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Alfonzetti, Giuseppe, Bellio, Ruggero, Chen, Yunxiao ORCID: 0000-0002-7215-2324 and Moustaki, Irini ORCID: 0000-0001-8371-1251 (2024) Pairwise stochastic approximation for confirmatory factor analysis of categorical data. British Journal of Mathematical and Statistical Psychology. ISSN 0007-1102
Alfonzetti, Giuseppe, Bellio, Ruggero, Chen, Yunxiao ORCID: 0000-0002-7215-2324 and Moustaki, Irini ORCID: 0000-0001-8371-1251 (2024) When composite likelihood meets stochastic approximation. Journal of the American Statistical Association. ISSN 0162-1459 (In Press)
Anthropelos, Michail and Kardaras, Constantinos ORCID: 0000-0001-6903-4506 (2024) Price impact under heterogeneous beliefs and restricted participation. Journal of Economic Theory, 215. ISSN 0022-0531
Azadkia, Mona ORCID: 0000-0001-5480-8791 and Balabdaoui, Fadoua (2024) Linear regression with unmatched data: a deconvolution perspective. Journal of Machine Learning Research, 25. ISSN 1532-4435
Baranowski, Rafal, Chen, Yining ORCID: 0000-0003-1697-1920 and Fryzlewicz, Piotr ORCID: 0000-0002-9676-902X (2024) Multiscale autoregression on adaptively detected timescales. Statistica Sinica. ISSN 1017-0405 (In Press)
Baurdoux, Erik J. ORCID: 0000-0002-5407-0683 and Pedraza, José M. (2024) Lp optimal prediction of the last zero of a spectrally negative Lévy process. Annals of Applied Probability, 34 (1B). 1350 - 1402. ISSN 1050-5164
Bian, Zeyu, Shi, Chengchun ORCID: 0000-0001-7773-2099, Qi, Zhengling and Wang, Lan (2024) Off-policy evaluation in doubly inhomogeneous environments. Journal of the American Statistical Association. ISSN 0162-1459
Bondi, Alessandro, Livieri, Giulia ORCID: 0000-0002-3777-7329 and Pulido, Sergio (2024) Affine Volterra processes with jumps. Stochastic Processes and Their Applications, 168. ISSN 0304-4149
Boylan, Sally, Arsenault, Catherine, Barreto, Marcos ORCID: 0000-0002-7818-1855, Bozza, Fernando A, Fonseca, Adalton, Forde, Eoghan, Hookham, Lauren, Humphreys, Georgina S, Ichihara, Maria Yury, Le doare, Kirsty, Liu, Xiao Fan, McNamara, Edel, Mugunga, Jean Claude, Oliveira, Juliane F, Ouma, Joseph, Postlethwaite, Neil, Retford, Matthew, Reyes, Luis Felipe, Morris, Andrew D and Wozencraft, Anne (2024) Data challenges for international health emergencies: lessons learned from ten international COVID-19 driver projects. The Lancet Digital Health, 6 (5). e354-e366. ISSN 2589-7500
Brokmann, Xavier, Itkin, David ORCID: 0000-0001-8643-574X, Muhle-Karbe, Johannes and Schmidt, Peter (2024) Tackling nonlinear price impact with linear strategies. Mathematical Finance. ISSN 0960-1627
Bynum, Lucius E.J., Loftus, Joshua R. ORCID: 0000-0002-2905-1632 and Stoyanovich, Julia (2024) A new paradigm for counterfactual reasoning in fairness and recourse. In: Larson, Kate, (ed.) Proceedings of the 33rd International Joint Conference on Artificial Intelligence, IJCAI 2024. IJCAI International Joint Conference on Artificial Intelligence. International Joint Conferences on Artificial Intelligence, pp. 7092-7100. ISBN 9781956792041
Cetin, Umut ORCID: 0000-0001-8905-853X (2024) Minimal subharmonic functions and related integral representations. Electronic Journal of Probability, 29. ISSN 1083-6489
Cetin, Umut ORCID: 0000-0001-8905-853X and Hok, Julien (2024) Speeding up the Euler scheme for killed diffusions. Finance and Stochastics, 28 (3). 663 - 707. ISSN 0949-2984
