metics can be intechangeably used, in this pape we will only pesent vaiogam plots. 2.2 Analysis of Data using Vaiogams In this section, we analyze the coelation stuctue of diffeent spatial pocesses and popose a simple model fo each of them. Moe specifically, we pesent a model fo independent data and fo data following the diffusion law. We then look at the coelation stuctue of a eal expeimental tace and popose a model to captue the spatial coelation in this data. This model combines the two pevious models. Using vaiogams, we show that the poposed model is able to captue the coelation in data. ACM Tansactions on Senso Netwoks, Vol. V, No. N, July 26.

6 6 A. Jindal and K. Psounis d= N- N Fig. 2. Linea Topology. The data value at node i is given by V i Vaiogam Values Vaiogam Values Vaiogam Values Oiginal Tace Tace geneated using Model Tace geneated using Model (a) (b) (c) Fig. 3. (a) Vaiogam fo an iid pocess. (b) Vaiogam fo a pocess which follows the diffusion law (λ =.). (c) Vaiogam of the expeimental data at a time snapshot. The x-axis is in units of distance. The models in this section assume a linea topology as shown in Figue 2. The data value at node i is given by V i Independent Data. If a pocess is independent and identically distibuted (iid), its vaiance will not change with distance and the vaiogam should be a staight line paallel to the x-axis. Figue 3(a) shows the vaiogam fo an iid pocess with the undelying andom vaiable being Gaussian with mean and standad deviation equal to. A model fo the data values which captues the statistical popeties of independent data is given by, V i = Y, whee Y is a nomal andom vaiable with mean and standad deviation equal to. The vaiogam fo this model can be easily evaluated as follows, γ() = 2 E[(V V ) 2 ]=σ 2 Y =, which is in accodance to Figue 3(a) Diffusion Model. When the phenomenon unde obsevation is being emitted fom a single souce it usually follows the diffusion popety with distance, i.e. f() whee f() is the magnitude of the event s effect at a distance λ ACM Tansactions on Senso Netwoks, Vol. V, No. N, July 26.

7 Modeling Spatially Coelated Data in Senso Netwoks 7 fom the souce and λ is the diffusion paamete that depends on the physical phenomenon. Figue 3(b) shows the vaiogam fo a pocess following the diffusion law with λ =.. Fo small λ (λ.), a model to populate the data values is given by, V i = V i + Z, whee Z is a andom vaiable with mean and vaiance σ 2 z. The vaiogam fo this model can be evaluated as, γ() = 2 E[(V V ) 2 ]= 2 E[(V V + Z) 2 ] = 2 E[(V 2 V + Z + Z) 2 ]= 2 E[(V V + Z + Z...+ Z) 2 ]= 2 σ2 z. which is in accodance to Figue 3(b) fo σ 2 z = 2. (The slope of the linea vaiogam, with espect to, fom the model is 2 σ2 z and equating it with the slope in Figue 3(b) yields σ 2 z = 2.) A eal data tace. The pocess unde obsevation seldom has a single souce and the pesence of multiple souces will equie us to calculate a phaso sum of data values at a node. Fo atmospheic data such as tempeatue, pecipitation and humidity, it is not even possible to define a souce. The data values at nodes close to each othe will be coelated, while fo lage the pocess will stat looking like an iid pocess. As an example, the vaiogam at a time snapshot of the S-Pol ada data is shown in Figue 3(c). The S-Pol ada data tace is a humidity data tace obtained fom emote sensing studies. A full desciption of the tace is povided in Section 5. It is obseved fom the plot that as the distance gows fom zeo the spatial coelation deceases. Also, fo distances lage than 6, the coelation is quite small. The coelation stuctue looks like that of the diffusion model fo smalle distances while it looks like that of independent data fo lage values of distance. Hence, we popose a model fo this data which combines both the pevious models. The data value at a node V i is deived eithe fom V i o fom a andom vaiable Y. { Vi + Z with pobability α V i =. Y w.p. α We efe to this model as Model. Afte some simple calculations simila to the ones above, the vaiogam of Model can be expessed by the following ecusive equation, γ() =αγ( ) + 2ασ 2 z, and γ() = 2ασz. 2 The vaiogam of Model with α =.945 and σz 2 =26.4 is shown in Figue 3(c). Note that the vaiogam does not depend on the statistics of Y. Y only effects the fist ode statistics of V i s and does not effect the coelation stuctue. Though Model is able to captue the tends, it is not a vey good match. So, we incease the depth of data dependency in Model to come up with the following ACM Tansactions on Senso Netwoks, Vol. V, No. N, July 26.

8 8 A. Jindal and K. Psounis model, V i + Z with pobability α V i = V i 2 + Z w. p. α 2. Y w.p. α α 2 Now, the data value at node V i is deived eithe fom V i o fom V i 2 o fom a andom vaiable Y. We efe to this model as Model 2. The vaiogam of Model 2foα =.48,α 2 =.47 and σz 2 =26.3 is plotted in Figue 3(c). Figue 3(c) shows that Model 2 is able to captue the coelation chaacteistics of the data. Remak: The eason why Model 2 is accuate in captuing the chaacteistics of the S-Pol ada data tace is intuitively the following: In eal taces, the data values of neaby nodes ae usually coelated and close to each othe, but not identical, wheeas the data values of fa-away nodes ae independent and can diffe a lot. The dependence of V i ove V i and V i 2 captues the coelation between the values of neaby nodes. The andom vaiable Z intoduces small deviations between the values of neaby nodes, since they ae close to each othe but not identical. And, the andom vaiable Y intoduces in an independent manne new data values that can diffe a lot fom pio values. In this section, we poposed simple models fo vey specific coelation stuctues (independent data, diffusion law with a small λ and one snapshot of the S-Pol ada data tace). In the next section, we will genealize the simple models used fo the S-Pol ada data tace, so that any given coelation stuctue can be modeled. Ou geneal model will follow the same pinciples as Model 2. A node will eithe deive its data value fom one of the neaby nodes plus a small deviation, o fom an independent andom vaiable. This appoach, as we will show, will accuately captue the coelation chaacteistics of a wide ange of spatially coelated data. 3. MODEL FOR AN IRREGULAR GRID In this section we intoduce ou model fo captuing the statistical popeties of senso netwoks data. Fo ease of notation, we use pola coodinates to define node locations. We assume that nodes ae distibuted in a disk of unit adius. Let V (, θ) be the data value at node (, θ) inside the unit adius disk. We assume that V (, θ) is a stationay isotopic pocess that has a unique fist ode distibution denoted by f V (v). Without loss of geneality and to simplify exposition, we assume that we want to geneate the data value at the oigin. We popose the following model to do so: V (, ) = I (U=T ) Y + I (U=H) (V (, θ)+z) whee: θ δ(r = )dδ(θ = θ R = )dθ, (5) a) U epesents a coin that when it lands heads (H), with pobability β, the oigin s data value is obtained fom neighboing nodes, and when it lands tails (T), with pobability β, it is obtained fom a andom vaiable Y. (I A denotes ACM Tansactions on Senso Netwoks, Vol. V, No. N, July 26.

9 Modeling Spatially Coelated Data in Senso Netwoks 9 (,) d dθ A Aea A = d dθ Fig. 4. The pobability that the data value at (, ) is deived fom a node in egion A is α() (θ 2 θ ). an indicato function that equals one when event A occus and equals zeo othewise.) b) Y and Z ae andom vaiables independent of each othe as well as V, with pdf s f Y (y) andf Z (z) espectively. Y models the situation whee the oigin s data value is not obtained fom neighboing nodes, Z captues the small diffeences between neighboing data values, and both of them detemine the distibution of V (f V (v)). c) R is a andom vaiable with pdf α(). When R =, the oigin s data value is obtained fom locations at distance fom the oigin. α()d is the pobability of this event. α() is a paamete of ou model. (δ(r = ) denotes a δ-function of R that is non-zeo when R =.) d) Θ is a andom vaiable with pdf f Θ (θ). When Θ = θ R =, the oigin s data value is obtained fom locations at angle θ given that thei distance fom the oigin is. f Θ R (θ )dθ is the pobability of this event. We assume that θ is unifomly distibuted between angles θ and θ 2.Thus, { f Θ R (θ ) = (θ θ 2 θ ) <θ<θ 2. othewise Given the above, the cdf of V (, ) can be expessed as follows, P (V (, ) v) =βp(y v)+( β) α() P (V (, θ)+z v) ddθ. (6) θ (θ 2 θ ) Equation (5) and (6) simply say that the pobability that the data value at a node is diectly deived fom a node lying in the shaded egion A in Figue 4 is α() (θ 2 θ ) ddθ. α()d is the pobability that a node s data value is deived fom any node at a distance away fom it. The numbe of nodes distance away and lying in an ac of (θ 2 θ ) is popotional to (θ 2 θ ). Now, given that the node s data value is deived fom a node distance away, the pobability that it is deived fomanodeinanacofdθ is dθ (θ 2 θ ). ACM Tansactions on Senso Netwoks, Vol. V, No. N, July 26.

