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

Lepton Mixing Patterns from a Scan of Finite Discrete Groups

The recent discovery of a non-zero value of the mixing angle theta_13 has ruled out tri-bimaximal mixing as the correct lepton mixing pattern generated by some discrete flavor symmetry (barring large next-to-leading order corrections in concrete models). In this work we assume that neutrinos are Majorana particles and perform a general scan of all finite discrete groups with order less than 1536 to obtain their predictions for lepton mixing angles. To our surprise, the scan of over one million groups only yields 3 interesting groups that give lepton mixing patterns which lie within 3-sigma of the current best global fit values. A systematic way to categorize such groups and the implications for flavor symmetry are discussed.Comment: 15 pages, 3 figures, references added and minor improvements, matches version to be appeared in Physics Letters

Dritter Wanderfalkenbrutplatz im Kreis Höxter

Nachdem der Wanderfalke 1965 (laut Aussagen des Ornithologen Ferdinand ROESRATH) im Kreis Höxter als Brutvogel verschwunden war, dauerte es bis 2001 zur Wiederbesiedlung. Im Jahr 2001 wurde zuerst genau jener 1965 zuletzt besiedelte Felsbrutplatz wieder besetzt (THIEL 2001). (Aus Artenschutzgründen unterbleiben im Artikel genaue Ortsangaben der Brutplätze.

Dynamical Electroweak Symmetry Breaking by a Neutrino Condensate

We show that the electroweak symmetry can be broken in a natural and phenomenologically acceptable way by a neutrino condensate. Therefore, we assume as particle content only the chiral fermions and gauge bosons of the Standard Model and in addition right-handed neutrinos. A fundamental Higgs field is absent. We assume instead that new interactions exist that can effectively be described as four-fermion interactions and that can become critical in the neutrino sector. We discuss in detail the coupled Dirac-Majorana gap equations which lead to a neutrino condensate, electroweak symmetry breaking and via the dynamical see-saw mechanism to small neutrino masses. We show that the effective Lagrangian is that of the Standard Model with massive neutrinos and with a composite Higgs particle. The mass predictions are consistent with data.Comment: 18 pages, 8 figures; minor clarifications; version to appear in Nucl. Phys.

Infinite Probabilistic Databases

Probabilistic databases (PDBs) model uncertainty in data in a quantitative way. In the established formal framework, probabilistic (relational) databases are finite probability spaces over relational database instances. This finiteness can clash with intuitive query behavior (Ceylan et al., KR 2016), and with application scenarios that are better modeled by continuous probability distributions (Dalvi et al., CACM 2009). We formally introduced infinite PDBs in (Grohe and Lindner, PODS 2019) with a primary focus on countably infinite spaces. 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. We argue that finite point processes are an appropriate model from probability theory for dealing with general probabilistic databases. This 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.Comment: This is the full version of the paper "Infinite Probabilistic Databases" presented at ICDT 2020 (arXiv:1904.06766

It was (not) me: Causal Inference of Agency in goal-directed actions

Summary: 
The perception of one’s own actions depends on both sensory information and predictions derived from internal forward models [1]. The integration of these information sources depends critically on whether perceptual consequences are associated with one’s own action (sense of agency) or with changes in the external world that are not related to the action. The perceived effects of actions should thus critically depend on the consistency between the predicted and the actual sensory consequences of actions. To test this idea, we used a virtual-reality setup to manipulate the consistency between pointing movements and their visual consequences and investigated the influence of this manipulation on self-action perception. We then asked whether a Bayesian causal inference model, which assumes a latent agency variable controlling the attributed influence of the own action on perceptual consequences [2,3], would account for the empirical data: if the percept was attributed to the own action, visual and internal information should fuse in a Bayesian optimal manner, while this should not be the case if the visual stimulus was attributed to external influences. The model correctly fits the data, showing that small deviations between predicted and actual sensory information were still attributed to one’s own action, while this was not the case for large deviations when subjects relied more on internal information. We discuss the performance of this causal inference model in comparison to alternative biologically feasible statistical models applying methods for Bayesian model comparison.

