MODEL SELECTION CRITERIA FOR ACOUSTIC SEGMENTATION
|
|
- Egbert Palmer
- 5 years ago
- Views:
Transcription
1 = = = MODEL SELECTION CRITERIA FOR ACOUSTIC SEGMENTATION Mauro Cettolo and Marcello Federico ITC-irst - Centro per la Ricerca Scientifica e Tecnoloica I-385 Povo, Trento, Italy ABSTRACT Robust acoustic sementation has become a critical issue in order to apply speech reconition to audio streams with variable acoustic content, e.. radio prorams. Many techniques in the literature base sementation on statistical model selection, by applyin the Bayesian Information Criterion. This work reviews alternative model selection criteria and presents comparative experiments both under controlled conditions and on a broadcast news corpus. 1. INTRODUCTION The problem of acoustic sementation and classification has become crucial to the application of automatic speech reconition to audio stream processin. For instance, in order to enerate transcripts of broadcast news prorams, it is necessary to isolate and filter out portions of the sinal which do not contain speech, e.. jinles and sinature tunes. Moreover, transcription accuracy can be sinificantly improved, by usin condition dependent acoustic models, if the speech sinal is semented and classified accordin to bandwidth, speaker ender, and speaker identity. In recent years, several alorithms have been presented which use a statistical decision criterion to detect spectral chanes (SCs) within the feature space of the sinal. Assumin that data are enerated by a Gaussian process, SCs are detected within a slidin window throuh a model selection method. The most likely SC is tested by comparin two hypothesis: (i) the window contains data enerated by the same distribution; (ii) the left and riht semi-windows, with respect to to the SC point, contain data drawn by two different distributions. The test is performed with a likelihood ratio that, besides the maximum likelihood of each hypothesis, takes into account the different size of the correspondin models. Usually, the Bayesian Information Criterion () [11] is applied to select the simplest and best fittin model. This paper reviews alternative model selection criteria and presents comparative experiments both on synthetic data and real audio data. 2. SEGMENTATION PROBLEM Acoustic sementation can be seen as a particular instance of the more eneral problem of partitionin data into distinct homoeneous reions [2]. The data partitionin problem arises in all applications which require to partition data into chunks, e.. imae processin, data minin, text processin, etc. The problem can be formulated as follows. Let be an ordered sample of data in the space. We assume that the data are enerated by a Gaussian process with at most transitions. The problem of sementation is that of detectin all the transition points in the data set. The eneral problem can be approached, without loss of enerality, by first considerin the simplest case. Sinle Transition Detection The search of one potential transition point oes throuh the definition of different statistical models: two-sement models ( ), each of them assumin: "!$#%# '&(*),+ - /. (1) 21!$#%# '&(*),+ - /. 3 (2) one sinle-sement model which assumes: 4 * 5! & ),+ -$ /. (3) The basic idea is to choose the model (6879$: ) that better fits the observations. The application of the maximum likelihood principle would however invariably lead to choosin one of the two-sement models, and hence to hypothesize a break point at some (;, as they have a hiher number of free parameters than the one-sement model. In order to take into account the notion of dimension of the model, the followin extension to the maximum likelihood principle was first proposed by Akaike [1]. The (Akaike s Information Criterion) suests to maximize the likelihood for each model < separately, obtainin say #> the model. # )?, and then choose the model for # EDF# is larest, where D*# is the dimension of Computations Given a sample G G G!$#%# H&IF),+ -$ /. the likelihood function achieves the maximum value [12]: = ) J )LKNM /O,PQ R(ST. S O,PRVU O XW (4)
2 D ] = at h - ji, the sample mean, and T. Name Author Year Reference Penalty Akaike 1972 [1] D Schwarz 1978 [11] Y Z%[F\ Bozdoan 1987 [3] Y Z%[F\ ^] Y F Bozdoan 1987 [3] D8]_Y Z`[*\ a] Z`[*\ SNb )dc S Rissanen 1987 [1] Y Z%[F\ ^] ) Y ]E Z%[F\ ) D8] K M Wallace & Freeman 1987 [14] ) e] Z%[F\ef ] Z`[*\ SNb )2c S Notation: Number of free parameters in the model. Size of the data sample. Dimension of the data space. b )dc Fisher Information matrix of the model. f Constant of the optimal -dimensional quantizin lattice [6]. k #%l ) #9nm ) #9nm po (5) the maximum-likelihood estimate of the covariance matrix. The number of free parameters of a multivariate normal distribution is equal to the dimension of the mean plus the number of variances and covariances to be estimated. For a full covariance matrix it is: Dq ) ]E K Table 1: Model Dimension Estimates. (6) Decision Rule Several model selection criteria have been proposed in the literature that can be applied to Akaike s framework of model selection. In eneral, each criterion proposes a penalty function r that takes into account the model dimension. By computin the likelihood function of each model, the followin decision rule can be derived. Look for the best two-sement model for the data: vqwnx 2l Xy{z{z{z y O S T. S } K then, take the one-sement model function: Z%[F\ = }r S T.