On state and parameter estimation in chaotic systems

State-of-the-art predictions of atmospheric states rely on large-scale numerical models of chaotic systems. This dissertation studies numerical methods for state and parameter estimation in such systems. The motivation comes from weather and climate models and a methodological perspective is adopted. The dissertation comprises three sections: state estimation, parameter estimation and chemical data assimilation with real atmospheric satellite data. In the state estimation part of this dissertation, a new filtering technique based on a combination of ensemble and variational Kalman filtering approaches, is presented, experimented and discussed. This new filter is developed for large-scale Kalman filtering applications. In the parameter estimation part, three different techniques for parameter estimation in chaotic systems are considered. The methods are studied using the parameterized Lorenz 95 system, which is a benchmark model for data assimilation. In addition, a dilemma related to the uniqueness of weather and climate model closure parameters is discussed. In the data-oriented part of this dissertation, data from the Global Ozone Monitoring by Occultation of Stars (GOMOS) satellite instrument are considered and an alternative algorithm to retrieve atmospheric parameters from the measurements is presented. The validation study presents first global comparisons between two unique satellite-borne datasets of vertical profiles of nitrogen trioxide (NO3), retrieved using GOMOS and Stratospheric Aerosol and Gas Experiment III (SAGE III) satellite instruments. The GOMOS NO3 observations are also considered in a chemical state estimation study in order to retrieve stratospheric temperature profiles. The main result of this dissertation is the consideration of likelihood calculations via Kalman filtering outputs. The concept has previously been used together with stochastic differential equations and in time series analysis. In this work, the concept is applied to chaotic dynamical systems and used together with Markov chain Monte Carlo (MCMC) methods for statistical analysis. In particular, this methodology is advocated for use in numerical weather prediction (NWP) and climate model applications. In addition, the concept is shown to be useful in estimating the filter-specific parameters related, e.g., to model error covariance matrix parameters.

Excessive functions, Appell polynomials and optimal stopping

The main topic of the thesis is optimal stopping. This is treated in two research articles. In the first article we introduce a new approach to optimal stopping of general strong Markov processes. The approach is based on the representation of excessive functions as expected suprema. We present a variety of examples, in particular, the Novikov-Shiryaev problem for Lévy processes. In the second article on optimal stopping we focus on differentiability of excessive functions of diffusions and apply these results to study the validity of the principle of smooth fit. As an example we discuss optimal stopping of sticky Brownian motion. The third research article offers a survey like discussion on Appell polynomials. The crucial role of Appell polynomials in optimal stopping of Lévy processes was noticed by Novikov and Shiryaev. They described the optimal rule in a large class of problems via these polynomials. We exploit the probabilistic approach to Appell polynomials and show that many classical results are obtained with ease in this framework. In the fourth article we derive a new relationship between the generalized Bernoulli polynomials and the generalized Euler polynomials.

Context-specific independence in graphical models

The theme of this thesis is context-speci c independence in graphical models. Considering a system of stochastic variables it is often the case that the variables are dependent of each other. This can, for instance, be seen by measuring the covariance between a pair of variables. Using graphical models, it is possible to visualize the dependence structure found in a set of stochastic variables. Using ordinary graphical models, such as Markov networks, Bayesian networks, and Gaussian graphical models, the type of dependencies that can be modeled is limited to marginal and conditional (in)dependencies. The models introduced in this thesis enable the graphical representation of context-speci c independencies, i.e. conditional independencies that hold only in a subset of the outcome space of the conditioning variables. In the articles included in this thesis, we introduce several types of graphical models that can represent context-speci c independencies. Models for both discrete variables and continuous variables are considered. A wide range of properties are examined for the introduced models, including identi ability, robustness, scoring, and optimization. In one article, a predictive classi er which utilizes context-speci c independence models is introduced. This classi er clearly demonstrates the potential bene ts of the introduced models. The purpose of the material included in the thesis prior to the articles is to provide the basic theory needed to understand the articles.