Experiment: 
Participants were seated in front of a horizontal board on which their right hand was placed with the index finger on a haptic marker, representing the starting point for each trial. Participants were instructed to execute straight, fast (quasi-ballistic) pointing movements of fixed amplitude, but without an explicit visual target. The hand was obstructed from the view of the participants, and visual feedback about the peripheral part of the movement was provided by a cursor. Feedback was either veridical or rotated against the true direction of the hand movement by predefined angles. After each trial participants were asked to report the subjectively experienced direction of the executed hand movement by placing a mouse-cursor into that direction.

Model: 
We compared two probabilistic models: Both include a binary random gating variable (agency) that models the sense of ‘agency’; that is the belief that the visual feedback is influenced by the subject’s motor action. The first model assumes that both the visual feedback xv and the internal motor state estimate xe are directly caused by the (unobserved) real motor state xt (Fig. 1). The second model assumes instead that the expected visual feedback depends on the perceived direction of the own motor action xe (Fig. 2). 
Results: Both models are in good agreement with the data. Fig. A shows the model fit for Model 1 superpositioned to the data from a single subject. Fig. B shows the belief that the visual stimulus was influenced by the own action, which decreases for large deviations between predicted and real visual feedback. Bayesian model comparison shows a better fit for model 1.
Citations
[1] Wolpert D.M, Ghahramani, Z, Jordan, M. (1995) Science, 269, 1880-1882.
[2] Körding KP, Beierholm E, Ma WJ, Quartz S, Tenenbaum JB, et al (2007) PLoS ONE 2(9): e943.
[3] Shams, L., Beierholm, U. (2010) TiCS, 14: 425-432.
Acknowledgements
This work was supported by the BCCN Tübingen (FKZ: 01GQ1002), the CIN Tübingen, the European Union (FP7-ICT-215866 project SEARISE), the DFG and the Hermann and Lilly Schilling Foundation

A Formalization of Kant's Second Formulation of the Categorical Imperative

We present a formalization and computational implementation of the second formulation of Kant's categorical imperative. This ethical principle requires an agent to never treat someone merely as a means but always also as an end. Here we interpret this principle in terms of how persons are causally affected by actions. We introduce Kantian causal agency models in which moral patients, actions, goals, and causal influence are represented, and we show how to formalize several readings of Kant's categorical imperative that correspond to Kant's concept of strict and wide duties towards oneself and others. Stricter versions handle cases where an action directly causally affects oneself or others, whereas the wide version maximizes the number of persons being treated as an end. We discuss limitations of our formalization by pointing to one of Kant's cases that the machinery cannot handle in a satisfying way

Causes of brain dysfunction in acute coma: a cohort study of 1027 patients in the emergency department

BACKGROUND: Coma of unknown etiology (CUE) is a major challenge in emergency medicine. CUE is caused by a wide variety of pathologies that require immediate and targeted treatment. However, there is little empirical data guiding rational and efficient management of CUE. We present a detailed investigation on the causes of CUE in patients presenting to the ED of a university hospital. METHODS: One thousand twenty-seven consecutive ED patients with CUE were enrolled. Applying a retrospective observational study design, we analyzed all clinical, laboratory and imaging findings resulting from a standardized emergency work-up of each patient. Following a predefined protocol, we identified main and accessory coma-explaining pathologies and related these with (i.a.) GCS and in-hospital mortality. RESULTS: On admission, 854 of the 1027 patients presented with persistent CUE. Their main diagnoses were classified into acute primary brain lesions (39%), primary brain pathologies without acute lesions (25%) and pathologies that affected the brain secondarily (36%). In-hospital mortality associated with persistent CUE amounted to 25%. 33% of patients with persistent CUE presented with more than one coma-explaining pathology. In 173 of the 1027 patients, CUE had already resolved on admission. However, these patients showed a spectrum of main diagnoses similar to persistent CUE and a significant in-hospital mortality of 5%. CONCLUSION: The data from our cohort show that the spectrum of conditions underlying CUE is broad and may include a surprisingly high number of coincidences of multiple coma-explaining pathologies. This finding has not been reported so far. Thus, significant pathologies may be masked by initial findings and only appear at the end of the diagnostic work-up. Furthermore, even transient CUE showed a significant mortality, thus rendering GCS cutoffs for selection of high- and low-risk patients questionable. Taken together, our data advocate for a standardized diagnostic work-up that should be triggered by the emergency symptom CUE and not by any suspected diagnosis. This standardized routine should always be completed - even when initial coma-explaining diagnoses may seem evident