~ S r (7) Z`[*\ S T. S r (8) and choose to sement the data at point o if and only if: ) Z%[F\ = s Z`[*\ = ) r s9r, ƒ (9) In the experimental part it will be shown that performance of the rule can be tuned by replacin the zero threshold with a value c to be empirically estimated. Multiple Transition Detection The extension of the method to an arbitrary lare number of potential sements requires considerin a number of competin models that combinatorially rows with and. In eneral, application dependent simplifications are introduced to reduce the complexity of the problem. For the acoustic sementation, the audio sinal can be semented throuh a slidin window. By keepin the window size sufficiently lare to reliably apply the method, and sufficiently short to avoid multiple transitions, a sementation alorithm can be devised that relies on the basic q case. In Fiure 1 an alorithm is proposed [5] that was derived by the one described in [7]. The main idea is to have a shiftin variable-size window in which a SC can be hypothesized accordin to (9). To reduce computations, the maximization (7) is not computed over all points q, but at a lower resolution rate. The resolution rate is increased when a potential SC is detected, in order to validate it and refine its time position. Let us refer to Fiure 1. The startin window (WinMin) has to be small to contain no more than one SC, but lare enouh to allow reliable statistics of the criterion to be computed. It is located at the beinnin of the input audio stream. Values of the criterion are computed with low resolution rate (ResLow), e.. every 3 observations (step 2.). The window is enlared (11.) until a potential SC is detected (3.), or a maximum size (WinMax) is reached (1.). In the first case, the potential SC is validated by computin the criterion values on the window centered around the candidate, and usin an hiher resolution rate (ResHih) (4.). In the second case, the window is shifted on the riht (13.). If the potential SC is validated (5.,7.) it is stored (6.), then, the window is set to the minimum size (8.) and placed just after the detected SC (9.). Steps 2-13 are repeated until all the input audio data have been processed (1.). 3. MODEL SELECTION CRITERIA Several model selection criteria have been proposed startin from the early 7s. As mentioned before, the seminal work of Akaike tried to extend the maximum likelihood principle with a term that estimates the dimension or complexity of the considered statistical model. Refinements to the Akaike s Information Criterion () were proposed by Schwarz [11], with the Bayesian Information Cri-
3 Parameters: WinMin: minimum window size WinMax: maximum window size WinDelta: window increase step WinStep: window shift step ResLow: low resolution ResHih: hih resolution N: input data lenth Thresh: threshold for the used criterion Variables: WinStart: left boundary of the window WinSize: current window size SC: detected spectral chanes Subroutine: MaxSearch(WinStart,WinSize,Res): returns the best potential SC and its score, computed by a iven criterion, inside the specified window at the iven resolution Res. Initialization: WinStart=1 WinSize=WinMin SC=() Alorithm: 1. while (WinStart+WinSize N) 2. (max,t)=maxsearch(winstart,winsize, ResLow) 3. if (max Thresh) 4. (max,t)= MaxSearch(t - WinSize/2,WinSize, ResHih) 5. if (max Thresh) 6. push SC t 7. if (max Thresh) 8. WinSize=WinMin 9. WinStart=t else if (WinSize WinMax) 11. WinSize=WinSize + WinDelta 12. else 13. WinStart=WinStart + WinStep Fiure 1: Alorithm for detectin multiple spectral chanes. terion (), and by Bozdoan [3], with the Consistent (), and the Consistent with Fisher information (F). By followin an information and codin theory approach to statistical modelin and stochastic complexity, Rissanen [1] and Wallace and Friedman [14] proposed in the 8s two different criteria, respectively called Minimum Description Lenth () and Minimum Messae Lenth (M). Without oin into the details of each method which would require too much space, the penalty terms derived by each of the mentioned criteria are iven in Table 1. For the sake of comparison, a version of the Hotellin s test and the maximum likelihood method are also considered. Hotellin s Test (T2) test [13] computes the maximum likelihood estimate of a chanin point of the mean in the sample by: The Hotellin s o ẅ ˆ \ vẅ x 2l /y{z{z{z y O ẅ ˆ \ vẅ x 2l /y{z{z{z y O (1) ) } K ) i ni o Š~O Œ ) i ni where Š Œ is the pooled variance: Š Œ K ). T ] ) }.~ T (11) and ) i. T and ) i. T 3 are, respectively, the sample means and covariance estimates on and 21. The hypothesis of a chanin point can aain be accepted with a confidence level ) Ž if: ƒ ) K s ƒ y O O Xy (12) where y O O Xy is upper Že * point of the F- distribution with (d,n-d-1) derees of freedom. Maximum Likelihood Test The Maximum Likelihood () criterion corresponds to a model selection criterion with a zero penalty function. Hence, a SC is detected if the two-sement model fits the data better than the sinle-sement model. 4. EVALUATION METRICS Sementin an audio stream, like a broadcast news proram, requires in eneral to detect spectral chanes reardin: acoustic sources, i.e. female/male speech, music acoustic channels, i.e. wide/narrow band. Accordin to [9], performance of automatic SC detection should be calculated with respect to a set of taret SCs. To each taret SC there is usually associated a time interval Š 4, rather than as a sinle point. This because silence or other non-speech events may occur between chanes. Tolerances in detectin SCs can be introduced by extendin such intervals. Hence, an hypothesized SC is considered correct if it falls inside one of the aumented taret intervals Š 6pAN@ ]špan@, where pan@ is the admitted tolerance. For comparin taret and hypothesized SCs, one can adopt the recall and precision measures: where recall ]œ precision ]Ÿž F (13) F (14) is the number of hypothesized SCs that fall inside the taret SC intervals, ž is the number of hypothesized SCs that do not fall inside any taret SC interval, and is the number of taret SC intervals which no hypothesized SC falls inside. 5. EXPERIMENTS UNDER CONTROLLED CONDITIONS Comparison of model selection criteria has been first performed under controlled conditions. Random samples of size j F were enerated accordin to different multivariate normal distributions, and for values of the dimension j?. In particular, random samples were enerated either by shiftin the mean or by scalin the variances of a standard normal distribution.
