Infinite Probabilistic Databases

Probabilistic databases (PDBs) are used to model uncertainty in data in a quantitative way. In the standard formal framework, PDBs are finite probability spaces over relational database instances. It has been argued convincingly that this is not compatible with an open-world semantics (Ceylan et al., KR 2016) and with application scenarios that are modeled by continuous probability distributions (Dalvi et al., CACM 2009). We recently introduced a model of PDBs as infinite probability spaces that addresses these issues (Grohe and Lindner, PODS 2019). While that work was mainly concerned with countably infinite probability spaces, our focus here is on uncountable spaces. Such an extension is necessary to model typical continuous probability distributions that appear in many applications. However, an extension beyond countable probability spaces raises nontrivial foundational issues concerned with the measurability of events and queries and ultimately with the question whether queries have a well-defined semantics. It turns out that so-called finite point processes are the appropriate model from probability theory for dealing with probabilistic databases. This model allows us to construct suitable (uncountable) probability spaces of database instances in a systematic way. Our main technical results are measurability statements for relational algebra queries as well as aggregate queries and Datalog queries

Continuous-time GARCH processes

A family of continuous-time generalized autoregressive conditionally heteroscedastic processes, generalizing the $\operatorname {COGARCH}(1,1)$ process of Kl\"{u}ppelberg, Lindner and Maller [J. Appl. Probab. 41 (2004) 601--622], is introduced and studied. The resulting $\operatorname {COGARCH}(p,q)$ processes, $q\ge p\ge 1$, exhibit many of the characteristic features of observed financial time series, while their corresponding volatility and squared increment processes display a broader range of autocorrelation structures than those of the $\operatorname {COGARCH}(1,1)$ process. We establish sufficient conditions for the existence of a strictly stationary nonnegative solution of the equations for the volatility process and, under conditions which ensure the finiteness of the required moments, determine the autocorrelation functions of both the volatility and the squared increment processes. The volatility process is found to have the autocorrelation function of a continuous-time autoregressive moving average process.Comment: Published at http://dx.doi.org/10.1214/105051606000000150 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

A Continuous Time GARCH Process of Higher Order

A continuous time GARCH model of order (p,q) is introduced, which is driven by a single Lévy process. It extends many of the features of discrete time GARCH(p,q) processes to a continuous time setting. When p=q=1, the process thus defined reduces to the COGARCH(1,1) process of Klüppelberg, Lindner and Maller (2004). We give sufficient conditions for the existence of stationary solutions and show that the volatility process has the same autocorrelation structure as a continuous time ARMA process. The autocorrelation of the squared increments of the process is also investigated, and conditions ensuring a positive volatility are discussed

Physikalische Chemie 2012

Zeitaufgelöste Experimente mit Freie-Elektronen-Lasern filmen chemische Reaktionen auf der Femto- und Pikosekundenskala mit atomarer Ortsauflösung. Wasserstoffbrückenbindungen brechen und ‧knüpfen auf einer Zeitskala von Pikosekunden. Mit zweidimensionaler Infrarotspektroskopie lässt sich die damit verbundene strukturelle Dynamik in Echtzeit beobachten

"Meet the farmer" : Kleinbauern, Regionalentwicklung und der neue globale Agrarmarkt

Lebensmittelkrisen wie BSE, Schweinepest, Vogelgrippe und der »Gammelfleischskandal« haben das Vertrauen der Verbraucher in den Agrarmarkt erschüttert. Deshalb verwenden Produzenten und Einzelhändler heute mehr Anstrengungen als jemals zuvor darauf, der verunsichernden Anonymität der global organisierten Produktion durch die Herstellung sozialer Nähe entgegenzuwirken. So suggerieren Herkunftszertifi kate für Regionalprodukte sowie eine schnell steigende Zahl von Hygiene-, Sozial- und Umweltstandards Verlässlichkeit aufgrund von geringen räumlichen Distanzen und unabhängiger Kontrolle, während Initiativen wie »Caretrace: Meet the Farmer« dadurch Vertrauen schaffen sollen, dass sich der Konsument im Internet über den individuellen Produzenten informieren kann. Doch die Folgen dieser Umbrüche für Produktionsweisen und Anbauregionen sind bislang nur wenig bekannt