Queries with Guarded Negation (full version)

A well-established and fundamental insight in database theory is that negation (also known as complementation) tends to make queries difficult to process and difficult to reason about. Many basic problems are decidable and admit practical algorithms in the case of unions of conjunctive queries, but become difficult or even undecidable when queries are allowed to contain negation. Inspired by recent results in finite model theory, we consider a restricted form of negation, guarded negation. We introduce a fragment of SQL, called GN-SQL, as well as a fragment of Datalog with stratified negation, called GN-Datalog, that allow only guarded negation, and we show that these query languages are computationally well behaved, in terms of testing query containment, query evaluation, open-world query answering, and boundedness. GN-SQL and GN-Datalog subsume a number of well known query languages and constraint languages, such as unions of conjunctive queries, monadic Datalog, and frontier-guarded tgds. In addition, an analysis of standard benchmark workloads shows that most usage of negation in SQL in practice is guarded negation

Guarded negation

International audienceWe consider restrictions of first-order logic and of fixpoint logic in which all occurrences of negation are required to be guarded by an atomic predicate. In terms of expressive power, the logics in question, called GNFO and GNFP, extend the guarded fragment of first-order logic and the guarded least fixpoint logic, respectively. They also extend the recently introduced unary negation fragments of first-order logic and of least fixpoint logic. We show that the satisfiability problem for GNFO and for GNFP is 2ExpTime-complete, both on arbitrary structures and on finite structures. We also study the complexity of the associated model checking problems. Finally, we show that GNFO and GNFP are not only computationally well behaved, but also model theoretically: we show that GNFO and GNFP have the tree-like model property and that GNFO has the finite model property, and we characterize the expressive power of GNFO in terms of invariance for an appropriate notion of bisimulation. Our complexity upper bounds for GNFO and GNFP hold true even for their " clique-guarded " extensions CGNFO and CGNFP, in which clique guards are allowed in the place of guards

Vascular Supply of the Metacarpophalangeal Joint

OBJECTIVE: To describe in detail the arterial vasculature of metacarpophalangeal joints 2–5 on cadaver specimens and to compare it to ultrasound imaging of healthy subjects. METHODS: Eighteen hands of donated human cadavers were arterially injected and investigated with either corrosion casting or cryosectioning. Each layer of cryosectioned specimens was photographed in high-resolution. Images were then segmented for arterial vessels of the metacarpophalangeal (MCP) joints 2–5. The arterial pattern of the joints was reconstructed from the segmented images and from the corrosion cast specimens. Both hands of ten adult healthy volunteers were scanned focusing on the vasculature of the same joints with high-end ultrasound imaging, including color Doppler. Measurements were made on both cryosectioned arteries and Doppler images. RESULTS: The arterial supply of MCP joints 2–5 divides into a metacarpal and a phalangeal territory, respectively. The metacarpal half receives arteries from the palmar metacarpal arteries or proper palmar digital arteries, while the phalangeal half is supplied by both proper and common palmar digital arteries. Comparing anatomical and ultrasonographic results, we determined the exact anatomic location of normal vessels using Doppler images acquired of healthy joints. All, except three branches, were found with less than 50% frequency using ultrasound. Doppler signals were identified significantly more frequently in MCP joints 2–3 than on 4–5 (p < 0.0001). Similarly, Doppler signals differed in the number of detectable small, intraarticular vessels (p < 0.009), but not that of the large extraarticular ones (p < 0.1373). When comparing measurements acquired by ultrasound and on cadaver vessels, measurements using the former technique were found to be larger in all joints (p < 0.0001). CONCLUSION: Using morphological and ultrasonographic techniques, our study provides a high-resolution anatomical maps and an essential reference data set on the entire arterial vasculature of healthy human MCP 2–5 joints. We found that Doppler signal could be detected in less than 50% of the vessels of healthy volunteers except three locations. Intraarticular branches were detected with ultrasound imaging significantly more frequently on healthy MCP 2–3 joints, which should be taken into account when inflammatory and normal Doppler signals are evaluated. Our study also provides reference data for future, higher-resolution imaging techniques

