The Multitarget/Multisensor Tracking Problem

Size: px
Start display at page:

Download "The Multitarget/Multisensor Tracking Problem"

Transcription

1 The Multitarget/Multisensor Tracking Problem Alexander Toet, Huub de Waard 11 April 1995 CALMA Report CALMA.TNO.WP31.AT.95d 1

2 CONTENTS Page SUMMARY 3 SAMENVATTING 4 1 INTRODUCTION 5 2 THE MULTITARGET/MULTISENSOR TRACKING PROBLEM 5 3 THE MULTIDIMENSIONAL ASSIGNMENT FORMULATION 7 4 CONCLUDING REMARKS 11 REFERENCES 13

3 The Multitarget/Multisensor Tracking Problem A. Toet and H. de Waard SUMMARY Various combinatorial optimization techniques are currently available. Most of these techniques have not been thourougly tested on realistic problems. The EUCLID (EUropean Cooperation for the Long term In Defence) CALMA (Combinatorial Algorithms for Military Applications) RTP (Research and Technology Project) 6.4 project has the main objective to investigate the relevance of various existing algorithmic optimization techniques to the actual solution of complex combinatorial problems arising in military applications. It has recently been shown that the data association problems arising both in multitarget/multisensor tracking and in multisensor data fusion can be formulated as multidimensional assignment problems (Poore, 1994). This report briefly reproduces the derivation of this formulation. No attempt is made to solve the multitarget/multisensor tracking and multisensor data fusion problems here. However, it is suggested that the assignment formulation turns these problems into good candidates for the testbed that is required for the last part of the CALMA study, which will be a comparative evaluation of the different optimization techniques that were studied and/or developed in the earlier stages of this project. The outcome of this comparative study may lead to a better understanding of the applicability of these methods.

4 Het Volgen van Meerdere Doelen A. Toet en H. de Waard SAMENVATTING Er zijn tegenwoordig verscheidene combinatorische optimalizatietechnieken beschikbaar. De meeste daarvan zijn niet volledig getest op realistische problemen. Het EUCLID (EUropean Cooperation for the Long term In Defence) CALMA (Combinatorial Algorithms for Military Applications) RTP (Research and Technology Project) 6.4 project heeft als voornaamste doel het onderzoeken van de bruikbaarheid van verschillende bestaande combinatorische optimalizatie technieken voor het oplossen van complexe combinatorische problemen zoals die voorkomen in militaire omgevingen. Recentelijk werd aangetoond dat de data associatie problemen die zowel in multitarget/multisensor tracking en in multisensor fusie voorkomen geformuleerd kunnen worden als een multidimensionaal toewijzings probleem. Dit rapport geeft een beknopte afleiding van deze formulering. De multitarget/multisensor tracking en multisensor data fusie problemen zelf worden in dit rapport niet opgelost. Er wordt slechts voorgestelt dat de herformulering van deze problemen als toewijzingsproblemen ze goed geschikt maakt om te dienen als een testomgeving waarin de verschillende optimalizatietechnieken, die in eerdere stadia van het CALMA project werden ontwikkeld en bestudeerd, met elkaar kunnen worden vergeleken. De uitkomst van een dergelijke excercitie kan mogelijk inzicht verschaffen in de praktische toepasbaarheid van deze technieken.

5 1 INTRODUCTION In military operations, problems in planning and scheduling often require feasible and close to optimal solutions with limited computing resources and within very short time periods. Various approaches to combinatorial problem solving have emerged over the last three decades. Most of these have only been tested on a few simplified problems (e.g. the Traveling Salesman Problem ). It is presently not known to what extent they can solve complex realistic problems as those arising in military appplications, and what the required computing resources are. The EUCLID (EUropean Cooperation for the Long term In Defence) CALMA (Combinatorial Algorithms for Military Applications) RTP (Research and Technology Project) 6.4 project has the main objective to investigate the relevance of the various existing algorithmic techniques to the actual solution of some of the most complex combinatorial problems arising in military applications. In the context of the CALMA project, the application of various existing algorithmic optimization techniques to some realistic problems of military relevance may serve to gain a better understanding of what makes a combinatorial problem solving approach adequate on some problems and inadequate on others. The various techniques may for instance be compared with respect to - the quality of the solution, - the runtime performances, - the tradeoff between quality and computing time, - the memory requirements, - the ease of implementation and the flexibility e.g. with respect to progressively adding new constraints to the problem, and - the stability with respect to small perturbations in the data. This report briefly reproduces the derivation of a multidimensional assignment formulation of the data association problems arising both in multitarget/multisensor tracking and in multisensor data fusion. This formulation was first presented by Poore (1994). It turns the abovementioned problems into optimization problems that may serve as testbeds to compare the relative performance of the combinatorial optimization techniques studied in the CALMA project. 2 THE MULTITARGET/MULTISENSOR TRACKING PROBLEM One of the key functions performed by a surveillance system is to keep track of all the targets of interest within the coverage region of its sensors. For military surveillance systems, the coverage region generally involves several thousand cubic miles containing several hundred targets. Typical sensors used in these surveillance systems (e.g. radars) cannot provide perfect information about the targets. In general, sensor measurements of the

6 targets tend to be ambiguous (it is not clear to which target a measurement corresponds), incorrect (reports of false targets), and imprecise (random errors in the measurements composing a report). The design of a multitarget/multisensor tracking algorithm for such surveillance systems poses a difficult problem. Multitarget tracking has many applications, both in military and in civilian areas. For instance, application areas include ballistic missile defense (reentry vehicles), air defense (enemy aircraft), air traffic control (civil air traffic), ocean surveillance (surface ships and submarines), and battlefield surveillance (ground vehicles and military units). The central problem of multitarget tracking is that of data association the problem of determining from which target, if any, a particular measurement originates (Bar-Shalom and Fortman, 1988; Blackman, 1986; Reid, 1979; Waltz and Llinas, 1990). The problem is especially difficult in situations where there are missing reports (probability of detection less than unity), unknown targets (requiring track initiation), and false reports (from clutter). Current methods for multitarget tracking generally fall into two categories: sequential and deferred logic. Methods based on sequential logic include nearest neighbour, one-to-one or few-to-many assignments, and all-to-one assignments (Bar-Shalom and Fortman, 1988). For track maintenance, the nearest neigbour method is valid in the absence of clutter when there is little or no track contention, i.e. when there is little chance of misallocation. Problems involving one-to-one or few-to-one assignments are generally formulated as (2D) assigment or multi-assignment problems, for which there are some excellent algorithms (Bertsekas, 1991; Bertsekas and Castañon,1992; Jonker and Volgenant, 1987). This methodology can be performed real-time, but can result in a large number of partial and incorrect assignments in dense and high contention scenarios, and thus incorrect track identification. The difficulty is that decisions, once made, are irrevocable, so that there is no mechanism to correct misassociations. The use of all observations in a scan or within a neighbourhood of a predicted track position to update a track has been successful in tracking a few targets in dense clutter (Bar-Shalom and Fortman, 1988). Deferred logic techniques consider several data sets or scans of data all at once in making data associations. At one extreme is batch processing, in which all observations (from all time) are processed together. This is computationally too intensive for real-time applications. The other extreme is sequential processing. The principal deferred logic method used to track large numbers of targets in low to moderate clutter is called multiple hypothesis tracking (MHT). This method builds a tree of posibilities, assigns a likelihood score to each track, develops an intricate pruning logic, and then solves the data association problem by an explicit enumeration scheme. The use of these enumeration schemes to solve this NP-hard combinatorial optimization problem in real-time is inevitably faulty in dense scenarios, since the time required to solve the problem optimally can grow exponentially in the size of the problem. Another important aspect in surveillance systems is the growing use of multisensor data fusion (Bar-Shalom, 1990; Blackman, 1990; Deb et al., 1993; Waltz and Llinas, 1990), in which one associates reports from multiple sensors together. Once matched, this more