Mathematical modeling and optimal control of malaria

Malaria continues to infect millions and kill hundreds of thousands of people worldwide each year, despite over a century of research and attempts to control and eliminate this infectious disease. Challenges such as the development and spread of drug resistant malaria parasites, insecticide resistance to mosquitoes, climate change, the presence of individuals with subpatent malaria infections which normally are asymptomatic and behavioral plasticity in the mosquito hinder the prospects of malaria control and elimination. In this thesis, mathematical models of malaria transmission and control that address the role of drug resistance, immunity, iron supplementation and anemia, immigration and visitation, and the presence of asymptomatic carriers in malaria transmission are developed. A within-host mathematical model of severe Plasmodium falciparum malaria is also developed. First, a deterministic mathematical model for transmission of antimalarial drug resistance parasites with superinfection is developed and analyzed. The possibility of increase in the risk of superinfection due to iron supplementation and fortification in malaria endemic areas is discussed. The model results calls upon stakeholders to weigh the pros and cons of iron supplementation to individuals living in malaria endemic regions. Second, a deterministic model of transmission of drug resistant malaria parasites, including the inflow of infective immigrants, is presented and analyzed. The optimal control theory is applied to this model to study the impact of various malaria and vector control strategies, such as screening of immigrants, treatment of drug-sensitive infections, treatment of drug-resistant infections, and the use of insecticide-treated bed nets and indoor spraying of mosquitoes. The results of the model emphasize the importance of using a combination of all four controls tools for effective malaria intervention. Next, a two-age-class mathematical model for malaria transmission with asymptomatic carriers is developed and analyzed. In development of this model, four possible control measures are analyzed: the use of long-lasting treated mosquito nets, indoor residual spraying, screening and treatment of symptomatic, and screening and treatment of asymptomatic individuals. The numerical results show that a disease-free equilibrium can be attained if all four control measures are used. A common pitfall for most epidemiological models is the absence of real data; model-based conclusions have to be drawn based on uncertain parameter values. In this thesis, an approach to study the robustness of optimal control solutions under such parameter uncertainty is presented. Numerical analysis of the optimal control problem in the presence of parameter uncertainty demonstrate the robustness of the optimal control approach that: when a comprehensive control strategy is used the main conclusions of the optimal control remain unchanged, even if inevitable variability remains in the control profiles. The results provide a promising framework for the design of cost-effective strategies for disease control with multiple interventions, even under considerable uncertainty of model parameters. Finally, a separate work modeling the within-host Plasmodium falciparum infection in humans is presented. The developed model allows re-infection of already-infected red blood cells. The model hypothesizes that in severe malaria due to parasite quest for survival and rapid multiplication, the Plasmodium falciparum can be absorbed in the already-infected red blood cells which accelerates the rupture rate and consequently cause anemia. Analysis of the model and parameter identifiability using Markov chain Monte Carlo methods is presented.

Optimization and Measuring Techniques for Collect-and-Place Machines in Printed Circuit Board Industry

This thesis considers optimization problems arising in printed circuit board assembly. Especially, the case in which the electronic components of a single circuit board are placed using a single placement machine is studied. Although there is a large number of different placement machines, the use of collect-and-place -type gantry machines is discussed because of their flexibility and increasing popularity in the industry. Instead of solving the entire control optimization problem of a collect-andplace machine with a single application, the problem is divided into multiple subproblems because of its hard combinatorial nature. This dividing technique is called hierarchical decomposition. All the subproblems of the one PCB - one machine -context are described, classified and reviewed. The derived subproblems are then either solved with exact methods or new heuristic algorithms are developed and applied. The exact methods include, for example, a greedy algorithm and a solution based on dynamic programming. Some of the proposed heuristics contain constructive parts while others utilize local search or are based on frequency calculations. For the heuristics, it is made sure with comprehensive experimental tests that they are applicable and feasible. A number of quality functions will be proposed for evaluation and applied to the subproblems. In the experimental tests, artificially generated data from Markov-models and data from real-world PCB production are used. The thesis consists of an introduction and of five publications where the developed and used solution methods are described in their full detail. For all the problems stated in this thesis, the methods proposed are efficient enough to be used in the PCB assembly production in practice and are readily applicable in the PCB manufacturing industry.

