Modeling and Predicting Popularity Dynamics via Reinforced Poisson Processes

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Modeling and Predicting Popularity Dynamics via Reinforced Poisson Processes"

Transcription

1 Proceeings of the Twenty-Eighth AAAI Conference on Artificial Intelligence Moeling an Preicting Popularity Dynamics via Reinforce Poisson Processes Huawei Shen 1, Dashun Wang 2, Chaoming Song 3, Albert-László Barabási 4 1 Institute of Computing Technology, Chinese Acaemy of Sciences, Beijing , China 2 IBM Thomas J. Watson Research Center, Yorktown Heights, New York 10598, USA 3 Department of Physics, University of Miami, Coral Gables, Floria 33146, USA 4 Center for Complex Network Research, Northeastern University, Boston, Massachusetts 02115, USA Abstract An ability to preict the popularity ynamics of iniviual items within a complex evolving system has important implications in an array of areas. Here we propose a generative probabilistic framework using a reinforce Poisson process to explicitly moel the process through which iniviual items gain their popularity. This moel istinguishes itself from existing moels via its capability of moeling the arrival process of popularity an its remarkable power at preicting the popularity of iniviual items. It possesses the flexibility of applying Bayesian treatment to further improve the preictive power using a conjugate prior. Extensive experiments on a longituinal citation ataset emonstrate that this moel consistently outperforms existing popularity preiction methos. Introuction Information explosion, from knowlege atabase to online meia, places attention economy in the center of this era. In the heart of attention economy lies a competing process through which a few items become popular while most are forgotten over time (Wu an Humberman 2007). For example, vieos on YouTube or stories on Digg gain their popularity by striving for views or votes (Szabo an Huberman 2010); papers increase their visibility by competing for citations from new papers (Ren et al. 2010; Wang, Song, an Barabási 2013); tweets or Hashtags in Twitter become more popular as being retweete (Hong, Dan, an Davison 2011) an so o webpages as being attache by incoming hyperlinks (Ratkiewicz et al. 2010). An ability to preict the popularity of iniviual items within a ynamically evolving system not only probes our unerstaning of complex systems, but also has important implications in a wie range of omains, from marketing an traffic control to policy making an risk management. Despite recent avances of empirical methos, we lack a general moeling framework to preict the popularity of iniviual items within a complex evolving system. Current moels fall into two main paraigms, each with known strengths an limitations. One focuses on reproucing certain statistical quantities over an aggregation of items (Barabási an Albert 2005; Kempe, Kleinberg, an Taros 2003; Backstrom et al. 2006; Dezso et al. 2006; Copyright c 2014, Association for the Avancement of Artificial Intelligence ( All rights reserve. Crane an Sornette 2008; Ratkiewicz et al. 2010). These moels have been successful in unerstaning the unerlying mechanisms of popularity ynamics. Yet, as they o not provie a way to extract item-specific parameters, these moels lack preictive power for the popularity ynamics of iniviual items. The other line of enquiry, in contrast, treats the popularity ynamics as time series, making preictions by either exploiting temporal correlations (Szabo an Huberman 2010; Yang an Leskovec 2010; Lerman an Hogg 2010; Yan et al. 2011; Yu et al. 2012; Bao et al. 2013b) or fitting to these time series certain classes of functions (Bass 1969; Mahajan, Muller, an Bass 1990; Vu et al. 2011; Matsubara et al. 2012; Lerman an Hogg 2012; Gomez-Roriguez, Leskovec, an Schölkopf 2013; Yang an Zha 2013). Despite their initial success in certain omains, these moels are eterministic, moeling the popularity ynamics in a mean-fiel, if heuristic, fashion by focusing on the average amount of attentions receive within a fixe time winow, ignoring the unerlying arrival process of attentions. Inee, to the best of our knowlege, we lack a probabilistic framework to moel an preict the popularity ynamics of iniviual items. The reason behin this is partly illustrate in Figure 1, suggesting that the ynamical processes governing iniviual items appear too noisy to be amenable to quantification. In this paper, we moel the stochastic popularity ynamics using reinforce Poisson processes, capturing simultaneously three key ingreients: fitness of an item, characterizing its inherent competitiveness against other items; a general temporal relaxation function, corresponing to the aging in the ability to attract new attentions; an a reinforcement mechanism, ocumenting the well-known rich-get-richer phenomenon. The benefit of the propose moel is threefol: (1) It moels the arrival process of iniviual attentions irectly in contrast to relying on aggregate popularity time series; (2) As a generative probabilistic moel, it can be easily incorporate into the Bayesian framework to account for external factors, hence leaing to improve preictive power; (3) The flexibility in its choice of specific relaxation functions makes it a general framework that can be aapte to moel the popularity ynamics in ifferent omains. Taking citation system as an exemplary case, we emonstrate the effectiveness of the propose framework using a ataset peculiar in its longituinality, spanning over

2 Citations Years after publication (a) Citations Frequency Hours after being poste (b) Hashtags Figure 1: Stochastic Popularity ynamics. (a) 20 papers ranomly selecte from Physical Review uring 1960s. (b) 20 Hashtags ranomly selecte from Twitter in years an containing all the papers ever publishe by American Physical Society. We fin the propose moel consistently outperforms competing methos. Moreover, the propose moel is general. Hence it is not limite to preicting citations, but with appropriate ajustments will likely apply to other omains riven by competing processes. Reinforce Poisson Process The popularity ynamics of iniviual item uring time perio [0,T] is characterize by a set of time moments {t i }(1 apple i apple n ) when each attention is receive, where n represents the total number of attentions. Without loss of generality, we have 0 = t 0 apple t 1 apple apple t i apple apple t n apple T. To moel the arrival process of {t i }, we consier two major phenomena confirme inepenently in previous stuies of population ynamics: (1) the reinforcement capturing the rich-get-richer mechanism, i.e., previous attention triggers more subsequent attentions (Crane an Sornette 2008); (2) the aging effect characterizing time-epenent attractiveness of iniviual items (Ulrich an Miller 1993; Wang, Song, an Barabási 2013). Taken these two factors together, for an iniviual item, we moel its popularity ynamics as a reinforce Poisson process (RPP) (Pemantle 2007) characterize by the rate function x (t) as x (t) = f (t; )i (t), (1) where is the intrinsic attractiveness, f (t; ) is the relaxation function that characterizes the temporal inhomogeneity ue to the aging effect moulate by parameters, an i (t) is the total number of attentions receive up to time t. From a Bayesian viewpoint, the total number of attentions i (t) is the sum of the number of real attentions an the effective number of attentions which plays the role of prior belief. Here, we assume that all items are create equal an hence the effective number of attentions for all items has the same value, enote by m. Therefore uring the time interval between the (i 1)th an ith attentions, we have i (t) =m + i 1, (2) where 1 apple i apple n. Accoringly, uring the time interval between the n th attention an T, the total number of attentions is m + n. The length of time interval between two consecutive attentions follows an inhomogeneous Poisson process. Therefore, given that the (i 1)th attention arrives at t i 1, the probability that the ith attention arrives at t i follows p 1 (t i t i 1) = f (t i ; )(m + i 1)! " p 1 p 0 t t ií1 t 1 i tn T 0 ií2 ií1 n í1 n Figure 2: Graphical representation of the generative moel for popularity ynamics via reinforce Poisson process. e R t i t i 1 f (t; )(m+i 1)t, (3) an the probability that no attention arrives between t n an T is p 0 (T t n ) = e R T t n f (t; )(m+n )t. (4) Incorporating Eqs. (3) an (4) with the fact that attentions uring ifferent time intervals are statistically inepenent, the likelihoo of observing the popularity ynamics {t i } uring time interval [0,T] follows Yn L(, ) = p 0 (T t n ) p 1 (t i t i 1) = n Yn (m + i 1)f (t i ; ) e ((m+n )F (T ; ) P n F (t i ; )), (5) where F (t; ) R t 0 f (t; )t an we have reorganize the terms on the exponent for simplicity. For clarity, we illustrate the propose RPP moel in the graphical representation (Figure 2). By maximizing the likelihoo function in Eq. (5), we obtain the most likely fitness parameter for item in close form: n = (m + n )F (T ; ) P n F (t i ; (6) ). The solution for epens on the specific form of relaxation function f (t; ). We save the iscussions about the estimation of for later. Next we show that, with the obtaine an, the moel can be use to preict the expecte number c (t) of attentions gathere by item up to any given time t. Inee, accoring to Eq. (1), for t T, this preiction task is equivalent to the following ifferential equation c (t) t = f (t; )(m + c (t)) (7) with the bounary conition c (T )=n. Solving this ifferential equation, we obtain the preiction function c (t) =(m + n )e F (t; ) F (T ; ) m. (8) 292