Cetin, Umut ORCID: 0000-0001-8905-853X and Larsen, Kasper (2024) Is Kyle’s equilibrium model stable? Mathematics and Financial Economics. ISSN 1862-9679
Chang, Jinyuan, Fang, Qin, Qiao, Xinghao ORCID: 0000-0002-6546-6595 and Yao, Qiwei ORCID: 0000-0003-2065-8486 (2024) On the modelling and prediction of high-dimensional functional time series. Journal of the American Statistical Association. ISSN 0162-1459
Chang, Jinyuan, Hu, Qiao, Kolaczyk, Eric D., Yao, Qiwei ORCID: 0000-0003-2065-8486 and Yi, Fengting (2024) Edge differentially private estimation in the β-model via jittering and method of moments. Annals of Statistics, 52 (2). 708 - 728. ISSN 0090-5364
Chatzilena, Anastasia, Demiris, Nikolas and Kalogeropoulos, Konstantinos ORCID: 0000-0002-0330-9105 (2024) A modeling framework for the analysis of the SARS-CoV2 transmission dynamics. Statistics in Medicine, 43 (23). 4542 - 4558. ISSN 0277-6715
Chen, Weilin and Lam, Clifford ORCID: 0000-0001-8972-9129 (2024) Rank and factor loadings estimation in time series tensor factor model by pre-averaging. Annals of Statistics, 52 (1). 364 - 391. ISSN 0090-5364
Chen, Yudong ORCID: 0000-0002-3034-4651 and Chen, Yining ORCID: 0000-0003-1697-1920 (2024) Yudong Chen and Yining Chen's contribution to the discussion of ‘the discussion meeting on probabilistic and statistical aspects of machine learning’. Journal of the Royal Statistical Society. Series B: Statistical Methodology, 86 (2). 316 – 317. ISSN 1369-7412
Chen, Yudong ORCID: 0000-0002-3034-4651, Wang, Tengyao ORCID: 0000-0003-2072-6645 and Samworth, Richard J. (2024) Inference in high-dimensional online changepoint detection. Journal of the American Statistical Association, 119 (546). 1461 - 1472. ISSN 0162-1459
Chen, Yunxiao ORCID: 0000-0002-7215-2324 and Li, Xiaoou (2024) A note on entrywise consistency for mixed-data matrix completion. Journal of Machine Learning Research, 25. ISSN 1532-4435
Chen, Zezhun Chen, Dassios, Angelos ORCID: 0000-0002-3968-2366 and Tzougas, George (2024) EM estimation for bivariate mixed poisson INAR(1) claim count regression models with correlated random effects. European Actuarial Journal, 14 (1). 225 – 255. ISSN 2190-9733
Duarte, Belmiro P. M., Atkinson, Anthony C., Pedrosa, David and van Munster, Marlena (2024) Compound optimum designs for clinical trials in personalized medicine. Mathematics, 12 (19). ISSN 2227-7390
Duarte, Belmiro P.M. and Atkinson, Anthony C. (2024) Optimum designs for clinical trials in personalized medicine when response variance depends on treatment. Journal of Biopharmaceutical Statistics. ISSN 1054-3406
Duarte, Belmiro P.M., Atkinson, Anthony C. and Oliveira, Nuno M.C. (2024) Using hierarchical information-theoretic criteria to optimize subsampling of extensive datasets. Chemometrics and Intelligent Laboratory Systems, 245. ISSN 0169-7439
Dubiel-Teleszynski, Tomasz, Kalogeropoulos, Konstantinos ORCID: 0000-0002-0330-9105 and Karouzakis, Nikolaos (2024) Sequential learning and economic benefits from dynamic term structure models. Management Science, 70 (4). 2236 - 2254. ISSN 0025-1909
do Espirito Santo, Jonatas Silva, da Conceição, Jackson Santos, da Costa, Lilia Carolina Carneiro, Fiaccone, Rosemeire Leovigildo, Barreto, Marcos ORCID: 0000-0002-7818-1855, Ichihara, Maria Yury and Ara, Anderson (2024) K-means DTW Barycenter Averaging: a clustering analysis of COVID-19 cases and deaths on the Brazilian federal units. International Journal of Data Science and Analytics. ISSN 2364-415X
