Answering Conjunctive Queries under Updates

We consider the task of enumerating and counting answers to $k$-ary conjunctive queries against relational databases that may be updated by inserting or deleting tuples. We exhibit a new notion of q-hierarchical conjunctive queries and show that these can be maintained efficiently in the following sense. During a linear time preprocessing phase, we can build a data structure that enables constant delay enumeration of the query results; and when the database is updated, we can update the data structure and restart the enumeration phase within constant time. For the special case of self-join free conjunctive queries we obtain a dichotomy: if a query is not q-hierarchical, then query enumeration with sublinear$^\ast$ delay and sublinear update time (and arbitrary preprocessing time) is impossible. For answering Boolean conjunctive queries and for the more general problem of counting the number of solutions of k-ary queries we obtain complete dichotomies: if the query's homomorphic core is q-hierarchical, then size of the the query result can be computed in linear time and maintained with constant update time. Otherwise, the size of the query result cannot be maintained with sublinear update time. All our lower bounds rely on the OMv-conjecture, a conjecture on the hardness of online matrix-vector multiplication that has recently emerged in the field of fine-grained complexity to characterise the hardness of dynamic problems. The lower bound for the counting problem additionally relies on the orthogonal vectors conjecture, which in turn is implied by the strong exponential time hypothesis. $^\ast)$ By sublinear we mean $O(n^{1-\varepsilon})$ for some $\varepsilon>0$, where $n$ is the size of the active domain of the current database

On the speed of constraint propagation and the time complexity of arc consistency testing

Establishing arc consistency on two relational structures is one of the most popular heuristics for the constraint satisfaction problem. We aim at determining the time complexity of arc consistency testing. The input structures $G$ and $H$ can be supposed to be connected colored graphs, as the general problem reduces to this particular case. We first observe the upper bound $O(e(G)v(H)+v(G)e(H))$, which implies the bound $O(e(G)e(H))$ in terms of the number of edges and the bound $O((v(G)+v(H))^3)$ in terms of the number of vertices. We then show that both bounds are tight up to a constant factor as long as an arc consistency algorithm is based on constraint propagation (like any algorithm currently known). Our argument for the lower bounds is based on examples of slow constraint propagation. We measure the speed of constraint propagation observed on a pair $G,H$ by the size of a proof, in a natural combinatorial proof system, that Spoiler wins the existential 2-pebble game on $G,H$. The proof size is bounded from below by the game length $D(G,H)$, and a crucial ingredient of our analysis is the existence of $G,H$ with $D(G,H)=\Omega(v(G)v(H))$. We find one such example among old benchmark instances for the arc consistency problem and also suggest a new, different construction.Comment: 19 pages, 5 figure

Graphs Identified by Logics with Counting

We classify graphs and, more generally, finite relational structures that are identified by C2, that is, two-variable first-order logic with counting. Using this classification, we show that it can be decided in almost linear time whether a structure is identified by C2. Our classification implies that for every graph identified by this logic, all vertex-colored versions of it are also identified. A similar statement is true for finite relational structures. We provide constructions that solve the inversion problem for finite structures in linear time. This problem has previously been shown to be polynomial time solvable by Martin Otto. For graphs, we conclude that every C2-equivalence class contains a graph whose orbits are exactly the classes of the C2-partition of its vertex set and which has a single automorphism witnessing this fact. For general k, we show that such statements are not true by providing examples of graphs of size linear in k which are identified by C3 but for which the orbit partition is strictly finer than the Ck-partition. We also provide identified graphs which have vertex-colored versions that are not identified by Ck.Comment: 33 pages, 8 Figure

Reduction Techniques for Graph Isomorphism in the Context of Width Parameters

We study the parameterized complexity of the graph isomorphism problem when parameterized by width parameters related to tree decompositions. We apply the following technique to obtain fixed-parameter tractability for such parameters. We first compute an isomorphism invariant set of potential bags for a decomposition and then apply a restricted version of the Weisfeiler-Lehman algorithm to solve isomorphism. With this we show fixed-parameter tractability for several parameters and provide a unified explanation for various isomorphism results concerned with parameters related to tree decompositions. As a possibly first step towards intractability results for parameterized graph isomorphism we develop an fpt Turing-reduction from strong tree width to the a priori unrelated parameter maximum degree.Comment: 23 pages, 4 figure