Regime-Switching in the Impact of Oil Price Shocks on Stock Market Volatility: Evidence from Oil-Importing and Oil-Exporting Countries

Research has highlighted the adequacy of Markov regime-switching model to address dynamic behavior in long term stock market movements. Employing a purposed Extended regime-switching GARCH(1,1) model, this thesis further investigates the regime dependent nonlinear relationship between changes in oil price and stock market volatility in Saudi Arabia, Norway and Singapore for the period of 2001-2014. Market selection is prioritized to national dependency on oil export or import, which also rationalizes the fitness of implied bivariate volatility model. Among two regimes identified by the mean model, high stock market return-low volatility regime reflects the stable economic growth periods. The other regime characterized by low stock market return-high volatility coincides with episodes of recession and downturn. Moreover, results of volatility model provide the evidence that shocks in stock markets are less persistent during the high volatility regime. While accelerated oil price rises the stock market volatility during recessions, it reduces the stock market risk during normal growth periods in Singapore. In contrast, oil price showed no significant notable impact on stock market volatility of target oil-exporting countries in either of the volatility regime. In light to these results, international investors and policy makers could benefit the risk management in relation to oil price fluctuation.

Parameter identification in time series models

Time series analysis can be categorized into three different approaches: classical, Box-Jenkins, and State space. Classical approach makes a basement for the analysis and Box-Jenkins approach is an improvement of the classical approach and deals with stationary time series. State space approach allows time variant factors and covers up a broader area of time series analysis. This thesis focuses on parameter identifiablity of different parameter estimation methods such as LSQ, Yule-Walker, MLE which are used in the above time series analysis approaches. Also the Kalman filter method and smoothing techniques are integrated with the state space approach and MLE method to estimate parameters allowing them to change over time. Parameter estimation is carried out by repeating estimation and integrating with MCMC and inspect how well different estimation methods can identify the optimal model parameters. Identification is performed in probabilistic and general senses and compare the results in order to study and represent identifiability more informative way.

Inverting ionospheric D-region electron density pro-file from riometer measurement

The aim of this work is to invert the ionospheric electron density profile from Riometer (Relative Ionospheric opacity meter) measurement. The newly Riometer instrument KAIRA (Kilpisjärvi Atmospheric Imaging Receiver Array) is used to measure the cosmic HF radio noise absorption that taking place in the D-region ionosphere between 50 to 90 km. In order to invert the electron density profile synthetic data is used to feed the unknown parameter Neq using spline height method, which works by taking electron density profile at different altitude. Moreover, smoothing prior method also used to sample from the posterior distribution by truncating the prior covariance matrix. The smoothing profile approach makes the problem easier to find the posterior using MCMC (Markov Chain Monte Carlo) method.

Kalman filter for computational market dynamics

Kalman filter is a recursive mathematical power tool that plays an increasingly vital role in innumerable fields of study. The filter has been put to service in a multitude of studies involving both time series modelling and financial time series modelling. Modelling time series data in Computational Market Dynamics (CMD) can be accomplished using the Jablonska-Capasso-Morale (JCM) model. Maximum likelihood approach has always been utilised to estimate the parameters of the JCM model. The purpose of this study is to discover if the Kalman filter can be effectively utilized in CMD. Ensemble Kalman filter (EnKF), with 50 ensemble members, applied to US sugar prices spanning the period of January, 1960 to February, 2012 was employed for this work. The real data and Kalman filter trajectories showed no significant discrepancies, hence indicating satisfactory performance of the technique. Since only US sugar prices were utilized, it would be interesting to discover the nature of results if other data sets are employed.

Initialization of Continuous Nonlinear Models Using Extended Kalman Filter

The two main objectives of Bayesian inference are to estimate parameters and states. In this thesis, we are interested in how this can be done in the framework of state-space models when there is a complete or partial lack of knowledge of the initial state of a continuous nonlinear dynamical system. In literature, similar problems have been referred to as diffuse initialization problems. This is achieved first by extending the previously developed diffuse initialization Kalman filtering techniques for discrete systems to continuous systems. The second objective is to estimate parameters using MCMC methods with a likelihood function obtained from the diffuse filtering. These methods are tried on the data collected from the 1995 Ebola outbreak in Kikwit, DRC in order to estimate the parameters of the system.