4 Mean Shiftin Random samples of size =3 were enerated accordin to the followin scheme: PR! & ),+/ b (15) PR 1 N 5! & ),+/ ]E Ž b (16) with Ž =.1,...,.5. Variance Scalin Random samples of size =3 were enerated accordin to the followin scheme: PR! &( ),+/ 9 b (17) PR 1! &( ),+/ 9 Ž> b (18) with Ž =.5,.6,...,.9. Experimental Conditions The basic sementation alorithm (} ) was applied to the above problems with a sliht variation. Two-sement models (7) were only evaluated on the central third of the data set, i.e. ª «š. This to reliably compute the model parameters. data samples were enerated for each focus condition. Finally, as for each condition the correct model has a diaonal covariance matrix, the number of free parameters D was set equal to K. Performance in terms of precision/recall were computed, for each condition, by assumin transition detections correct if they fall within the interval ` 3. Moreover, each method was also evaluated on homoeneous data samples enerated accordin to a standard normal distribution. Hence, the statistic ž of equation (14) was estimated by countin the number of hypothesized transition points found in the homoeneous samples. Finally, the T2 method was only applied to detect mean shifts in the data, with a confidence level Ž *. Experimental Results Experimental results are reported in Fiure 2. The three vertical plots on the left size correspond to experiments applyin mean shifts, while the three plots on the riht correspond to experiments applyin variance scalins. Increasin values of the dimension of the data are considered oin from the top to the bottom plots. Each sinle plot shows precision versus recall performance of each criterion, under different shiftin/scalin conditions. Vertical slices correspond, oin rihtward, to easier sementation tasks. Accordin to the definition of the precision/recall measures, best performin methods are those which are closest to the top-riht corner of a slice. By lookin at the two upper plots, which correspondin to dimension n, it results that the best two performin criteria are and. M follows with a lower recall, which ets closer to the best methods as the task ets easier. With a slihtly better precision, but much lower recall,, T2 (just for mean shiftin), and follow in the order. F often keeps abreast of the best methods, in terms of recall, but scores much lower in terms of precision. Results sinificantly chane by lookin at dimension and :. performs sinificantly better than, especially for the mean shiftin case. M worsens sinificantly and ets close to the best methods just in the easiest variance scalin case. T2 provides the best precision/recall trade-off on the mean shiftin conditions. shows a ood precision-recall trade-off on both dimensions and conditions. In particular, shows the hihest precision on the most difficult conditions (left most plot slices). 6. EXPERIMENTS ON REAL DATA Experiments with all the sementation criteria were performed on audio data comin from a broadcast news data base. The aim is to detect spectral chanes that occur within the sinal that are mainly due to channel and source switches. The IBNC Corpus For testin purposes, data from the IBNC (Italian Broadcast News Corpus) database, developed at ITC-irst [8], were employed. The IBNC consists of 3 hours of radio news recordins, which were manually transcribed, semented and labeled. The test set consists of six radio news prorams (about minutes of audio sinal) that were selected as a representative sample of the whole corpus, with respect to all the issues concernin automatic broadcast news transcription [4]. Table 2 reports statistics on the test set reardin sements. A sement is defined as a contiuous portion of audio sinal, homoeneous in terms of acoustic source and channel. # averae duration (s) music sements speech sements Table 2: Statistics of sements in the test set. The test set contains a total of 212 SCs (218 sements distributed amon six news prorams). Experimental Conditions Multivariate observations of dimension 13 were used, i.e. 12 mel-scaled cepstral coefficients and the lo-enery. SCs detections was performed by usin a tolerance value of 5ms. Multiple SC detection was performed by means of the alorithm shown in Fiure 1. Moreover, in order to compute a precision/recall operatin curve of each method, an empirical threshold was introduced in the decision criteria (9) and (12). In fact, the threshold can be seen as an empirically estimated additional penalty to the method. Different values of the threshold were tested and the resultin precision/recall statistics were computed. Experimental Results Precision vs. recall points of each method are shown in Fiure 3. As a reference, complete curves are plotted for the and T2 methods. The left most points of all the model selection criteria correspond to settin the threshold
5 to the oriinal value, i.e. zero. By lookin at Fiure 3 the followin can be observed: straihtforward application of the methods on audio data provides hih recall but very low precision; by suitably tunin the threshold value, on each sinle method, much better performance can be achieved; optimal values of the threshold make all methods, with the exception of T2, perform comparably well; T2 performs sinificantly worse than all other methods. Moreover, no improvement was achieved even by usin a universal pooled variance estimated as suested in [15];,, and confirm to be amon the best performin methods; the pure empirically tuned method performs as well as the best model selection methods; 7. CONCLUSIONS Several model selection methods for acoustic sementation were presented and tested, both on synthetic and real audio data. Tanible differences amon the methods appeared in experiments performed under controlled conditions. In particular, methods with simple penalty functions showed to perform better with multivariate data. Methods based on the Fisher information (i.e. M and F) did not result competitive versus easier methods, at least on the here considered sementation problems. Application of any method on real audio data requires introducin an empirical threshold on the decision criterion. Tunin the threshold on each method permits to achieve sinificantly better retrieval performance. Almost all the considered methods reached very similar optimal performance. Besides, methods which best performed on the synthetic data sets also worked well on the audio data. To conclude, a major point in applyin the considered methods on audio data concerns their robustness with respect to the normality assumption on the data source. By the introduction of an empirical threshold in the decision criterion, all the tested selection criteria showed to be reasonably robust. Future work will be devoted to the development and evaluation of non parametric methods for the acoustic sementation problem. [2] R. A. Baxter. Minimum Messae Lenht Inference: Theory and Applications. PhD thesis, Department of Computer Science Monash University, Clayton, Victoria, Australia, [3] H. Bozdoan. Model selection and the Akaike s information criterion (): the eneral theory and its analytical extensions. Psychometrika, 52(3):345 37, [4] F. Brunara, M. Cettolo, M. Federico, and D. Giuliani. A system for the sementation and transcription of Italian radio news. In Proceedins of RIAO Content-Based Multimedia Information Access, Paris, France, 2. [5] M. Cettolo. Sementation, classification and clusterin of an Italian broadcast news corpus. In Proceedins of the RIAO International Conference, Paris, France, 2. [6] J. H. Conway and N. J. A. Sloane. Sphere Packin, Lattices and Groups. Spriner Verla, Berlin, Germany, [7] P. Delacourt, D. Kryze, and C. J. Wellekens. Speaker-based sementation for audio data indexin. In Proceedins of the ESCA ETRW workshop Accessin Information in Spoken Audio, Cambride, UK, [8] M. Federico, D. Giordani, and P. Coletti. Development and Evaluation of an Italian Broadcast News Corpus. In Proceedins of the Second International Conference on Lanuae Resources and Evaluation (LREC), Athens, Greece, 2. [9] D. Liu and F. Kubala. Fast speaker chane detection for broadcast news transcription and indexin. In Proceedins of the 6th European Conference on Speech Communication and Technoloy, paes , Budapest, Hunary, [1] J. Rissanen. Stochastic complexity. Journal of the Royal Statistical Society, B, 49(3): , [11] G. Schwarz. Estimatin the dimension of a model. The Annals of Statistics, 6(2): , [12] G. A. F. Seber. Multivariate Observations. John Wiley & Sons, New York, NY, [13] M. S. Srivastava and E. M. Carter. An Introduction to Applied Multivariate Statistics. North-Holland, New York, NY, [14] C. S. Wallace and P. R. Freeman. Estimation and inference by compact codin. Journal of the Royal Statistical Society, B, 49(3):24 265, [15] S. Wemann, P. Zhan, and L. Gillick. Proress in broadcast news transcription at Draon Systems. In Proceedins of the IEEE International Conference on Acoustics, Speech and Sinal Processin, volume I, paes 33 36, Phoenix, AZ, ACKNOWLEDGMENTS The here presented work was carried out within the European project CORETEX (IST ). The authors thank R. A. Baxter and D. Giuliani for their help and useful suestions. REFERENCES [1] H. Akaike. On entropy maximization principle. In P. R. Krishnaiah, editor, Applications of Statistics, paes North-Holland, Amsterdam, Nederlands, 1977.