3 $ #! :1 N Figure 3: Probabilistic graphical moel for reinforce Poisson process with conjugate prior. Reinforce Poisson Process with prior Maximum likelihoo parameter estimation suffers from the overfitting problem for small sample size. For example, Eq. (6) gives =0when n =0, an results in a null forecasting of future popularity, i.e., c (t) =0at any future time t. Moreover, the exponential epenency of c (t) on in Eq. (8) leas to a large uncertainty in the preiction of c (t). In this section, to overcome the rawback of the parameter estimation in Eq. (6), we aopt the Bayesian treatment for popularity preiction by introucing a conjugate prior for the fitness parameter, leaing to a further improvement of the preiction accuracy of the propose RPP moel. The likelihoo function in Eq. (5) is a prouct of a power function an an exponential function of. Therefore, the conjugate prior for follows the gamma istribution p(, )= ( ) t " 1 e. (9) Note that this conjugate prior is the prior istribution of fitness parameters for all N items rather than for certain iniviual item. Hereafter, for convenience, we use ~ t {t i } to enote all the arrival time of attentions gathere by item. After introucing the conjugate prior, the graphical representation of moel is epicte in Figure 3. Using Bayes theorem an combining Eqs. (5) an (9), we obtain the posterior istribution of p( ~ t,,, ) = p( t ~, )p(, ) R p( t ~, )p(, ) = ( + X) +n +n 1 e ( +X), (10) ( + n ) P n where X (m + n )F (T ; ) F (t i ; ). With the obtaine posterior istribution of, the expecte number of attentions c (t), as shown in Eq. (8), can be preicte using its mean over the posterior istribution as Z hc (t)i = c (t)p( t ~,,, ) = (m + n ) +n + X + X Y m,(11) where Y F (t; ) F (T ; ). When! inf, the preiction function reuces to a naive metho, i.e., preicting that the popularity keeps constant in future. Eq. (11) is the Bayesian preiction function, preicting c (t) using the posterior istribution of instea of using a single value of obtaine by maximum likelihoo estimation. Neither X, corresponing to empirical observations, nor Y, reflecting the rate ifference in reinforce Poisson process, is in the exponent, inicating the robustness of this preiction function. We now iscuss how to etermine the parameters an of prior istribution. In principle, the values of prior parameters coul be tune by checking the accuracy of preiction function with respect to prior parameters on so-calle valiation set. Yet, this requires us to know the future popularity of some items to etermine prior parameters, hence may not be practical in scenarios where such information is not available. One alternative solution is the fully Bayesian approach which introuces hyperprior for prior parameters. Although the fully Bayesian approach is theoretically elegant, the inference of prior parameters is intractable in most cases. Approximation methos or Monte Carlo methos have to be aopte. As a result, the benefit of fully Bayesian approach is iscounte by approximation gap in approximation methos or high computational cost of Monte Carlo methos. In this paper, we etermine the value of prior parameters by aopting maximum likelihoo estimation with latent variable. Specifically, we choose the an values that maximize the following logarithmic likelihoo function L(, ) = =1 Z ln p( ~ t )p(, ). (12) Here, is not explicitly written to keep the notation uncluttere. In sum, an are obtaine accoring to ) = = N N X = N(ln 0( )) + + =1, (13) ln + n =1 0( + n ), (14) 0 is the igamma function an the latent variable is + n +(m + n )F (T ; ) P n F (t i ; ). (15) Comparing Eq. (15) an Eq. (6), we can see that the fitness parameter is ajuste by prior parameters an. Note that the parameters for all items are also etermine by maximizing the likelihoo function in Eq. (12). The calculation epens on the specific form of relaxation function f (t; ), which is given in experiments on real ataset. Experiments In this section, we emonstrate the effectiveness of the propose RPP moel, with an without prior. 293

4 Experiment setup Dataset. We conuct experiments on an excellent longituinal ataset, containing all papers an citations publishe by American Physical Society between 1893 an We choose this ataset for two main reasons: (1) It covers an extene perio of time, spanning 117 years, ieal for moeling an preicting temporal ynamics; (2) Treating papers as items, their popularity is well-efine, characterize by citations. Statistics about this ataset are shown in Table 1. Relaxation function. When formalizing the moel for popularity ynamics, we introuce a general relaxation function f (t; ) an skippe the iscussion of parameter. Here, when applying this moel to a specific case, i.e., to citation system, we nee to etermine the specific form of the relaxation function as well as. Previous stuies (Raicchi, Fortunato, an Castellano 2008; Wang, Song, an Barabási 2013) on citation ynamics suggest that the aging of papers is capture by a log-normal relaxation function 1 (ln t f (t; µ, ) = p 2 t exp µ ) 2, (16) 2 2 a common relaxation function, which is also observe in other omains such as messages in microblogging networks (Bao et al. 2013a). For item with log-normal relaxation function, is replace by parameters µ an, which can be calculate by maximizing the logarithmic likelihoo L in Eq. (12) an Eq. (5) for the propose RPP moel with an without prior, respectively. In this paper, we maximize logarithmic likelihoo using optimization methos which = 1 ( n X h i i ( i ) + (n + m) ( ) ), (17) = 1 X n h i i i i ( i + (n + m) ( ) n ), (18) where is the probability ensity function of stanar normal istribution, i (ln t i µ )/ an (ln T µ )/. Therefore, we can use Eqs. (17) an (18) together with Eqs. (13) an (14) to maximize the logarithmic likelihoo in Eq. (12) for the RPP moel with prior, together with Eq. (6) to maximize the likelihoo in Eq. (5) for the RPP moel without prior. Baseline moels an evaluation metrics. We compare the RPP moel with three wiely-use moels for popularity preiction: the classic autoregression () metho (Box, Jenkins, an Reinsel 2008), the linear regression metho of logarithmic popularity () (Szabo an Huberman 2010), an the WSB moel (Wang, Song, an Barabási 2013), which is equivalent to the propose RPP moel without prior when the log-normal relaxation function is aopte. We aopt two stanar measurements as evaluation metrics: Table 1: Basic statistics of ataset. Journal #Papers #Citations Perio PRSI 1, PR 47, , PRA 53, , PRB 137, 999 1, 191, PRC 29, , PRD 56, , PRE 35, , PRL 95, 516 1, 507, RMP 2, , PRSTAB 1, 257 2, PRSTPER Total 463, 348 4, 710, Mean Absolute Percentage Error (MAPE) measures the average eviation between preicte an empirical popularity over an aggregation of items. Denoting with c (t) the preicte number of citations for a paper up to time t an with r (t) its real number of citations, we obtain the MAPE over N papers MAP E = 1 c (t) r (t) N r. (t) =1 Accuracy measures the fraction of papers correctly preicte for a given error tolerance. Hence the accuracy of popularity preiction on N papers is 1 N { : =1 c (t) r (t) r (t) apple }. We set the threshol =0.1 in this paper. Experiment Results In this section, we report two sets of experiments: (1) We compare the preictive power of RPP moel with other competing methos, fining that RPP consistently outperforms other moels; (2) We perform etaile analysis to unerstan the factors that coul affect the performance of RPP moel, incluing the length of training perio, the effective number of attentions, an the prior parameters. Popularity preiction. We evaluate the preiction results on three collections of papers: (a) papers publishe in Physical Review (PR) from 1960 to 1969; (b) papers publishe in Physical Review Letters (PRL) from 1970 to 1979; (c) papers publishe in Physical Review B (PRB) from 1980 to These samples vary in timeframes an scopes, spanning three ecaes an covering three types of journals. Using papers with more than 10 citations uring the first five years after publication, we compare the RPP moel with an without prior against the an moels. The number of papers in the three collections is 3242, 2017 an 3732, respectively. The training perio is 10 years an we preict the citation counts for each paper from the 1st to 20th year after the training perio. For collection (c), we preict the citation counts up to the 10th year after training perio ue to the cutoff year of the ata (2009). We set the parameter m = 30 for now, corresponing to the typical number of 294