10 A. Jindal and K. Psounis The paametes of the model ae α(), β, f Y (y) andf Z (z). The values of θ and θ 2 depend on the method used to populate data. We will explain thei ole in moe detail in Section 3.. Since coelation is a function of distance only (as the pocess is isotopic), α is a function of only and not θ. α() will be a deceasing function of as the coelation between nodes deceases as thei distance inceases. Thoughout this pape, we assume that α() is zeo fo max fo some value of max. Now, since the pdf s should integate out to, we get the following equation, max θ2 θ α() ddθ = (θ 2 θ ) max α() =. (7) 3. Instantiation of the model In a eal life scenaio, the exact node locations detemined though some location distibution will be given as an input and the use should be able to geneate data values at these nodes using the model. In this section we descibe how to geneate the data using an instantiation of the model. (a) (b) (,) (,) R Fig. 5. Two methods to populate data. (a) Semi Cicula Dependence: The data value at node (, ) can be diectly deived fom any node lying in the semi cicula egion. (b) Quate Cicula Dependence: The data value at node (, ) can be diectly deived fom any node lying in the quate cicula egion. Befoe we poceed, we look at how the values of θ and θ 2 effect the population of data. A couple of examples ae given in Figue 5. The fist method coesponds to population of data using a semi cicula data dependence while the second method coesponds to a quate cicula data dependence. Quate cicula data dependence implies that a node s data value can be diectly deived fom only those nodes which lie in the shaded egion R which is quate of a cicle centeed at the node. The values of θ and θ 2 ae π and 3π 2 fo quate cicula dependence and π and 2π espectively fo semi cicula dependence. Which method to choose will depend on the physical phenomenon being modeled. The default data population method in the est of the pape is going to be the quate cicula data dependence (θ = π and θ 2 = 3π 2 ). As an example, conside the node locations given by Figue 6. Let the node location of node i be ( i,θ i ), i, and let the data values at these nodes be ACM Tansactions on Senso Netwoks, Vol. V, No. N, July 26.

11 Modeling Spatially Coelated Data in Senso Netwoks (, ) Fig. 6. An example topology. denoted by V ( i,θ i ). The instantiation of the model fo node (, ) fo a quate cicula data dependence is as follows: V (,θ )+Z with pobability c α() V ( 2,θ 2 )+Z V (, ) = V ( 3,θ 3 )+Z V ( 4,θ 4 )+Z Y w.p. c α(2) 2 w.p. c α(3) 3 w.p. c α(4) 4 w.p. cβ, (8) whee j denotes the distance between nodes (, ) and ( j,θ j )andc is a scaling constant which is pesent to make the sum of pobabilities go to one. Equation 8 assumes that the data values at nodes lying in the data dependence egion of V (, ) have aleady been populated. Thus, an ode of populating data has implicitly been assumed. A valid odeing to populate data will ensue that when a data value at a node is populated, the data value at all the nodes lying in its data dependence egion have aleady been populated. Note that this implies that a full cicula data dependence (θ =andθ 2 =2π) cannot be used fo populating data. Also, befoe stating to populate the data we andomly initialize the values that ae within the data dependence egion of the fist node we populate. Remak: Note that Equation (8) implies that the poposed model is Makovian. To see this, assume a valid ode fo populating the data. Then, if the state is defined to be a vecto of data values at nodes which lie in the dependence aea of any node whose value has not yet been populated, the Makovian popety holds as we populate the node values one by one because the next state depends only on the pevious one. The dependence between the two states is chaacteized by the model paametes. 3.2 Instantiation of the model on a gid topology Though the instantiation on a gid topology can be constucted in a manne simila to the pevious section, the inheent egulaity in the topology allows us to simplify the exposition. So, we devote this section to constuct the model on gid topologies. A moe compehensive teatment of the model on gid topologies can be found in [Jindal and Psounis 24]. ACM Tansactions on Senso Netwoks, Vol. V, No. N, July 26.

12 2 A. Jindal and K. Psounis 3 Fo ease of notation we use Catesian coodinates to define node locations. Fist we descibe why a gid topology simplifies the exposition. Since the distance to the neaest node is the same fo evey node and is equal to the size of the gid, the L o manhattan distance is a meaningful way to measue distances between two nodes. The L distance between two nodes (x,y ) and (x 2,y 2 ) is given by = x x 2 + y y 2. Thus, the distances between nodes on a gid ae in multiples of the gid size. This simplifies the model stuctue as the vaiogam as well as α() can now be viewed as discete functions of distance. In this pape, we denote a discete function f as f[x] and a continuous function as f(x). Let the data value at node (x, y) be given by V (x, y). Let N[] denote the numbe of nodes at a distance fom (x, y). Let V denote the data value at a node which is distance away fom (x, y), and V k denote the data value at the k th node ( k N[]) at a distance fom (x, y). Following is the model fo geneating the data values, V + Z with pobability cα[] N[]. V N[] cα[] + Z w.p. V (x, y) = V 2 + Z w.p.. V N[2] 2 + Z w.p.. V max + Z w.p.. V N[max ] N[] cα[2] N[2] cα[2] N[2] cα[ max ] N[ max ] cα[ max ] N[ max ] max + Z w.p. Y w.p. cβ, (9) whee c is a scaling constant pesent to make the pobabilities sum to one. The above equation simply says that the pobability that V (x, y) is deived fom the value of any node which is distance away fom (x, y) isα[]. Futhe, the pobability that V (x, y) is deived fom the value of a paticula such node is α[] N[]. The value of N[] will depend on whethe the data is populated using a semi cicula dependence (N[] = 2) o a quate cicula dependence (N[] = + ). 3.3 How the model paametes affect coelation The pesence of many paametes in the model gives us geat flexibility to model diffeent spatial pocesses. In this section, we study how diffeent paametes affect the coelation popeties of the geneated data. We use the simple linea topology shown in Figue 2. Synthetic taces ae geneated using the model unde a 2 node scenaio. We assume Y N(, ) and Z N(,σ z ). 3 Fo ease of notation, wheneve we ae dealing with iegula gids, we will assume pola coodinate system while wheneve we deal with gid topologies, we assume Catesian coodinates. ACM Tansactions on Senso Netwoks, Vol. V, No. N, July 26.

13 Modeling Spatially Coelated Data in Senso Netwoks 3 Vaiogam Values β = 6 β =.2 4 β =.4 β =.6 2 β =.8 β = Vaiogam Values max = 3 max = 7 max = max = 5 max = 9 max = Vaiogam Values σ z = 8 σ z = 2 σ z = 3 6 σ z = 4 4 σ = 5 z σ z = (a) (b) (c) Fig. 7. (a) Effect on the coelation stuctue of the data when β is vaied keeping all the othe paametes constant. (b) Effect on the coelation stuctue of the data when max is vaied keeping all the othe paametes constant. (c) Effect on the coelation stuctue of the data when σ z is vaied keeping all the othe paametes constant. The x-axis is in units of distance 3.3. Effect of β. Since β govens the pobability with which a node will choose a andom value independent of evey othe node, it is expected that a lowe value of β will lead to a highe value of coelation. Also, a vaiation in β will change the distibution of V. The exact elationship between the two is deived in Appendix A.3. Figue 7(a) plots the vaiogam fo taces geneated using diffeent values of β. The othe paametes ae: max =2,α() =λ2 fo << max and othewise, and σ z = 3. Any deceasing function of can seve as α(). We choose one of these fo these case studies. The plots show that as the value of β deceases, not only does the distance at which the vaiogam levels off (the distance beyond which the nodes ae uncoelated) incease, but also the y-value to which it levels off inceases. Figue 8 shows the actual data values fo a sample of the topology fo two values of β. Foβ =.95, the data values look petty andom implying low spatial coelation in data while fo β =.5, the data values at close by nodes show high coelation Effect of max. If the distance between the nodes is moe than max, then they cannot be diectly deived fom each othe. Hence, we expect that inceasing max will incease the distance at which the vaiogam levels off. Figue 7(b) plots the vaiogam fo taces geneated using diffeent values of max. The othe paametes ae: α() =λ2 fo << max and othewise, β =.4 andσ z = 4. A look at the vaiogams tells us that coelation between the data values is independent of the value of max. This obsevation is contay to ou initial intuition and hence equies a moe detailed explanation. We take this oppotunity to highlight a key chaacteistic of ou model. If node 2 is deived fom node, and node 3 is deived fom node ACM Tansactions on Senso Netwoks, Vol. V, No. N, July 26.

14 4 A. Jindal and K. Psounis 4 β =.95 Data Value nodeid β =.5 Data Value nodeid Fig. 8. The actual data values fo a sample of the topology fo two values of β. β =.95 coesponds to vey low coelation while β =.5 coesponds to vey high coelation. 2, then node and node 3 will show a stong coelation too. So, even if max is small, when β is small, nodes having distances much lage than max will have high coelation. Thus, we infe that the distance at which the vaiogam levels off depends pimaily on β Effect of σ z. Finally, we study whethe changing f Z (z) will effect the coelation in data. We had assumed f Z (z) toben(,σ z ). Taces fo diffeent values of σ z ae geneated and thei vaiogams ae plotted in Figue 7(c). The othe paametes ae: max =2,α() =λ2 fo << max and othewise, and β =.4. It can be easily seen fom the plots that σ z does not effect the coelation stuctue of the data, though it has a significant effect on the distibution of V. The value at which the vaiogam satuates to, which is the vaiance of V, inceases as σ z inceases. Remak: When one geneates tace and uses them to evaluate the pefomance of an algoithm fo diffeent coelation stuctues, it is useful to have a single tunable paamete whose value detemines the level of coelation in data. Fo ou model, this tunable paamete is β. Taces with diffeent coelation stuctues can be geneated by tuning β fom to and the pefomance of the algoithm can be plotted against β. 4. INFERRING MODEL PARAMETERS In this section, we pesent techniques fo infeing model paametes fom eal taces. This section shows that the model paametes can be infeed fom the fist ode statistics and second ode moments of the tace. The model paametes to be infeed ae α(), β, f Y (y), max and f Z (z). Without loss of geneality, fom now onwads we will assume that Z is a nomal andom ACM Tansactions on Senso Netwoks, Vol. V, No. N, July 26.

