When are Stochastic Transition Systems Tameable?

A decade ago, Abdulla, Ben Henda and Mayr introduced the elegant concept of decisiveness for denumerable Markov chains [1]. Roughly speaking, decisiveness allows one to lift most good properties from finite Markov chains to denumerable ones, and therefore to adapt existing verification algorithms to infinite-state models. Decisive Markov chains however do not encompass stochastic real-time systems, and general stochastic transition systems (STSs for short) are needed. In this article, we provide a framework to perform both the qualitative and the quantitative analysis of STSs. First, we define various notions of decisiveness (inherited from [1]), notions of fairness and of attractors for STSs, and make explicit the relationships between them. Then, we define a notion of abstraction, together with natural concepts of soundness and completeness, and we give general transfer properties, which will be central to several verification algorithms on STSs. We further design a generic construction which will be useful for the analysis of {\omega}-regular properties, when a finite attractor exists, either in the system (if it is denumerable), or in a sound denumerable abstraction of the system. We next provide algorithms for qualitative model-checking, and generic approximation procedures for quantitative model-checking. Finally, we instantiate our framework with stochastic timed automata (STA), generalized semi-Markov processes (GSMPs) and stochastic time Petri nets (STPNs), three models combining dense-time and probabilities. This allows us to derive decidability and approximability results for the verification of these models. Some of these results were known from the literature, but our generic approach permits to view them in a unified framework, and to obtain them with less effort. We also derive interesting new approximability results for STA, GSMPs and STPNs.Comment: 77 page

Analysing Decisive Stochastic Processes

In 2007, Abdulla et al. introduced the elegant concept of decisive Markov chain. Intuitively, decisiveness allows one to lift the good properties of finite Markov chains to infinite Markov chains. For instance, the approximate quantitative reachability problem can be solved for decisive Markov chains (enjoying reasonable effectiveness assumptions) including probabilistic lossy channel systems and probabilistic vector addition systems with states. In this paper, we extend the concept of decisiveness to more general stochastic processes. This extension is non trivial as we consider stochastic processes with a potentially continuous set of states and uncountable branching (common features of real-time stochastic processes). This allows us to obtain decidability results for both qualitative and quantitative verification problems on some classes of real-time stochastic processes, including generalized semi-Markov processes and stochastic timed automat

dAcquisition setting optimization and quantitative imaging for 124I studies with the Inveon microPET-CT system

International audienceABSTRACT: BACKGROUND: Noninvasive multimodality imaging is essential for preclinical evaluation of the biodistribution and pharmacokinetics of radionuclide therapy and for monitoring tumor response. Imaging with nonstandard positron-emission tomography [PET] isotopes such as 124I is promising in that context but requires accurate activity quantification. The decay scheme of 124I implies an optimization of both acquisition settings and correction processing. The PET scanner investigated in this study was the Inveon PET/CT system dedicated to small animal imaging. METHODS: The noise equivalent count rate [NECR], the scatter fraction [SF], and the gamma-prompt fraction [GF] were used to determine the best acquisition parameters for mouse- and rat-sized phantoms filled with 124I. An image-quality phantom as specified by the National Electrical Manufacturers Association NU 4-2008 protocol was acquired and reconstructed with two-dimensional filtered back projection, 2D ordered-subset expectation maximization [2DOSEM], and 3DOSEM with maximum a posteriori [3DOSEM/MAP] algorithms, with and without attenuation correction, scatter correction, and gamma-prompt correction (weighted uniform distribution subtraction). RESULTS: Optimal energy windows were established for the rat phantom (390 to 550 keV) and the mouse phantom (400 to 590 keV) by combining the NECR, SF, and GF results. The coincidence time window had no significant impact regarding the NECR curve variation. Activity concentration of 124I measured in the uniform region of an image-quality phantom was underestimated by 9.9% for the 3DOSEM/MAP algorithm with attenuation and scatter corrections, and by 23% with the gamma-prompt correction. Attenuation, scatter, and gamma-prompt corrections decreased the residual signal in the cold insert. CONCLUSIONS: The optimal energy windows were chosen with the NECR, SF, and GF evaluation. Nevertheless, an image quality and an activity quantification assessment were required to establish the most suitable reconstruction algorithm and corrections for 124I small animal imaging

A new technique for assessing arterial pressure wave forms and central pressure with tissue Doppler

BACKGROUND: Non-invasive assessment of arterial pressure wave forms using applanation tonometry of the radial or carotid arteries can be technically challenging and has not found wide clinical application. 2D imaging of the common carotid arteries is routinely used and we sought to determine whether arterial waveform measurements could be derived from tissue Doppler imaging (TDI) of the carotid artery. METHODS: We studied 91 subjects (52 men, age 52 ± 14 years) with and without cardiovascular disease. Tonometry was performed on the carotid artery simultaneously with pulsed wave Doppler of the LVOT and acquired digitally. Longitudinal 2D images of the common carotid artery with and without TDI were also acquired digitally and both TDI and tonometry were calibrated using mean and diastolic cuff pressure and analysed off line. RESULTS: Correlation between central pressure by TDI and tonometry was excellent for maximum pressure (r = 0.97, p < 0.0001). The mean differences between central pressures derived by TDI and tonometry were minimal (systolic 5.36 ± 5.5 mmHg; diastolic 1.2 ± 1.2 mmHg). CONCLUSION: Imaging of the common carotid artery motion with tissue Doppler may permit acquisition of a waveform analogous to that from tonometry. This method may simplify estimation of central arterial pressure and calculation of total arterial compliance