Novel control, haptic and calibration methods for teleoperated electrohydraulic servo systems

The aim of this thesis is to propose a novel control method for teleoperated electrohydraulic servo systems that implements a reliable haptic sense between the human and manipulator interaction, and an ideal position control between the manipulator and the task environment interaction. The proposed method has the characteristics of a universal technique independent of the actual control algorithm and it can be applied with other suitable control methods as a real-time control strategy. The motivation to develop this control method is the necessity for a reliable real-time controller for teleoperated electrohydraulic servo systems that provides highly accurate position control based on joystick inputs with haptic capabilities. The contribution of the research is that the proposed control method combines a directed random search method and a real-time simulation to develop an intelligent controller in which each generation of parameters is tested on-line by the real-time simulator before being applied to the real process. The controller was evaluated on a hydraulic position servo system. The simulator of the hydraulic system was built based on Markov chain Monte Carlo (MCMC) method. A Particle Swarm Optimization algorithm combined with the foraging behavior of E. coli bacteria was utilized as the directed random search engine. The control strategy allows the operator to be plugged into the work environment dynamically and kinetically. This helps to ensure the system has haptic sense with high stability, without abstracting away the dynamics of the hydraulic system. The new control algorithm provides asymptotically exact tracking of both, the position and the contact force. In addition, this research proposes a novel method for re-calibration of multi-axis force/torque sensors. The method makes several improvements to traditional methods. It can be used without dismantling the sensor from its application and it requires smaller number of standard loads for calibration. It is also more cost efficient and faster in comparison to traditional calibration methods. The proposed method was developed in response to re-calibration issues with the force sensors utilized in teleoperated systems. The new approach aimed to avoid dismantling of the sensors from their applications for applying calibration. A major complication with many manipulators is the difficulty accessing them when they operate inside a non-accessible environment; especially if those environments are harsh; such as in radioactive areas. The proposed technique is based on design of experiment methodology. It has been successfully applied to different force/torque sensors and this research presents experimental validation of use of the calibration method with one of the force sensors which method has been applied to.

Bayesian analysis of SEIR epidemic models

This thesis concerns the analysis of epidemic models. We adopt the Bayesian paradigm and develop suitable Markov Chain Monte Carlo (MCMC) algorithms. This is done by considering an Ebola outbreak in the Democratic Republic of Congo, former Zaïre, 1995 as a case of SEIR epidemic models. We model the Ebola epidemic deterministically using ODEs and stochastically through SDEs to take into account a possible bias in each compartment. Since the model has unknown parameters, we use different methods to estimate them such as least squares, maximum likelihood and MCMC. The motivation behind choosing MCMC over other existing methods in this thesis is that it has the ability to tackle complicated nonlinear problems with large number of parameters. First, in a deterministic Ebola model, we compute the likelihood function by sum of square of residuals method and estimate parameters using the LSQ and MCMC methods. We sample parameters and then use them to calculate the basic reproduction number and to study the disease-free equilibrium. From the sampled chain from the posterior, we test the convergence diagnostic and confirm the viability of the model. The results show that the Ebola model fits the observed onset data with high precision, and all the unknown model parameters are well identified. Second, we convert the ODE model into a SDE Ebola model. We compute the likelihood function using extended Kalman filter (EKF) and estimate parameters again. The motivation of using the SDE formulation here is to consider the impact of modelling errors. Moreover, the EKF approach allows us to formulate a filtered likelihood for the parameters of such a stochastic model. We use the MCMC procedure to attain the posterior distributions of the parameters of the SDE Ebola model drift and diffusion parts. In this thesis, we analyse two cases: (1) the model error covariance matrix of the dynamic noise is close to zero , i.e. only small stochasticity added into the model. The results are then similar to the ones got from deterministic Ebola model, even if methods of computing the likelihood function are different (2) the model error covariance matrix is different from zero, i.e. a considerable stochasticity is introduced into the Ebola model. This accounts for the situation where we would know that the model is not exact. As a results, we obtain parameter posteriors with larger variances. Consequently, the model predictions then show larger uncertainties, in accordance with the assumption of an incomplete model.