15 Modeling Spatially Coelated Data in Senso Netwoks f V (v) v Fig. 9. Distibution of V V fo samples fom a time snapshot of the S-Pol ada data whee V ae the sample values at nodes at a unit distance away fom V. vaiable with zeo mean and standad deviation σ = σ z. The S-Pol ada data justifies ou assumption. In paticula, Figue 9 shows the distibution of V V, whee V epesents the sample values at nodes at a unit distance away fom V and, as it is evident fom the plot, this distibution can be vey closely appoximated by a Gaussian distibution. Note that the distibution of Z need not necessaily be Gaussian; any othe distibution will not effect the model, though the analysis pesented in this section will be modified. Remak: If Z is not Gaussian, then the model paametes cannot be detemined fom just the fist ode statistics and the second ode moments; they will depend on highe ode statistics too. Since all the eal taces we studied wee accuately modelled with a Gaussian Z, we do not discuss the model fo a non-gaussian Z in this pape. In Section 4., we state the elationship between f V (v), f Y (y) andσ z. Note that f V (v) can be easily estimated by its empiical distibution. Then, in Section 4.2 we pesent a igoous pocedue to infe α(), β, max and σ z fom a eal tace. But, this pocedue involves solving integal equations of the fist kind [Kanwal 997], [Pote and Stiling 99] and hence, it is not always possible to obtain a closed fom expession fo the model paametes. Futhe, even though seveal numeical techniques exist in the liteatue to solve integal equations with no closed fom solutions, integal equations of the fist kind ae inheently ill posed poblems [Kythe and Pui 22]. As a esult, thei solutions ae geneally unstable and pone to lage eos. Motivated by this, in Section 4.3 we descibe a pocedue to infe the model paametes fo data values on nodes on a gid topology, and then, in Section 4.4 we pesent a simple, pactical method which uses the gid topology solution to infe the model paametes on any topology. 4. Relationship between the distibutions of V, Y and Z Lemma 4.. V = Y + L whee L is a andom vaiable with a chaacteistic function given by β Φ L (jω)=. () ( β)e [ σz 2 ω 2 2 ] Poof: See Appendix A.3. The distibution of Y, f Y (y), can be infeed fom Lemma 4.. The following ACM Tansactions on Senso Netwoks, Vol. V, No. N, July 26.

16 6 A. Jindal and K. Psounis subsections pesent pocedues to infe the est of the model paametes. 4.2 A igoous pocedue to infe the model paametes In this section, we pesent a igoous method to infe the est of the model paametes, α(), β, σ z and max. To infe these paametes, we fist compute the vaiogam γ() using the model and then equate it with its estimate γ () obtained fom the eal tace. Using Equation (2), γ() = 2π 2 2π E [ (V (, ) V (, θ)) 2] dθ = ( β) 2 2π max θ2 E [ (V (,θ )+Z V (, θ)) 2] α( ) d dθ dθ 2π θ θ 2 θ + 2π β 2 2π E[(Y V (, θ))2 ]dθ. () The tem E [ (V (,θ )+Z V (, θ)) 2] in the above equation can be expanded as, E [ (V (,θ )+Z V (, θ)) 2] = E [ (V (,θ ) V (, θ)) 2] ( ) +E[Z 2 ]=2γ cos(θ θ ) + σz. 2 The second tem in Equation () E[(Y V (, θ)) 2 ] is equal to E[L 2 ]. Using Equation (), E[L 2 ] is evaluated to be ( β)σ2 z β. Substituting all of the above in Equation (), max θ2 2π γ() =( β)σz 2 α( ) +( β) θ 2π θ 2 θ ( ) γ cos(θ θ ) dθdθ d. (2) Equation (2) gives the elationship between the vaiogam and the model paametes α(), β, σ z and max. Substituting γ() with its estimate γ () inequation (2) gives us an integal equation of the fist kind [Kanwal 997], [Pote and Stiling 99], which along with the bounday conditions max α()d =and α( max ) = fom a system of equations with one unknown function α() and thee unknown constants β,σ z and max. Solving these equations gives us the model paametes. Afte obtaining σ z and β, f Y (y) is obtained though Equation (25). In Equation (2), the unknown function α() is inside an integal. In geneal, it is not possible to find closed fom solutions fo α() fo evey vaiogam function. In the next section, we assume a specific vaiogam function that coesponds to a covaiance function commonly used in the senso netwoks liteatue, and solve fo α() Case Study. In this section, we will the find model paametes fo a tace having the following vaiogam, γ() = c( e λ2 )<<R, (3) ACM Tansactions on Senso Netwoks, Vol. V, No. N, July 26.

17 Modeling Spatially Coelated Data in Senso Netwoks 7 whee R is detemined by the aea in which the nodes ae distibuted and λ is a paamete which govens how fast the coelation decays. The coesponding covaiance is C() =ce λ2 which is a vey commonly assumed coelation stuctue fo spatially coelated data in the senso netwoks liteatue, see, fo example, [Cistescu and Vetteli 25], [Maco et al. 23]. Note that these papes also assume the data to be jointly Gaussian, wheeas we don t make any such assumption hee. Actually, the jointly Gaussian scenaio is a subcase of ou model, as discussed in Section 6. To find the model paametes, we have to solve the following integal equation: max θ2 2π α( ) c( e λ2 )=( β) θ 2π θ 2 θ ( ) c e λ( cos(θ θ )) dθdθ d +( β)σz. 2 (4) Befoe ventuing into the solution of the above equation, we fist integate out θ and θ, θ2 2π θ 2π ( ) c e λ2 e λ 2 e 2λ cos(θ θ )) dθdθ. (5) θ 2 θ To obtain a closed fom appoximation fo the model paametes, we assume that 2λ < and hence, by neglecting the squae tems and beyond, the last tem in the above equation can be appoximated by, e 2λ cos(θ θ )) =+2λ cos(θ θ ). We assume the semi cicula data dependence to populate data, hence ( θ = π and θ 2 =2π. With the above appoximation, Equation (5) educes to c e λ2 e λ 2). Substituting in Equation (4), max ( c( e λ2 )=c( β) α( ) e λ2 e λ 2) d +( β)σ 2 z. (6) Using the method descibed in [Kanwal 997] to solve fo integal equations, we detemine that α() has the fom a + be λ2 whee a and b ae constants to be detemined by the bounday conditions max α()d =andα( max )=. ( πef( Solving them yields b = λmax) 2 λ max e max) λ2 and a = be λ 2 max, whee Ef(x) is the eo function defined as Ef(x) = 2 x π e t2 dt. Now substituting α() =a+be λ2 in Equation (6) gives β = 4 λ π (2aEf( λ max )+ 2bEf( 2λmax )) and σz 2 = cβ β. We still need to detemine the value of max. Any value of max would do, as long as the esulting β is between and -since it is a pobability-, and the esulting α() is positive fo all -since it is a pdf-. In this example, we choose the lagest max value that satisfies both constaints. In paticula, we stat with max = R, and keep on educing its value till we obtain a positive value of β. Fo R =, λ = 2 and c =, the model paametes tun out to be, max =2, β =.52 and σz 2 =.4. The coesponding α() is plotted in Figue (a). ACM Tansactions on Senso Netwoks, Vol. V, No. N, July 26.

18 8 A. Jindal and K. Psounis α() Vaiogam Values Oiginal Tace Synthetic Tace (a) (b) Fig.. (a) α() obtained afte solving the Integal Equation 4. (b) The given vaiogam γ() = ( e λ2 ) and the vaiogam of a synthetic tace geneated using the paametes deived in Section nodes nodes (x, y)... nodes nodes Total numbe of nodes i distance away fom (x, y) = 4 i Fig.. Gid Topology. To veify that these paametes captue the coelation chaacteistics, we plot the vaiogam of Equation (3) and the vaiogam of a synthetic tace geneated using these paametes in Figue (b). Both the cuves match closely. 4.3 Infeing model paametes fo the gid topology As discussed in Section 3.2, the gid topology simplifies the exposition because both the vaiogam and the model paametes ae now discete functions of distance. The mathematical pocedue to infe model paametes on a gid is simila to the one descibed in Section 4.2, but now since all the functions ae discete instead of continuous, the integals will be eplaced by sums. ACM Tansactions on Senso Netwoks, Vol. V, No. N, July 26.

19 Modeling Spatially Coelated Data in Senso Netwoks 9 Fo a gid topology, Equation () is ewitten as, γ[] = 2 4 i= 4 E [ (X X i ) 2] = 2 α[j] N[j] E [ (X k j + Z X i ) 2] i= 4 i= 4 max j= N[j] k= 4 βe [ (Y X i ) 2], (7) whee, because α[ max ] =, the second sum is up to max only. As seen in Figue, the numbe of nodes at a distance away ae equal to 4, and the fist sum is to be taken ove all nodes at a distance away, so the fist sum is ove 4 nodes. Using simila expansions as in Section 4.2, Equation (7) educes to, γ[] =( β)σz i= max j= N[j] k= α[j] N[j] γ[d ij k ] (8) whee d ij k denotes the distance between the nodes X i and Xj k. Equating γ [] =γ[] fo i max gives max equations. These equations along with the equation β + max α[i] =fomasystemof max + non linea i= equations with max + unknowns, the α[] s, β and σ 2 z. The above non linea system can be easily conveted to a linea system by a change of vaiables.. Substitute c = ( β)σz 2 in Equation (8) to get a system of max linea equations with max vaiables, the α[] s and c. 2. Afte solving this linea system, Equation β + max α[i] = is used to obtain i= β. 3. Given the value of c and β, get the value of σz 2 = c β. Afte solving the above system, f Y (y) can be obtained though Equation (25). This pocedue implicitly assumes that the value of max is known. Thus we need a method to detemine the value of max. As a stating point, we choose a vey lage value fo max. In theoy, oveestimating max, which esults in a lage system, would still find the coect paametes. Howeve, in pactice, lage max values leads to moe ounding and statistical eos, hence to small negative α[] s in the solution of the non linea system. A solution to this is to stat fom an oveestimated max, and lowe its value until all the α[] s ae positive. We illustate the pocedue though an example in Section A simple method to infe the model paametes fo an iegula topology In this section we pesent a simple pocedue than the one pesented in Section 4.2 to infe the model paametes fo any given topology. The igoous pocedue equies to solve integal equations of the fist kind and hence, it is not always possible ACM Tansactions on Senso Netwoks, Vol. V, No. N, July 26.