5 MAPE MAPE MAPE Years after Training Perio (a) Physical Review (1960s) Years after Training Perio (b) Physical Review Letters (1970s) Years after Training Perio (c) Physical Review B (1980s) Accuracy Accuracy Accuracy Years after Training Perio () Physical Review (1960s) Years after Training Perio (e) Physical Review Letters (1970s) Years after Training Perio (f) Physical Review B (1980s) 10 2 real preicte 10 2 real preicte 10 2 real preicte # papers 10 1 # papers 10 1 # papers # citations (g) Physical Review (1960s) # citations (h) Physical Review Letters (1970s) # citations (i) Physical Review B (1980s) Figure 4: The performance comparison in popularity preiction. references for a paper, leaving the effect of varying m on the performance of RPP moel for later iscussions. We fin the RPP moel, propose in this paper, achieves higher accuracy than the an methos (Figure 4). Yet in absence of prior it only exhibits moest performance in terms of MAPE, inicating that the RPP moel without prior performs well on most papers but can be skewe by large errors on a hanful of papers. This is mainly cause by its exponential epenence on the fitness parameter that sometimes yiels overfitting problem when maximum likelihoo parameter estimation is aopte. This problem is nicely avoie by incorporating conjugate prior for the fitness parameter, ocumente by the fact that the RPP moel with prior consistently outperforms the other three methos on all collections. The superiority of the RPP moel with prior, compare to the an methos, increases with the number of years after the training perio. This improvement is roote in the methoological avantage: the RPP moel is a generative probabilistic moel that explicitly moels the arrival process of attentions, while the two baseline methos only capture the correlation between early popularity an future popularity, linearly or logarithmically. In aition, the reinforce Poisson process coul moel the rich-get-richer phenomenon in popularity ynamics an thus coul characterize the logarithmic correlation between early popularity an future popularity. Therefore, when compare with the metho, the superiority is more obvious than being compare with the metho. This is because of the linear nature of the metho, while the metho works in a logarithmic manner. Furthermore, the RPP moels with an without prior are traine only on the popularity ynamics uring training perio while the training of the an moels epen on the knowlege of future popularity ynamics. When training these two moels, we employ the leave-one-out technique 295

6 Mean of Prior Distribution Mean Variance <MAPE> Years for Training Figure 5: Effect of training perio length. which uses all papers except the target paper for preiction. Yet, in most cases, it is unrealistic to know future popularity ynamics when training the moel, limiting their applications in real scenarios. Finally, being a generative moel, the RPP moel is able to reprouce the citation istribution. Inee, as shown in Figure 4 (g-i), the istribution of citations preicte by the RPP moel with prior matches very well with that of real citations on all stuie collections, inicating that the RPP moel can also be use to moel aggregate properties of a system. Moreover, for completeness, we offer the values of prior parameters an for the three collections of papers: =5.322 an =6.796 for collection (a); =5.703 an = for collection (b); = an = for collection (c). Analysis of relevant factors. The superior preictive power in the RPP moel with prior raises an interesting question: what are the possible factors that affect its preictive power? In this section, we stuy a number of factors which coul affect the performance of the RPP moel with prior. Hereafter, we use hmapei to enote the average MAPEs for preictions from the 1st to 10th year after training perio. The training perio is 10 years except when we iscuss the effect of varying training perio length. The parameter m is set to be 30 except when we iscuss the effect of changing m. First, we stuy the preiction accuracy of the RPP moel with prior by varying the length of training perio. Experiments are conucte on the paper collection (a). As shown in Figure 5, hmapei ecreases as the training perio increases. Hence increasing the training perio improves the preiction accuracy. However, the rate at which hmapei iminishes slows own quickly, inicating the marginal gain of increasing training perio. We also fin that the mean of prior istribution stays almost constant as the length of training perio increases from 5 years to 15 years, inicating the expecte fitness parameter learne by the RPP moel is robust against varying training perio. At the same time, increasing training perio reuces the role of prior in preiction, partly explaining the role of prior in overcoming the overfitting problem, as the variance in the prior istributions increases with the length of training perio. Secon, we investigate the effect of parameter m, i.e., the effective number of attentions by conucting experiments on the paper collection (a). Intuitively, m balances the strength in the reinforcement mechanism. Inee, as shown in Ta- <MAPE> / Variance of Prior Distribution Table 2: Effect of the number of conceive attentions (m). m Mean ( / ) Variance ( / 2 ) hmapei Table 3: Performance on RMP papers over four ecaes. Perio / hmapei 1950s s s s ble 2, the mean an variance of the prior istribution ecay with m, emonstrating these parameters are mainly etermine by papers with fewer citations. We also fin that ecreasing m reuces hmapei, inicating that the isparity in citations is capture appropriately by the reinforcement mechanism in our moel, as a larger m implies a weaker role of the reinforcement mechanism. Taken together, Table 2 confirms that the reinforcement mechanism is crucial to moeling popularity ynamics in citation system. Finally, we use papers publishe in Reviews of Moern Physics (RMP) to illustrate the change of prior parameter an over four ecaes an their influence on the preiction accuracy of the RPP moel with prior. As shown in Table 3, the mean of prior istribution (i.e., / ) increases with the increasing magnitue of both an over the four ecaes. This inicates that the expecte citations for papers in this prestigious journal steaily increases uring the secon half of the 20th century. Meanwhile, the hmapei of the RPP moel also increases. Hence it becomes more ifficult to preict the citations of these papers, as a result of the increasing isparity in citation istribution (Barabási et al. 2012). Conclusions Taken together, we presente a general framework to moel an preict popularity ynamics base on a reinforce Poisson process. This moel incorporates three key ingreients of popularity ynamics: the fitness parameter characterizing intrinsic attractiveness, the temporal relaxation function explaining the aging effect in attracting new attentions, an the reinforcement mechanism corresponing to the richget-richer effect in popularity ynamics. Being a generative probabilistic framework, it explicitly moels the stochastic process of gaining popularity for each item, in contrast to existing eterministic approaches. We evelope optimization methos to train the propose RPP moel with an without priors. The RPP moel with prior allows us to apply the Bayesian treatment, resulting in more robust an accurate preictions for popularity ynamics. We empirically valiate our moel on an excellent longituinal ataset on citations, spanning more than one hunre years, emonstrating its clear avantages over competing methos. 296