6 MEAN SHIFTING VARIANCE SCALING α=.1 - α=.2 - α=.3 - α=.4 - α=.5 - α=.9 - α=.8 - α=.7 - α=.6 - α=.5 - d=1 d=1 RECALL RECALL RECALL 5 F M T α=.1 α=.2 α=.3 α=.4 α=.5 α=.9 α=.8 α=.7 α=.6 α=.5 d=5 d=5 5 d=1 5 F M T α=.1 α=.2 α=.3 α=.4 α= F M F M α=.9 α=.8 α=.7 α=.6 α=.5 d=1 F M T PRECISION F M PRECISION Fiure 2: Results of experiments under controlled conditions.
7 95 9 RECALL 85 8 aic bic caic caicf mdl ml mml t PRECISION Fiure 3: Precision vs. recall curve by different methods on an audio sementation task.
MODEL SELECTION CRITERIA FOR ACOUSTIC SEGMENTATION
ISCA Archive MODEL SELECTION CRITERIA FOR ACOUSTIC SEGMENTATION Mauro Cettolo and Marcello Federico ITC-irst - Centro per la Ricerca Scientifica e Tecnologica I-385 Povo, Trento, Italy ABSTRACT Robust
More informationRobust Semiparametric Optimal Testing Procedure for Multiple Normal Means
Veterinary Dianostic and Production Animal Medicine Publications Veterinary Dianostic and Production Animal Medicine 01 Robust Semiparametric Optimal Testin Procedure for Multiple Normal Means Pen Liu
More informationA Mathematical Model for the Fire-extinguishing Rocket Flight in a Turbulent Atmosphere
A Mathematical Model for the Fire-extinuishin Rocket Fliht in a Turbulent Atmosphere CRISTINA MIHAILESCU Electromecanica Ploiesti SA Soseaua Ploiesti-Tiroviste, Km 8 ROMANIA crismihailescu@yahoo.com http://www.elmec.ro
More informationStrong Interference and Spectrum Warfare
Stron Interference and Spectrum Warfare Otilia opescu and Christopher Rose WILAB Ruters University 73 Brett Rd., iscataway, J 8854-86 Email: {otilia,crose}@winlab.ruters.edu Dimitrie C. opescu Department
More informationAdjustment of Sampling Locations in Rail-Geometry Datasets: Using Dynamic Programming and Nonlinear Filtering
Systems and Computers in Japan, Vol. 37, No. 1, 2006 Translated from Denshi Joho Tsushin Gakkai Ronbunshi, Vol. J87-D-II, No. 6, June 2004, pp. 1199 1207 Adjustment of Samplin Locations in Rail-Geometry
More informationPHY 133 Lab 1 - The Pendulum
3/20/2017 PHY 133 Lab 1 The Pendulum [Stony Brook Physics Laboratory Manuals] Stony Brook Physics Laboratory Manuals PHY 133 Lab 1 - The Pendulum The purpose of this lab is to measure the period of a simple
More informationLP Rounding and Combinatorial Algorithms for Minimizing Active and Busy Time
LP Roundin and Combinatorial Alorithms for Minimizin Active and Busy Time Jessica Chan, Samir Khuller, and Koyel Mukherjee University of Maryland, Collee Park {jschan,samir,koyelm}@cs.umd.edu Abstract.
More informationStatistics Hotelling s T Gary W. Oehlert School of Statistics 313B Ford Hall
\ C f C E A tatistics 5041 11 Hotellin s T Gary W ehlert chool of tatistics 313B Ford Hall 612-625-155 ary@statumnedu Let s think about the univariate -test First recall that there are one-sample tests,
More informationStat260: Bayesian Modeling and Inference Lecture Date: March 10, 2010
Stat60: Bayesian Modelin and Inference Lecture Date: March 10, 010 Bayes Factors, -priors, and Model Selection for Reression Lecturer: Michael I. Jordan Scribe: Tamara Broderick The readin for this lecture
More informationMinimum message length estimation of mixtures of multivariate Gaussian and von Mises-Fisher distributions
Minimum message length estimation of mixtures of multivariate Gaussian and von Mises-Fisher distributions Parthan Kasarapu & Lloyd Allison Monash University, Australia September 8, 25 Parthan Kasarapu
More informationA Constant Complexity Fair Scheduler with O(log N) Delay Guarantee
A Constant Complexity Fair Scheduler with O(lo N) Delay Guarantee Den Pan and Yuanyuan Yan 2 Deptment of Computer Science State University of New York at Stony Brook, Stony Brook, NY 79 denpan@cs.sunysb.edu
More informationEfficient method for obtaining parameters of stable pulse in grating compensated dispersion-managed communication systems
3 Conference on Information Sciences and Systems, The Johns Hopkins University, March 12 14, 3 Efficient method for obtainin parameters of stable pulse in ratin compensated dispersion-manaed communication
More informationConvergence of DFT eigenvalues with cell volume and vacuum level
Converence of DFT eienvalues with cell volume and vacuum level Sohrab Ismail-Beii October 4, 2013 Computin work functions or absolute DFT eienvalues (e.. ionization potentials) requires some care. Obviously,
More informationMODIFIED SPHERE DECODING ALGORITHMS AND THEIR APPLICATIONS TO SOME SPARSE APPROXIMATION PROBLEMS. Przemysław Dymarski and Rafał Romaniuk
MODIFIED SPHERE DECODING ALGORITHMS AND THEIR APPLICATIONS TO SOME SPARSE APPROXIMATION PROBLEMS Przemysław Dymarsi and Rafał Romaniu Institute of Telecommunications, Warsaw University of Technoloy ul.