7 varied information has the potential to greatly enhance target identification and state estimation (Blackman, 1990). The central problem is again that of data association and the principal method employed is multiple hypothesis tracking. Similar data association problems occur in other fields of research, such as edge grouping and contour segmentation in image analysis (e.g. Cox et al., 1993). Some general classes of data association problems in multitarget tracking and multisensor data fusion have recently been formulated as multidimensional assignment problems (Pattipati et al., 1990; Poore, 1994). The objective function is derived from a composite negative log posterior or likelihood function for each of the track reports. This formulation covers the popular multiple hypothesis tracking method introduced by Reid (1979) and modified by Kurien (1990) to include maneuvering targets and terminations, and the work of Deb et al. (1993) on centralized multisensor data fusion. The only known method to solve the NP-hard multidimensional assignment problems is branch-and-bound. However, this approach is too computationally intensive to produce real time solutions, especially in dense scenarios. Since the objective function is generally noisy due to various sources of errors (e.g. plant noise, observation errors, and uncertainty about the exact values of various probability parameters), one only needs to solve these problems to or just below the noise level in the problem. The goal of algorithm development is therefore the computation of high quality and near optimal solutions. Several algorithms based on Lagrangian relaxation have been and continue to be developed (Poore and Rijavic, 1993, 1994). These algorithms are near optimal, provide a lower and upper bound on the optimal value, and work real time for many scenarios. 3 THE MULTIDIMENSIONAL ASSIGNMENT FORMULATION In tracking, a common surveillance problem is to estimate the past, current, or future state of a collection of objects (e.g. airplanes), moving in three dimensional space, from a sequence of measurements made of the surveillance region by one or more sensors. The objects will be called targets. The dynamics of these targets are generally modeled from physical laws of motion. However, there may be noise measurementsz(k)=fzkikgmk in the dynamics and certain parameters of the motion may be unknown. At timet=0 one or more sensors are turned on to observe the region. In an ideal situation measurements are taken at a finite sequence of timesftkgnk=0, where 0=t0<t1<<tn. Due to the finite amount of time required for a sensor to sweep the surveillance region, measurements are generally made asynchronously, i.e. not at the same time, so that a time tag is associated with each measurement. At each time tkthe sensor produces a sequence of where eachzkikis ik=1 a vector of noise contaminated measurements. The actual type of measurement is sensor dependent. For example, a 2D radar measures range and azimuth of each potential target, a 3D radar measures range, azimuth, and elevation, a 3D radar with Doppler measures these together with the time derivative of the range, and a 2D passive sensor measures the azimuth and elevation angle. Some of the measurements may be false, and the number of targets and which measurement emanates from which target are not known a priori. The

8 problems are then(a)to determine the number of targets, which measurements go with which targets and which are false (i.e. the data association problem), and(b)to estimate the state of each target given a sequence of measurements that emanate from that target. As part of posing the data association problem one must estimate the state of a potential target fzkikgmk given a particular sequence of measurements from the data setsfz(k)gnk=1. Thus, the two problems of data association and state estimation are inseparable parts of the same problem. Z(k)=fzkikgMk ZN=fZ(1);:::;Z(N)g (1) In the surveillance example, the data sets are measurements made of the surveillance region. To allow for more general types of data such as tracks and target descriptions, the elements in the data sets will be called reports (Reid,1979). LetZ(k)denote a data set ofmkreports and letzndenote the cumulative data set ofnsuch sets defined by ik=1 and ik=1 respectively. In multisensor data fusion and multitarget tracking the data setsz(k)may represent different classes of objects. For track initiation in multitarget tracking the objects are measurements that must be partitioned into tracks and false alarms. For track maintenance, one data set will be tracks, and the remaining data sets will be measurements which are either(a)assigned IN=fI(1);I(2);:::;I(N)g to existing tracks,(b)marked as false measurements, or(c)used to initiate new tracks. Now it will be defined by=f1;:::;n()j8i:i6=;g; I(k)=fikgMk (2) what is meant by a partition of the cumulative data setznin Equation 1. Since this partition is to be independent of the actual data in the data setzn, the partition will be defined on the set of indices inzn. Let i\j=; where IN=n() i6=j; ik=1 denote the indices in the data sets (1). A partitionofinand the collection of all such partitions Γis defined (3) for (4) Γ=fjsatisfies(3)?(5)g: (6) [j=1j; (5) Here,iin Equation 3 represents a track, so thatn()denotes the number of tracks (or elements) Clearly,Zi\Zj=;fori6=jandZN=Sn() (7) in the partition. A2Γis called a set partitioning of the indicesinif properties (3) (5) are valid, a set covering ofinif property (4) is omitted but the other two properties (3) and (5) are retained, and a set packing if (5) is omitted but (3) and (4) are retained. A partition2γof the index setininduces a partition of the data setznvia j=1zj. EachZjwill be called a track of data. The definition of a partition in Equations 3 and 7 implies that each actual report Z=fZ1;:::;Zn()gwhereZi=ffzkikgik2igNk=1: belongs to at most one track of reportsziin a partitionzof the cumulative data set.

9 Max(P(Γ=jZN) P(Γ=0jZN)j2Γ) (8) The combinatorial optimization problem that governs a large number of data association problems in multitarget tracking and multisensor data fusion is generally posed as Γ ZN where representsndata sets (1), is a partition of the indices of the data (Eqs. 2 and 3), is the finite collection of all such partitions (3), Γ is a discrete random element defined on Γ, 0 is a reference partition, and P(Γ=jZN)is the P(Γ=jZN)=p(ZNjΓ=)PΓ(Γ=) posterior probability of a partitionbeing true given the datazn. The objective function in the optimization problem (8) can be converted into an equivalent linear one by making some independence assumptions for the density functionp(znjγ= p(znjγ=)=y p(zn) : (9) )and the probabilitypγ(γ=)in Bayes formula p(zijγ=)=p(zijγ=!)8;!2γ; PΓ(Γ=)=Cn() These assumptions are respectively (11) i2p(zijγ=); Yi=1G(i); (10) (12) where Cis a constant independent of the partition2γ, and Gis a probability distribution on the set of tracksiin Equation 3. A probabilistic framework that illustrates each of these assumptions was presented by Poore (1994). Since for each2γ,zcorresponds P(Γ=jZN)= p(zn)p(znjγ=)pγ(γ=) to a partition of the data inton()feasible tracks of data, Equation 10 says that then()tracks of data,z1;:::;zn(), are independent if is the true track. (There will of course be dependence between reports within a single track.) Equation 11 states that these tracks are independent across all partitions of the data. Substitution of Equation 10 in Bayes formula (Eq. 9) gives 1 (13)