Fahrenwaldt, Matthias, Furrer, Christian, Hiabu, Munir Eberhardt, Huang, Fei, Jørgensen, Frederik Hytting, Lindholm, Mathias, Loftus, Joshua ORCID: 0000-0002-2905-1632, Steffensen, Mogens and Tsanakas, Andreas (2024) Fairness: plurality, causality, and insurability. European Actuarial Journal, 14 (2). 317 - 328. ISSN 2190-9733
Fang, Qin, Guo, Shaojun and Qiao, Xinghao ORCID: 0000-0002-6546-6595 (2024) Adaptive functional thresholding for sparse covariance function estimation in high dimensions. Journal of the American Statistical Association, 119 (546). 1473 - 1485. ISSN 0162-1459
Fryzlewicz, Piotr ORCID: 0000-0002-9676-902X (2024) Book review: Telling stories with data: with applications in R. American Statistician. ISSN 0003-1305
Fryzlewicz, Piotr ORCID: 0000-0002-9676-902X (2024) Robust Narrowest Significance Pursuit: inference for multiple change-points in the median. Journal of Business and Economic Statistics, 42 (4). pp. 1389-1402. ISSN 0735-0015
Gascoigne, Connor, Jeffery, Annie, Shao, Zejing, Geneletti, Sara ORCID: 0000-0001-6456-7258, Kirkbride, James B., Baio, Gianluca and Blangiardo, Marta (2024) A Bayesian interrupted time series framework for evaluating policy change on mental well-being: an application to England's welfare reform. Spatial and Spatio-temporal Epidemiology, 50. ISSN 1877-5845
Gavioli-Akilagun, Shakeel ORCID: 0009-0003-8501-5737 (2024) Shakeel Gavioli-Akilagun's contribution to the discussion of the discussion meeting on probabilistic and statistical aspects of machine learning. Journal of the Royal Statistical Society. Series B: Statistical Methodology, 86 (2). 312 - 313. ISSN 1369-7412
Guastadisegni, Lucia, Moustaki, Irini ORCID: 0000-0001-8371-1251 and Vasdekis, Vassilis (2024) The generalized Hausman test for detecting non-normality in the latent variable distribution of the two-parameter IRT model. British Journal of Mathematical and Statistical Psychology. ISSN 0007-1102 (In Press)
Hao, Meiling, Su, Pingfan, Hu, Liyuan, Szabo, Zoltan ORCID: 0000-0001-6183-7603, Zhao, Qianyu and Shi, Chengchun ORCID: 0000-0001-7773-2099 (2024) Forward and backward state abstractions for off-policy evaluation. . arXiv. (Submitted)
Horvath, Blanka, Jacquier, Antoine, Muguruza, Aitor and Søjmark, Andreas ORCID: 0000-0001-7488-0221 (2024) Functional central limit theorems for rough volatility. Finance and Stochastics, 28 (3). 615 - 661. ISSN 0949-2984
Iglesias, Rodrigo, Mohammadi, Fatemah, Pascual-Ortigosa, Patricia, Sáenz-de-Cabezón, Eduardo and Wynn, Henry ORCID: 0000-0002-6448-1080 (2024) Stable coherent systems. Applicable Algebra in Engineering, Communication and Computing. ISSN 0938-1279
Jamil, Haziq, Moustaki, Irini ORCID: 0000-0001-8371-1251 and Skinner, Chris J. (2024) Pairwise likelihood estimation and limited-information goodness-of-fit test statistics for binary factor analysis models under complex survey sampling. British Journal of Mathematical and Statistical Psychology. ISSN 0007-1102
Jeffery, Annie, Gascoigne, Connor, Dykxhoorn, Jennifer, Blangiardo, Marta, Geneletti, Sara ORCID: 0000-0001-6456-7258, Baio, Gianluca and Kirkbride, James B. (2024) The effect of immigration policy reform on mental health in people from minoritised ethnic groups in England: an interrupted time series analysis of longitudinal data from the UK Household Longitudinal Study cohort. The Lancet Psychiatry, 11 (3). 183 - 192. ISSN 2215-0366