20 2 A. Jindal and K. Psounis to get a closed fom expession fo the model paamete. So, we pesent a pactical simple method which uses the discete model to infe the model paametes and the continuous model to populate the data and geneate taces.. The fist step is to obtain a discetized vaiogam, which coesponds to the continuous vaiogam sampled at multiples of the aveage neaest neighbo distance. The second method descibed in Section 2 is used to obtain an estimate of the continuous vaiogam. Recall that one of the standad vaiogam models is fitted to the vaiogam samples to get the continuous vaiogam. This vaiogam is then sampled at multiples of the aveage neaest neighbo distance to get the discetized vaiogam. 2. The second step is to use the method descibed in Section 4.3 to obtain a discete vesion α[] ofα(), which coesponds to the continuous α() sampled at multiples of the aveage neighbo distance. 3. Finally, the α[] s ae intepolated o cuve fitted and then scaled to obtain the continuous α(). The scaling is caied out to ensue max α()d =. 4. Afte obtaining the model paametes, we use the model descibed in Section 3 to geneate synthetic taces. We illustate the pocedue using an example in Section 5. This pocedue fomulates the poblem in continuous domain, convets it to the discete domain by sampling, solves it in the discete domain and tansfoms the solution back to the continuous domain by intepolation. Intuitively, this pocedue is vey simila to seveal signal pocessing techniques, fo example using the FFT to find the Fouie tansfom of a continuous signal. Obviously, as in the signal pocessing techniques, the distance between the two neighboing samples (which is the aveage neaest neighbo distance fo the given pocedue) has an impotant ole to play. The lage the numbe of samples in an aea, the smalle the aveage neaest-neighbo distance, and the moe accuate is the estimation of the model paametes. 5. MODEL VERIFICATION AND VALIDATION In this section, the model paametes fo expeimental taces ae infeed using the method descibed in Section 4. Then these model paametes ae used to geneate synthetic taces. We veify ou model by compaing the vaiogams of the oiginal expeimental taces and the coesponding synthetic taces, and then we validate it by compaing the pefomance of algoithms which exploit spatial coelation, against both the taces. 5. Data Set Desciption In this section, we descibe the diffeent expeimental taces we use to veify and validate ou model. The fist two taces we use, the Pecipitation Data Set [Widmann and Betheton ] and the S-Pol Rada Data Set 4 wee obtained fom emote 4 S-Pol ada data wee collected duing the IHOP 22 poject ( pojects/ihop_22/spol/). S-Pol is fielded by the Atmospheic Technology Division of the National Cente fo Atmospheic Reseach. We acknowledge NCAR and its sponso, the National Science Foundation, fo povision of the S-Pol data set. ACM Tansactions on Senso Netwoks, Vol. V, No. N, July 26.

21 Modeling Spatially Coelated Data in Senso Netwoks 2 sensing studies and have been used in the senso netwoks liteatue as expeimental taces to evaluate algoithm pefomance, see, fo example [Yu et al. 23], [Pattem et al. 24], [Ganesan et al. 22]. 5.. Pecipitation Data Set. This data set consists of the daily ainfall pecipitation fo the Pacific Nothwest fom The final measuement points in the data set fomed a egula gid of 5 km 5 km egions ove the egion unde study. We select a subset of data that has no missing values. Specifically, each snapshot of data is a 8 8 spatial gid data with a 5 km esolution S-Pol Rada Data Set. The esampled S-Pol ada data, povided by NCAR, ecods the intensity of eflectivity of atmosphee in dbz, whee Z is popotional to the etuned powe fo a paticula ada and a paticula ange. The oiginal data wee ecoded in the pola coodinate system. Samples wee taken at evey.7 degees in azimuth and 8 sample locations (appoximately 5 metes between neighboing samples) in ange, esulting in a total of 5 8 samples fo each 36 degee azimuthal sweep. They wee conveted to the Catesian gid using the neaest neighboing esampling method [Venables and Ripley 22]. In this pape, we have selected a spatial subset of the oiginal data and 259 time snapshots acoss 2 days in May 22. The distance between the sensing nodes fo these taces is hundeds of metes which is not epesentative of actual senso netwoks in which the inte senso distance is a few metes. The only publicly available senso netwok taces which the authos ae awae of ae the SHM Tace [Paek et al. 25] and Intel Lab Data [int 24] SHM Tace. One of the eal wold expeiments whee eal senso netwok taces have been collected afte deploying a senso netwok is epoted in [Paek et al. 25]. A 4 MicaZ node senso netwok was deployed in a lage seismic test stuctue used by civil enginees to study stuctual health monitoing (SHM). Acceleometes on the sensos collected vibation samples fom the stuctue and send them to a base station using a data acquisition system called Wisden. We use a time snapshot of this tace to veify and validate ou model Intel Lab Data. Anothe eal wold expeiment whee eal senso netwok taces have been collected was pefomed in Intel Bekeley Reseach Lab [int 24]. 54 sensos measuing tempeatue wee deployed in a lab. We use a time snapshot of this tace to veify and validate ou model. Due to the lack of the publicly available taces, we collected ou own taces using MICA2 motes with MTS3CA senso boads attached to them. We used the light sensos on the senso boad to take light intensity measuements. Two taces in two diffeently lighted envionments wee collected using these motes Tace. 44 senso nodes ae deployed in a feet squae aea. The location of each node is andomly chosen accoding to a unifom location distibution. We use a maste mote to send a message to evey mote. When a senso node eceives the message, it samples the light intensity of the envionment. Thus all sensos take the eadings at the same time. Thus, we get a spatially coelated ACM Tansactions on Senso Netwoks, Vol. V, No. N, July 26.

Modeling spatially-correlated data of sensor networks with irregular topologies

Modeling spatially-correlated data of sensor networks with irregular topologies This full text pape was pee eviewed at the diection of IEEE Communications Society subject matte expets fo publication in the IEEE SECON 25 poceedings Modeling spatially-coelated data of senso netwoks

More information

A modal estimation based multitype sensor placement method

A modal estimation based multitype sensor placement method A modal estimation based multitype senso placement method *Xue-Yang Pei 1), Ting-Hua Yi 2) and Hong-Nan Li 3) 1),)2),3) School of Civil Engineeing, Dalian Univesity of Technology, Dalian 116023, China;

More information

Journal of World s Electrical Engineering and Technology J. World. Elect. Eng. Tech. 1(1): 12-16, 2012

Journal of World s Electrical Engineering and Technology J. World. Elect. Eng. Tech. 1(1): 12-16, 2012 2011, Scienceline Publication www.science-line.com Jounal of Wold s Electical Engineeing and Technology J. Wold. Elect. Eng. Tech. 1(1): 12-16, 2012 JWEET An Efficient Algoithm fo Lip Segmentation in Colo

More information

Segmentation of Casting Defects in X-Ray Images Based on Fractal Dimension

Segmentation of Casting Defects in X-Ray Images Based on Fractal Dimension 17th Wold Confeence on Nondestuctive Testing, 25-28 Oct 2008, Shanghai, China Segmentation of Casting Defects in X-Ray Images Based on Factal Dimension Jue WANG 1, Xiaoqin HOU 2, Yufang CAI 3 ICT Reseach

More information

Lecture # 04. Image Enhancement in Spatial Domain

Lecture # 04. Image Enhancement in Spatial Domain Digital Image Pocessing CP-7008 Lectue # 04 Image Enhancement in Spatial Domain Fall 2011 2 domains Spatial Domain : (image plane) Techniques ae based on diect manipulation of pixels in an image Fequency

More information

HISTOGRAMS are an important statistic reflecting the

HISTOGRAMS are an important statistic reflecting the JOURNAL OF L A T E X CLASS FILES, VOL. 14, NO. 8, AUGUST 2015 1 D 2 HistoSketch: Disciminative and Dynamic Similaity-Peseving Sketching of Steaming Histogams Dingqi Yang, Bin Li, Laua Rettig, and Philippe

More information

Optical Flow for Large Motion Using Gradient Technique

Optical Flow for Large Motion Using Gradient Technique SERBIAN JOURNAL OF ELECTRICAL ENGINEERING Vol. 3, No. 1, June 2006, 103-113 Optical Flow fo Lage Motion Using Gadient Technique Md. Moshaof Hossain Sake 1, Kamal Bechkoum 2, K.K. Islam 1 Abstact: In this

More information

Topological Characteristic of Wireless Network

Topological Characteristic of Wireless Network Topological Chaacteistic of Wieless Netwok Its Application to Node Placement Algoithm Husnu Sane Naman 1 Outline Backgound Motivation Papes and Contibutions Fist Pape Second Pape Thid Pape Futue Woks Refeences