7 Acknowlegments This work was fune by the National Basic Research Program of China (973 Program) uner grant number 2014CB340401, the National High-tech R&D Program of China (863 Program) uner grant number 2014AA015103, an the National Natural Science Founation of China uner grant numbers , This work was also partly fune by the Beijing Natural Science Founation uner grant number DW, CS, ALB are supporte by Lockhee Martin Corporation (SRA ), the Network Science Collaborative Technology Alliance is sponsore by the U.S. Army Research Laboratory uner agreement W911NF , Defence Avance Research Projects Agency uner agreement , an the Future an Emerging Technologies Project Multiplex finance by the European Commission. References Backstrom, L.; Huttenlocher, D.; Kleinberg, J.; an Lan, X Group formation in large social networks: Membership, growth, an evolution. In KDD 06, Bao, P.; Shen, H. W.; Chen, W.; an Cheng, X. Q. 2013a. Cumulative effect in information iffusion: empirical stuy on a microblogging network. PLoS ONE 8(10):e Bao, P.; Shen, H. W.; Huang, J.; an Cheng, X. Q. 2013b. Popularity preiction in microblogging network: A case stuy on sina weibo. In WWW 13, Barabási, A. L., an Albert, R Emergence of scaling in ranom networks. Science 286(5439): Barabási, A. L.; Song, C.; an Wang, D Publishing: Hanful of papers ominates citation. Nature, 491(7422): Bass, F. M A new prouct growth for moel consumer urables. Management Science 15(5): Box, G. E. P.; Jenkins, G. M.; an Reinsel, G. C Time Series Analysis: Forecasting an Control. Wiley, 4th eition. Crane, R., an Sornette, D Robust ynamic classes reveale by measuring the response function of a social system. PNAS 105(41): Dezso, Z.; Almaas, E.; Lukács, A.; Rácz, B.; Szakaát, I.; an Barabási, A. L Dynamics of information access on the web. Physical Review E 73: Gomez-Roriguez, M.; Leskovec, J.; an Schölkopf, B Moeling information propagation with survival theory. In ICML 13. Hong, L.; Dan, O.; an Davison, B. D Preicting popular messages in twitter. In WWW 11, Kempe, D.; Kleinberg, J.; an Taros, E Maximizing the sprea of influence through a social network. In KDD 03, Lerman, K., an Hogg, T Using a moel of social ynamics to preict popularity of news. In WWW 10, Lerman, K., an Hogg, T Using stochastic moels to escribe an preict social ynamics of web users. ACM Transactions on Intelligent Systems an Technology 3(4):62. Mahajan, V.; Muller, E.; an Bass, F. M New prouct iffusion moels in marketing: A review an irections for research. The Journal of Marketing 54:1 26. Matsubara, Y.; Sakurai, Y.; Prakash, B. A.; Li, L.; an Faloutsos, C Rise an fall patterns of information iffusion: Moel an implications. In KDD 12, Pemantle, R A survey of ranom processes with reinforcement. Probability Surveys 4:1 79. Raicchi, F.; Fortunato, S.; an Castellano, C Universality of citation istribution: towar an objective measure of scientific impact. PNAS 105(45): Ratkiewicz, J.; Fortunato, S.; Flammini, A.; Menczer, F.; an Vespignani, A Characterizing an moeling the ynamics of online popularity. Physical Review Letters 105(15): Ren, F. X.; Shen, H. W.; an Cheng, X. Q Moeling the clustering in citation networks. Physica A 391(12): Szabo, G., an Huberman, B. A Preicting the popularity of online content. Communications of the ACM 53(8): Ulrich, R., an Miller, J Information processing moels generating lognormally istribute reaction times. J. Math. Psychol. 37(4): Vu, D. Q.; Asuncion, A. U.; Hunter, D. R.; an Smyth, P Dynamic egocentric moels for citation networks. In ICML 11, Wang, D.; Song, C.; an Barabási, A. L Quantifying long-term scientific impact. Science 342: Wu, F., an Humberman, B Novelty an collective attention. PNAS 104(45): Yan, R.; Tang, J.; Liu, X.; Shan, D.; an Li, X Citation count preiction: learning to estimate future citations for literature. In CIKM 11, Yang, J., an Leskovec, J Moeling information iffusion in implict networks. In ICDM 10, Yang, S. H., an Zha, H Mixture of mutually exciting processes for viral iffusion. In ICML 13, 1 9. Yu, X.; Gu, Q.; Zhou, M.; an Han, J Citation preiction in heterogeneous bibliographic networks. In SDM 12,

State of Louisiana Office of Information Technology. Change Management Plan

State of Louisiana Office of Information Technology. Change Management Plan State of Louisiana Office of Information Technology Change Management Plan Table of Contents Change Management Overview Change Management Plan Key Consierations Organizational Transition Stages Change

More information

Risk Management for Derivatives

Risk Management for Derivatives Risk Management or Derivatives he Greeks are coming the Greeks are coming! Managing risk is important to a large number o iniviuals an institutions he most unamental aspect o business is a process where

More information

MASSACHUSETTS INSTITUTE OF TECHNOLOGY 6.436J/15.085J Fall 2008 Lecture 14 10/27/2008 MOMENT GENERATING FUNCTIONS

MASSACHUSETTS INSTITUTE OF TECHNOLOGY 6.436J/15.085J Fall 2008 Lecture 14 10/27/2008 MOMENT GENERATING FUNCTIONS MASSACHUSETTS INSTITUTE OF TECHNOLOGY 6.436J/15.085J Fall 2008 Lecture 14 10/27/2008 MOMENT GENERATING FUNCTIONS Contents 1. Moment generating functions 2. Sum of a ranom number of ranom variables 3. Transforms

More information

Ch 10. Arithmetic Average Options and Asian Opitons

Ch 10. Arithmetic Average Options and Asian Opitons Ch 10. Arithmetic Average Options an Asian Opitons I. Asian Option an the Analytic Pricing Formula II. Binomial Tree Moel to Price Average Options III. Combination of Arithmetic Average an Reset Options

More information

Digital barrier option contract with exponential random time

Digital barrier option contract with exponential random time IMA Journal of Applie Mathematics Avance Access publishe June 9, IMA Journal of Applie Mathematics ) Page of 9 oi:.93/imamat/hxs3 Digital barrier option contract with exponential ranom time Doobae Jun

More information

The one-year non-life insurance risk

The one-year non-life insurance risk The one-year non-life insurance risk Ohlsson, Esbjörn & Lauzeningks, Jan Abstract With few exceptions, the literature on non-life insurance reserve risk has been evote to the ultimo risk, the risk in the

More information

Optimal Control Policy of a Production and Inventory System for multi-product in Segmented Market

Optimal Control Policy of a Production and Inventory System for multi-product in Segmented Market RATIO MATHEMATICA 25 (2013), 29 46 ISSN:1592-7415 Optimal Control Policy of a Prouction an Inventory System for multi-prouct in Segmente Market Kuleep Chauhary, Yogener Singh, P. C. Jha Department of Operational

More information

UCLA STAT 13 Introduction to Statistical Methods for the Life and Health Sciences. Chapter 9 Paired Data. Paired data. Paired data

UCLA STAT 13 Introduction to Statistical Methods for the Life and Health Sciences. Chapter 9 Paired Data. Paired data. Paired data UCLA STAT 3 Introuction to Statistical Methos for the Life an Health Sciences Instructor: Ivo Dinov, Asst. Prof. of Statistics an Neurology Chapter 9 Paire Data Teaching Assistants: Jacquelina Dacosta

More information

Sensitivity Analysis of Non-linear Performance with Probability Distortion

Sensitivity Analysis of Non-linear Performance with Probability Distortion Preprints of the 19th Worl Congress The International Feeration of Automatic Control Cape Town, South Africa. August 24-29, 214 Sensitivity Analysis of Non-linear Performance with Probability Distortion

More information

ISSN: 2277-3754 ISO 9001:2008 Certified International Journal of Engineering and Innovative Technology (IJEIT) Volume 3, Issue 12, June 2014

ISSN: 2277-3754 ISO 9001:2008 Certified International Journal of Engineering and Innovative Technology (IJEIT) Volume 3, Issue 12, June 2014 ISSN: 77-754 ISO 900:008 Certifie International Journal of Engineering an Innovative echnology (IJEI) Volume, Issue, June 04 Manufacturing process with isruption uner Quaratic Deman for Deteriorating Inventory

More information

Data Center Power System Reliability Beyond the 9 s: A Practical Approach

Data Center Power System Reliability Beyond the 9 s: A Practical Approach Data Center Power System Reliability Beyon the 9 s: A Practical Approach Bill Brown, P.E., Square D Critical Power Competency Center. Abstract Reliability has always been the focus of mission-critical

More information

5 Isotope effects on vibrational relaxation and hydrogen-bond dynamics in water

5 Isotope effects on vibrational relaxation and hydrogen-bond dynamics in water 5 Isotope effects on vibrational relaxation an hyrogen-bon ynamics in water Pump probe experiments HDO issolve in liqui H O show the spectral ynamics an the vibrational relaxation of the OD stretch vibration.