10 p(zn)24n() = p(zn)y C Yi=1p(Zi)35P(Γ=) 1 (14) Equation 13 is Bayes formula. IfPΓ(Γ=)=C, a constant, over all partitions2γ, then Equation 14 is proportional to the likelihood function. Otherwise, the expansion (15) follows from Equation 12. Thus, Equation 15 includes both the likelihood function with the idenficationc=1 andg(i)=1 and the posterior function for a more general probability distributiongon the tracks. This equation will now be transformed into an assignment formulation. Zi=Zi1:::in(z1i1;:::;zNiN) i=(i1;:::;in) For notational convenience in representing tracks, a zero index is added to each of the index setsi(k)(k=1;:::;n)in Equation 2, a dummy reportzk0 to each of the data sets in Equation 1, while (16) byi=(0;:::;0;ik;0;:::;0)andzi= whereikandzkikcan now adopt the values 0 andzk0 respectively. The dummy report serves several purposes in the representation of missing data, false reports, initiating and terminating tracks. IfZiis missing actual report from the data setz(k), theni=(i1;:::;ik?1;0;ik+1;:::;in)andzi=fz1i1;:::;zk?1 ik?1;0;zk+1 ik+1;:::;zning. A zk0 false reportzkik(ik>0)is represented fz1 0;:::;zk?1 (17) there is but one actual report. The partition 0 of the data in which all reports are declared to be false reports is defined by Z0=fZ0:::0ik0:::0z1 0;:::;zk?1 Let each data setz(k)represent a scan of measurements. A track that initiates on scan m>1 will contain only the dummy reportzk0 from each of the data setsz(k)for each k=1;:::;m?1. Likewise, a track that terminates on scanmonly has the dummy report from each of the data sets fork>m. The cumlative (i1;:::;ik?1;ik+1;:::;in)=(0;:::;0)zi1:::in=1forik=1;:::;mkandk=1;:::;n: (M1;:::;Mk?1;Mk+1;:::;MN) X data setzncan be seen as a set of equality constraints with the help (18) of a binary 0-1 variable zi1:::in=1;if(i1;:::;in)2, 0;otherwise which transforms Equations 3 17 into P(Γ=0jZN)L P(Γ=jZN) (i1:::in)2li1:::in Y (19) Equation 15 can be written as a likelihood ratio: i2p(zi)g(i) (15) 0;:::;zN0jik=1;:::;Mk;k=1;:::;Ng: 0;zkik;zk+1 0;:::;zN0gin which 0;zkik;zk+1

11 Li1:::iN= QNk=1;ik6=0p(Zo:::0ik0:::0)G(Zo:::0ik0:::0): p(zi1:::in)g(zi1:::in)?ln"p(jzn) P(0jZN)#= ci1:::in=?lnli1:::in; (i1:::in)2ci1:::in: X Let Xi1=0MN in=0ci1:::inzi1:::in X i2=0pmn in=0zi1:::in=1;i1=1;:::;m1; ik+1=0pmn in?1=0zi1:::in=1;in=1;:::;mn; PM2 i1;:::;in; PM1 i1=0pmk?1 ik?1=0pmk+1 in=0zi1:::in=1;for ik=1;:::;mkandk=2;:::;n?1, PM1 i1=0pmn?1 zi1:::in2f0;1gfor all (21) (20) where (22) so that (23) The optimization problem (8) can now be written as the following N-dimensional assignment problem: MinM1 subject to wherec0:::0 is arbitrarily defined to be zero. The complexity of the optimization problem (23) makes its formulation and solution formidable. In fact, it is NP-hard (Garvey and Johnson, 1979). The computation of all the cost coefficients can be a time consuming task. For example, six scans of measurements with one hundred measurements per scan requires the computation of one trillion cost coefficients for track initiation. Thus preprocessing is essential to reduce the complexity. One class of preprocessing methods for sensor fusion and tracking is called gating (Bar-Shalom and Fortman, 1988; Blackman, 1986). The idea of gating is to compute only those cost coefficients that are feasible for the underlying physical problem, thereby removing unlikely pairings of measurements. Another commonly used complexity reducing technique is that of clustering (Bar-Shalom, 1990; Blackman, 1990). This method decomposes the problem into a number of smaller independent problems. 4 CONCLUDING REMARKS The data association problems arising both in multitarget/multisensor tracking and in multisensor data fusion are actual real-time defence industry problems with a large number of military and civilian appplications. The multidimensional assignment formulation of

12 these problems (Pattipati et al., 1990; Poore, 1994) turns them into good candidates for the testbed that is required for the last part of the CALMA study, which will be a comparative evaluation of the different optimization techniques that were studied and/or developed in the earlier stages of this project. The outcome of the comparative study may lead to a better understanding of the applicability of these optimization methods.

13 REFERENCES Bar-Shalom, Y. (Ed., 1990) Multitarget-multisensor Tracking: Advanced Applications. Artech House, Norwood, MA. Bar-Shalom, Y. and Fortman, T.E. (1988). Tracking and Data Association. Academic Press, Boston. Bertsekas, D.P. (1991). Linear Network Optimization: Algorithms and Code. MIT Press, Cambridge, Mass. Bertsekas, D.P. and Castañon, D.A. (1991). A forward/reverse auction algorithm for asymmetric assignment problems. Computational Optimization and Applications 1, pp Blackman, S.S. (1986). Multiple Target Tracking with Applications. Artech House, Norwood, MA. Blackman, S.S. (1990). Association and fusion of multiple sensor data. In: Bar-Shalom, Y. (Ed.), Multitarget-multisensor Tracking: Advanced Applications. Artech House, Norwood, MA, pp Cox, I.J., Rehg, J.M. and Hingorani, S. (1993). A Bayesian multiple hypothesis approach to contour grouping and segmentation. Int. J. of Computer Vision 11, pp Deb, S., Pattipati, K.R., and Bar-Shalom, Y. (1993). A multisensor-multitarget data asociation algorithm for heterogeneous systems. IEEE Tr. on Aerospace and Electronic Systems 29, pp Garvey, M.R. and Johnson, D.S.(1979). Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman and Co., CA. Jonker, R. and Volgenant, T. (1987). A shortest augmenting path algorithm for dense and sparse linear assignment problems. Computing 38, pp Kurien, T. (1990). Issues in the designing of practical multitarget tracking algorithms. In: Bar- Shalom, Y. (Ed.), Multitarget-multisensor Tracking: Advanced Applications. Artech House, Norwood, MA, pp Pattipati, K.R., Deb, S., and Bar-Shalom, Y. (1990). Passive multisensor data association using a new relaxation algorithm. In: Bar-Shalom, Y. (Ed.), Multitarget-multisensor Tracking: Advanced Applications. Artech House, Norwood, MA, pp Poore, A.B. (1994). Multidimensional assignment formulation of data association problems arising from multitarget and multisensor tracking. Computational Optimization and Applications 3, pp Poore, A.B. and Rijavic, N. (1993). A Lagrangian relaxation algorithm for multidimensional assignment problems. In: Drummond, O.E. (Ed.), Proc. of the 1991 SPIE Conf. on Signal and Data Processing of Small Targets, vol. 1481, pp Poore, A.B. and Rijavic, N. (1994). Partitioning multiple data sets: multidimensional assignments and Lagrangian relaxation. To appear in: DIMACS Series in Discrete Mathematics and Theoretical Computer Science. Reid, D.B. (1979). An algorithm for tracking multiple targets. IEEE Tr. on Automatic Control AC-24, pp

14 Waltz, E. and Llinas, J. (1990). Multisensor Data Fusion. Artech House, Boston. Soesterberg, 11 April 1995 Dr. A. Toet

15 30 woorden abstract Er wordt een beknopte afleiding gegeven van de manier waarop het probleem van het volgen van meerdere doelen, met gebruikmaking van meerdere sensoren, kan worden herschreven als een optimalizatie probleem (en wel een meer-dimensionaal toewijzingsprobleem). In deze formulering kan dit probleem goed dienen als een testomgeving waarin de verschillende optimalizatietechnieken, die in eerdere stadia van het CALMA project werden ontwikkeld en bestudeerd, met elkaar kunnen worden vergeleken. Descriptors Target Acquisition Identifiers multiple hypothesis testing multiple target tracking multisensor fusion optimization