Offline-tila web-sovelluksissa

Selainpohjaiset sovellukset ovat yleistyneet viimeisen kymmenen vuoden aikana. Samanaikaisesti ympäristö, jossa ihmiset käyttävät sovelluksia, on muuttunut. Nykyään sovelluksia käytetään yhä enenevissä määrin myös mobiililaitteilla, joissa verkkoyhteyden luotettavuus on huomattavasti heikompi kuin työpöytäympäristössä. Verkkoyhteyden toiminta on ehdoton edellytys web- sovelluksen toiminnalle. Kun verkkoyhteyttä ei ole, sovellusta ei useimmiten voi käyttää. Tilanne on käyttäjän kannalta sama myös, jos verkkoyhteyden laatu on hyvin heikko. Tämä uusi käyttöympäristö asettaa web-sovelluksen saavutettavuudelle haasteen, johon sovelluskehittäjien tulisi pystyä vastaamaan uusien teknologioiden avulla ja mahdollisesti sovelluksen arkkitehtuuria muuttamalla. Johdantona aiheeseen kerrotaan mitä hyötyjä offline-tilan tukemisesta on. Selainpohjaiset sovellukset kilpailevat jossain määrin mobiilialustojen natiivisovellusten kanssa. Web-sovelluksia on verrattu natiivisovelluksiin niiltä osin miten ne toimivat offline-tilassa. Pohjustuksena offline-tilan mahdollistavien teknologioiden arvioinnille esitellään Web-sovelluksen arkkitehtuuri yleisellä tasolla. Tässä tutkielmassa on esitelty muutamia offline-tilan asettamia vaatimuksia sovellukselle. Sovelluksen on kyettävä tunnistamaan, onko laitteella internet-yhteyttä. Yhteyden tilan tarkastukseen esitellään muutama vaihtoehto. Käyttäjän luoma tieto on myös tallennettava paikallisesti. Kun käyttäjä luo uutta sisältöä, se pitää tallentaa väliaikaisesti tai pysyvästi selaimeen. Ainakin osa sovelluksessa käsiteltävästä tiedosta pitäisi olla koko ajan saatavilla, käyttäjän internet-yhteyden tilasta riippumatta. Tähän tarkoitukseen selaimissa on nykyään käytettävissä muutamia erityyppisiä tietovarastoja. Kun selain on online-tilassa, sovelluksen tarvitsemat resurssit on tallennettava offline-tilaa varten. Tähän tarkoitukseen on luotu kaksi eri teknologiaa, HTML5 Application cache ja Service worker. Niiden avulla voi toteuttaa selaimen sisäisen välipalvelimen, joka vastaa sovelluksen tekemiin verkkopyyntöihin. Tutkielmassa esitellään näiden teknologioiden toimintaa teknisten määrittelydokumenttien ja verkkoartikkelien pohjalta. Mainittuja teknologoita vertaillaan keskenään toiminnallisten vaatimusten pohjalta. Tutkimuksen perusteella voidaan päätellä, että esitellyillä teknologioilla voidaan toteuttaa offline-tuki web-sovellukseen. Service worker osoittautuu paremmaksi vaihtoehdoksi kuin Application cache toiminnallisuudeltaan.

Parameter estimation for Chaotic or Stochastic Dynamics

Since its discovery, chaos has been a very interesting and challenging topic of research. Many great minds spent their entire lives trying to give some rules to it. Nowadays, thanks to the research of last century and the advent of computers, it is possible to predict chaotic phenomena of nature for a certain limited amount of time. The aim of this study is to present a recently discovered method for the parameter estimation of the chaotic dynamical system models via the correlation integral likelihood, and give some hints for a more optimized use of it, together with a possible application to the industry. The main part of our study concerned two chaotic attractors whose general behaviour is diff erent, in order to capture eventual di fferences in the results. In the various simulations that we performed, the initial conditions have been changed in a quite exhaustive way. The results obtained show that, under certain conditions, this method works very well in all the case. In particular, it came out that the most important aspect is to be very careful while creating the training set and the empirical likelihood, since a lack of information in this part of the procedure leads to low quality results.

Legendarius per circulum anni, pars.