Kalinke, Florian and Szabo, Zoltan ORCID: 0000-0001-6183-7603 (2024) The minimax rate of HSIC estimation for translation-invariant kernel. In: 38th Annual Conference on Neural Information Processing Systems, 2024-12-10 - 2024-12-15, Vancouver Convention Center, Vancouver, Canada, CAN. (In Press)
Kalinke, Florian, Szabo, Zoltan ORCID: 0000-0001-6183-7603 and Sriperumbudur, Bharath K. (2024) Nyström Kernel Stein Discrepancy. . arXiv. (Submitted)
Karch, Julian D., Perez-Alonso, Andres F. and Bergsma, Wicher P. ORCID: 0000-0002-2422-2359 (2024) Beyond Pearson’s correlation: modern nonparametric independence tests for psychological research. Multivariate Behavioral Research, 59 (5). 957 - 977. ISSN 0027-3171
Kardaras, Constantinos ORCID: 0000-0001-6903-4506 (2024) Stochastic integration with respect to arbitrary collections of continuous semimartingales and applications to mathematical finance. Annals of Applied Probability, 34 (3). 2566 - 2599. ISSN 1050-5164
Li, Jie, Fearnhead, Paul, Fryzlewicz, Piotr ORCID: 0000-0002-9676-902X and Wang, Tengyao ORCID: 0000-0003-2072-6645 (2024) Authors' reply to the discussion of 'Automatic change-point detection in time series via deep learning' at the discussion meeting on 'Probabilistic and statistical aspects of machine learning'. Journal of the Royal Statistical Society. Series B: Statistical Methodology, 86 (2). 332 - 334. ISSN 1369-7412
Li, Jie, Fearnhead, Paul, Fryzlewicz, Piotr ORCID: 0000-0002-9676-902X and Wang, Tengyao ORCID: 0000-0003-2072-6645 (2024) Automatic change-point detection in time series via deep learning. Journal of the Royal Statistical Society. Series B: Statistical Methodology, 86 (2). 273 - 285. ISSN 1369-7412
Li, Jing Jing, Shi, Chengchun ORCID: 0000-0001-7773-2099, Li, Lexin and Collins, Anne G.E. (2024) Dynamic noise estimation: a generalized method for modeling noise fluctuations in decision-making. Journal of Mathematical Psychology, 119. ISSN 0022-2496
Li, Ting, Shi, Chengchun ORCID: 0000-0001-7773-2099, Lu, Zhaohua, Li, Yi and Zhu, Hongtu (2024) Evaluating dynamic conditional quantile treatment effects with applications in ridesharing. Journal of the American Statistical Association, 119 (547). 1736 - 1750. ISSN 0162-1459
Li, Ting, Shi, Chengchun ORCID: 0000-0001-7773-2099, Wen, Qianglin, Sui, Yang, Qin, Yongli, Lai, Chunbo and Zhu, Hongtu (2024) Combining experimental and historical data for policy evaluation. Proceedings of Machine Learning Research, 235. pp. 28630-28656. ISSN 2640-3498
Livieri, Giulia ORCID: 0000-0002-3777-7329, Radi, Davide and Smaniotto, Elia (2024) Pricing transition risk with a jump-diffusion credit risk model: evidences from the CDS market. Review of Corporate Finance, 4 (1–2). 177 - 201. ISSN 2693-9312
Loftus, Joshua R. ORCID: 0000-0002-2905-1632 (2024) Position: the causal revolution needs scientific pragmatism. Proceedings of Machine Learning Research, 235. pp. 32671-32679. ISSN 1938-7228
Luo, Shikai, Yang, Ying, Shi, Chengchun ORCID: 0000-0001-7773-2099, Yao, Fang, Ye, Jieping and Zhu, Hongtu (2024) Policy evaluation for temporal and/or spatial dependent experiments. Journal of the Royal Statistical Society. Series B: Statistical Methodology, 86 (3). 623 - 649. ISSN 1369-7412
Ma, Tao ORCID: 0000-0002-8062-9217, Yang, Xuzhi and Szabo, Zoltan ORCID: 0000-0001-6183-7603 (2024) To switch or not to switch? Balanced policy switching in offline reinforcement learning. . arXiv. (Submitted)