16 MANAGEMENT UITTREKSEL Er zijn tegenwoordig verscheidene combinatorische optimalizatietechnieken beschikbaar. De meeste daarvan zijn niet volledig getest op realistische problemen. Het EUCLID (EUropean Cooperation for the Long term In Defence) CALMA (Combinatorial Algorithms for Military Applications) RTP (Research and Technology Project) 6.4 project heeft als voornaamste doel het onderzoeken van de bruikbaarheid van verschillende bestaande combinatorische optimalizatie technieken voor het oplossen van complexe combinatorische problemen zoals die voorkomen in militaire omgevingen. Het volgen van meerdere doelen heeft veel toepassingen, zowel in de militaire als ook in de civiele sfeer. Toepassingen zijn o.a. de verdediging tegen raketaanvallen (reentry vehicles), luchtverdedigingssytemen (tegen vijandige vliegtuigen), lucht verkeerscontrole (civiele luchtvaart), bewaking van zeegebieden (voor oppervlakte verkeer en duikboten), en slagveld bewaking (de detectie van voertuigen en militaire eenheden). Een van de belangrijkste functies van een surveillance systeem is het volgen van alle interessante doelen binnen het door de sensoren bestreken gebied. Voor militaire systemen beslaat dit gebied vaak enkele duizenden kubieke kilometers die honderden doelen kunnen bevatten. Doorgaans geven de gebruikte sensoren (bijv. radar) geen perfecte informatie over de doelen. De sensor metingen zijn vaak ambigu (het is niet duidelijk van welk doel een meting afkomstig is), incorrect (een meting correspondeert met een vals alarm), en onnauwkeurig (random fouten in de meetwaarden). Deze problemen maken het ontwerpen van algoritmen voor het volgen van meerdere doelen met gebruikmaking van meerdere sensoren tot een complexe taak. Recentelijk werd aangetoond dat de data associatie problemen, die zowel in multitarget/multisensor tracking en in multisensor fusie voorkomen, geformuleerd kunnen worden als een multidimensionaal toewijzings probleem. Dit rapport geeft een beknopte afleiding van deze herformulering. Het probleem zelf wordt in dit rapport niet opgelost. Er wordt slechts voorgestelt dat de herformulering van deze problemen als toewijzingsproblemen ze goed geschikt maakt om te dienen als een testomgeving waarin de verschillende optimalizatietechnieken, die in eerdere stadia van het CALMA project werden ontwikkeld en bestudeerd, met elkaar kunnen worden vergeleken. De uitkomst van een dergelijke excercitie kan mogelijk inzicht verschaffen in de praktische toepasbaarheid van deze technieken.

GMP-Z Annex 15: Kwalificatie en validatie

GMP-Z Annex 15: Kwalificatie en validatie -Z Annex 15: Kwalificatie en validatie item Gewijzigd richtsnoer -Z Toelichting Principle 1. This Annex describes the principles of qualification and validation which are applicable to the manufacture

More information

Information Theory and Coding Prof. S. N. Merchant Department of Electrical Engineering Indian Institute of Technology, Bombay

Information Theory and Coding Prof. S. N. Merchant Department of Electrical Engineering Indian Institute of Technology, Bombay Information Theory and Coding Prof. S. N. Merchant Department of Electrical Engineering Indian Institute of Technology, Bombay Lecture - 17 Shannon-Fano-Elias Coding and Introduction to Arithmetic Coding

More information

Exploiting A Constellation of Narrowband RF Sensors to Detect and Track Moving Targets

Exploiting A Constellation of Narrowband RF Sensors to Detect and Track Moving Targets Exploiting A Constellation of Narrowband RF Sensors to Detect and Track Moving Targets Chris Kreucher a, J. Webster Stayman b, Ben Shapo a, and Mark Stuff c a Integrity Applications Incorporated 900 Victors

More information

Understanding and Applying Kalman Filtering

Understanding and Applying Kalman Filtering Understanding and Applying Kalman Filtering Lindsay Kleeman Department of Electrical and Computer Systems Engineering Monash University, Clayton 1 Introduction Objectives: 1. Provide a basic understanding

More information

SPECIAL PERTURBATIONS UNCORRELATED TRACK PROCESSING

SPECIAL PERTURBATIONS UNCORRELATED TRACK PROCESSING AAS 07-228 SPECIAL PERTURBATIONS UNCORRELATED TRACK PROCESSING INTRODUCTION James G. Miller * Two historical uncorrelated track (UCT) processing approaches have been employed using general perturbations

More information

Multisensor Data Fusion and Applications

Multisensor Data Fusion and Applications Multisensor Data Fusion and Applications Pramod K. Varshney Department of Electrical Engineering and Computer Science Syracuse University 121 Link Hall Syracuse, New York 13244 USA E-mail: varshney@syr.edu

More information

CSRQ Center Rapport over schoolhervormingsmodellen voor basisscholen Samenvatting voor onderwijsgevenden

CSRQ Center Rapport over schoolhervormingsmodellen voor basisscholen Samenvatting voor onderwijsgevenden CSRQ Center Rapport over schoolhervormingsmodellen voor basisscholen Samenvatting voor onderwijsgevenden Laatst bijgewerkt op 25 november 2008 Nederlandse samenvatting door TIER op 29 juni 2011 Welke schoolverbeteringsprogramma

More information

A Statistical Framework for Operational Infrasound Monitoring

A Statistical Framework for Operational Infrasound Monitoring A Statistical Framework for Operational Infrasound Monitoring Stephen J. Arrowsmith Rod W. Whitaker LA-UR 11-03040 The views expressed here do not necessarily reflect the views of the United States Government,

More information

Message-passing sequential detection of multiple change points in networks

Message-passing sequential detection of multiple change points in networks Message-passing sequential detection of multiple change points in networks Long Nguyen, Arash Amini Ram Rajagopal University of Michigan Stanford University ISIT, Boston, July 2012 Nguyen/Amini/Rajagopal

More information

24. The Branch and Bound Method

24. The Branch and Bound Method 24. The Branch and Bound Method It has serious practical consequences if it is known that a combinatorial problem is NP-complete. Then one can conclude according to the present state of science that no

More information

Probability Hypothesis Density filter versus Multiple Hypothesis Tracking

Probability Hypothesis Density filter versus Multiple Hypothesis Tracking Probability Hypothesis Density filter versus Multiple Hypothesis Tracing Kusha Panta a, Ba-Ngu Vo a, Sumeetpal Singh a and Arnaud Doucet b a Co-operative Research Centre for Sensor and Information Processing

More information

Course: Model, Learning, and Inference: Lecture 5

Course: Model, Learning, and Inference: Lecture 5 Course: Model, Learning, and Inference: Lecture 5 Alan Yuille Department of Statistics, UCLA Los Angeles, CA 90095 yuille@stat.ucla.edu Abstract Probability distributions on structured representation.

More information

CO-BRANDING RICHTLIJNEN

CO-BRANDING RICHTLIJNEN A minimum margin surrounding the logo keeps CO-BRANDING RICHTLIJNEN 22 Last mei revised, 2013 30 April 2013 The preferred version of the co-branding logo is white on a Magenta background. Depending on

More information

The Kendall Rank Correlation Coefficient

The Kendall Rank Correlation Coefficient The Kendall Rank Correlation Coefficient Hervé Abdi Overview The Kendall (955) rank correlation coefficient evaluates the degree of similarity between two sets of ranks given to a same set of objects.