More informationLinearized optimal power flow
Linearized optimal power flow. Some introductory comments The advantae of the economic dispatch formulation to obtain minimum cost allocation of demand to the eneration units is that it is computationally
More informationStochastic learning feedback hybrid automata for dynamic power management in embedded systems
Electrical and Computer Enineerin Faculty Publications Electrical & Computer Enineerin 2005 Stochastic learnin feedback hybrid automata for dynamic power manaement in embedded systems T. Erbes Eurecom
More informationNing Wu Institute for Traffic Engineering Ruhr University Bochum, Germany Tel: ; Fax: ;
MODELLING THE IMPACT OF SIDE-STREET TRAFFIC VOLUME ON MAJOR- STREET GREEN TIME AT ISOLATED SEMI-ACTUATED INTERSECTIONS FOR SIGNAL COORDINATION DECISIONS Donmei Lin, Correspondin Author Center for Advanced
More information10log(1/MSE) log(1/MSE)
IROVED MATRI PENCIL METHODS Biao Lu, Don Wei 2, Brian L Evans, and Alan C Bovik Dept of Electrical and Computer Enineerin The University of Texas at Austin, Austin, T 7872-84 fblu,bevans,bovik@eceutexasedu
More informationBidirectional Clustering of Weights for Finding Succinct Multivariate Polynomials
IJCSNS International Journal of Computer Science and Network Security, VOL.8 No.5, May 28 85 Bidirectional Clusterin of Weihts for Findin Succinct Multivariate Polynomials Yusuke Tanahashi and Ryohei Nakano
More informationUSE OF FILTERED SMITH PREDICTOR IN DMC
Proceedins of the th Mediterranean Conference on Control and Automation - MED22 Lisbon, Portual, July 9-2, 22. USE OF FILTERED SMITH PREDICTOR IN DMC C. Ramos, M. Martínez, X. Blasco, J.M. Herrero Predictive
More informationEquivalent rocking systems: Fundamental rocking parameters
Equivalent rockin systems: Fundamental rockin parameters M.J. DeJon University of Cambride, United Kindom E.G. Dimitrakopoulos The Hon Kon University of Science and Technoloy SUMMARY Early analytical investiations
More informationLecture 5 Processing microarray data
Lecture 5 Processin microarray data (1)Transform the data into a scale suitable for analysis ()Remove the effects of systematic and obfuscatin sources of variation (3)Identify discrepant observations Preprocessin
More informationAsymptotic Behavior of a t Test Robust to Cluster Heterogeneity
Asymptotic Behavior of a t est Robust to Cluster Heteroeneity Andrew V. Carter Department of Statistics University of California, Santa Barbara Kevin. Schnepel and Doulas G. Steierwald Department of Economics
More informationGeneralized Distance Metric as a Robust Similarity Measure for Mobile Object Trajectories
Generalized Distance Metric as a Robust Similarity Measure for Mobile Object rajectories Garima Pathak, Sanjay Madria Department of Computer Science University Of Missouri-Rolla Missouri-6541, USA {madrias}@umr.edu
More informationDecomposing compositional data: minimum chi-squared reduced-rank approximations on the simplex
Decomposin compositional data: minimum chi-squared reduced-rank approximations on the simplex Gert Jan Welte Department of Applied Earth Sciences Delft University of Technoloy PO Box 508 NL-600 GA Delft
More informationLP Rounding and Combinatorial Algorithms for Minimizing Active and Busy Time
LP Roundin and Combinatorial Alorithms for Minimizin Active and Busy Time Jessica Chan University of Maryland Collee Park, MD, USA jschan@umiacs.umd.edu Samir Khuller University of Maryland Collee Park,
More informationIEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING 1
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING 1 Intervention in Gene Reulatory Networks via a Stationary Mean-First-Passae-Time Control Policy Golnaz Vahedi, Student Member, IEEE, Babak Faryabi, Student
More informationHEAT TRANSFER IN EXHAUST SYSTEM OF A COLD START ENGINE AT LOW ENVIRONMENTAL TEMPERATURE
THERMAL SCIENCE: Vol. 14 (2010) Suppl. pp. S219 S232 219 HEAT TRANSFER IN EXHAUST SYSTEM OF A COLD START ENGINE AT LOW ENVIRONMENTAL TEMPERATURE by Snežana D. PETKOVIĆ a Radivoje B. PEŠIĆ b b and Jovanka
More informationA NEW INFORMATION THEORETIC APPROACH TO ORDER ESTIMATION PROBLEM. Massachusetts Institute of Technology, Cambridge, MA 02139, U.S.A.
A EW IFORMATIO THEORETIC APPROACH TO ORDER ESTIMATIO PROBLEM Soosan Beheshti Munther A. Dahleh Massachusetts Institute of Technology, Cambridge, MA 0239, U.S.A. Abstract: We introduce a new method of model
More informationREAL-TIME TIME-FREQUENCY BASED BLIND SOURCE SEPARATION. Scott Rickard, Radu Balan, Justinian Rosca
REAL-TIME TIME-FREQUENCY BASED BLIND SOURCE SEARATION Scott Rickard, Radu Balan, Justinian Rosca Siemens Corporate Research rinceton, NJ scott.rickard,radu.balan,justinian.rosca @scr.siemens.com ABSTRACT
More informationCorrelated Component Regression: A Fast Parsimonious Approach for Predicting Outcome Variables from a Large Number of Predictors
Correlated Component Reression: A Fast Parsimonious Approach for Predictin Outcome Variables from a Lare Number of Predictors Jay Maidson, Ph.D. Statistical Innovations COMPTSTAT 2010, Paris, France 1
More informationExperiment 3 The Simple Pendulum
PHY191 Fall003 Experiment 3: The Simple Pendulum 10/7/004 Pae 1 Suested Readin for this lab Experiment 3 The Simple Pendulum Read Taylor chapter 5. (You can skip section 5.6.IV if you aren't comfortable
More informationWhat Causes Image Intensity Changes?