More information

On Adaboost and Optimal Betting Strategies

On Adaboost and Optimal Betting Strategies On Aaboost an Optimal Betting Strategies Pasquale Malacaria 1 an Fabrizio Smerali 1 1 School of Electronic Engineering an Computer Science, Queen Mary University of Lonon, Lonon, UK Abstract We explore

More information

JON HOLTAN. if P&C Insurance Ltd., Oslo, Norway ABSTRACT

JON HOLTAN. if P&C Insurance Ltd., Oslo, Norway ABSTRACT OPTIMAL INSURANCE COVERAGE UNDER BONUS-MALUS CONTRACTS BY JON HOLTAN if P&C Insurance Lt., Oslo, Norway ABSTRACT The paper analyses the questions: Shoul or shoul not an iniviual buy insurance? An if so,

More information

Stock Market Value Prediction Using Neural Networks

Stock Market Value Prediction Using Neural Networks Stock Market Value Preiction Using Neural Networks Mahi Pakaman Naeini IT & Computer Engineering Department Islamic Aza University Paran Branch e-mail: m.pakaman@ece.ut.ac.ir Hamireza Taremian Engineering

More information

Cross-Over Analysis Using T-Tests

Cross-Over Analysis Using T-Tests Chapter 35 Cross-Over Analysis Using -ests Introuction his proceure analyzes ata from a two-treatment, two-perio (x) cross-over esign. he response is assume to be a continuous ranom variable that follows

More information

Product Differentiation for Software-as-a-Service Providers

Product Differentiation for Software-as-a-Service Providers University of Augsburg Prof. Dr. Hans Ulrich Buhl Research Center Finance & Information Management Department of Information Systems Engineering & Financial Management Discussion Paper WI-99 Prouct Differentiation

More information

Optimizing Multiple Stock Trading Rules using Genetic Algorithms

Optimizing Multiple Stock Trading Rules using Genetic Algorithms Optimizing Multiple Stock Traing Rules using Genetic Algorithms Ariano Simões, Rui Neves, Nuno Horta Instituto as Telecomunicações, Instituto Superior Técnico Av. Rovisco Pais, 040-00 Lisboa, Portugal.

More information

Improving Direct Marketing Profitability with Neural Networks

Improving Direct Marketing Profitability with Neural Networks Volume 9 o.5, September 011 Improving Direct Marketing Profitability with eural etworks Zaiyong Tang Salem State University Salem, MA 01970 ABSTRACT Data mining in irect marketing aims at ientifying the

More information

Consumer Referrals. Maria Arbatskaya and Hideo Konishi. October 28, 2014

Consumer Referrals. Maria Arbatskaya and Hideo Konishi. October 28, 2014 Consumer Referrals Maria Arbatskaya an Hieo Konishi October 28, 2014 Abstract In many inustries, rms rewar their customers for making referrals. We analyze the optimal policy mix of price, avertising intensity,

More information

A Generalization of Sauer s Lemma to Classes of Large-Margin Functions

A Generalization of Sauer s Lemma to Classes of Large-Margin Functions A Generalization of Sauer s Lemma to Classes of Large-Margin Functions Joel Ratsaby University College Lonon Gower Street, Lonon WC1E 6BT, Unite Kingom J.Ratsaby@cs.ucl.ac.uk, WWW home page: http://www.cs.ucl.ac.uk/staff/j.ratsaby/

More information

Robust Reading of Ambiguous Writing

Robust Reading of Ambiguous Writing In submission; please o not istribute. Abstract A given entity, representing a person, a location or an organization, may be mentione in text in multiple, ambiguous ways. Unerstaning natural language requires

More information

Identification and Tracing of Ambiguous Names: Discriminative and Generative Approaches

Identification and Tracing of Ambiguous Names: Discriminative and Generative Approaches Ientification an Tracing of Ambiguous Names: Discriminative an Generative Approaches Xin Li Paul Morie Dan Roth Department of Computer Science University of Illinois, Urbana, IL 61801 {xli1,morie,anr}@uiuc.eu

More information

Patch Complexity, Finite Pixel Correlations and Optimal Denoising

Patch Complexity, Finite Pixel Correlations and Optimal Denoising Patch Complexity, Finite Pixel Correlations an Optimal Denoising Anat Levin Boaz Naler Freo Duran William T. Freeman Weizmann Institute MIT CSAIL Abstract. Image restoration tasks are ill-pose problems,

More information

A Theory of Exchange Rates and the Term Structure of Interest Rates

A Theory of Exchange Rates and the Term Structure of Interest Rates Review of Development Economics, 17(1), 74 87, 013 DOI:10.1111/roe.1016 A Theory of Exchange Rates an the Term Structure of Interest Rates Hyoung-Seok Lim an Masao Ogaki* Abstract This paper efines the

More information

MSc. Econ: MATHEMATICAL STATISTICS, 1995 MAXIMUM-LIKELIHOOD ESTIMATION

MSc. Econ: MATHEMATICAL STATISTICS, 1995 MAXIMUM-LIKELIHOOD ESTIMATION MAXIMUM-LIKELIHOOD ESTIMATION The General Theory of M-L Estimation In orer to erive an M-L estimator, we are boun to make an assumption about the functional form of the istribution which generates the

More information

10.2 Systems of Linear Equations: Matrices

10.2 Systems of Linear Equations: Matrices SECTION 0.2 Systems of Linear Equations: Matrices 7 0.2 Systems of Linear Equations: Matrices OBJECTIVES Write the Augmente Matrix of a System of Linear Equations 2 Write the System from the Augmente Matrix

More information

Emergence of heterogeneity in acute leukemias

Emergence of heterogeneity in acute leukemias Stiehl et al. Biology Direct (2016) 11:51 DOI 10.1186/s13062-016-0154-1 RESEARCH Open Access Emergence of heterogeneity in acute leukemias Thomas Stiehl 1,2,3*, Christoph Lutz 4 an Anna Marciniak-Czochra

More information

Optimal Energy Commitments with Storage and Intermittent Supply

Optimal Energy Commitments with Storage and Intermittent Supply Submitte to Operations Research manuscript OPRE-2009-09-406 Optimal Energy Commitments with Storage an Intermittent Supply Jae Ho Kim Department of Electrical Engineering, Princeton University, Princeton,

More information

CHAPTER 5 : CALCULUS

CHAPTER 5 : CALCULUS Dr Roger Ni (Queen Mary, University of Lonon) - 5. CHAPTER 5 : CALCULUS Differentiation Introuction to Differentiation Calculus is a branch of mathematics which concerns itself with change. Irrespective

More information

Seeing the Unseen: Revealing Mobile Malware Hidden Communications via Energy Consumption and Artificial Intelligence

Seeing the Unseen: Revealing Mobile Malware Hidden Communications via Energy Consumption and Artificial Intelligence Seeing the Unseen: Revealing Mobile Malware Hien Communications via Energy Consumption an Artificial Intelligence Luca Caviglione, Mauro Gaggero, Jean-François Lalane, Wojciech Mazurczyk, Marcin Urbanski

More information

DETERMINING OPTIMAL STOCK LEVEL IN MULTI-ECHELON SUPPLY CHAINS

DETERMINING OPTIMAL STOCK LEVEL IN MULTI-ECHELON SUPPLY CHAINS HUNGARIAN JOURNA OF INDUSTRIA CHEMISTRY VESZPRÉM Vol. 39(1) pp. 107-112 (2011) DETERMINING OPTIMA STOCK EVE IN MUTI-ECHEON SUPPY CHAINS A. KIRÁY 1, G. BEVÁRDI 2, J. ABONYI 1 1 University of Pannonia, Department

More information

Enterprise Resource Planning

Enterprise Resource Planning Enterprise Resource Planning MPC 6 th Eition Chapter 1a McGraw-Hill/Irwin Copyright 2011 by The McGraw-Hill Companies, Inc. All rights reserve. Enterprise Resource Planning A comprehensive software approach

More information

Heat-And-Mass Transfer Relationship to Determine Shear Stress in Tubular Membrane Systems Ratkovich, Nicolas Rios; Nopens, Ingmar

Heat-And-Mass Transfer Relationship to Determine Shear Stress in Tubular Membrane Systems Ratkovich, Nicolas Rios; Nopens, Ingmar Aalborg Universitet Heat-An-Mass Transfer Relationship to Determine Shear Stress in Tubular Membrane Systems Ratkovich, Nicolas Rios; Nopens, Ingmar Publishe in: International Journal of Heat an Mass Transfer

More information

Forecasting and Staffing Call Centers with Multiple Interdependent Uncertain Arrival Streams

Forecasting and Staffing Call Centers with Multiple Interdependent Uncertain Arrival Streams Forecasting an Staffing Call Centers with Multiple Interepenent Uncertain Arrival Streams Han Ye Department of Statistics an Operations Research, University of North Carolina, Chapel Hill, NC 27599, hanye@email.unc.eu

More information

6.3 Microbial growth in a chemostat

6.3 Microbial growth in a chemostat 6.3 Microbial growth in a chemostat The chemostat is a wiely-use apparatus use in the stuy of microbial physiology an ecology. In such a chemostat also known as continuous-flow culture), microbes such

More information

An intertemporal model of the real exchange rate, stock market, and international debt dynamics: policy simulations

An intertemporal model of the real exchange rate, stock market, and international debt dynamics: policy simulations This page may be remove to conceal the ientities of the authors An intertemporal moel of the real exchange rate, stock market, an international ebt ynamics: policy simulations Saziye Gazioglu an W. Davi

More information

Di usion on Social Networks. Current Version: June 6, 2006 Appeared in: Économie Publique, Numéro 16, pp 3-16, 2005/1.