Légendier disposé dans l'ordre du calendrier liturgique du 20 juillet au 25 novembre et contenant les saints suivants: ss. Margarita, Maria Magdelene, Jacobus major ap., Stephanus, Laurentius, Hippolytus, assumptio b. Mariae, Bartholomaeus, Augustinus, Johannes Baptista, Aegidius, nativitas b. Mariae, Gorgonius, Protus et Hyacinthus, exaltatio s. Crucis, Euphemia, Matthaeus, Mauritius, Cosmas et Damianus, Michael archangelus, Hieronymus, Leodegarius, Dionysius, Lucas, Simon et Judas, Martinus, Caecilia, Clemens, Catharina. F. 1-130. Legendarius. F. 1-3v. "... passio sancte Margarete virginis"; cf. B.H.L. n° 5306. F. 3v-6v. "... vita sancte Marie Magdalene" [ODO Cluniacensis abbas, sermo 2, excerptum] (P.L. 133, 714B-719C); cf. B.H.L. n° 5440. F. 6v-8v. "... passio sancti Jacobi [majoris] apostoli" incomplet des lignes finales par lacune matérielle, à partir de "decollandi erant dixit [Jacobus...]" [Virtutes apostolorum, de s. Jacobo majore] (Mombritius, 2a ed., II, 37-40 lig. 15); cf. B.H.L. n° 4057; C.A.N.T. n° 272. F. 9-12. "Inventio sancti Stephani prothomartyris" [LUCIANUS presbyter, interprete AVITO presbytero Bracarensi ]. "Domino venerabili Nimpsio [sic] episcopo... [Julianus exponctué et corrigé en] Lucianus... Revelationem que mihi ostensa est...-... aperire dignatus est..." recensio mixta suivie d'un court épilogue: "Bovem appellatum... declarata sunt"; cf. C.P.L. n° 575; B.H.L. Suppl. n° 7851n (E. Vanderlinden, Rev. des études byzantines, IV, 1946, 190-216, version A'; ne fait pas partie des mss. recensés pour l'édition). F. 12-16. "... passio sancti [Sixti et sancti] Laurentii". "In illo tempore Decius Caesar et Valerianus prefectus jusserunt...-... participati sunt omnes"; cf. B.H.L. Suppl. n° 7801 avec var. incipit et n° 4754. F. 16-18. "... passio sancti Ypoliti et sociorum ejus". "Egressus itaque Ypolitus post tercium diem...-... vivere male et regnare cum Christo "; cf. B.H.L. n° 3961 avec var. incipit et explicit. F. 18-31. "... [sermo] beati Ieronimi in assumptione sancte Virginis" [PASCHASIUS RADBERTUS, De Adsumptione b. Mariae] (C.C.C.M., LVI C 109-162; édité aussi parmi les apocryphes de saint Jérôme, P.L., XXX, 126-147); cf. C.P.L. n° 633, ep. 9 (18-29). F. 29-31. Addition contemporaine : "In vigilia assumptionis beate Marie legatur: Secundum Lucam (Lc 11, 27). [M]agne devocionis et fidei...-... ubera que suxisti" [BEDA, In Lc, l. IV, excerptum] divisé en trois paragraphes, correspondant sans doute à trois leçons (P.L., XCII, 479 C-480 B; C.C.S.L., CXX, 236-237 lig. 213-244) (29). — "Sermo iste legatur in nativitate beate Marie virginis"; cf. infra f. 56v. "[A]pprobate consuetudinis est apud christianos...-... pacta cessare" [FULBERTUS CARNOTENSIS, sermo 4] incomplet de la fin qui a été laissée en blanc (P.L. CXLI, 320-324 A; J.M. Canal, dans Rech. théol. anc. méd., XXX (1963), 56-61 lig. 168); ne fait pas partie des mss. répertoriés par J.M. Canal, ibid., XXIX (1962), 36-37; division marginale en neuf, puis en trois fois trois leçons; en marge du titre, une note difficilement lisible identifie l'auteur: "sermo Fulberti ep. Carnotensis" (29v-31). F. 32-35. "... vita [sic pro passio] sancti Bartholomei apostoli" [Virtutes apostolorum, de s. Bartholomaeo]; cf. B.H.L. Suppl. n° 1002a; C.A.N.T. n° 259. F. 35-49v. "[Vita s.] Augustini episcopi", sans prologue [POSSIDIUS]. "Ex provincia affricana civitate...