Frequency drift in MR spectroscopy at 3T

Purpose: Heating of gradient coils and passive shim components is a common cause of instability in the B0 field, especially when gradient intensive sequences are used. The aim of the study was to set a benchmark for typical drift encountered during MR spectroscopy (MRS) to assess the need for real-time field-frequency locking on MRI scanners by comparing field drift data from a large number of sites. Method: A standardized protocol was developed for 80 participating sites using 99 3T MR scanners from 3 major vendors. Phantom water signals were acquired before and after an EPI sequence. The protocol consisted of: minimal preparatory imaging; a short pre-fMRI PRESS; a ten-minute fMRI acquisition; and a long post-fMRI PRESS acquisition. Both pre- and post-fMRI PRESS were non-water suppressed. Real-time frequency stabilization/adjustment was switched off when appropriate. Sixty scanners repeated the protocol for a second dataset. In addition, a three-hour post-fMRI MRS acquisition was performed at one site to observe change of gradient temperature and drift rate. Spectral analysis was performed using MATLAB. Frequency drift in pre-fMRI PRESS data were compared with the first 5:20 minutes and the full 30:00 minutes of data after fMRI. Median (interquartile range) drifts were measured and showed in violin plot. Paired t-tests were performed to compare frequency drift pre- and post-fMRI. A simulated in vivo spectrum was generated using FID-A to visualize the effect of the observed frequency drifts. The simulated spectrum was convolved with the frequency trace for the most extreme cases. Impacts of frequency drifts on NAA and GABA were also simulated as a function of linear drift. Data from the repeated protocol were compared with the corresponding first dataset using Pearson\u27s and intraclass correlation coefficients (ICC). Results: Of the data collected from 99 scanners, 4 were excluded due to various reasons. Thus, data from 95 scanners were ultimately analyzed. For the first 5:20 min (64 transients), median (interquartile range) drift was 0.44 (1.29) Hz before fMRI and 0.83 (1.29) Hz after. This increased to 3.15 (4.02) Hz for the full 30 min (360 transients) run. Average drift rates were 0.29 Hz/min before fMRI and 0.43 Hz/min after. Paired t-tests indicated that drift increased after fMRI, as expected (p \u3c 0.05). Simulated spectra convolved with the frequency drift showed that the intensity of the NAA singlet was reduced by up to 26%, 44 % and 18% for GE, Philips and Siemens scanners after fMRI, respectively. ICCs indicated good agreement between datasets acquired on separate days. The single site long acquisition showed drift rate was reduced to 0.03 Hz/min approximately three hours after fMRI. Discussion: This study analyzed frequency drift data from 95 3T MRI scanners. Median levels of drift were relatively low (5-min average under 1 Hz), but the most extreme cases suffered from higher levels of drift. The extent of drift varied across scanners which both linear and nonlinear drifts were observed

Frequency drift in MR spectroscopy at 3T

Purpose: Heating of gradient coils and passive shim components is a common cause of instability in the B-0 field, especially when gradient intensive sequences are used. The aim of the study was to set a benchmark for typical drift encountered during MR spectroscopy (MRS) to assess the need for real-time field-frequency locking on MRI scanners by comparing field drift data from a large number of sites.Method: A standardized protocol was developed for 80 participating sites using 99 3T MR scanners from 3 major vendors. Phantom water signals were acquired before and after an EPI sequence. The protocol consisted of: minimal preparatory imaging; a short pre-fMRI PRESS; a ten-minute fMRI acquisition; and a long post-fMRI PRESS acquisition. Both pre- and post-fMRI PRESS were non-water suppressed. Real-time frequency stabilization/adjustment was switched off when appropriate. Sixty scanners repeated the protocol for a second dataset. In addition, a three-hour post-fMRI MRS acquisition was performed at one site to observe change of gradient temperature and drift rate. Spectral analysis was performed using MATLAB. Frequency drift in pre-fMRI PRESS data were compared with the first 5:20 minutes and the full 30:00 minutes of data after fMRI. Median (interquartile range) drifts were measured and showed in violin plot. Paired t-tests were performed to compare frequency drift pre- and post-fMRI. A simulated in vivo spectrum was generated using FID-A to visualize the effect of the observed frequency drifts. The simulated spectrum was convolved with the frequency trace for the most extreme cases. Impacts of frequency drifts on NAA and GABA were also simulated as a function of linear drift. Data from the repeated protocol were compared with the corresponding first dataset using Pearson's and intraclass correlation coefficients (ICC).Results: Of the data collected from 99 scanners, 4 were excluded due to various reasons. Thus, data from 95 scanners were ultimately analyzed. For the first 5:20 min (64 transients), median (interquartile range) drift was 0.44 (1.29) Hz before fMRI and 0.83 (1.29) Hz after. This increased to 3.15 (4.02) Hz for the full 30 min (360 transients) run. Average drift rates were 0.29 Hz/min before fMRI and 0.43 Hz/min after. Paired t-tests indicated that drift increased after fMRI, as expected (p &lt; 0.05). Simulated spectra convolved with the frequency drift showed that the intensity of the NAA singlet was reduced by up to 26%, 44 % and 18% for GE, Philips and Siemens scanners after fMRI, respectively. ICCs indicated good agreement between datasets acquired on separate days. The single site long acquisition showed drift rate was reduced to 0.03 Hz/min approximately three hours after fMRI.Discussion: This study analyzed frequency drift data from 95 3T MRI scanners. Median levels of drift were relatively low (5-min average under 1 Hz), but the most extreme cases suffered from higher levels of drift. The extent of drift varied across scanners which both linear and nonlinear drifts were observed.</p