More information

Illumination methods for optical wear detection

Illumination methods for optical wear detection Illumination methods fo optical wea detection 1 J. Zhang, 2 P.P.L.Regtien 1 VIMEC Applied Vision Technology, Coy 43, 5653 LC Eindhoven, The Nethelands Email: jianbo.zhang@gmail.com 2 Faculty Electical

More information

RANDOM IRREGULAR BLOCK-HIERARCHICAL NETWORKS: ALGORITHMS FOR COMPUTATION OF MAIN PROPERTIES

RANDOM IRREGULAR BLOCK-HIERARCHICAL NETWORKS: ALGORITHMS FOR COMPUTATION OF MAIN PROPERTIES RANDOM IRREGULAR BLOCK-HIERARCHICAL NETWORKS: ALGORITHMS FOR COMPUTATION OF MAIN PROPERTIES Svetlana Avetisyan Mikayel Samvelyan* Matun Kaapetyan Yeevan State Univesity Abstact In this pape, the class

More information

ADDING REALISM TO SOURCE CHARACTERIZATION USING A GENETIC ALGORITHM

ADDING REALISM TO SOURCE CHARACTERIZATION USING A GENETIC ALGORITHM ADDING REALISM TO SOURCE CHARACTERIZATION USING A GENETIC ALGORITHM Luna M. Rodiguez*, Sue Ellen Haupt, and Geoge S. Young Depatment of Meteoology and Applied Reseach Laboatoy The Pennsylvania State Univesity,

More information

Communication vs Distributed Computation: an alternative trade-off curve

Communication vs Distributed Computation: an alternative trade-off curve Communication vs Distibuted Computation: an altenative tade-off cuve Yahya H. Ezzeldin, Mohammed amoose, Chistina Fagouli Univesity of Califonia, Los Angeles, CA 90095, USA, Email: {yahya.ezzeldin, mkamoose,

More information

Image Enhancement in the Spatial Domain. Spatial Domain

Image Enhancement in the Spatial Domain. Spatial Domain 8-- Spatial Domain Image Enhancement in the Spatial Domain What is spatial domain The space whee all pixels fom an image In spatial domain we can epesent an image by f( whee x and y ae coodinates along

More information

IP Network Design by Modified Branch Exchange Method

IP Network Design by Modified Branch Exchange Method Received: June 7, 207 98 IP Netwok Design by Modified Banch Method Kaiat Jaoenat Natchamol Sichumoenattana 2* Faculty of Engineeing at Kamphaeng Saen, Kasetsat Univesity, Thailand 2 Faculty of Management

More information

Point-Biserial Correlation Analysis of Fuzzy Attributes

Point-Biserial Correlation Analysis of Fuzzy Attributes Appl Math Inf Sci 6 No S pp 439S-444S (0 Applied Mathematics & Infomation Sciences An Intenational Jounal @ 0 NSP Natual Sciences Publishing o Point-iseial oelation Analysis of Fuzzy Attibutes Hao-En hueh

More information

Controlled Information Maximization for SOM Knowledge Induced Learning

Controlled Information Maximization for SOM Knowledge Induced Learning 3 Int'l Conf. Atificial Intelligence ICAI'5 Contolled Infomation Maximization fo SOM Knowledge Induced Leaning Ryotao Kamimua IT Education Cente and Gaduate School of Science and Technology, Tokai Univeisity

More information

= dv 3V (r + a 1) 3 r 3 f(r) = 1. = ( (r + r 2

= dv 3V (r + a 1) 3 r 3 f(r) = 1. = ( (r + r 2 Random Waypoint Model in n-dimensional Space Esa Hyytiä and Joma Vitamo Netwoking Laboatoy, Helsinki Univesity of Technology, Finland Abstact The andom waypoint model (RWP) is one of the most widely used

More information

Fifth Wheel Modelling and Testing

Fifth Wheel Modelling and Testing Fifth heel Modelling and Testing en Masoy Mechanical Engineeing Depatment Floida Atlantic Univesity Boca aton, FL 4 Lois Malaptias IFMA Institut Fancais De Mechanique Advancee ampus De lemont Feand Les

More information

Assessment of Track Sequence Optimization based on Recorded Field Operations

Assessment of Track Sequence Optimization based on Recorded Field Operations Assessment of Tack Sequence Optimization based on Recoded Field Opeations Matin A. F. Jensen 1,2,*, Claus G. Søensen 1, Dionysis Bochtis 1 1 Aahus Univesity, Faculty of Science and Technology, Depatment

More information

A Minutiae-based Fingerprint Matching Algorithm Using Phase Correlation

A Minutiae-based Fingerprint Matching Algorithm Using Phase Correlation A Minutiae-based Fingepint Matching Algoithm Using Phase Coelation Autho Chen, Weiping, Gao, Yongsheng Published 2007 Confeence Title Digital Image Computing: Techniques and Applications DOI https://doi.og/10.1109/dicta.2007.4426801

More information

Extract Object Boundaries in Noisy Images using Level Set. Final Report

Extract Object Boundaries in Noisy Images using Level Set. Final Report Extact Object Boundaies in Noisy Images using Level Set by: Quming Zhou Final Repot Submitted to Pofesso Bian Evans EE381K Multidimensional Digital Signal Pocessing May 10, 003 Abstact Finding object contous

More information

An Unsupervised Segmentation Framework For Texture Image Queries

An Unsupervised Segmentation Framework For Texture Image Queries An Unsupevised Segmentation Famewok Fo Textue Image Queies Shu-Ching Chen Distibuted Multimedia Infomation System Laboatoy School of Compute Science Floida Intenational Univesity Miami, FL 33199, USA chens@cs.fiu.edu

More information

Analysis of Wired Short Cuts in Wireless Sensor Networks

Analysis of Wired Short Cuts in Wireless Sensor Networks Analysis of Wied Shot Cuts in Wieless Senso Netwos ohan Chitaduga Depatment of Electical Engineeing, Univesity of Southen Califonia, Los Angeles 90089, USA Email: chitadu@usc.edu Ahmed Helmy Depatment

More information

Color Correction Using 3D Multiview Geometry

Color Correction Using 3D Multiview Geometry Colo Coection Using 3D Multiview Geomety Dong-Won Shin and Yo-Sung Ho Gwangju Institute of Science and Technology (GIST) 13 Cheomdan-gwagio, Buk-ku, Gwangju 500-71, Republic of Koea ABSTRACT Recently,

More information

Performance Optimization in Structured Wireless Sensor Networks

Performance Optimization in Structured Wireless Sensor Networks 5 The Intenational Aab Jounal of Infomation Technology, Vol. 6, o. 5, ovembe 9 Pefomance Optimization in Stuctued Wieless Senso etwoks Amine Moussa and Hoda Maalouf Compute Science Depatment, ote Dame

More information

Positioning of a robot based on binocular vision for hand / foot fusion Long Han

Positioning of a robot based on binocular vision for hand / foot fusion Long Han 2nd Intenational Confeence on Advances in Mechanical Engineeing and Industial Infomatics (AMEII 26) Positioning of a obot based on binocula vision fo hand / foot fusion Long Han Compute Science and Technology,

More information

Conservation Law of Centrifugal Force and Mechanism of Energy Transfer Caused in Turbomachinery

Conservation Law of Centrifugal Force and Mechanism of Energy Transfer Caused in Turbomachinery Poceedings of the 4th WSEAS Intenational Confeence on luid Mechanics and Aeodynamics, Elounda, Geece, August 1-3, 006 (pp337-34) Consevation Law of Centifugal oce and Mechanism of Enegy Tansfe Caused in

More information

Mobility Pattern Recognition in Mobile Ad-Hoc Networks

Mobility Pattern Recognition in Mobile Ad-Hoc Networks Mobility Patten Recognition in Mobile Ad-Hoc Netwoks S. M. Mousavi Depatment of Compute Engineeing, Shaif Univesity of Technology sm_mousavi@ce.shaif.edu H. R. Rabiee Depatment of Compute Engineeing, Shaif

More information

INFORMATION DISSEMINATION DELAY IN VEHICLE-TO-VEHICLE COMMUNICATION NETWORKS IN A TRAFFIC STREAM

INFORMATION DISSEMINATION DELAY IN VEHICLE-TO-VEHICLE COMMUNICATION NETWORKS IN A TRAFFIC STREAM INFORMATION DISSEMINATION DELAY IN VEHICLE-TO-VEHICLE COMMUNICATION NETWORKS IN A TRAFFIC STREAM LiLi Du Depatment of Civil, Achitectual, and Envionmental Engineeing Illinois Institute of Technology 3300

More information

A Novel Automatic White Balance Method For Digital Still Cameras

A Novel Automatic White Balance Method For Digital Still Cameras A Novel Automatic White Balance Method Fo Digital Still Cameas Ching-Chih Weng 1, Home Chen 1,2, and Chiou-Shann Fuh 3 Depatment of Electical Engineeing, 2 3 Gaduate Institute of Communication Engineeing

More information

Transmission Lines Modeling Based on Vector Fitting Algorithm and RLC Active/Passive Filter Design

Transmission Lines Modeling Based on Vector Fitting Algorithm and RLC Active/Passive Filter Design Tansmission Lines Modeling Based on Vecto Fitting Algoithm and RLC Active/Passive Filte Design Ahmed Qasim Tuki a,*, Nashien Fazilah Mailah b, Mohammad Lutfi Othman c, Ahmad H. Saby d Cente fo Advanced