Machado, Tiago Fernandes, das Chagas Barros Neto, Francisco, de Souza Gonçalves, Marilda, Barbosa, Cynara Gomes and Barreto, Marcos Ennes ORCID: 0000-0002-7818-1855 (2024) Exploring machine learning algorithms in sickle cell disease patient data: a systematic review. PLOS ONE, 19 (11). ISSN 1932-6203
Mitrodima, Gelly ORCID: 0009-0007-5360-5221 and Oberoi, Jaideep (2024) CAViaR models for Value-at-Risk and Expected Shortfall with long range dependency features. Journal of the Royal Statistical Society. Series C: Applied Statistics, 73 (1). 1 - 27. ISSN 0035-9254
Mohammadi, Fatemeh, Pascual-Ortigosa, Patricia, Sáenz-de-Cabezón, Eduardo and Wynn, Henry P. ORCID: 0000-0002-6448-1080 (2024) Overview of the algebraic reliability of binary and multistate k-out-of-n and related systems. In: Ram, Mangey, (ed.) Developments in Reliability Engineering. Advances in Reliability Science. Elsevier, 687 - 730. ISBN 9780443132414
Noah, Abdurafiu Olaiya, Adhikari, Pawan and Liew, Pik Kun ORCID: 0000-0002-9135-4183 (2024) Environmental and social accountability in emerging economies: strategic pressures from and responses to vulnerable local communities. Accounting Forum. ISSN 0155-9982
Pillinger, Rebecca, Steele, Fiona ORCID: 0000-0001-6417-7444, Leckie, George and Jenkins, Jennifer (2024) A dynamic social relations model for clustered longitudinal dyadic data with continuous or ordinal responses. Journal of the Royal Statistical Society. Series A: Statistics in Society, 187 (2). 338 - 357. ISSN 0964-1998
Qu, Yan, Dassios, Angelos ORCID: 0000-0002-3968-2366, Liu, Anxin and Zhao, Hongbiao (2024) Exact simulation of quadratic intensity models. Informs Journal on Computing. ISSN 1091-9856
Sallai, Dorottya ORCID: 0000-0003-3411-4818, Cardoso Silva, Jon ORCID: 0000-0002-9566-7400 and Barreto, Marcos ORCID: 0000-0002-7818-1855 (2024) To improve their courses, educators should respond to how students actually use AI. Impact of Social Sciences Blog (22 May 2024). Blog Entry.
Sparago, Pietro (2024) Note on the weak convergence of hyperplane α-quantile functionals and their continuity in the Skorokhod J1 topology. Journal of Theoretical Probability, 38 (1). ISSN 0894-9840
Steele, Fiona ORCID: 0000-0001-6417-7444, Zhang, Siliang ORCID: 0000-0002-2641-4944, Grundy, Emily ORCID: 0000-0002-9633-1116 and Burchardt, Tania ORCID: 0000-0003-4822-4954 (2024) Longitudinal analysis of exchanges of support between parents and children in the UK. Journal of the Royal Statistical Society. Series A: Statistics in Society, 187 (2). 279 - 304. ISSN 0964-1998
Toth, Csaba, Oberhauser, Harald and Szabo, Zoltan ORCID: 0000-0001-6183-7603 (2024) Random Fourier signature features. SIAM Journal on Mathematics of Data Science. ISSN 2577-0187 (In Press)
Wallin, Gabriel, Chen, Yunxiao ORCID: 0000-0002-7215-2324 and Moustaki, Irini ORCID: 0000-0001-8371-1251 (2024) DIF analysis with unknown groups and anchor items. Psychometrika, 89 (1). 267 - 295. ISSN 0033-3123
Wang, Tengyao ORCID: 0000-0003-2072-6645, Dobriban, Edgar, Gataric, Milana and Samworth, Richard J. (2024) Sharp-SSL: selective high-dimensional axis-aligned random projections for semi-supervised learning. Journal of the American Statistical Association. ISSN 0162-1459
Wang, Yiliu, Chen, Wei and Vojnovic, Milan ORCID: 0000-0003-1382-022X (2024) Combinatorial bandits for maximum value reward function under value-index feedback. In: ICLR 2024 The Twelfth International Conference on Learning Representations, 2024-05-07 - 2024-05-11, Messe Wien Exhibition and Congress Center, Vienna, Austria, AUT.