-... perfruar"; cf. B.H.L. n° 785; C.P.L. n° 358 (35-49a lig. 7); suivi de la liste des livres de s. Augustin dans l'ordre des Retractations : "Libros vero quod edidit hic breviter enumerare vel annotare non omissi. Et hoc indicium librorum omnium sancti Augustini. Contra paganos achademicos [sic] libri III. De beata vita liber I. De ordine sacro libri II. De soliloquiis...-... et gratia liber. Requievit autem... V. kal. septembris..." (C.C.S.L., LVII (1984), 1-4, var.); texte proche du ms. lat. 5276, ff. 136v-137, répertorié par A. Wilmart, Miscellanea Agostiniana, Roma, 1931, 157 (Testi e studi, 2) (49a lig. 7-49v). F. 49v-52v. "Inventio capitis sancti Johannis Baptiste"; cf. B.H.L. n° 4296 (49v-51). — "De translatione ejusdem [Angeriacum]"; cf. B.H.L. n° 4297 (51-52v). F. 52v-56v. "... vita sancti Egidii"; cf. B.H.L. n° 93. F. 56v-59v. "De nativitate sancte Marie". "Petis a me petitiunculam opere...-... prefationem habuisse"; cf. B.H.L. Suppl. n° 5345 (56v a-b lig. 27) ; suivi de: "Petitis a me...-... scribi potuerunt. Igitur beata et gloriosissima semper virgo Maria..-... docuerunt Dominum..." (éd. parmi les apocryphes de s. Jérôme, P.L., XXX, 2a ed., 307-317); cf. B.H.L. n° 5344-5343; C.P.L., n° 633, ep. 50 (56v b lig. 27-59v). L'attribution à Paschase Radbert des deux lettres regroupées en une seule faite par C. Lambot, dans Rev. bénéd., XLVI (1934), 271-282, est réfutée par R. Beyers, dans Rev. Théol. et Philos., CXXII (1990), 171-188. Voir sa nouv. éd. dans CC Apocrypha, 10. F. 59v-61v. "Passio sancti Gorgonii [et Dorothei]; cf. B.H.L. n° 3617. F. 61v-62. "[Passio ss.] Prothi et Jacincti"; cf. B.H.L. n° 6977. F. 62-63v. "De exaltatione sancte Crucis". "Tempore illo postquam Constantino Augusto contra Maxentium..."; cf. B.H.L. n° 4178, avec var. incipit. F. 64-68v. "[Passio s.] Eufemie virginis". "Quinto persecutionis anno Diocletiani...-... Completum est autem martyrium... Prisco proconsule Europe..."; cf. B.H.L. n° 2709, avec var. explicit. F. 68v-72v. "[Passio] sancti Mathei apostoli" [Virtutes apostolorum, de s. Jacobo majore]; cf. C.A.N.T. n° 270; B.H.L. n° 5690, avec var. explicit de l'épilogue: "Zaroes autem...-... passio eorum ostendit". F. 72v-76. "[Passio s.] [Marcii corrigé en] Mauricii con [sic] sociis suis" [s. EUCHERIUS LUGDUNENSIS] sans le prologue; cf. B.H.L. n° 5738; C.P.L. n° 490. F. 76-79v. "[Passio ss.] Cosme et Damiani"; cf. B.H.L. Suppl. n° 1975. F. 79v-80. "[In festivitate s.] Michaelis archangeli". "Angelorum quippe et hominum naturam...-... medicina Dei." [GREGORIUS MAGNUS, Hom. in Ev., 34, excerptum]; C.P.L. n° 1711 (P.L., LXXVI, 1249 C-1251 A, §§ 6, fin-9 début) divisé en 8 paragraphes; une interpolation a été ajoutée dans la marge inférieure du f. 79v par une main contemporaine qui a également numéroté les paragraphes en IX leçons, le texte ajouté formant la lectio IIa : "[N]ovem esse angelorum ordines ad Dei judicia...