Integrity Constraints Revisited: From Exact to Approximate Implication

Integrity constraints such as functional dependencies (FD), and multi-valued dependencies (MVD) are fundamental in database schema design. Likewise, probabilistic conditional independences (CI) are crucial for reasoning about multivariate probability distributions. The implication problem studies whether a set of constraints (antecedents) implies another constraint (consequent), and has been investigated in both the database and the AI literature, under the assumption that all constraints hold exactly. However, many applications today consider constraints that hold only approximately. In this paper we define an approximate implication as a linear inequality between the degree of satisfaction of the antecedents and consequent, and we study the relaxation problem: when does an exact implication relax to an approximate implication? We use information theory to define the degree of satisfaction, and prove several results. First, we show that any implication from a set of data dependencies (MVDs+FDs) can be relaxed to a simple linear inequality with a factor at most quadratic in the number of variables; when the consequent is an FD, the factor can be reduced to 1. Second, we prove that there exists an implication between CIs that does not admit any relaxation; however, we prove that every implication between CIs relaxes "in the limit". Finally, we show that the implication problem for differential constraints in market basket analysis also admits a relaxation with a factor equal to 1. Our results recover, and sometimes extend, several previously known results about the implication problem: implication of MVDs can be checked by considering only 2-tuple relations, and the implication of differential constraints for frequent item sets can be checked by considering only databases containing a single transaction

The 4-particle hydrogen-antihydrogen system revisited: twofold Hamiltonian symmetry and natural atom antihydrogen

Modern ab initio treatments of H-Hbar systems are inconsistent with the logic behind algebraic Hamiltonians H(+-)=H(0)+/-deltaH for charge-symmetrical and charge-asymmetrical 4 unit charge systems like H(2) and HHbar. Since these 2 Hamiltonians are mutually exclusive, only the attractive one can apply for stable natural molecular H(2). A wrong choice leads to problems with antiatom Hbar. In line with earlier results on band and line spectra, we now prove that HL chose the wrong Hamiltonian for H(2). Their theory explains the stability of attractive system H(2) with a repulsive Hamiltonian instead of with the attractive one, representative for charge-asymmetrical system HHbar. A new second order symmetry effect is detected. Repulsive HL Hamiltonian H(+) applies at long range but at the critical distance, attractive charge-inverted Hamiltonian H(-)takes over and leads to bond H(2) but in reality, HHbar, for which we give an analytical proof. Another wrong asymptote choice in the past also applies for atomic antihydrogen Hbar, which has hidden the Mexican hat potential for natural hydrogen. This generic solution removes most problems, physicists and chemists experience with atomic Hbar and molecular HHbar, including the problem with antimatter in the Universe.Comment: at the instituional UGent archive, 37 pag, 10 fig, tabb, version as submitted, abstract shortene

Characterizations of User Web Revisit Behavior

In this article we update and extend on earlier long-term studies on user's page revisit behavior. Revisits ar

Research ethics and participatory research in an interdisciplinary technology-enhanced learning project

This account identifies some of the tensions that became apparent in a large interdisciplinary technology-enhanced learning project as its members attempted to maintain their commitment to responsive, participatory research and development in naturalistic research settings while also ‘enacting’ these commitments in formal research review processes. It discusses how these review processes were accompanied by a commitment to continuing discussion and elaboration across an extended research team and to a view of ethical practice as an aspect of phronesis or ‘practical wisdom’ which demands understanding of specific situations and reference to prior experience. In this respect the interdisciplinary nature of the project allows the diverse experience of the project team to be brought into play, with ethical issues a joint point of focus for continuing interdisciplinary discours