More information

Topic -3 Image Enhancement

Topic -3 Image Enhancement Topic -3 Image Enhancement (Pat 1) DIP: Details Digital Image Pocessing Digital Image Chaacteistics Spatial Spectal Gay-level Histogam DFT DCT Pe-Pocessing Enhancement Restoation Point Pocessing Masking

More information

Topic 7 Random Variables and Distribution Functions

Topic 7 Random Variables and Distribution Functions Definition of a Random Vaiable Distibution Functions Popeties of Distibution Functions Topic 7 Random Vaiables and Distibution Functions Distibution Functions 1 / 11 Definition of a Random Vaiable Distibution

More information

Detection and Recognition of Alert Traffic Signs

Detection and Recognition of Alert Traffic Signs Detection and Recognition of Alet Taffic Signs Chia-Hsiung Chen, Macus Chen, and Tianshi Gao 1 Stanfod Univesity Stanfod, CA 9305 {echchen, macuscc, tianshig}@stanfod.edu Abstact Taffic signs povide dives

More information

Methods for history matching under geological constraints Jef Caers Stanford University, Petroleum Engineering, Stanford CA , USA

Methods for history matching under geological constraints Jef Caers Stanford University, Petroleum Engineering, Stanford CA , USA Methods fo histoy matching unde geological constaints Jef Caes Stanfod Univesity, Petoleum Engineeing, Stanfod CA 9435-222, USA Abstact Two geostatistical methods fo histoy matching ae pesented. Both ely

More information

Lecture 27: Voronoi Diagrams

Lecture 27: Voronoi Diagrams We say that two points u, v Y ae in the same connected component of Y if thee is a path in R N fom u to v such that all the points along the path ae in the set Y. (Thee ae two connected components in the

More information

On the Forwarding Area of Contention-Based Geographic Forwarding for Ad Hoc and Sensor Networks

On the Forwarding Area of Contention-Based Geographic Forwarding for Ad Hoc and Sensor Networks On the Fowading Aea of Contention-Based Geogaphic Fowading fo Ad Hoc and Senso Netwoks Dazhi Chen Depatment of EECS Syacuse Univesity Syacuse, NY dchen@sy.edu Jing Deng Depatment of CS Univesity of New

More information

UCLA Papers. Title. Permalink. Authors. Publication Date. Localized Edge Detection in Sensor Fields. https://escholarship.org/uc/item/3fj6g58j

UCLA Papers. Title. Permalink. Authors. Publication Date. Localized Edge Detection in Sensor Fields. https://escholarship.org/uc/item/3fj6g58j UCLA Papes Title Localized Edge Detection in Senso Fields Pemalink https://escholashipog/uc/item/3fj6g58j Authos K Chintalapudi Govindan Publication Date 3-- Pee eviewed escholashipog Poweed by the Califonia

More information

DISTRIBUTION MIXTURES

DISTRIBUTION MIXTURES Application Example 7 DISTRIBUTION MIXTURES One fequently deals with andom vaiables the distibution of which depends on vaious factos. One example is the distibution of atmospheic paametes such as wind

More information

POMDP: Introduction to Partially Observable Markov Decision Processes Hossein Kamalzadeh, Michael Hahsler

POMDP: Introduction to Partially Observable Markov Decision Processes Hossein Kamalzadeh, Michael Hahsler POMDP: Intoduction to Patially Obsevable Makov Decision Pocesses Hossein Kamalzadeh, Michael Hahsle 2019-01-02 The R package pomdp povides an inteface to pomdp-solve, a solve (witten in C) fo Patially

More information

WIRELESS sensor networks (WSNs), which are capable

WIRELESS sensor networks (WSNs), which are capable IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS, VOL. XX, NO. XX, XXX 214 1 Lifetime and Enegy Hole Evolution Analysis in Data-Gatheing Wieless Senso Netwoks Ju Ren, Student Membe, IEEE, Yaoxue Zhang, Kuan

More information

Concomitants of Upper Record Statistics for Bivariate Pseudo Weibull Distribution

Concomitants of Upper Record Statistics for Bivariate Pseudo Weibull Distribution Available at http://pvamuedu/aam Appl Appl Math ISSN: 93-9466 Vol 5, Issue (Decembe ), pp 8 9 (Peviously, Vol 5, Issue, pp 379 388) Applications and Applied Mathematics: An Intenational Jounal (AAM) Concomitants

More information

ANALYTIC PERFORMANCE MODELS FOR SINGLE CLASS AND MULTIPLE CLASS MULTITHREADED SOFTWARE SERVERS

ANALYTIC PERFORMANCE MODELS FOR SINGLE CLASS AND MULTIPLE CLASS MULTITHREADED SOFTWARE SERVERS ANALYTIC PERFORMANCE MODELS FOR SINGLE CLASS AND MULTIPLE CLASS MULTITHREADED SOFTWARE SERVERS Daniel A Menascé Mohamed N Bennani Dept of Compute Science Oacle, Inc Geoge Mason Univesity 1211 SW Fifth

More information

A Two-stage and Parameter-free Binarization Method for Degraded Document Images

A Two-stage and Parameter-free Binarization Method for Degraded Document Images A Two-stage and Paamete-fee Binaization Method fo Degaded Document Images Yung-Hsiang Chiu 1, Kuo-Liang Chung 1, Yong-Huai Huang 2, Wei-Ning Yang 3, Chi-Huang Liao 4 1 Depatment of Compute Science and

More information

AUTOMATED LOCATION OF ICE REGIONS IN RADARSAT SAR IMAGERY

AUTOMATED LOCATION OF ICE REGIONS IN RADARSAT SAR IMAGERY AUTOMATED LOCATION OF ICE REGIONS IN RADARSAT SAR IMAGERY Chistophe Waceman (1), William G. Pichel (2), Pablo Clement-Colón (2) (1) Geneal Dynamics Advanced Infomation Systems, P.O. Box 134008 Ann Abo

More information

Bo Gu and Xiaoyan Hong*

Bo Gu and Xiaoyan Hong* Int. J. Ad Hoc and Ubiquitous Computing, Vol. 11, Nos. /3, 1 169 Tansition phase of connectivity fo wieless netwoks with gowing pocess Bo Gu and Xiaoyan Hong* Depatment of Compute Science, Univesity of

More information

Multi-azimuth Prestack Time Migration for General Anisotropic, Weakly Heterogeneous Media - Field Data Examples

Multi-azimuth Prestack Time Migration for General Anisotropic, Weakly Heterogeneous Media - Field Data Examples Multi-azimuth Pestack Time Migation fo Geneal Anisotopic, Weakly Heteogeneous Media - Field Data Examples S. Beaumont* (EOST/PGS) & W. Söllne (PGS) SUMMARY Multi-azimuth data acquisition has shown benefits

More information

MapReduce Optimizations and Algorithms 2015 Professor Sasu Tarkoma

MapReduce Optimizations and Algorithms 2015 Professor Sasu Tarkoma apreduce Optimizations and Algoithms 2015 Pofesso Sasu Takoma www.cs.helsinki.fi Optimizations Reduce tasks cannot stat befoe the whole map phase is complete Thus single slow machine can slow down the

More information

A ROI Focusing Mechanism for Digital Cameras

A ROI Focusing Mechanism for Digital Cameras A ROI Focusing Mechanism fo Digital Cameas Chu-Hui Lee, Meng-Feng Lin, Chun-Ming Huang, and Chun-Wei Hsu Abstact With the development and application of digital technologies, the digital camea is moe popula

More information

Comparisons of Transient Analytical Methods for Determining Hydraulic Conductivity Using Disc Permeameters

Comparisons of Transient Analytical Methods for Determining Hydraulic Conductivity Using Disc Permeameters Compaisons of Tansient Analytical Methods fo Detemining Hydaulic Conductivity Using Disc Pemeametes 1,,3 Cook, F.J. 1 CSRO Land and Wate, ndoooopilly, Queensland The Univesity of Queensland, St Lucia,

More information

Analysis of uniform illumination system with imperfect Lambertian LEDs

Analysis of uniform illumination system with imperfect Lambertian LEDs Optica Applicata, Vol. XLI, No. 3, 2011 Analysis of unifom illumination system with impefect Lambetian LEDs JIAJIE TAN 1, 2, KECHENG YANG 1*, MIN XIA 1, YING YANG 1 1 Wuhan National Laboatoy fo Optoelectonics,

More information

Separability and Topology Control of Quasi Unit Disk Graphs

Separability and Topology Control of Quasi Unit Disk Graphs Sepaability and Topology Contol of Quasi Unit Disk Gaphs Jiane Chen, Anxiao(Andew) Jiang, Iyad A. Kanj, Ge Xia, and Fenghui Zhang Dept. of Compute Science, Texas A&M Univ. College Station, TX 7784. {chen,

More information

A Memory Efficient Array Architecture for Real-Time Motion Estimation

A Memory Efficient Array Architecture for Real-Time Motion Estimation A Memoy Efficient Aay Achitectue fo Real-Time Motion Estimation Vasily G. Moshnyaga and Keikichi Tamau Depatment of Electonics & Communication, Kyoto Univesity Sakyo-ku, Yoshida-Honmachi, Kyoto 66-1, JAPAN

More information

COMPARISON OF CHIRP SCALING AND WAVENUMBER DOMAIN ALGORITHMS FOR AIRBORNE LOW FREQUENCY SAR DATA PROCESSING

COMPARISON OF CHIRP SCALING AND WAVENUMBER DOMAIN ALGORITHMS FOR AIRBORNE LOW FREQUENCY SAR DATA PROCESSING COMPARISON OF CHIRP SCALING AND WAVENUMBER DOMAIN ALGORITHMS FOR AIRBORNE LOW FREQUENCY SAR DATA PROCESSING A. Potsis a, A. Reigbe b, E. Alivisatos a, A. Moeia c,and N. Uzunoglu a a National Technical