Reconstruction multiclasse pour l'imagerie TEP 3-photons

This contribution addresses the problem of image reconstruction of radioactivity distribution for which the available information arises from several classes of data, each associated with a specific combination of detections. We introduce a theoretical framework to measure the amount of information brought by each class and we develop an iterative algorithm dedicated to multi-class reconstruction based on maximum likelihood.We apply our approach to the XEMIS2 camera, a preclinical prototype of a Compton telescope dedicated to 3-photon PET imaging for which four distinct classes of partial detections coexist with the full detection class.Based on Monte Carlo simulations, we present the first elements of our model.Comment: in French language, GRETSI'23, Groupe de Recherche et d'Etudes de Traitement du Signal et des Images, Aug 2023, Grenoble, Franc

Etude de la solution interstitielle des pâtes de ciment : extraction par injection de gaz et calcul de la conductivité électrique

Dès le gâchage du ciment, l'eau devient multiforme dans la matrice cimentaire durcie, nous distinguons quatre types : l'eau adsorbée, l'eau capillaire, l'eau chimiquement liée et l'eau libre. Au cours de la prise et du durcissement, certains produits de l'hydratation (KOH, NaOH et Ca(OH)2) restent dissous dans la solution aqueuse interstitielle. Les teneurs en alcalins Na+ et K+ sont supérieurs à celles en Ca2+ à cause de l'insolubilité de Ca(OH)2 en milieu très alcalin et c'est la présence d'ions OH? qui contrôle le pH basique compris entre 12 et 13 de la solution. La composition de la solution interstitielle constituée par l'eau libre varie avec l'âge du matériau, au terme des réactions d'hydratation, elle contient quelques mmol/L de calcium, une dizaine de mmol/L de sulfates et plusieurs centaines de mmol/L d'alcalins. La solution porale des pâtes de ciment portland est initialement riche en Na, K, Ca, sulfate et ions hydroxyde. L'étude et la connaissance de l'évolution de ces ions au cours du temps jouent un rôle très important dans la durabilité des matériaux cimentaires. D'un point de vue structural, l'évaluation de la concentration des ions chlorure par exemple permet d'évaluer l'état des armatures dans le béton. Ainsi la connaissance de la concentration des ions présents dans la solution porale permet de calculer la conductivité électrique et le pH de celle-ci qui est un indicateur de durabilité des matériaux cimentaires. Par ailleurs la conductivité de la solution porale elle-même joue un rôle important dans le calcul du coe?cient de di?usion des espèces ioniques présentes dans celle-ci. Ce papier présente les résultats de l'analyse chimique de la solution interstitielle sachant que la connaissance de cette donnée peut être utiliser comme paramètre de modèle ou avoir directement une conséquence sur le comportement mécanique des structures. Il existe deux techniques qui permettent d'extraire la solution porale : la première est par compression, une méthode destructive qui a été développé par Longuet et al., et elle consiste à placer des fragments d'échantillon, en général de la matrice cimentaire, dans une cellule d'extraction. Le matériau est comprimé à l'aide d'une presse mécanique, et la solution porale sera recueillie par une seringue en passant par le drain du montage pour e?ectuer les analyses chimiques. La deuxième méthode est celle d'un perméamètre haute pression (Hassler Cell permeability) : c'est une méthode non destructive. Elle a été développée par Green et al., le principe consiste à placer un échantillon dans un noyau cylindrique ,et la pression est assurée par l'injection de l'eau déminéralisée. Un dispositif d'extraction de la solution interstitielle en appliquant une pression de gaz inerte sera présenté dans cette étude. L'avantage principal de cette méthode est qu'elle est non destructive, l'échantillon peut être récupéré et réutilisé pour des autres essais. Les analyses chimiques ont été réalisés à l'aide d'un spéctromètre d'émission atomique. L'étude a montré que l'application d'une pression d'injection de 20 MPa et d'une pression de con?nement de 23 MPa est su?sante pour l'extraction de la solution porale des pâtes de ciment de rapport E/C = 0,6 et 0,7 et du mortier de rapport E/C = 0,7. Pour les matériaux de faible rapport E/C, quelques gouttes d'eau ont été recueillies sur la face inférieure de l'échantillon montrant ainsi la limitation de la méthode.  Le calcul de la résistivité électrique par le modèle analytique, à partir de l'analyse chimique des ions présents dans la solution extraite, met en évidence que celle ci diminue avec la diminution du rapport E/C. L'intérêt d'avoir ce modèle analytique permet d'estimer la conductivité électrique d'une solution extraite de petite quantité avec précision