More information

INTEGER PROGRAMMING. Integer Programming. Prototype example. BIP model. BIP models

INTEGER PROGRAMMING. Integer Programming. Prototype example. BIP model. BIP models Integer Programming INTEGER PROGRAMMING In many problems the decision variables must have integer values. Example: assign people, machines, and vehicles to activities in integer quantities. If this is

More information

JUST-IN-TIME SCHEDULING WITH PERIODIC TIME SLOTS. Received December May 12, 2003; revised February 5, 2004

JUST-IN-TIME SCHEDULING WITH PERIODIC TIME SLOTS. Received December May 12, 2003; revised February 5, 2004 Scientiae Mathematicae Japonicae Online, Vol. 10, (2004), 431 437 431 JUST-IN-TIME SCHEDULING WITH PERIODIC TIME SLOTS Ondřej Čepeka and Shao Chin Sung b Received December May 12, 2003; revised February

More information

JUST THE MATHS UNIT NUMBER 8.5. VECTORS 5 (Vector equations of straight lines) A.J.Hobson

JUST THE MATHS UNIT NUMBER 8.5. VECTORS 5 (Vector equations of straight lines) A.J.Hobson JUST THE MATHS UNIT NUMBER 8.5 VECTORS 5 (Vector equations of straight lines) by A.J.Hobson 8.5.1 Introduction 8.5. The straight line passing through a given point and parallel to a given vector 8.5.3

More information

A REVIEW ON KALMAN FILTER FOR GPS TRACKING

A REVIEW ON KALMAN FILTER FOR GPS TRACKING A REVIEW ON KALMAN FILTER FOR GPS TRACKING Ms. SONAL(Student, M.Tech ), Dr. AJIT SINGH (Professor in CSE & IT) Computer Science & Engg. (Network Security) BPS Mahila Vishwavidyalaya Khanpur Kalan, Haryana

More information

NP-Completeness and Cook s Theorem

NP-Completeness and Cook s Theorem NP-Completeness and Cook s Theorem Lecture notes for COM3412 Logic and Computation 15th January 2002 1 NP decision problems The decision problem D L for a formal language L Σ is the computational task:

More information

An Optimization Approach for Cooperative Communication in Ad Hoc Networks

An Optimization Approach for Cooperative Communication in Ad Hoc Networks An Optimization Approach for Cooperative Communication in Ad Hoc Networks Carlos A.S. Oliveira and Panos M. Pardalos University of Florida Abstract. Mobile ad hoc networks (MANETs) are a useful organizational

More information

Motivated by a problem faced by a large manufacturer of a consumer product, we

Motivated by a problem faced by a large manufacturer of a consumer product, we A Coordinated Production Planning Model with Capacity Expansion and Inventory Management Sampath Rajagopalan Jayashankar M. Swaminathan Marshall School of Business, University of Southern California, Los

More information

A Performance Comparison of Five Algorithms for Graph Isomorphism

A Performance Comparison of Five Algorithms for Graph Isomorphism A Performance Comparison of Five Algorithms for Graph Isomorphism P. Foggia, C.Sansone, M. Vento Dipartimento di Informatica e Sistemistica Via Claudio, 21 - I 80125 - Napoli, Italy {foggiapa, carlosan,

More information

Annotation Guidelines for Dutch-English Word Alignment

Annotation Guidelines for Dutch-English Word Alignment Annotation Guidelines for Dutch-English Word Alignment version 1.0 LT3 Technical Report LT3 10-01 Lieve Macken LT3 Language and Translation Technology Team Faculty of Translation Studies University College

More information

Common Core Unit Summary Grades 6 to 8

Common Core Unit Summary Grades 6 to 8 Common Core Unit Summary Grades 6 to 8 Grade 8: Unit 1: Congruence and Similarity- 8G1-8G5 rotations reflections and translations,( RRT=congruence) understand congruence of 2 d figures after RRT Dilations

More information

Offline 1-Minesweeper is NP-complete

Offline 1-Minesweeper is NP-complete Offline 1-Minesweeper is NP-complete James D. Fix Brandon McPhail May 24 Abstract We use Minesweeper to illustrate NP-completeness proofs, arguments that establish the hardness of solving certain problems.

More information

Experiments on the local load balancing algorithms; part 1

Experiments on the local load balancing algorithms; part 1 Experiments on the local load balancing algorithms; part 1 Ştefan Măruşter Institute e-austria Timisoara West University of Timişoara, Romania maruster@info.uvt.ro Abstract. In this paper the influence

More information

Why? A central concept in Computer Science. Algorithms are ubiquitous.

Why? A central concept in Computer Science. Algorithms are ubiquitous. Analysis of Algorithms: A Brief Introduction Why? A central concept in Computer Science. Algorithms are ubiquitous. Using the Internet (sending email, transferring files, use of search engines, online

More information

Performance Level Descriptors Grade 6 Mathematics

Performance Level Descriptors Grade 6 Mathematics Performance Level Descriptors Grade 6 Mathematics Multiplying and Dividing with Fractions 6.NS.1-2 Grade 6 Math : Sub-Claim A The student solves problems involving the Major Content for grade/course with

More information

Specification by Example (methoden, technieken en tools) Remco Snelders Product owner & Business analyst

Specification by Example (methoden, technieken en tools) Remco Snelders Product owner & Business analyst Specification by Example (methoden, technieken en tools) Remco Snelders Product owner & Business analyst Terminologie Specification by Example (SBE) Acceptance Test Driven Development (ATDD) Behaviour

More information

PATTERN RECOGNITION AND MACHINE LEARNING CHAPTER 4: LINEAR MODELS FOR CLASSIFICATION

PATTERN RECOGNITION AND MACHINE LEARNING CHAPTER 4: LINEAR MODELS FOR CLASSIFICATION PATTERN RECOGNITION AND MACHINE LEARNING CHAPTER 4: LINEAR MODELS FOR CLASSIFICATION Introduction In the previous chapter, we explored a class of regression models having particularly simple analytical

More information

Discrete Optimization

Discrete Optimization Discrete Optimization [Chen, Batson, Dang: Applied integer Programming] Chapter 3 and 4.1-4.3 by Johan Högdahl and Victoria Svedberg Seminar 2, 2015-03-31 Todays presentation Chapter 3 Transforms using

More information

On the Traffic Capacity of Cellular Data Networks. 1 Introduction. T. Bonald 1,2, A. Proutière 1,2

On the Traffic Capacity of Cellular Data Networks. 1 Introduction. T. Bonald 1,2, A. Proutière 1,2 On the Traffic Capacity of Cellular Data Networks T. Bonald 1,2, A. Proutière 1,2 1 France Telecom Division R&D, 38-40 rue du Général Leclerc, 92794 Issy-les-Moulineaux, France {thomas.bonald, alexandre.proutiere}@francetelecom.com

More information

Relationele Databases 2002/2003

Relationele Databases 2002/2003 1 Relationele Databases 2002/2003 Hoorcollege 5 22 mei 2003 Jaap Kamps & Maarten de Rijke April Juli 2003 Plan voor Vandaag Praktische dingen 3.8, 3.9, 3.10, 4.1, 4.4 en 4.5 SQL Aantekeningen 3 Meer Queries.

More information

Mapping an Application to a Control Architecture: Specification of the Problem

Mapping an Application to a Control Architecture: Specification of the Problem Mapping an Application to a Control Architecture: Specification of the Problem Mieczyslaw M. Kokar 1, Kevin M. Passino 2, Kenneth Baclawski 1, and Jeffrey E. Smith 3 1 Northeastern University, Boston,

More information

Offline sorting buffers on Line

Offline sorting buffers on Line Offline sorting buffers on Line Rohit Khandekar 1 and Vinayaka Pandit 2 1 University of Waterloo, ON, Canada. email: rkhandekar@gmail.com 2 IBM India Research Lab, New Delhi. email: pvinayak@in.ibm.com

More information

Support Vector Machines with Clustering for Training with Very Large Datasets

Support Vector Machines with Clustering for Training with Very Large Datasets Support Vector Machines with Clustering for Training with Very Large Datasets Theodoros Evgeniou Technology Management INSEAD Bd de Constance, Fontainebleau 77300, France theodoros.evgeniou@insead.fr Massimiliano

More information

Math Review. for the Quantitative Reasoning Measure of the GRE revised General Test

Math Review. for the Quantitative Reasoning Measure of the GRE revised General Test Math Review for the Quantitative Reasoning Measure of the GRE revised General Test www.ets.org Overview This Math Review will familiarize you with the mathematical skills and concepts that are important