Di usion on Social Networks. Current Version: June 6, 2006 Appeared in: Économie Publique, Numéro 16, pp 3-16, 2005/1. Di usion on Social Networks Matthew O. Jackson y Caltech Leeat Yariv z Caltech Current Version: June 6, 2006 Appeare in: Économie Publique, Numéro 16, pp 3-16, 2005/1. Abstract. We analyze a moel of i

More information

Robust Reading: Identification and Tracing of Ambiguous Names

Robust Reading: Identification and Tracing of Ambiguous Names Robust Reaing: Ientification an Tracing of Ambiguous Names Xin Li Paul Morie Dan Roth Department of Computer Science University of Illinois, Urbana, IL 61801 {xli1,morie,anr}@uiuc.eu Abstract A given entity,

More information

Applications of Global Positioning System in Traffic Studies. Yi Jiang 1

Applications of Global Positioning System in Traffic Studies. Yi Jiang 1 Applications of Global Positioning System in Traffic Stuies Yi Jiang 1 Introuction A Global Positioning System (GPS) evice was use in this stuy to measure traffic characteristics at highway intersections

More information

Performance And Analysis Of Risk Assessment Methodologies In Information Security

Performance And Analysis Of Risk Assessment Methodologies In Information Security International Journal of Computer Trens an Technology (IJCTT) volume 4 Issue 10 October 2013 Performance An Analysis Of Risk Assessment ologies In Information Security K.V.D.Kiran #1, Saikrishna Mukkamala

More information

An Introduction to Event-triggered and Self-triggered Control

An Introduction to Event-triggered and Self-triggered Control An Introuction to Event-triggere an Self-triggere Control W.P.M.H. Heemels K.H. Johansson P. Tabuaa Abstract Recent evelopments in computer an communication technologies have le to a new type of large-scale

More information

Cost Efficient Datacenter Selection for Cloud Services

Cost Efficient Datacenter Selection for Cloud Services Cost Efficient Datacenter Selection for Clou Services Hong u, Baochun Li henryxu, bli@eecg.toronto.eu Department of Electrical an Computer Engineering University of Toronto Abstract Many clou services

More information

A Case Study of Applying SOM in Market Segmentation of Automobile Insurance Customers

A Case Study of Applying SOM in Market Segmentation of Automobile Insurance Customers International Journal of Database Theory an Application, pp.25-36 http://x.oi.org/10.14257/ijta.2014.7.1.03 A Case Stuy of Applying SOM in Market Segmentation of Automobile Insurance Customers Vahi Golmah

More information

Study on the Price Elasticity of Demand of Beijing Subway

Study on the Price Elasticity of Demand of Beijing Subway Journal of Traffic an Logistics Engineering, Vol, 1, No. 1 June 2013 Stuy on the Price Elasticity of Deman of Beijing Subway Yanan Miao an Liang Gao MOE Key Laboratory for Urban Transportation Complex

More information

Option Pricing for Inventory Management and Control

Option Pricing for Inventory Management and Control Option Pricing for Inventory Management an Control Bryant Angelos, McKay Heasley, an Jeffrey Humpherys Abstract We explore the use of option contracts as a means of managing an controlling inventories

More information

Optimal Control Of Production Inventory Systems With Deteriorating Items And Dynamic Costs

Optimal Control Of Production Inventory Systems With Deteriorating Items And Dynamic Costs Applie Mathematics E-Notes, 8(2008), 194-202 c ISSN 1607-2510 Available free at mirror sites of http://www.math.nthu.eu.tw/ amen/ Optimal Control Of Prouction Inventory Systems With Deteriorating Items

More information

Detecting Possibly Fraudulent or Error-Prone Survey Data Using Benford s Law

Detecting Possibly Fraudulent or Error-Prone Survey Data Using Benford s Law Detecting Possibly Frauulent or Error-Prone Survey Data Using Benfor s Law Davi Swanson, Moon Jung Cho, John Eltinge U.S. Bureau of Labor Statistics 2 Massachusetts Ave., NE, Room 3650, Washington, DC

More information

Modelling and Resolving Software Dependencies

Modelling and Resolving Software Dependencies June 15, 2005 Abstract Many Linux istributions an other moern operating systems feature the explicit eclaration of (often complex) epenency relationships between the pieces of software

More information

Automatic Long-Term Loudness and Dynamics Matching

Automatic Long-Term Loudness and Dynamics Matching Automatic Long-Term Louness an Dynamics Matching Earl ickers Creative Avance Technology Center Scotts alley, CA, USA earlv@atc.creative.com ABSTRACT Traitional auio level control evices, such as automatic

More information

The most common model to support workforce management of telephone call centers is

The most common model to support workforce management of telephone call centers is Designing a Call Center with Impatient Customers O. Garnett A. Manelbaum M. Reiman Davison Faculty of Inustrial Engineering an Management, Technion, Haifa 32000, Israel Davison Faculty of Inustrial Engineering

More information

A New Evaluation Measure for Information Retrieval Systems

A New Evaluation Measure for Information Retrieval Systems A New Evaluation Measure for Information Retrieval Systems Martin Mehlitz martin.mehlitz@ai-labor.e Christian Bauckhage Deutsche Telekom Laboratories christian.bauckhage@telekom.e Jérôme Kunegis jerome.kunegis@ai-labor.e

More information

A New Pricing Model for Competitive Telecommunications Services Using Congestion Discounts

A New Pricing Model for Competitive Telecommunications Services Using Congestion Discounts A New Pricing Moel for Competitive Telecommunications Services Using Congestion Discounts N. Keon an G. Ananalingam Department of Systems Engineering University of Pennsylvania Philaelphia, PA 19104-6315

More information

Unsteady Flow Visualization by Animating Evenly-Spaced Streamlines

Unsteady Flow Visualization by Animating Evenly-Spaced Streamlines EUROGRAPHICS 2000 / M. Gross an F.R.A. Hopgoo Volume 19, (2000), Number 3 (Guest Eitors) Unsteay Flow Visualization by Animating Evenly-Space Bruno Jobar an Wilfri Lefer Université u Littoral Côte Opale,

More information

ThroughputScheduler: Learning to Schedule on Heterogeneous Hadoop Clusters

ThroughputScheduler: Learning to Schedule on Heterogeneous Hadoop Clusters ThroughputScheuler: Learning to Scheule on Heterogeneous Haoop Clusters Shehar Gupta, Christian Fritz, Bob Price, Roger Hoover, an Johan e Kleer Palo Alto Research Center, Palo Alto, CA, USA {sgupta, cfritz,

More information

Hull, Chapter 11 + Sections 17.1 and 17.2 Additional reference: John Cox and Mark Rubinstein, Options Markets, Chapter 5

Hull, Chapter 11 + Sections 17.1 and 17.2 Additional reference: John Cox and Mark Rubinstein, Options Markets, Chapter 5 Binomial Moel Hull, Chapter 11 + ections 17.1 an 17.2 Aitional reference: John Cox an Mark Rubinstein, Options Markets, Chapter 5 1. One-Perio Binomial Moel Creating synthetic options (replicating options)