Peptide Bond Distortions from Planarity: New Insights from Quantum Mechanical Calculations and Peptide/Protein Crystal Structures

By combining quantum-mechanical analysis and statistical survey of peptide/protein structure databases we here report a thorough investigation of the conformational dependence of the geometry of peptide bond, the basic element of protein structures. Different peptide model systems have been studied by an integrated quantum mechanical approach, employing DFT, MP2 and CCSD(T) calculations, both in aqueous solution and in the gas phase. Also in absence of inter-residue interactions, small distortions from the planarity are more a rule than an exception, and they are mainly determined by the backbone ψ dihedral angle. These indications are fully corroborated by a statistical survey of accurate protein/peptide structures. Orbital analysis shows that orbital interactions between the σ system of Cα substituents and the π system of the amide bond are crucial for the modulation of peptide bond distortions. Our study thus indicates that, although long-range inter-molecular interactions can obviously affect the peptide planarity, their influence is statistically averaged. Therefore, the variability of peptide bond geometry in proteins is remarkably reproduced by extremely simplified systems since local factors are the main driving force of these observed trends. The implications of the present findings for protein structure determination, validation and prediction are also discussed

The nucleotide addition cycle of RNA polymerase is controlled by two molecular hinges in the Bridge Helix domain

Abstract Background Cellular RNA polymerases (RNAPs) are complex molecular machines that combine catalysis with concerted conformational changes in the active center. Previous work showed that kinking of a hinge region near the C-terminus of the Bridge Helix (BH-HC) plays a critical role in controlling the catalytic rate. Results Here, new evidence for the existence of an additional hinge region in the amino-terminal portion of the Bridge Helix domain (BH-HN) is presented. The nanomechanical properties of BH-HN emerge as a direct consequence of the highly conserved primary amino acid sequence. Mutations that are predicted to influence its flexibility cause corresponding changes in the rate of the nucleotide addition cycle (NAC). BH-HN displays functional properties that are distinct from BH-HC, suggesting that conformational changes in the Bridge Helix control the NAC via two independent mechanisms. Conclusions The properties of two distinct molecular hinges in the Bridge Helix of RNAP determine the functional contribution of this domain to key stages of the NAC by coordinating conformational changes in surrounding domains.</p

Scenario Analysis as a Tool for Informing the Design of Behaviour Change Interventions

This article presents the design process behind the specification of a behaviour change intervention method to promote energy saving. The amount of energy used for food preparation is highly influenced by people’s behaviours. A user-centred design approach based on scenario analysis was applied to provide understanding of context of use and specification of user requirements. This knowledge was applied to the design of behaviour change interventions to motivate sustainable behaviours

Atherogenesis and plaque rupture, surface/interface-related phenomena

In atherogenesis, free oxygen radicals cause a lipid peroxidation of apoB100-containing lipoproteins in the blood, at the blood–endothelium-interface and in the subendothelial space. These lipoproteins easily aggregate, bind to their receptor heparan sulfate proteoglycan and calcify to arteriosclerotic nanoplaques (ternary complexes). Nanoplaque formation was measured by ellipsometry, both in vitro on an HS-PG coated hydrophobic silica surface and also in vivo on living human coronary endothelial cells, which had overgrown the silica surface. Reversely, we show with the same techniques that, in dependence on the degree of peroxidation and epitope in concern, oxLDL attacks its molecular receptor and thus can induce degradation of arteriosclerotic plaques and, in a combined action with inflammatory processes, even a plaque rupture. In order to delay or stop this process, cytokines circulating in the blood such as TNFα and TGFβ upregulate PML-NB especially in the vulnerable shoulder region of the plaque. PML-NB influences via two transcription factors, CIITA and NFκB, the collagen and proteoglycan synthesis both negatively and positively. We could prove that the purely negative effect of CIITA does not play any role, while the altogether positive effect of NFκB predominates. NFκB is inhibited with the help of the transcription mediator SMAD4 within this molecular feedback control circuit; simultaneously, NFκB inhibits the collagen and proteoglycan synthesis in the fibrous cap of the plaque. This double check (disinhibition) causes a stabilization of the fibrous cap through a specially strong collagen and proteoglycan production, which in addition is supported by circulating TGFβ. TGFβ furthers also calcification, so that fibrous cap tensile strength and resistance to shear stress are imparted. This way, a plaque rupture can possibly be averted