More information

Load Balancing and Switch Scheduling

Load Balancing and Switch Scheduling EE384Y Project Final Report Load Balancing and Switch Scheduling Xiangheng Liu Department of Electrical Engineering Stanford University, Stanford CA 94305 Email: liuxh@systems.stanford.edu Abstract Load

More information

Simulating Variable Message Signs Influencing dynamic route choice in microsimulation

Simulating Variable Message Signs Influencing dynamic route choice in microsimulation Simulating Variable Message Signs Influencing dynamic route choice in microsimulation N.D. Cohn, Grontmij Traffic & Transport, nick.cohn@grontmij.nl P. Krootjes, International School of Breda, pronos@ricardis.tudelft.nl

More information

Detection of changes in variance using binary segmentation and optimal partitioning

Detection of changes in variance using binary segmentation and optimal partitioning Detection of changes in variance using binary segmentation and optimal partitioning Christian Rohrbeck Abstract This work explores the performance of binary segmentation and optimal partitioning in the

More information

Social Media Mining. Data Mining Essentials

Social Media Mining. Data Mining Essentials Introduction Data production rate has been increased dramatically (Big Data) and we are able store much more data than before E.g., purchase data, social media data, mobile phone data Businesses and customers

More information

Machine Learning. Chapter 18, 21. Some material adopted from notes by Chuck Dyer

Machine Learning. Chapter 18, 21. Some material adopted from notes by Chuck Dyer Machine Learning Chapter 18, 21 Some material adopted from notes by Chuck Dyer What is learning? Learning denotes changes in a system that... enable a system to do the same task more efficiently the next

More information

Doorstroommogelijkheden in 3TU-verband in 2008 en 2009

Doorstroommogelijkheden in 3TU-verband in 2008 en 2009 Doorstroommogelijkheden in 3TU-verband in 2008 en 2009 Toelichting: In het onderstaande overzicht is per technische bacheloropleiding aangegeven welke masteropleidingen een drempelloze toelating, dan wel

More information

Tracking based on graph of pairs of plots

Tracking based on graph of pairs of plots INFORMATIK 0 - Informati schafft Communities 4. Jahrestagung der Gesellschaft für Informati, 4.-7.0.0, Berlin www.informati0.de Tracing based on graph of pairs of plots Frédéric Livernet, Aline Campillo-Navetti

More information

Another Look at Sensitivity of Bayesian Networks to Imprecise Probabilities

Another Look at Sensitivity of Bayesian Networks to Imprecise Probabilities Another Look at Sensitivity of Bayesian Networks to Imprecise Probabilities Oscar Kipersztok Mathematics and Computing Technology Phantom Works, The Boeing Company P.O.Box 3707, MC: 7L-44 Seattle, WA 98124

More information

OGH: : 11g in de praktijk

OGH: : 11g in de praktijk OGH: : 11g in de praktijk Real Application Testing SPREKER : E-MAIL : PATRICK MUNNE PMUNNE@TRANSFER-SOLUTIONS.COM DATUM : 14-09-2010 WWW.TRANSFER-SOLUTIONS.COM Real Application Testing Uitleg Real Application

More information

2004 Networks UK Publishers. Reprinted with permission.

2004 Networks UK Publishers. Reprinted with permission. Riikka Susitaival and Samuli Aalto. Adaptive load balancing with OSPF. In Proceedings of the Second International Working Conference on Performance Modelling and Evaluation of Heterogeneous Networks (HET

More information

Enhancing the SNR of the Fiber Optic Rotation Sensor using the LMS Algorithm

Enhancing the SNR of the Fiber Optic Rotation Sensor using the LMS Algorithm 1 Enhancing the SNR of the Fiber Optic Rotation Sensor using the LMS Algorithm Hani Mehrpouyan, Student Member, IEEE, Department of Electrical and Computer Engineering Queen s University, Kingston, Ontario,

More information

Synthetic Aperture Radar: Principles and Applications of AI in Automatic Target Recognition

Synthetic Aperture Radar: Principles and Applications of AI in Automatic Target Recognition Synthetic Aperture Radar: Principles and Applications of AI in Automatic Target Recognition Paulo Marques 1 Instituto Superior de Engenharia de Lisboa / Instituto de Telecomunicações R. Conselheiro Emídio

More information

ruimtelijk ontwikkelingsbeleid

ruimtelijk ontwikkelingsbeleid 38 S a n d e r O u d e E l b e r i n k Digitale bestemmingsplannen 3D MODELLING OF TOPOGRAPHIC Geo-informatie OBJECTS en BY FUSING 2D MAPS AND LIDAR DATA ruimtelijk ontwikkelingsbeleid in Nederland INTRODUCTION

More information

An Overview of Knowledge Discovery Database and Data mining Techniques

An Overview of Knowledge Discovery Database and Data mining Techniques An Overview of Knowledge Discovery Database and Data mining Techniques Priyadharsini.C 1, Dr. Antony Selvadoss Thanamani 2 M.Phil, Department of Computer Science, NGM College, Pollachi, Coimbatore, Tamilnadu,

More information

Bayesian Statistics: Indian Buffet Process

Bayesian Statistics: Indian Buffet Process Bayesian Statistics: Indian Buffet Process Ilker Yildirim Department of Brain and Cognitive Sciences University of Rochester Rochester, NY 14627 August 2012 Reference: Most of the material in this note

More information

The Problem of Scheduling Technicians and Interventions in a Telecommunications Company

The Problem of Scheduling Technicians and Interventions in a Telecommunications Company The Problem of Scheduling Technicians and Interventions in a Telecommunications Company Sérgio Garcia Panzo Dongala November 2008 Abstract In 2007 the challenge organized by the French Society of Operational

More information

BINOMIAL OPTIONS PRICING MODEL. Mark Ioffe. Abstract

BINOMIAL OPTIONS PRICING MODEL. Mark Ioffe. Abstract BINOMIAL OPTIONS PRICING MODEL Mark Ioffe Abstract Binomial option pricing model is a widespread numerical method of calculating price of American options. In terms of applied mathematics this is simple

More information

Proprietary Kroll Ontrack. Data recovery Data management Electronic Evidence

Proprietary Kroll Ontrack. Data recovery Data management Electronic Evidence Data recovery Data management Electronic Evidence Back-up migratie of consolidatie TAPE SERVICES Overview The Legacy Tape Environment Common Legacy Tape Scenarios Available Options Tape Service Components

More information

The Conference Call Search Problem in Wireless Networks

The Conference Call Search Problem in Wireless Networks The Conference Call Search Problem in Wireless Networks Leah Epstein 1, and Asaf Levin 2 1 Department of Mathematics, University of Haifa, 31905 Haifa, Israel. lea@math.haifa.ac.il 2 Department of Statistics,

More information

5 INTEGER LINEAR PROGRAMMING (ILP) E. Amaldi Fondamenti di R.O. Politecnico di Milano 1

5 INTEGER LINEAR PROGRAMMING (ILP) E. Amaldi Fondamenti di R.O. Politecnico di Milano 1 5 INTEGER LINEAR PROGRAMMING (ILP) E. Amaldi Fondamenti di R.O. Politecnico di Milano 1 General Integer Linear Program: (ILP) min c T x Ax b x 0 integer Assumption: A, b integer The integrality condition

More information

A Constraint Programming based Column Generation Approach to Nurse Rostering Problems

A Constraint Programming based Column Generation Approach to Nurse Rostering Problems Abstract A Constraint Programming based Column Generation Approach to Nurse Rostering Problems Fang He and Rong Qu The Automated Scheduling, Optimisation and Planning (ASAP) Group School of Computer Science,

More information

Real Time Traffic Monitoring With Bayesian Belief Networks

Real Time Traffic Monitoring With Bayesian Belief Networks Real Time Traffic Monitoring With Bayesian Belief Networks Sicco Pier van Gosliga TNO Defence, Security and Safety, P.O.Box 96864, 2509 JG The Hague, The Netherlands +31 70 374 02 30, sicco_pier.vangosliga@tno.nl

More information

Solution of Linear Systems

Solution of Linear Systems Chapter 3 Solution of Linear Systems In this chapter we study algorithms for possibly the most commonly occurring problem in scientific computing, the solution of linear systems of equations. We start

More information

A Spectral Clustering Approach to Validating Sensors via Their Peers in Distributed Sensor Networks

A Spectral Clustering Approach to Validating Sensors via Their Peers in Distributed Sensor Networks A Spectral Clustering Approach to Validating Sensors via Their Peers in Distributed Sensor Networks H. T. Kung Dario Vlah {htk, dario}@eecs.harvard.edu Harvard School of Engineering and Applied Sciences

More information

PRACTICE BOOK COMPUTER SCIENCE TEST. Graduate Record Examinations. This practice book contains. Become familiar with. Visit GRE Online at www.gre.