More information

A Data Placement Strategy in Scientific Cloud Workflows

A Data Placement Strategy in Scientific Cloud Workflows A Data Placement Strategy in Scientific Clou Workflows Dong Yuan, Yun Yang, Xiao Liu, Jinjun Chen Faculty of Information an Communication Technologies, Swinburne University of Technology Hawthorn, Melbourne,

More information

If you have ever spoken with your grandparents about what their lives were like

If you have ever spoken with your grandparents about what their lives were like CHAPTER 7 Economic Growth I: Capital Accumulation an Population Growth The question of growth is nothing new but a new isguise for an age-ol issue, one which has always intrigue an preoccupie economics:

More information

INFLUENCE OF GPS TECHNOLOGY ON COST CONTROL AND MAINTENANCE OF VEHICLES

INFLUENCE OF GPS TECHNOLOGY ON COST CONTROL AND MAINTENANCE OF VEHICLES 1 st Logistics International Conference Belgrae, Serbia 28-30 November 2013 INFLUENCE OF GPS TECHNOLOGY ON COST CONTROL AND MAINTENANCE OF VEHICLES Goran N. Raoičić * University of Niš, Faculty of Mechanical

More information

Predicting Television Ratings and Its Application to Taiwan Cable TV Channels

Predicting Television Ratings and Its Application to Taiwan Cable TV Channels 2n International Symposium on Computer, Communication, Control an Automation (3CA 2013) Preicting Television Ratings an Its Application to Taiwan Cable TV Channels Hui-Ling Huang Department of Biological

More information

_Mankiw7e_CH07.qxp 3/2/09 9:40 PM Page 189 PART III. Growth Theory: The Economy in the Very Long Run

_Mankiw7e_CH07.qxp 3/2/09 9:40 PM Page 189 PART III. Growth Theory: The Economy in the Very Long Run 189-220_Mankiw7e_CH07.qxp 3/2/09 9:40 PM Page 189 PART III Growth Theory: The Economy in the Very Long Run 189-220_Mankiw7e_CH07.qxp 3/2/09 9:40 PM Page 190 189-220_Mankiw7e_CH07.qxp 3/2/09 9:40 PM Page

More information

A Blame-Based Approach to Generating Proposals for Handling Inconsistency in Software Requirements

A Blame-Based Approach to Generating Proposals for Handling Inconsistency in Software Requirements International Journal of nowlege an Systems Science, 3(), -7, January-March 0 A lame-ase Approach to Generating Proposals for Hanling Inconsistency in Software Requirements eian Mu, Peking University,

More information

Mathematics Review for Economists

Mathematics Review for Economists Mathematics Review for Economists by John E. Floy University of Toronto May 9, 2013 This ocument presents a review of very basic mathematics for use by stuents who plan to stuy economics in grauate school

More information

Linking ICT related Innovation. Adoption and Productivity: results from micro-aggregated versus firm-level data

Linking ICT related Innovation. Adoption and Productivity: results from micro-aggregated versus firm-level data 08 09 0 Linking ICT relate Innovation Aoption an Prouctivity: results from micro-aggregate versus firm-level ata 4 5 Explanation of symbols. ata not available * provisional figure ** revise provisional

More information

Lagrangian and Hamiltonian Mechanics

Lagrangian and Hamiltonian Mechanics Lagrangian an Hamiltonian Mechanics D.G. Simpson, Ph.D. Department of Physical Sciences an Engineering Prince George s Community College December 5, 007 Introuction In this course we have been stuying

More information

n-parameter families of curves

n-parameter families of curves 1 n-parameter families of curves For purposes of this iscussion, a curve will mean any equation involving x, y, an no other variables. Some examples of curves are x 2 + (y 3) 2 = 9 circle with raius 3,

More information

FAST JOINING AND REPAIRING OF SANDWICH MATERIALS WITH DETACHABLE MECHANICAL CONNECTION TECHNOLOGY

FAST JOINING AND REPAIRING OF SANDWICH MATERIALS WITH DETACHABLE MECHANICAL CONNECTION TECHNOLOGY FAST JOINING AND REPAIRING OF SANDWICH MATERIALS WITH DETACHABLE MECHANICAL CONNECTION TECHNOLOGY Jörg Felhusen an Sivakumara K. Krishnamoorthy RWTH Aachen University, Chair an Insitute for Engineering

More information

Differentiability of Exponential Functions

Differentiability of Exponential Functions Differentiability of Exponential Functions Philip M. Anselone an John W. Lee Philip Anselone (panselone@actionnet.net) receive his Ph.D. from Oregon State in 1957. After a few years at Johns Hopkins an

More information

Internal relative humidity distribution in concrete considering self-desiccation at early ages

Internal relative humidity distribution in concrete considering self-desiccation at early ages International Journal of the Physical Sciences Vol. 6(7), pp. 14-16, 4 April, 11 Available online at http://www.acaemicjournals.org/ijps DOI:.5897/IJPS11.8 ISSN 1992-19 11 Acaemic Journals Full Length

More information

Open World Face Recognition with Credibility and Confidence Measures

Open World Face Recognition with Credibility and Confidence Measures Open Worl Face Recognition with Creibility an Confience Measures Fayin Li an Harry Wechsler Department of Computer Science George Mason University Fairfax, VA 22030 {fli, wechsler}@cs.gmu.eu Abstract.

More information

Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices

Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices THE JOURNAL OF FINANCE VOL LIII, NO. 2 APRIL 1998 Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices YACINE AÏT-SAHALIA an ANDREW W. LO* ABSTRACT Implicit in the prices

More information

MODELLING OF TWO STRATEGIES IN INVENTORY CONTROL SYSTEM WITH RANDOM LEAD TIME AND DEMAND

MODELLING OF TWO STRATEGIES IN INVENTORY CONTROL SYSTEM WITH RANDOM LEAD TIME AND DEMAND art I. robobabilystic Moels Computer Moelling an New echnologies 27 Vol. No. 2-3 ransport an elecommunication Institute omonosova iga V-9 atvia MOEING OF WO AEGIE IN INVENOY CONO YEM WIH ANOM EA IME AN

More information

Purpose of the Experiments. Principles and Error Analysis. ε 0 is the dielectric constant,ε 0. ε r. = 8.854 10 12 F/m is the permittivity of

Purpose of the Experiments. Principles and Error Analysis. ε 0 is the dielectric constant,ε 0. ε r. = 8.854 10 12 F/m is the permittivity of Experiments with Parallel Plate Capacitors to Evaluate the Capacitance Calculation an Gauss Law in Electricity, an to Measure the Dielectric Constants of a Few Soli an Liqui Samples Table of Contents Purpose

More information

Towards a Framework for Enterprise Architecture Frameworks Comparison and Selection

Towards a Framework for Enterprise Architecture Frameworks Comparison and Selection Towars a Framework for Enterprise Frameworks Comparison an Selection Saber Aballah Faculty of Computers an Information, Cairo University Saber_aballah@hotmail.com Abstract A number of Enterprise Frameworks

More information

Hardness Evaluation of Polytetrafluoroethylene Products

Hardness Evaluation of Polytetrafluoroethylene Products ECNDT 2006 - Poster 111 Harness Evaluation of Polytetrafluoroethylene Proucts T.A.KODINTSEVA, A.M.KASHKAROV, V.A.KALOSHIN NPO Energomash Khimky, Russia A.P.KREN, V.A.RUDNITSKY, Institute of Applie Physics

More information

Estimating the drilling rate in Ahvaz oil field

Estimating the drilling rate in Ahvaz oil field J Petrol Explor Pro Technol (2013) 3:169 173 DOI 10.1007/s13202-013-0060-3 ORIGINAL PAPER - PRODUCTION ENGINEERING Estimating the rilling rate in Ahvaz oil fiel Masou Cheraghi Seifaba Peyman Ehteshami

More information

Unbalanced Power Flow Analysis in a Micro Grid

Unbalanced Power Flow Analysis in a Micro Grid International Journal of Emerging Technology an Avance Engineering Unbalance Power Flow Analysis in a Micro Gri Thai Hau Vo 1, Mingyu Liao 2, Tianhui Liu 3, Anushree 4, Jayashri Ravishankar 5, Toan Phung