Wang, Zezhi, Zhu, Junxian, Wang, Xueqin, Zhu, Jin ORCID: 0000-0001-8550-5822, Peng, Huiyang, Chen, Peng, Wang, Anran and Zhang, Xiaoke (2024) skscope: fast sparsity-constrained optimization in Python. Journal of Machine Learning Research, 25. ISSN 1532-4435
Wen, Kaiyue, Wang, Tengyao ORCID: 0000-0003-2072-6645 and Wang, Yuhao (2024) Residual permutation test for regression coefficient testing. Annals of Statistics. ISSN 0090-5364 (In Press)
Wouters, Olivier J. ORCID: 0000-0002-2514-476X, Kesselheim, Aaron S., Kuha, Jouni ORCID: 0000-0002-1156-8465 and Luyten, Jeroen (2024) Sales revenues for new therapeutic agents approved by the United States Food and Drug Administration from 1995 to 2014: a retrospective study. Value in Health, 27 (10). 1373 - 1381. ISSN 1098-3015
Wouters, Olivier J. ORCID: 0000-0002-2514-476X and Kuha, Jouni ORCID: 0000-0002-1156-8465 (2024) Low- and middle-income countries experienced delays accessing new essential medicines, 1982–2024. Health Affairs, 43 (10). 1410 - 1419. ISSN 0278-2715
Yang, Xuzhi and Wang, Tengyao ORCID: 0000-0003-2072-6645 (2024) Multiple-output composite quantile regression through an optimal transport lens. Proceedings of Machine Learning Research, 247. pp. 5076-5122. ISSN 2640-3498
Younes, Younes R., Cron, Nicholas ORCID: 0000-0001-9591-2210, Field, Benjamin C.T., Nayyar, Vidhu, Clark, James, Zachariah, Sunil, Lakshmipathy, Kavitha, Isuga, Jimboy O., Maghsoodi, Negar and Emmanuel, Julian (2024) Proposed treatment strategy for reactive hypoglycaemia. Frontiers in Endocrinology, 15. ISSN 1664-2392
Yu, Shuguang, Fang, Shuxing, Peng, Ruixin, Qi, Zhengling, Zhou, Fan and Shi, Chengchun ORCID: 0000-0001-7773-2099 (2024) Two-way deconfounder for off-policy evaluation in causal reinforcement learning. In: 38th Annual Conference on Neural Information Processing Systems, 2024-12-10 - 2024-12-15, Vancouver Convention Center, Vancouver, Canada, CAN. (In Press)
Zhang, Junyi ORCID: 0000-0001-8986-6588 and Dassios, Angelos ORCID: 0000-0002-3968-2366 (2024) Posterior sampling from truncated Ferguson-Klass representation of normalised completely random measure mixtures. Bayesian Analysis. ISSN 1936-0975
Zhang, Pengcheng, Chen, Zezhun, Tzougas, George, Calderín–Ojeda, Enrique, Dassios, Angelos ORCID: 0000-0002-3968-2366 and Wu, Xueyuan (2024) Multivariate zero-inflated INAR(1) model with an application in automobile insurance. North American Actuarial Journal. ISSN 1092-0277
Zhang, Siliang ORCID: 0000-0002-2641-4944 and Chen, Yunxiao ORCID: 0000-0002-7215-2324 (2024) A note on Ising network analysis with missing data. Psychometrika, 89 (4). 1186 - 1202. ISSN 0033-3123
Zhang, Siliang ORCID: 0000-0002-2641-4944, Kuha, Jouni ORCID: 0000-0002-1156-8465 and Steele, Fiona ORCID: 0000-0001-6417-7444 (2024) Modelling correlation matrices in multivariate data, with application to reciprocity and complementarity of child-parent exchanges of support. Annals of Applied Statistics, 18 (4). 3024 - 3049. ISSN 1932-6157
Zhao, Puyang, Liu, Xinhui, Yue, Zhiyi, Zhao, Qianyu, Liu, Xinzhi, Deng, Yuhui and Wu, Jingjin (2024) DiGAN breakthrough: advancing diabetic data analysis with innovative GAN-based imbalance correction techniques. Computer Methods and Programs in Biomedicine Update, 5. ISSN 2666-9900
Zhu, Jin ORCID: 0000-0001-8550-5822, Wan, Runzhe, Qi, Zhengling, Luo, Shikai and Shi, Chengchun ORCID: 0000-0001-7773-2099 (2024) Robust offline reinforcement learning with heavy-tailed rewards. In: Dasgupta, Sanjoy, Mandt, Stephan and Li, Yingzhen, (eds.) Proceedings of the 27th International Conference on Artificial Intelligence and Statistics (AISTATS) 2024. International Conference on Machine Learning, Valencia, Spain, 541 - 549.