PRACTICE BOOK COMPUTER SCIENCE TEST. Graduate Record Examinations. This practice book contains. Become familiar with. Visit GRE Online at www.gre. This book is provided FREE with test registration by the Graduate Record Examinations Board. Graduate Record Examinations This practice book contains one actual full-length GRE Computer Science Test test-taking

More information

EMERGENCIES IVAO BE 28 OCT. 2006. by Bob van der Flier IVAO-TA12 & PATCO

EMERGENCIES IVAO BE 28 OCT. 2006. by Bob van der Flier IVAO-TA12 & PATCO De afbeelding kan niet worden weergegeven. Het is mogelijk dat er onvoldoende geheugen beschikbaar is op de computer om de afbeelding te openen of dat de afbeelding beschadigd is. Start de computer opnieuw

More information

Dynamic Programming and Graph Algorithms in Computer Vision

Dynamic Programming and Graph Algorithms in Computer Vision Dynamic Programming and Graph Algorithms in Computer Vision Pedro F. Felzenszwalb and Ramin Zabih Abstract Optimization is a powerful paradigm for expressing and solving problems in a wide range of areas,

More information

Signal Detection. Outline. Detection Theory. Example Applications of Detection Theory

Signal Detection. Outline. Detection Theory. Example Applications of Detection Theory Outline Signal Detection M. Sami Fadali Professor of lectrical ngineering University of Nevada, Reno Hypothesis testing. Neyman-Pearson (NP) detector for a known signal in white Gaussian noise (WGN). Matched

More information

Security-Aware Beacon Based Network Monitoring

Security-Aware Beacon Based Network Monitoring Security-Aware Beacon Based Network Monitoring Masahiro Sasaki, Liang Zhao, Hiroshi Nagamochi Graduate School of Informatics, Kyoto University, Kyoto, Japan Email: {sasaki, liang, nag}@amp.i.kyoto-u.ac.jp

More information

Marketing Mix Modelling and Big Data P. M Cain

Marketing Mix Modelling and Big Data P. M Cain 1) Introduction Marketing Mix Modelling and Big Data P. M Cain Big data is generally defined in terms of the volume and variety of structured and unstructured information. Whereas structured data is stored

More information

Risk Management for IT Security: When Theory Meets Practice

Risk Management for IT Security: When Theory Meets Practice Risk Management for IT Security: When Theory Meets Practice Anil Kumar Chorppath Technical University of Munich Munich, Germany Email: anil.chorppath@tum.de Tansu Alpcan The University of Melbourne Melbourne,

More information

Risk-Based Monitoring

Risk-Based Monitoring Risk-Based Monitoring Evolutions in monitoring approaches Voorkomen is beter dan genezen! Roelf Zondag 1 wat is Risk-Based Monitoring? en waarom doen we het? en doen we het al? en wat is lastig hieraan?

More information

A Network Flow Approach in Cloud Computing

A Network Flow Approach in Cloud Computing 1 A Network Flow Approach in Cloud Computing Soheil Feizi, Amy Zhang, Muriel Médard RLE at MIT Abstract In this paper, by using network flow principles, we propose algorithms to address various challenges

More information

LOAD BALANCING IN WDM NETWORKS THROUGH DYNAMIC ROUTE CHANGES

LOAD BALANCING IN WDM NETWORKS THROUGH DYNAMIC ROUTE CHANGES LOAD BALANCING IN WDM NETWORKS THROUGH DYNAMIC ROUTE CHANGES S.Ramanathan 1, G.Karthik 1, Ms.G.Sumathi 2 1 Dept. of computer science Sri Venkateswara College of engineering, Sriperumbudur, 602 105. 2 Asst.professor,

More information

Uw partner in system management oplossingen

Uw partner in system management oplossingen Uw partner in system management oplossingen User Centric IT Bring your Own - Corporate Owned Onderzoek Forrester Welke applicatie gebruik je het meest op mobiele devices? Email 76% SMS 67% IM / Chat 48%

More information

100 Series Keyboard Tray Pivot

100 Series Keyboard Tray Pivot 00 Series Keyboard Tray Pivot INSTALLATION MANUAL USA -800-888-8458 Europe +3 0 3.9.39 A B 3/3" 4x 8-3 x 5/6" Ergonomics Ergonomía Ergonomie Ergonomi 888-99-04 REMOVE PIVOT COVERS IF ALREADY ATTACHED.

More information

International Journal of Computer Science Trends and Technology (IJCST) Volume 3 Issue 3, May-June 2015

International Journal of Computer Science Trends and Technology (IJCST) Volume 3 Issue 3, May-June 2015 RESEARCH ARTICLE OPEN ACCESS Data Mining Technology for Efficient Network Security Management Ankit Naik [1], S.W. Ahmad [2] Student [1], Assistant Professor [2] Department of Computer Science and Engineering

More information

The CUSUM algorithm a small review. Pierre Granjon

The CUSUM algorithm a small review. Pierre Granjon The CUSUM algorithm a small review Pierre Granjon June, 1 Contents 1 The CUSUM algorithm 1.1 Algorithm............................... 1.1.1 The problem......................... 1.1. The different steps......................

More information

TCOM 370 NOTES 99-4 BANDWIDTH, FREQUENCY RESPONSE, AND CAPACITY OF COMMUNICATION LINKS

TCOM 370 NOTES 99-4 BANDWIDTH, FREQUENCY RESPONSE, AND CAPACITY OF COMMUNICATION LINKS TCOM 370 NOTES 99-4 BANDWIDTH, FREQUENCY RESPONSE, AND CAPACITY OF COMMUNICATION LINKS 1. Bandwidth: The bandwidth of a communication link, or in general any system, was loosely defined as the width of

More information

A Game Theoretical Framework for Adversarial Learning

A Game Theoretical Framework for Adversarial Learning A Game Theoretical Framework for Adversarial Learning Murat Kantarcioglu University of Texas at Dallas Richardson, TX 75083, USA muratk@utdallas Chris Clifton Purdue University West Lafayette, IN 47907,

More information

IMPROVING DATA INTEGRATION FOR DATA WAREHOUSE: A DATA MINING APPROACH

IMPROVING DATA INTEGRATION FOR DATA WAREHOUSE: A DATA MINING APPROACH IMPROVING DATA INTEGRATION FOR DATA WAREHOUSE: A DATA MINING APPROACH Kalinka Mihaylova Kaloyanova St. Kliment Ohridski University of Sofia, Faculty of Mathematics and Informatics Sofia 1164, Bulgaria

More information

DYNAMIC RANGE IMPROVEMENT THROUGH MULTIPLE EXPOSURES. Mark A. Robertson, Sean Borman, and Robert L. Stevenson

DYNAMIC RANGE IMPROVEMENT THROUGH MULTIPLE EXPOSURES. Mark A. Robertson, Sean Borman, and Robert L. Stevenson c 1999 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or

More information

user checks! improve your design significantly"

user checks! improve your design significantly user checks! improve your design significantly" Workshop by Userneeds - Anouschka Scholten Assisted by ArjanneAnouk Interact Arjanne de Wolf AmsterdamUX Meet up - June 3, 2015 Make people s lives better.