Invariants of Automatic Presentations and Semi−Synchronous Transductions

Automatic structures are countable structures finitely presentable by a collection of automata. We study questions related to properties invariant with respect to the choice of an automatic presentation. We give a negative answer to a question of Rubin concerning definability of intrinsically regular relations by showing that order-invariant first-order logic can be stronger than first-order logic with counting on automatic structures. We introduce a notion of equivalence of automatic presentations, define semi-synchronous transductions, and show how these concepts correspond. Our main result is that a one-to-one function on words preserves regularity as well as non-regularity of all relations iff it is a semi-synchronous transduction. We also characterize automatic presentations of the complete structures of Blumensath and Gr�del

Automatic Presentations of Infinite Structures

The work at hand studies the possibilities and limitations of the use of finite automata in the description of infinite structures. An automatic presentation of a countable structure consists of a labelling of the elements of the structure by finite words over a finite alphabet in a consistent way so as to allow each of the relations of the structure to be recognised, given the labelling, by a synchronous multi-tape automaton. The collection of automata involved constitutes a finite presentation of the structure up to isomorphism. More generally, one can consider presentations over finite trees or over infinite words or trees, based on the appropriate model of automata. In the latter models, uncountable structures are also representable. Automatic presentations allow for effective evaluation of first-order formulas over the represented structure in line with the strong correspondence between automata and logics. Accordingly, automatic presentations can be recast in logical terms using various notions of interpretations. The simplicity and robustness of the model coupled with the diversity of automatic structures makes automatic presentations interesting subject of investigation within the scope of algorithmic model theory. Although automata have been in use in representations of infinite structures in computational group theory, in the analysis of numeration systems and finitely generated infinite sequences as well as in the theory of term rewriting systems, a systematic investigation of automatic structures using model theoretic methods has only just begun in the last twelve years. There are two main lines of research in this field. One would like to have a classification of automatic models of certain first-order theories of common interest, such as linear orderings, trees, boolean algebras, groups, etc. Though efforts aimed at obtaining structure theorems have produced considerable advancement in recent years, this programme is still in an early stage. Even further lacking is our understanding of the richness of automatic presentations of key individual structures. A prominent result in this area is the deep theorem of Cobham and Semenov concerning numeration systems. In this style, one would like to know the degree of freedom in choosing automatic presentations of a particular structure. In this thesis we present contributions to both of these problem areas. We also study restricted notions of presentations and clarify the relationship of automatic presentations over finite and infinite words. The peculiarities of using automata to represent structures up to isomorphism introduce problems out of the range of classical automata theory. We present some new techniques developed to tackle these difficulties

Semi−synchronous transductions

Semi-synchronously rational relations generalise synchronised rational relations in a natural way. We discuss here some of their basic properties, among them a \"Cobham-Semenov-like\" dichotomy theorem. Our main result is a characterisation of bijective semi-synchronously rational transductions as those bijections mapping regular relations to regular ones and non-regular relations to non-regular ones