Ede Detection l Why Detect Edes? u Information reduction l Replace imae by a cartoon in which objects and surface markins are outlined create line drawin description l These are the most informative parts
More informationTHE SIGNAL ESTIMATOR LIMIT SETTING METHOD
' THE SIGNAL ESTIMATOR LIMIT SETTING METHOD Shan Jin, Peter McNamara Department of Physics, University of Wisconsin Madison, Madison, WI 53706 Abstract A new method of backround subtraction is presented
More informationOptimal Maintenance Strategies for Wind Turbine Systems Under Stochastic Weather Conditions
IEEE TRANSACTIONS ON RELIABILITY 1 Optimal Maintenance Strateies for Wind Turbine Systems Under Stochastic Weather Conditions Eunshin Byon, Student Member, IEEE, Lewis Ntaimo, and Yu Din, Member, IEEE
More informationEnergizing Math with Engineering Applications
Enerizin Math with Enineerin Applications Understandin the Math behind Launchin a Straw-Rocket throuh the use of Simulations. Activity created by Ira Rosenthal (rosenthi@palmbeachstate.edu) as part of
More informationAMERICAN INSTITUTES FOR RESEARCH
AMERICAN INSTITUTES FOR RESEARCH LINKING RASCH SCALES ACROSS GRADES IN CLUSTERED SAMPLES Jon Cohen, Mary Seburn, Tamas Antal, and Matthew Gushta American Institutes for Research May 23, 2005 000 THOMAS
More informationSTOCHASTICALLY GENERATED MULTIGROUP DIFFUSION COEFFICIENTS
STOCHASTICALLY GENERATED MULTIGROUP DIFFUSION COEFFICIENTS A Thesis Presented to The Academic Faculty by Justin M. Pounders In Partial Fulfillment of the Requirements for the Deree Master of Science in
More informationOn K-Means Cluster Preservation using Quantization Schemes
On K-Means Cluster Preservation usin Quantization Schemes Deepak S. Turaa Michail Vlachos Olivier Verscheure IBM T.J. Watson Research Center, Hawthorne, Y, USA IBM Zürich Research Laboratory, Switzerland
More informationStochastic simulations of genetic switch systems
Stochastic simulations of enetic switch systems Adiel Loiner, 1 Azi Lipshtat, 2 Nathalie Q. Balaban, 1 and Ofer Biham 1 1 Racah Institute of Physics, The Hebrew University, Jerusalem 91904, Israel 2 Department
More informationIndeterminacy in discrete-time infinite-horizon models with non linear utility and endogenous labor
Indeterminacy in discrete-time infinite-horizon models with non linear utility and endoenous labor Kazuo NISHIMURA Institute of Economic Research, Kyoto University, Japan and Alain VENDII CNRS - GREQAM,
More informationLevenberg-Marquardt-based OBS Algorithm using Adaptive Pruning Interval for System Identification with Dynamic Neural Networks
Proceedins of the 29 IEEE International Conference on Systems, Man, and Cybernetics San Antonio, X, USA - October 29 evenber-marquardt-based OBS Alorithm usin Adaptive Prunin Interval for System Identification
More informationCausal Bayesian Networks
Causal Bayesian Networks () Ste7 (2) (3) Kss Fus3 Ste2 () Fiure : Simple Example While Bayesian networks should typically be viewed as acausal, it is possible to impose a causal interpretation on these
More informationREPORT DOCUMENTATION PAGE
REPORT DOCMENTATION PAGE Form Approved OMB No. 74-88 Public reportin burden for this collection of information is estimated to averae hour per response, includin the time for reviewin instructions, searchin
More informationGenetic Algorithm Approach to Nonlinear Blind Source Separation
Genetic Alorithm Approach to Nonlinear Blind Source Separation F. Roas, C.G. Puntonet, I.Roas, J. Ortea, A. Prieto Dept. of Computer Architecture and Technoloy, University of Granada. fernando@atc.ur.es,
More informationn j u = (3) b u Then we select m j u as a cross product between n j u and û j to create an orthonormal basis: m j u = n j u û j (4)
4 A Position error covariance for sface feate points For each sface feate point j, we first compute the normal û j by usin 9 of the neihborin points to fit a plane In order to create a 3D error ellipsoid
More informationModeling for control of a three degrees-of-freedom Magnetic. Levitation System
Modelin for control of a three derees-of-freedom Manetic evitation System Rafael Becerril-Arreola Dept. of Electrical and Computer En. University of Toronto Manfredi Maiore Dept. of Electrical and Computer
More informationExperimental and Computational Studies of Gas Mixing in Conical Spouted Beds
Refereed Proceedins The 1th International Conference on Fluidization - New Horizons in Fluidization Enineerin Enineerin Conferences International Year 007 Experimental and Computational Studies of Gas
More informationWire antenna model of the vertical grounding electrode
Boundary Elements and Other Mesh Reduction Methods XXXV 13 Wire antenna model of the vertical roundin electrode D. Poljak & S. Sesnic University of Split, FESB, Split, Croatia Abstract A straiht wire antenna
More informationEvaluation of the SONAR Meter in Wet Gas Flow for an Offshore Field Development
Evaluation of the SONAR Meter in Wet Gas Flow for an Offshore Field Development Anela Floyd, BP Siddesh Sridhar and Gabriel Dranea, Expro Meters 1 INTRODUCTION The ABC project is a hih pressure as condensate
More informationActive filter synthesis based on nodal admittance matrix expansion
Tan et al. EURASIP Journal on Wireless Communications and Networkin (1) 1:9 DOI 1.118/s18-1-881-8 RESEARCH Active filter synthesis based on nodal admittance matrix expansion Linlin Tan, Yunpen Wan and
More informationSparse principal component analysis and its l 1 -relaxation
Sparse principal component analysis and its l 1 -relaxation Santanu S. Dey s, Rahul Mazumder p, Marco Molinaro c, and Guanyi Wan a a,s School of Industrial and Systems Enineerin, Georia Institute of Technoloy
More informationNumerical and Experimental Investigations of Lateral Cantilever Shaft Vibration of Passive-Pitch Vertical-Axis Ocean Current
R. Hantoro, et al. / International Enery Journal 1 (011) 191-00 191 Numerical and Experimental Investiations of Lateral Cantilever Shaft Vibration of Passive-Pitch Vertical-Axis Ocean Current R. Hantoro
More informationMinimum Message Length Autoregressive Model Order Selection
Minimum Message Length Autoregressive Model Order Selection Leigh J. Fitzgibbon School of Computer Science and Software Engineering, Monash University Clayton, Victoria 38, Australia leighf@csse.monash.edu.au
More informationScheduling non-preemptive hard real-time tasks with strict periods
Schedulin non-preemptive hard real-time tasks with strict periods Mohamed MAROUF INRIA Rocquencourt Domaine de Voluceau BP 05 785 Le Chesnay Cedex - France Email: mohamed.marouf@inria.fr Yves SOREL INRIA
More informationAmplitude Adaptive ASDM without Envelope Encoding
Amplitude Adaptive ASDM without Envelope Encodin Kaspars Ozols and Rolands Shavelis Institute of Electronics and Computer Science 14 Dzerbenes Str., LV-16, Ria, Latvia Email: kaspars.ozols@edi.lv, shavelis@edi.lv