More information

On Error Estimation in Runge-Kutta Methods

On Error Estimation in Runge-Kutta Methods Leonado Jounal of Sciences ISSN 1583-0233 Issue 18, Januay-June 2011 p. 1-10 On Eo Estimation in Runge-Kutta Methods Ochoche ABRAHAM 1,*, Gbolahan BOLARIN 2 1 Depatment of Infomation Technology, 2 Depatment

More information

Haptic Glove. Chan-Su Lee. Abstract. This is a final report for the DIMACS grant of student-initiated project. I implemented Boundary

Haptic Glove. Chan-Su Lee. Abstract. This is a final report for the DIMACS grant of student-initiated project. I implemented Boundary Physically Accuate Haptic Rendeing of Elastic Object fo a Haptic Glove Chan-Su Lee Abstact This is a final epot fo the DIMACS gant of student-initiated poject. I implemented Bounday Element Method(BEM)

More information

Augmented Reality. Integrating Computer Graphics with Computer Vision Mihran Tuceryan. August 16, 1998 ICPR 98 1

Augmented Reality. Integrating Computer Graphics with Computer Vision Mihran Tuceryan. August 16, 1998 ICPR 98 1 Augmented Reality Integating Compute Gaphics with Compute Vision Mihan Tuceyan August 6, 998 ICPR 98 Definition XCombines eal and vitual wolds and objects XIt is inteactive and eal-time XThe inteaction

More information

Image Registration among UAV Image Sequence and Google Satellite Image Under Quality Mismatch

Image Registration among UAV Image Sequence and Google Satellite Image Under Quality Mismatch 0 th Intenational Confeence on ITS Telecommunications Image Registation among UAV Image Sequence and Google Satellite Image Unde Quality Mismatch Shih-Ming Huang and Ching-Chun Huang Depatment of Electical

More information

AN ANALYSIS OF COORDINATED AND NON-COORDINATED MEDIUM ACCESS CONTROL PROTOCOLS UNDER CHANNEL NOISE

AN ANALYSIS OF COORDINATED AND NON-COORDINATED MEDIUM ACCESS CONTROL PROTOCOLS UNDER CHANNEL NOISE AN ANALYSIS OF COORDINATED AND NON-COORDINATED MEDIUM ACCESS CONTROL PROTOCOLS UNDER CHANNEL NOISE Tolga Numanoglu, Bulent Tavli, and Wendi Heinzelman Depatment of Electical and Compute Engineeing Univesity

More information

Slotted Random Access Protocol with Dynamic Transmission Probability Control in CDMA System

Slotted Random Access Protocol with Dynamic Transmission Probability Control in CDMA System Slotted Random Access Potocol with Dynamic Tansmission Pobability Contol in CDMA System Intaek Lim 1 1 Depatment of Embedded Softwae, Busan Univesity of Foeign Studies, itlim@bufs.ac.k Abstact In packet

More information

Effective Missing Data Prediction for Collaborative Filtering

Effective Missing Data Prediction for Collaborative Filtering Effective Missing Data Pediction fo Collaboative Filteing Hao Ma, Iwin King and Michael R. Lyu Dept. of Compute Science and Engineeing The Chinese Univesity of Hong Kong Shatin, N.T., Hong Kong { hma,

More information

3D Reconstruction from 360 x 360 Mosaics 1

3D Reconstruction from 360 x 360 Mosaics 1 CENTER FOR MACHINE PERCEPTION 3D Reconstuction fom 36 x 36 Mosaics CZECH TECHNICAL UNIVERSITY {bakstein, pajdla}@cmp.felk.cvut.cz REPRINT Hynek Bakstein and Tomáš Pajdla, 3D Reconstuction fom 36 x 36 Mosaics,

More information

Erasure-Coding Based Routing for Opportunistic Networks

Erasure-Coding Based Routing for Opportunistic Networks Easue-Coding Based Routing fo Oppotunistic Netwoks Yong Wang, Sushant Jain, Magaet Matonosi, Kevin Fall Pinceton Univesity, Univesity of Washington, Intel Reseach Bekeley ABSTRACT Routing in Delay Toleant

More information

Frequency Domain Approach for Face Recognition Using Optical Vanderlugt Filters

Frequency Domain Approach for Face Recognition Using Optical Vanderlugt Filters Optics and Photonics Jounal, 016, 6, 94-100 Published Online August 016 in SciRes. http://www.scip.og/jounal/opj http://dx.doi.og/10.436/opj.016.68b016 Fequency Domain Appoach fo Face Recognition Using

More information

Adaptation of Motion Capture Data of Human Arms to a Humanoid Robot Using Optimization

Adaptation of Motion Capture Data of Human Arms to a Humanoid Robot Using Optimization ICCAS25 June 2-5, KINTEX, Gyeonggi-Do, Koea Adaptation of Motion Captue Data of Human Ams to a Humanoid Robot Using Optimization ChangHwan Kim and Doik Kim Intelligent Robotics Reseach Cente, Koea Institute

More information

Title. Author(s)NOMURA, K.; MOROOKA, S. Issue Date Doc URL. Type. Note. File Information

Title. Author(s)NOMURA, K.; MOROOKA, S. Issue Date Doc URL. Type. Note. File Information Title CALCULATION FORMULA FOR A MAXIMUM BENDING MOMENT AND THE TRIANGULAR SLAB WITH CONSIDERING EFFECT OF SUPPO UNIFORM LOAD Autho(s)NOMURA, K.; MOROOKA, S. Issue Date 2013-09-11 Doc URL http://hdl.handle.net/2115/54220

More information

Elliptic Generation Systems

Elliptic Generation Systems 4 Elliptic Geneation Systems Stefan P. Spekeijse 4.1 Intoduction 4.1 Intoduction 4.2 Two-Dimensional Gid Geneation Hamonic Maps, Gid Contol Maps, and Poisson Systems Discetization and Solution Method Constuction

More information

5 4 THE BERNOULLI EQUATION

5 4 THE BERNOULLI EQUATION 185 CHATER 5 the suounding ai). The fictional wok tem w fiction is often expessed as e loss to epesent the loss (convesion) of mechanical into themal. Fo the idealied case of fictionless motion, the last

More information

Lifetime and Energy Hole Evolution Analysis in Data-Gathering Wireless Sensor Networks

Lifetime and Energy Hole Evolution Analysis in Data-Gathering Wireless Sensor Networks 788 IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS, VOL. 12, NO. 2, APRIL 2016 Lifetime and Enegy Hole Evolution Analysis in Data-Gatheing Wieless Senso Netwoks Ju Ren, Student Membe, IEEE, Yaoxue Zhang,

More information

Towards Adaptive Information Merging Using Selected XML Fragments

Towards Adaptive Information Merging Using Selected XML Fragments Towads Adaptive Infomation Meging Using Selected XML Fagments Ho-Lam Lau and Wilfed Ng Depatment of Compute Science and Engineeing, The Hong Kong Univesity of Science and Technology, Hong Kong {lauhl,

More information

COLOR EDGE DETECTION IN RGB USING JOINTLY EUCLIDEAN DISTANCE AND VECTOR ANGLE

COLOR EDGE DETECTION IN RGB USING JOINTLY EUCLIDEAN DISTANCE AND VECTOR ANGLE COLOR EDGE DETECTION IN RGB USING JOINTLY EUCLIDEAN DISTANCE AND VECTOR ANGLE Slawo Wesolkowski Systems Design Engineeing Univesity of Wateloo Wateloo (Ont.), Canada, NL 3G s.wesolkowski@ieee.og Ed Jenigan

More information

Clustering Interval-valued Data Using an Overlapped Interval Divergence

Clustering Interval-valued Data Using an Overlapped Interval Divergence Poc. of the 8th Austalasian Data Mining Confeence (AusDM'9) Clusteing Inteval-valued Data Using an Ovelapped Inteval Divegence Yongli Ren Yu-Hsn Liu Jia Rong Robet Dew School of Infomation Engineeing,

More information

Obstacle Avoidance of Autonomous Mobile Robot using Stereo Vision Sensor

Obstacle Avoidance of Autonomous Mobile Robot using Stereo Vision Sensor Obstacle Avoidance of Autonomous Mobile Robot using Steeo Vision Senso Masako Kumano Akihisa Ohya Shin ichi Yuta Intelligent Robot Laboatoy Univesity of Tsukuba, Ibaaki, 35-8573 Japan E-mail: {masako,

More information

IP Multicast Simulation in OPNET

IP Multicast Simulation in OPNET IP Multicast Simulation in OPNET Xin Wang, Chien-Ming Yu, Henning Schulzinne Paul A. Stipe Columbia Univesity Reutes Depatment of Compute Science 88 Pakway Dive South New Yok, New Yok Hauppuage, New Yok

More information

THE THETA BLOCKCHAIN

THE THETA BLOCKCHAIN THE THETA BLOCKCHAIN Theta is a decentalized video steaming netwok, poweed by a new blockchain and token. By Theta Labs, Inc. Last Updated: Nov 21, 2017 esion 1.0 1 OUTLINE Motivation Reputation Dependent

More information

Accurate Diffraction Efficiency Control for Multiplexed Volume Holographic Gratings. Xuliang Han, Gicherl Kim, and Ray T. Chen