-... principantur."; il s'agit d'un court extrait du sermon Legimus in ecclesiasticis historiis édité par J. E. Cross, dans Traditio, 33 (1977), 108-109 lig. 41-47 (Beda, Homilia subditia 71, P.L., XCIV, 453 C); cf. C.P.P.M., I, 4046. F. 80-82v. "[Vita s.] Jeronimi presbiteri". "Hieronimus noster [corrigé en: presbiter] in oppido Stridonis...-... etatis sue anno in Domino requievit cui..." extraits de la Vie apocryphe de Gennadius (P.L., XXII, 175-184, passim, avec var.); cf. C.P.L. n° 623; B.H.L. n° 3869; Lambert, B.H.M., IIIA, 630 (80-81b lig. 26); suivi du miracle du lion extrait de la Vie du Ps. Sebastianus Casinensis: "Contigit autem hujusmodi miraculum in monasterio... Quadam namque die ingens leo... - asserendo narrantur" (P.L., XXII, 210 lig. 11-213 lig. 11); cf. C.P.L. n° 622; B.H.L. n° 3872 avec var. incipit; Lambert, B.H.M., IIIA, 630 (81b lig. 26-82v). F. 82v-88v. "[Vita s.] Leodegarii". "Igitur sanctus Leodegarius ex progenie...-... postmodum cecum. ... adnecteret opera ibidem" [URSINUS LOGOGIACENSIS] sans le prologue et incomplet de la fin (C.C.S.L., CXVII, 589-632 lig. 14, avec var.); cf. C.P.L. n° 1079a; B.H.L. n° 4851; suivi d'un court extrait omis à sa place plus haut dans le texte: "Deinde vero ire ceperunt... Dei opera ibidem" (ed. cit., 631 § 31 lig. 3-7). F. 88v-98. "[Passio] sancti Dyonisii martyris", texte incomplet par suite de la perte de 2 ff. entre les ff. 96 et 97, le texte s'arrête à "...fideliter adhe[-rebat]" et reprend à "[Domitia-]no per tres Cesares..." (P.L., CVI, 23-40 C et 48 A-50); cf. B.H.L. n° 2175. F. 98-100v. "[Laudatio s.] Luce evvangeliste". "Gloriosus igitur evvangelista Jhesu Christi Lucas natione Syrus...-... ubique confluunt qui ..." [PAULUS DIACONUS, hom. 59] incomplet du prologue (P.L., XCV, 1530-1535, avec var.); cf. B.H.L. n° 4974, d'après ce ms. F. 100v-106. "[Passio ss.] Symonis et Jude apostolorum" avec l'épilogue [ABDIAS, Virtutes Simonis et Judae Thaddaei]; cf. B.H.L. n° 7750-7751; C.A.N.T. n° 284. F. 106-107v. "[Laudatio] sancti Martini archiepiscopi" [ALCUINUS, De vita s. Martini, pars I]; cf. B.H.L. n° 5625. — GREGORIUS TURONENSIS, De virtutibus s. Martini; cf. B.H.L. n° 5618; seule l'adresse du prologue, introduite par une initiale filigranée, a été copiée au bas du f. 107v, col. b: "Domnis sanctis et in Christi amore dulcissimis fratribus... Gregorius peccator", le texte lui-même manque, soit en raison de la perte du cahier suivant, soit qu'il n'ait pas été copié. F. 108-115v. "[Passio s.] Cecilie virginis et martyris"; cf. B.H.L. Suppl. n° 1495a. F. 115v-118v. "[Passio s.] Clementis pape". [Prologus] "Postquam igitur beatus Petrus apostolus in Antiochia cathedram... -... passio secuta est"; cf. B.H.L. Suppl. n° 1849, d'après ce ms. (115v-116a, lig. 11); — "Tunc sanctus Clemens romane ecclesie episcopus disciplinam...-... Cersone Licie provincie"; C.P.L. n° 2177; B.H.L. n° 1848 (Mombritius, 2a ed., I, 341-344, var. à l'incipit et à l'explicit); suivi de: "Oremus fratres ut Dominus... participes. Per..." (116a, lig. 11-118v). F.118v-130. "[Passio] sancte Katerine virginis et martyris"; cf. B.H.L. n° 1663, sans le prologue. F. 130-130v. Additions. Table des saints contenus dans le volume, XIVe s. (130). — Prière latine en 10 strophes de deux vers, XVe s.: "Jhesu tue matris prece ab Orci me serva nece...-... ab inferi atris" (130v).