More informationJournal of Inequalities in Pure and Applied Mathematics
Journal of Inequalities in Pure and Applied Mathematics L HOSPITAL TYPE RULES FOR OSCILLATION, WITH APPLICATIONS IOSIF PINELIS Department of Mathematical Sciences, Michian Technoloical University, Houhton,
More informationINFLUENCE OF TUBE BUNDLE GEOMETRY ON HEAT TRANSFER TO FOAM FLOW
HEFAT7 5 th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics Sun City, South Africa Paper number: GJ1 INFLUENCE OF TUBE BUNDLE GEOMETRY ON HEAT TRANSFER TO FOAM FLOW Gylys
More informationRound-off Error Free Fixed-Point Design of Polynomial FIR Predictors
Round-off Error Free Fixed-Point Desin of Polynomial FIR Predictors Jarno. A. Tanskanen and Vassil S. Dimitrov Institute of Intellient Power Electronics Department of Electrical and Communications Enineerin
More informationFourier Optics and Image Analysis
Laboratory instruction to Fourier Optics and Imae Analysis Sven-Göran Pettersson and Anders Persson updated by Maïté Louisy and Henrik Ekerfelt This laboratory exercise demonstrates some important applications
More informationEmotional Optimized Design of Electro-hydraulic Actuators
Sensors & Transducers, Vol. 77, Issue 8, Auust, pp. 9-9 Sensors & Transducers by IFSA Publishin, S. L. http://www.sensorsportal.com Emotional Optimized Desin of Electro-hydraulic Actuators Shi Boqian,
More informationMulti-sample structural equation models with mean structures, with special emphasis on assessing measurement invariance in cross-national research
1 Multi-sample structural equation models with mean structures, with special emphasis on assessin measurement invariance in cross-national research Measurement invariance measurement invariance: whether
More informationDetection of Outliers in Regression Analysis by Information Criteria
Detection of Outliers in Regression Analysis by Information Criteria Seppo PynnÄonen, Department of Mathematics and Statistics, University of Vaasa, BOX 700, 65101 Vaasa, FINLAND, e-mail sjp@uwasa., home
More informationDecentralized Control Design for Interconnected Systems Based on A Centralized Reference Controller
Decentralized Control Desin for Interconnected Systems Based on A Centralized Reference Controller Javad Lavaei and Amir G Ahdam Department of Electrical and Computer Enineerin, Concordia University Montréal,
More informationTranslations on graphs with neighborhood preservation
1 Translations on raphs with neihborhood preservation Bastien Pasdeloup, Vincent Gripon, Nicolas Grelier, Jean-harles Vialatte, Dominique Pastor arxiv:1793859v1 [csdm] 12 Sep 217 Abstract In the field
More informationREVIEW: Going from ONE to TWO Dimensions with Kinematics. Review of one dimension, constant acceleration kinematics. v x (t) = v x0 + a x t
Lecture 5: Projectile motion, uniform circular motion 1 REVIEW: Goin from ONE to TWO Dimensions with Kinematics In Lecture 2, we studied the motion of a particle in just one dimension. The concepts of
More informationLTI Systems, Additive Noise, and Order Estimation
LTI Systems, Additive oise, and Order Estimation Soosan Beheshti, Munther A. Dahleh Laboratory for Information and Decision Systems Department of Electrical Engineering and Computer Science Massachusetts
More informationMatrix multiplication: a group-theoretic approach
CSG399: Gems of Theoretical Computer Science. Lec. 21-23. Mar. 27-Apr. 3, 2009. Instructor: Emanuele Viola Scribe: Ravi Sundaram Matrix multiplication: a roup-theoretic approach Given two n n matrices
More informationThermo-Mechanical Damage Modeling of Polymer Matrix Composite Structures in Fire
Thermo-Mechanical Damae Modelin of Polymer Matrix Composite Structures in Fire CHANGSONG LUO, and JIM LUA Global Enineerin and Materials, Inc. One Airport Place, Suite One Princeton, NJ 08540 USA ABSTRACT
More information(a) Find the function that describes the fraction of light bulbs failing by time t e (0.1)x dx = [ e (0.1)x ] t 0 = 1 e (0.1)t.
1 M 13-Lecture March 8, 216 Contents: 1) Differential Equations 2) Unlimited Population Growth 3) Terminal velocity and stea states Voluntary Quiz: The probability density function of a liht bulb failin
More informationLecture 8: Pesudorandom Generators (II) 1 Pseudorandom Generators for Bounded Computation
Expander Graphs in Computer Science WS 2010/2011 Lecture 8: Pesudorandom Generators (II) Lecturer: He Sun 1 Pseudorandom Generators for Bounded Computation Definition 8.1 Let M be a randomized TM that
More informationFLUID flow in a slightly inclined rectangular open
Numerical Solution of de St. Venant Equations with Controlled Global Boundaries Between Unsteady Subcritical States Aldrin P. Mendoza, Adrian Roy L. Valdez, and Carlene P. Arceo Abstract This paper aims
More information1. Introduction. ) exceeded the terminal velocity (U t
Excerpt from the Proceedins of the COMOL Conference 010 India Cluster Diameter Determination of Gas-solid Dispersed Particles in a Fluidized Bed Reactor *Mitali Das Department of Biotechnoloy, PEIT Banalore
More informationMathematical Analysis of Efficiencies in Hydraulic Pumps for Automatic Transmissions
TECHNICAL PAPER Mathematical Analysis of Efficiencies in Hydraulic Pumps for Automatic Transmissions N. YOSHIDA Y. INAGUMA This paper deals with a mathematical analysis of pump effi ciencies in an internal
More informationA Multigrid-like Technique for Power Grid Analysis
A Multirid-like Technique for Power Grid Analysis Joseph N. Kozhaya, Sani R. Nassif, and Farid N. Najm 1 Abstract Modern sub-micron VLSI desins include hue power rids that are required to distribute lare
More informationV DD. M 1 M 2 V i2. V o2 R 1 R 2 C C
UNVERSTY OF CALFORNA Collee of Enineerin Department of Electrical Enineerin and Computer Sciences E. Alon Homework #3 Solutions EECS 40 P. Nuzzo Use the EECS40 90nm CMOS process in all home works and projects
More informationA Performance Comparison Study with Information Criteria for MaxEnt Distributions
A Performance Comparison Study with nformation Criteria for MaxEnt Distributions Ozer OZDEMR and Aslı KAYA Abstract n statistical modelin, the beinnin problem that has to be solved is the parameter estimation
More informationAn EM Algorithm for the Student-t Cluster-Weighted Modeling
An EM Alorithm for the Student-t luster-weihted Modelin Salvatore Inrassia, Simona. Minotti, and Giuseppe Incarbone Abstract luster-weihted Modelin is a flexible statistical framework for modelin local
More information41903: Group-Based Inference
41903: Clusterin and Fama-MacBeth Notes 4 Dependent Data in Economics Many real-world data sets plausibly exhibit complicated dependence structures Consider areate panel data model: y it = x itβ + α i
More information5 Shallow water Q-G theory.