Accurate Diffraction Efficiency Control for Multiplexed Volume Holographic Gratings. Xuliang Han, Gicherl Kim, and Ray T. Chen Accuate Diffaction Efficiency Contol fo Multiplexed Volume Hologaphic Gatings Xuliang Han, Gichel Kim, and Ray T. Chen Micoelectonic Reseach Cente Depatment of Electical and Compute Engineeing Univesity

More information

Scaling Location-based Services with Dynamically Composed Location Index

Scaling Location-based Services with Dynamically Composed Location Index Scaling Location-based Sevices with Dynamically Composed Location Index Bhuvan Bamba, Sangeetha Seshadi and Ling Liu Distibuted Data Intensive Systems Laboatoy (DiSL) College of Computing, Geogia Institute

More information

17/5/2009. Introduction

17/5/2009. Introduction 7/5/9 Steeo Imaging Intoduction Eample of Human Vision Peception of Depth fom Left and ight eye images Diffeence in elative position of object in left and ight eyes. Depth infomation in the views?? 7/5/9

More information

A Recommender System for Online Personalization in the WUM Applications

A Recommender System for Online Personalization in the WUM Applications A Recommende System fo Online Pesonalization in the WUM Applications Mehdad Jalali 1, Nowati Mustapha 2, Ali Mamat 2, Md. Nasi B Sulaiman 2 Abstact foeseeing of use futue movements and intentions based

More information

Experimental and numerical simulation of the flow over a spillway

Experimental and numerical simulation of the flow over a spillway Euopean Wate 57: 253-260, 2017. 2017 E.W. Publications Expeimental and numeical simulation of the flow ove a spillway A. Seafeim *, L. Avgeis, V. Hissanthou and K. Bellos Depatment of Civil Engineeing,

More information

4.2. Co-terminal and Related Angles. Investigate

4.2. Co-terminal and Related Angles. Investigate .2 Co-teminal and Related Angles Tigonometic atios can be used to model quantities such as

More information

Hierarchical Region Mean-Based Image Segmentation

Hierarchical Region Mean-Based Image Segmentation Hieachical Region Mean-Based Image Segmentation Slawo Wesolkowski and Paul Fieguth Systems Design Engineeing Univesity of Wateloo Wateloo, Ontaio, Canada, N2L-3G1 s.wesolkowski@ieee.og, pfieguth@uwateloo.ca

More information

A Shape-preserving Affine Takagi-Sugeno Model Based on a Piecewise Constant Nonuniform Fuzzification Transform

A Shape-preserving Affine Takagi-Sugeno Model Based on a Piecewise Constant Nonuniform Fuzzification Transform A Shape-peseving Affine Takagi-Sugeno Model Based on a Piecewise Constant Nonunifom Fuzzification Tansfom Felipe Fenández, Julio Gutiéez, Juan Calos Cespo and Gacián Tiviño Dep. Tecnología Fotónica, Facultad

More information

A VECTOR PERTURBATION APPROACH TO THE GENERALIZED AIRCRAFT SPARE PARTS GROUPING PROBLEM

A VECTOR PERTURBATION APPROACH TO THE GENERALIZED AIRCRAFT SPARE PARTS GROUPING PROBLEM Accepted fo publication Intenational Jounal of Flexible Automation and Integated Manufactuing. A VECTOR PERTURBATION APPROACH TO THE GENERALIZED AIRCRAFT SPARE PARTS GROUPING PROBLEM Nagiza F. Samatova,

More information

And Ph.D. Candidate of Computer Science, University of Putra Malaysia 2 Faculty of Computer Science and Information Technology,

And Ph.D. Candidate of Computer Science, University of Putra Malaysia 2 Faculty of Computer Science and Information Technology, (IJCSIS) Intenational Jounal of Compute Science and Infomation Secuity, Efficient Candidacy Reduction Fo Fequent Patten Mining M.H Nadimi-Shahaki 1, Nowati Mustapha 2, Md Nasi B Sulaiman 2, Ali B Mamat

More information

ISyE 4256 Industrial Robotic Applications

ISyE 4256 Industrial Robotic Applications ISyE 456 Industial Robotic Applications Quiz # Oct. 9, 998 Name This is a closed book, closed notes exam. Show wok fo poblem questions ) ( pts) Please cicle one choice fo each item. a) In an application,

More information

Event-based Location Dependent Data Services in Mobile WSNs

Event-based Location Dependent Data Services in Mobile WSNs Event-based Location Dependent Data Sevices in Mobile WSNs Liang Hong 1, Yafeng Wu, Sang H. Son, Yansheng Lu 3 1 College of Compute Science and Technology, Wuhan Univesity, China Depatment of Compute Science,

More information

Approximating Euclidean Distance Transform with Simple Operations in Cellular Processor Arrays

Approximating Euclidean Distance Transform with Simple Operations in Cellular Processor Arrays 00 th Intenational Wokshop on Cellula Nanoscale Netwoks and thei Applications (CNNA) Appoximating Euclidean Distance Tansfom with Simple Opeations in Cellula Pocesso Aas Samad Razmjooei and Piot Dudek

More information

Desired Attitude Angles Design Based on Optimization for Side Window Detection of Kinetic Interceptor *

Desired Attitude Angles Design Based on Optimization for Side Window Detection of Kinetic Interceptor * Poceedings of the 7 th Chinese Contol Confeence July 6-8, 008, Kunming,Yunnan, China Desied Attitude Angles Design Based on Optimization fo Side Window Detection of Kinetic Intecepto * Zhu Bo, Quan Quan,

More information

A New and Efficient 2D Collision Detection Method Based on Contact Theory Xiaolong CHENG, Jun XIAO a, Ying WANG, Qinghai MIAO, Jian XUE

A New and Efficient 2D Collision Detection Method Based on Contact Theory Xiaolong CHENG, Jun XIAO a, Ying WANG, Qinghai MIAO, Jian XUE 5th Intenational Confeence on Advanced Mateials and Compute Science (ICAMCS 2016) A New and Efficient 2D Collision Detection Method Based on Contact Theoy Xiaolong CHENG, Jun XIAO a, Ying WANG, Qinghai

More information

(a, b) x y r. For this problem, is a point in the - coordinate plane and is a positive number.

(a, b) x y r. For this problem, is a point in the - coordinate plane and is a positive number. Illustative G-C Simila cicles Alignments to Content Standads: G-C.A. Task (a, b) x y Fo this poblem, is a point in the - coodinate plane and is a positive numbe. a. Using a tanslation and a dilation, show

More information

Improved Fourier-transform profilometry

Improved Fourier-transform profilometry Impoved Fouie-tansfom pofilomety Xianfu Mao, Wenjing Chen, and Xianyu Su An impoved optical geomety of the pojected-finge pofilomety technique, in which the exit pupil of the pojecting lens and the entance

More information

Hierarchically Clustered P2P Streaming System

Hierarchically Clustered P2P Streaming System Hieachically Clusteed P2P Steaming System Chao Liang, Yang Guo, and Yong Liu Polytechnic Univesity Thomson Lab Booklyn, NY 11201 Pinceton, NJ 08540 Abstact Pee-to-pee video steaming has been gaining populaity.

More information

2. PROPELLER GEOMETRY

2. PROPELLER GEOMETRY a) Fames of Refeence 2. PROPELLER GEOMETRY 10 th Intenational Towing Tank Committee (ITTC) initiated the pepaation of a dictionay and nomenclatue of ship hydodynamic tems and this wok was completed in

More information

A Mathematical Implementation of a Global Human Walking Model with Real-Time Kinematic Personification by Boulic, Thalmann and Thalmann.

A Mathematical Implementation of a Global Human Walking Model with Real-Time Kinematic Personification by Boulic, Thalmann and Thalmann. A Mathematical Implementation of a Global Human Walking Model with Real-Time Kinematic Pesonification by Boulic, Thalmann and Thalmann. Mashall Badley National Cente fo Physical Acoustics Univesity of

More information

Adaptation of TDMA Parameters Based on Network Conditions

Adaptation of TDMA Parameters Based on Network Conditions Adaptation of TDMA Paametes Based on Netwok Conditions Boa Kaaoglu Dept. of Elect. and Compute Eng. Univesity of Rocheste Rocheste, NY 14627 Email: kaaoglu@ece.ocheste.edu Tolga Numanoglu Dept. of Elect.

More information

Spiral Recognition Methodology and Its Application for Recognition of Chinese Bank Checks

Spiral Recognition Methodology and Its Application for Recognition of Chinese Bank Checks Spial Recognition Methodology and Its Application fo Recognition of Chinese Bank Checks Hanshen Tang 1, Emmanuel Augustin 2, Ching Y. Suen 1, Olivie Baet 2, Mohamed Cheiet 3 1 Cente fo Patten Recognition

More information

Module 6 STILL IMAGE COMPRESSION STANDARDS

Module 6 STILL IMAGE COMPRESSION STANDARDS Module 6 STILL IMAE COMPRESSION STANDARDS Lesson 17 JPE-2000 Achitectue and Featues Instuctional Objectives At the end of this lesson, the students should be able to: 1. State the shotcomings of JPE standad.

More information

View Synthesis using Depth Map for 3D Video

View Synthesis using Depth Map for 3D Video View Synthesis using Depth Map fo 3D Video Cheon Lee and Yo-Sung Ho Gwangju Institute of Science and Technology (GIST) 1 Oyong-dong, Buk-gu, Gwangju, 500-712, Republic of Koea E-mail: {leecheon, hoyo}@gist.ac.k

More information

Gravitational Shift for Beginners

Gravitational Shift for Beginners Gavitational Shift fo Beginnes This pape, which I wote in 26, fomulates the equations fo gavitational shifts fom the elativistic famewok of special elativity. Fist I deive the fomulas fo the gavitational

More information