More information

A Monte Carlo Simulation of Multivariate General

A Monte Carlo Simulation of Multivariate General A Monte Carlo Simulation of Multivariate General Pareto Distribution an its Application 1 1 1 1 1 1 1 1 0 1 Luo Yao 1, Sui Danan, Wang Dongxiao,*, Zhou Zhenwei, He Weihong 1, Shi Hui 1 South China Sea

More information

Learning-Based Summarisation of XML Documents

Learning-Based Summarisation of XML Documents Learning-Base Summarisation of XML Documents Massih R. Amini Anastasios Tombros Nicolas Usunier Mounia Lalmas {name}@poleia.lip6.fr {first name}@cs.qmul.ac.uk University Pierre an Marie Curie Queen Mary,

More information

DEVELOPMENT OF A BRAKING MODEL FOR SPEED SUPERVISION SYSTEMS

DEVELOPMENT OF A BRAKING MODEL FOR SPEED SUPERVISION SYSTEMS DEVELOPMENT OF A BRAKING MODEL FOR SPEED SUPERVISION SYSTEMS Paolo Presciani*, Monica Malvezzi #, Giuseppe Luigi Bonacci +, Monica Balli + * FS Trenitalia Unità Tecnologie Materiale Rotabile Direzione

More information

Mathematical Models of Therapeutical Actions Related to Tumour and Immune System Competition

Mathematical Models of Therapeutical Actions Related to Tumour and Immune System Competition Mathematical Moels of Therapeutical Actions Relate to Tumour an Immune System Competition Elena De Angelis (1 an Pierre-Emmanuel Jabin (2 (1 Dipartimento i Matematica, Politecnico i Torino Corso Duca egli

More information

Risk Adjustment for Poker Players

Risk Adjustment for Poker Players Risk Ajustment for Poker Players William Chin DePaul University, Chicago, Illinois Marc Ingenoso Conger Asset Management LLC, Chicago, Illinois September, 2006 Introuction In this article we consier risk

More information

Mandate-Based Health Reform and the Labor Market: Evidence from the Massachusetts Reform

Mandate-Based Health Reform and the Labor Market: Evidence from the Massachusetts Reform Manate-Base Health Reform an the Labor Market: Evience from the Massachusetts Reform Jonathan T. Kolsta Wharton School, University of Pennsylvania an NBER Amana E. Kowalski Department of Economics, Yale

More information

The mean-field computation in a supermarket model with server multiple vacations

The mean-field computation in a supermarket model with server multiple vacations DOI.7/s66-3-7-5 The mean-fiel computation in a supermaret moel with server multiple vacations Quan-Lin Li Guirong Dai John C. S. Lui Yang Wang Receive: November / Accepte: 8 October 3 SpringerScienceBusinessMeiaNewYor3

More information

9.3. Diffraction and Interference of Water Waves

9.3. Diffraction and Interference of Water Waves Diffraction an Interference of Water Waves 9.3 Have you ever notice how people relaxing at the seashore spen so much of their time watching the ocean waves moving over the water, as they break repeately

More information

1 High-Dimensional Space

1 High-Dimensional Space Contents High-Dimensional Space. Properties of High-Dimensional Space..................... 4. The High-Dimensional Sphere......................... 5.. The Sphere an the Cube in Higher Dimensions...........

More information

Monitoring of Slope Stability by Using Global Positioning System (GPS)

Monitoring of Slope Stability by Using Global Positioning System (GPS) Monitoring of Slope Stability by Using Global Positioning System (GPS) Eric Ma 1, Yongqi Chen 2, Xiaoli Ding 3 Department of Lan Surveying an Geo-Informatics Hong Kong Polytechnic University, Hung Hom,

More information

Chapter 2 Review of Classical Action Principles

Chapter 2 Review of Classical Action Principles Chapter Review of Classical Action Principles This section grew out of lectures given by Schwinger at UCLA aroun 1974, which were substantially transforme into Chap. 8 of Classical Electroynamics (Schwinger

More information

Modeling RED with Idealized TCP Sources

Modeling RED with Idealized TCP Sources Moeling RED with Iealize TCP Sources P. Kuusela, P. Lassila, J. Virtamo an P. Key Networking Laboratory Helsinki University of Technology (HUT) P.O.Box 3000, FIN-02015 HUT, Finlan Email: {Pirkko.Kuusela,

More information

Average-Case Analysis of a Nearest Neighbor Algorithm. Moett Field, CA USA. in accuracy. neighbor.

Average-Case Analysis of a Nearest Neighbor Algorithm. Moett Field, CA USA. in accuracy. neighbor. From Proceeings of the Thirteenth International Joint Conference on Articial Intelligence (1993). Chambery, France: Morgan Kaufmann Average-Case Analysis of a Nearest Neighbor Algorithm Pat Langley Learning

More information

The Elastic Capacitor and its Unusual Properties

The Elastic Capacitor and its Unusual Properties 1 The Elastic Capacitor an its Unusual Properties Michael B. Partensky, Department of Chemistry, Braneis University, Waltham, MA 453 partensky@attbi.com The elastic capacitor (EC) moel was first introuce

More information

A Universal Sensor Control Architecture Considering Robot Dynamics

A Universal Sensor Control Architecture Considering Robot Dynamics International Conference on Multisensor Fusion an Integration for Intelligent Systems (MFI2001) Baen-Baen, Germany, August 2001 A Universal Sensor Control Architecture Consiering Robot Dynamics Frierich

More information

Predictive Modeling in a VoIP System

Predictive Modeling in a VoIP System Paper Preictive Moeling in a VoIP System Ana-Maria Simionovici a, Alexanru-Arian Tantar a, Pascal Bouvry a, an Loic Dielot b a Computer Science an Communications University of Luxembourg, Luxembourg b

More information

Exploratory Optimal Latin Hypercube Designs for Computer Simulated Experiments

Exploratory Optimal Latin Hypercube Designs for Computer Simulated Experiments Thailan Statistician July 0; 9() : 7-93 http://statassoc.or.th Contribute paper Exploratory Optimal Latin Hypercube Designs for Computer Simulate Experiments Rachaaporn Timun [a,b] Anamai Na-uom* [a,b]

More information

Guidelines for the use of UHPLC Instruments

Guidelines for the use of UHPLC Instruments Guielines for the use of UHPLC Instruments Requirements for UHPLC instruments, metho evelopment in UHPLC an metho transfer from regular HPLC to UHPLC Authors: Dr. Davy Guillarme, Prof. Jean-Luc Veuthey

More information

Characterizing the Influence of Domain Expertise on Web Search Behavior

Characterizing the Influence of Domain Expertise on Web Search Behavior Characterizing the Influence of Domain Expertise on Web Search Behavior Ryen W. White Microsoft Research One Microsoft Way Remon, WA 98052 ryenw@microsoft.com Susan T. Dumais Microsoft Research One Microsoft

More information

Math 230.01, Fall 2012: HW 1 Solutions

Math 230.01, Fall 2012: HW 1 Solutions Math 3., Fall : HW Solutions Problem (p.9 #). Suppose a wor is picke at ranom from this sentence. Fin: a) the chance the wor has at least letters; SOLUTION: All wors are equally likely to be chosen. The

More information

Minimum-Energy Broadcast in All-Wireless Networks: NP-Completeness and Distribution Issues

Minimum-Energy Broadcast in All-Wireless Networks: NP-Completeness and Distribution Issues Minimum-Energy Broacast in All-Wireless Networks: NP-Completeness an Distribution Issues Mario Čagal LCA-EPFL CH-05 Lausanne Switzerlan mario.cagal@epfl.ch Jean-Pierre Hubaux LCA-EPFL CH-05 Lausanne Switzerlan

More information

Liquidity and Corporate Debt Market Timing

Liquidity and Corporate Debt Market Timing Liquiity an Corporate Debt Market Timing Marina Balboa Faculty of Economics University of Alicante Phone: +34 965903621 Fax: +34 965903621 marina.balboa@ua.es Belén Nieto (Corresponing author) Faculty

More information

Web Appendices of Selling to Overcon dent Consumers

Web Appendices of Selling to Overcon dent Consumers Web Appenices of Selling to Overcon ent Consumers Michael D. Grubb A Option Pricing Intuition This appenix provies aitional intuition base on option pricing for the result in Proposition 2. Consier the

More information