5 Shallow water Q-G theory. So far we have discussed the fact that lare scale motions in the extra-tropical atmosphere are close to eostrophic balance i.e. the Rossby number is small. We have examined
More informationInvestigation of ternary systems
Investiation of ternary systems Introduction The three component or ternary systems raise not only interestin theoretical issues, but also have reat practical sinificance, such as metallury, plastic industry
More informationarxiv:cond-mat/ v1 [cond-mat.stat-mech] 17 Sep 1999
Shape Effects of Finite-Size Scalin Functions for Anisotropic Three-Dimensional Isin Models Kazuhisa Kaneda and Yutaka Okabe Department of Physics, Tokyo Metropolitan University, Hachioji, Tokyo 92-397,
More informationStrategies for Sustainable Development Planning of Savanna System Using Optimal Control Model
Strateies for Sustainable Development Plannin of Savanna System Usin Optimal Control Model Jiabao Guan Multimedia Environmental Simulation Laboratory School of Civil and Environmental Enineerin Georia
More informationTermination criteria in the Moore-Skelboe Algorithm for Global Optimization by Interval Arithmetic
To appear in series Nonconvex Global Optimization and Its Applications Kluwer Academic Publishers Termination criteria in the Moore-Skelboe Alorithm for Global Optimization by Interval Arithmetic M.H.
More informationIN this paper we investigate a propagative impact model. A propagative model of simultaneous impact: existence, uniqueness, and design consequences
1 A propaative model of simultaneous impact: existence, uniqueness, and desin consequences Vlad Sehete, Student Member, IEEE, Todd D. Murphey, Member, IEEE Abstract This paper presents existence and uniqueness
More informationOPTIMAL BEAMFORMING AS A TIME DOMAIN EQUALIZATION PROBLEM WITH APPLICATION TO ROOM ACOUSTICS
OPTIMAL BEAMFORMING AS A TIME DOMAIN EQUALIZATION PROBLEM WITH APPLICATION TO ROOM ACOUSTICS Mark R P Thomas, Ivan J Tashev Microsoft Research Redmond, WA 985, USA {markth, ivantash}@microsoftcom Felicia
More informationA Maximum Entropy Approach to Classifying Gene Array Data Sets
Workshop on Data Minin for Genomics, First SIAM International Conference on Data Minin A Maximum Entropy Approach to Classifyin Gene Array Data Sets Shumei Jian, Chun Tan, Li Zhan and Aidon Zhan Department
More informationAnalysis of Outage and Throughput for Opportunistic Cooperative HARQ Systems over Time Correlated Fading Channels
Analysis of Outae and Throuhput for Opportunistic Cooperative HARQ Systems over Time Correlated Fadin Channels Xuanxuan Yan, Haichuan Din,3, Zhen Shi, Shaodan Ma, and Su Pan Department of Electrical and
More informationLazy Suspect-Set Computation: Fault Diagnosis for Deep Electrical Bugs
Lazy Suspect-Set Computation: Fault Dianosis for Deep Electrical Bus Dipanjan Senupta Dept. Elec. & Comp. En. University of Toronto Toronto, Canada dipanjan@eec.toronto.edu Flavio M. de Paula Dept. of
More informationConical Pendulum: Part 2 A Detailed Theoretical and Computational Analysis of the Period, Tension and Centripetal Forces
European J of Physics Education Volume 8 Issue 1 1309-70 Dean onical Pendulum: Part A Detailed heoretical and omputational Analysis of the Period, ension and entripetal orces Kevin Dean Physics Department,
More informationExamination of rapid depressurization phenomena modeling problems in VHTR following sudden DLOFC event
Examination of rapid depressurization phenomena modelin problems in VHTR followin sudden DLOFC event Izabela Gutowska, Brian G. Woods 1, Warsaw University of Technoloy Institute of Heat Enineerin Nowowiejska
More informationDeformations Preserving Gauß Curvature
Deformations Preservin Gauß Curvature Anne Berres, Hans Haen, Stefanie Hahmann To cite this version: Anne Berres, Hans Haen, Stefanie Hahmann. Deformations Preservin Gauß Curvature. Bennett, Janine; Vivodtzev,
More informationGeneralized Least-Squares Regressions V: Multiple Variables
City University of New York (CUNY) CUNY Academic Works Publications Research Kinsborouh Community Collee -05 Generalized Least-Squares Reressions V: Multiple Variables Nataniel Greene CUNY Kinsborouh Community
More informationResearch, Education and Problem Solving as a Virtuous Circle
The nd International Symposium on Interatin Research, Education, Problem Solvin: IREPS 01 Research, Education Problem Solvin as a Virtuous Circle Horacio E. Bosch Mercedes S. Berero Mario Di Blasi Maria
More informationTeams to exploit spatial locality among agents
Teams to exploit spatial locality amon aents James Parker and Maria Gini Department of Computer Science and Enineerin, University of Minnesota Email: [jparker,ini]@cs.umn.edu Abstract In many situations,
More informationMATHCHEM 1.0. By Madhavan Narayanan Graduate Student, Department of Chemistry, Temple University
MATHCHEM.0 By Madhavan Narayanan Graduate Student, Department of Chemistry, Temple University Preface I dedicate this document to my beloved parents and my teachers without whom I would not have had the
More informationAvailable online at ScienceDirect. Procedia Computer Science 57 (2015 )
vailable online at www.sciencedirect.com ScienceDirect Procedia Computer Science 57 (25 ) 99 28 3 rd International Conference on Recent Trends in Computin 25 (ICRTC - 25) Efficient desin and analysiss
More informationarxiv: v1 [cs.ai] 15 Nov 2013
Inferrin Multilateral Relations from Dynamic Pairwise Interactions arxiv:1311.3982v1 [cs.ai] 15 Nov 2013 Aaron Schein, Juston Moore, Hanna Wallach School of Computer Science University of Massachusetts
More informationUsing Quasi-Newton Methods to Find Optimal Solutions to Problematic Kriging Systems
Usin Quasi-Newton Methos to Fin Optimal Solutions to Problematic Kriin Systems Steven Lyster Centre for Computational Geostatistics Department of Civil & Environmental Enineerin University of Alberta Solvin
More information1 CHAPTER 7 PROJECTILES. 7.1 No Air Resistance
CHAPTER 7 PROJECTILES 7 No Air Resistance We suppose that a particle is projected from a point O at the oriin of a coordinate system, the y-axis bein vertical and the x-axis directed alon the round The
More information