More information

Cloud Computing is NP-Complete

Cloud Computing is NP-Complete Working Paper, February 2, 20 Joe Weinman Permalink: http://www.joeweinman.com/resources/joe_weinman_cloud_computing_is_np-complete.pdf Abstract Cloud computing is a rapidly emerging paradigm for computing,

More information

Chapter 14 Managing Operational Risks with Bayesian Networks

Chapter 14 Managing Operational Risks with Bayesian Networks Chapter 14 Managing Operational Risks with Bayesian Networks Carol Alexander This chapter introduces Bayesian belief and decision networks as quantitative management tools for operational risks. Bayesian

More information

Protein Protein Interaction Networks

Protein Protein Interaction Networks Functional Pattern Mining from Genome Scale Protein Protein Interaction Networks Young-Rae Cho, Ph.D. Assistant Professor Department of Computer Science Baylor University it My Definition of Bioinformatics

More information

Performance of networks containing both MaxNet and SumNet links

Performance of networks containing both MaxNet and SumNet links Performance of networks containing both MaxNet and SumNet links Lachlan L. H. Andrew and Bartek P. Wydrowski Abstract Both MaxNet and SumNet are distributed congestion control architectures suitable for

More information

Time-Series Prediction with Applications to Traffic and Moving Objects Databases

Time-Series Prediction with Applications to Traffic and Moving Objects Databases Time-Series Prediction with Applications to Traffic and Moving Objects Databases Bo Xu Department of Computer Science University of Illinois at Chicago Chicago, IL 60607, USA boxu@cs.uic.edu Ouri Wolfson

More information

Tracking Groups of Pedestrians in Video Sequences

Tracking Groups of Pedestrians in Video Sequences Tracking Groups of Pedestrians in Video Sequences Jorge S. Marques Pedro M. Jorge Arnaldo J. Abrantes J. M. Lemos IST / ISR ISEL / IST ISEL INESC-ID / IST Lisbon, Portugal Lisbon, Portugal Lisbon, Portugal

More information

Example: Credit card default, we may be more interested in predicting the probabilty of a default than classifying individuals as default or not.

Example: Credit card default, we may be more interested in predicting the probabilty of a default than classifying individuals as default or not. Statistical Learning: Chapter 4 Classification 4.1 Introduction Supervised learning with a categorical (Qualitative) response Notation: - Feature vector X, - qualitative response Y, taking values in C

More information

Statistics in Retail Finance. Chapter 6: Behavioural models

Statistics in Retail Finance. Chapter 6: Behavioural models Statistics in Retail Finance 1 Overview > So far we have focussed mainly on application scorecards. In this chapter we shall look at behavioural models. We shall cover the following topics:- Behavioural

More information

Compression algorithm for Bayesian network modeling of binary systems

Compression algorithm for Bayesian network modeling of binary systems Compression algorithm for Bayesian network modeling of binary systems I. Tien & A. Der Kiureghian University of California, Berkeley ABSTRACT: A Bayesian network (BN) is a useful tool for analyzing the

More information

Dynamic Stochastic Optimization of Relocations in Container Terminals

Dynamic Stochastic Optimization of Relocations in Container Terminals Dynamic Stochastic Optimization of Relocations in Container Terminals Setareh Borjian Vahideh H. Manshadi Cynthia Barnhart Patrick Jaillet June 25, 2013 Abstract In this paper, we present a mathematical

More information

princeton univ. F 13 cos 521: Advanced Algorithm Design Lecture 6: Provable Approximation via Linear Programming Lecturer: Sanjeev Arora

princeton univ. F 13 cos 521: Advanced Algorithm Design Lecture 6: Provable Approximation via Linear Programming Lecturer: Sanjeev Arora princeton univ. F 13 cos 521: Advanced Algorithm Design Lecture 6: Provable Approximation via Linear Programming Lecturer: Sanjeev Arora Scribe: One of the running themes in this course is the notion of

More information

COMPUTING CLOUD MOTION USING A CORRELATION RELAXATION ALGORITHM Improving Estimation by Exploiting Problem Knowledge Q. X. WU

COMPUTING CLOUD MOTION USING A CORRELATION RELAXATION ALGORITHM Improving Estimation by Exploiting Problem Knowledge Q. X. WU COMPUTING CLOUD MOTION USING A CORRELATION RELAXATION ALGORITHM Improving Estimation by Exploiting Problem Knowledge Q. X. WU Image Processing Group, Landcare Research New Zealand P.O. Box 38491, Wellington

More information

Principles of Fund Governance BNP Paribas Investment Partners Funds (Nederland) N.V.

Principles of Fund Governance BNP Paribas Investment Partners Funds (Nederland) N.V. Principles of Fund Governance BNP Paribas Investment Partners Funds (Nederland) N.V. Versie november 2012 Inleiding Het doel van de Principles of Fund Governance (verder Principles ) is het geven van nadere

More information

Examen Software Engineering 2010-2011 05/09/2011

Examen Software Engineering 2010-2011 05/09/2011 Belangrijk: Schrijf je antwoorden kort en bondig in de daartoe voorziene velden. Elke theorie-vraag staat op 2 punten (totaal op 24). De oefening staan in totaal op 16 punten. Het geheel staat op 40 punten.

More information

IP-NBM. Copyright Capgemini 2012. All Rights Reserved

IP-NBM. Copyright Capgemini 2012. All Rights Reserved IP-NBM 1 De bescheidenheid van een schaker 2 Maar wat betekent dat nu 3 De drie elementen richting onsterfelijkheid Genomics Artifical Intelligence (nano)robotics 4 De impact van automatisering en robotisering

More information

Introduction to Mobile Robotics Bayes Filter Particle Filter and Monte Carlo Localization

Introduction to Mobile Robotics Bayes Filter Particle Filter and Monte Carlo Localization Introduction to Mobile Robotics Bayes Filter Particle Filter and Monte Carlo Localization Wolfram Burgard, Maren Bennewitz, Diego Tipaldi, Luciano Spinello 1 Motivation Recall: Discrete filter Discretize

More information

Assuring the Cloud. Hans Bootsma Deloitte Risk Services hbootsma@deloitte.nl +31 (0)6 1098 0182

Assuring the Cloud. Hans Bootsma Deloitte Risk Services hbootsma@deloitte.nl +31 (0)6 1098 0182 Assuring the Cloud Hans Bootsma Deloitte Risk Services hbootsma@deloitte.nl +31 (0)6 1098 0182 Need for Assurance in Cloud Computing Demand Fast go to market Support innovation Lower costs Access everywhere

More information

State of Stress at Point

State of Stress at Point State of Stress at Point Einstein Notation The basic idea of Einstein notation is that a covector and a vector can form a scalar: This is typically written as an explicit sum: According to this convention,

More information

MAYORGAME (BURGEMEESTERGAME)

MAYORGAME (BURGEMEESTERGAME) GATE Pilot Safety MAYORGAME (BURGEMEESTERGAME) Twan Boerenkamp Who is it about? Local council Beleidsteam = GBT or Regional Beleidsteam = RBT Mayor = Chairman Advisors now = Voorlichting? Official context

More information

On the k-path cover problem for cacti

On the k-path cover problem for cacti On the k-path cover problem for cacti Zemin Jin and Xueliang Li Center for Combinatorics and LPMC Nankai University Tianjin 300071, P.R. China zeminjin@eyou.com, x.li@eyou.com Abstract In this paper we

More information