Essential Constraints of Edge-Constrained Proximity Graphs

Given a plane forest $F = (V, E)$ of $|V| = n$ points, we find the minimum set $S \subseteq E$ of edges such that the edge-constrained minimum spanning tree over the set $V$ of vertices and the set $S$ of constraints contains $F$. We present an $O(n \log n )$-time algorithm that solves this problem. We generalize this to other proximity graphs in the constraint setting, such as the relative neighbourhood graph, Gabriel graph, $\beta$-skeleton and Delaunay triangulation. We present an algorithm that identifies the minimum set $S\subseteq E$ of edges of a given plane graph $I=(V,E)$ such that $I \subseteq CG_\beta(V, S)$ for $1 \leq \beta \leq 2$, where $CG_\beta(V, S)$ is the constraint $\beta$-skeleton over the set $V$ of vertices and the set $S$ of constraints. The running time of our algorithm is $O(n)$, provided that the constrained Delaunay triangulation of $I$ is given.Comment: 24 pages, 22 figures. A preliminary version of this paper appeared in the Proceedings of 27th International Workshop, IWOCA 2016, Helsinki, Finland. It was published by Springer in the Lecture Notes in Computer Science (LNCS) serie

The complexity of theorem proving in circumscription and minimal entailment

We provide the first comprehensive proof-complexity analysis of different proof systems for propositional circumscription. In particular, we investigate two sequent-style calculi: MLK defined by Olivetti [28] and CIRC introduced by Bonatti and Olivetti [8], and the tableaux calculus NTAB suggested by Niemelä [26]. In our analysis we obtain exponential lower bounds for the proof size in NTAB and CIRC and show a polynomial simulation of CIRC by MLK. This yields a chain NTAB < CIRC < MLK of proof systems for circumscription of strictly increasing strength with respect to lengths of proofs

On unification of QBF resolution-based calculi

Several calculi for quantified Boolean formulas (QBFs) exist, but relations between them are not yet fully understood. This paper defines a novel calculus, which is resolution-based and enables unification of the principal existing resolution-based QBF calculi, namely Q-resolution, long-distance Q-resolution and the expansion-based calculus Exp+Res. All these calculi play an important role in QBF solving. This paper shows simulation results for the new calculus and some of its variants. Further, we demonstrate how to obtain winning strategies for the universal player from proofs in the calculus. We believe that this new proof system provides an underpinning necessary for formal analysis of modern QBF solvers. © 2014 Springer-Verlag Berlin Heidelberg

Feasible Interpolation for QBF Resolution Calculi

In sharp contrast to classical proof complexity we are currently short of lower bound techniques for QBF proof systems. In this paper we establish the feasible interpolation technique for all resolution-based QBF systems, whether modelling CDCL or expansion-based solving. This both provides the first general lower bound method for QBF proof systems as well as largely extends the scope of classical feasible interpolation. We apply our technique to obtain new exponential lower bounds to all resolution-based QBF systems for a new class of QBF formulas based on the clique problem. Finally, we show how feasible interpolation relates to the recently established lower bound method based on strategy extraction

Understanding Cutting Planes for QBFs

We define a cutting planes system CP+8red for quantified Boolean formulas (QBF) and analyse the proof-theoretic strength of this new calculus. While in the propositional case, Cutting Planes is of intermediate strength between resolution and Frege, our findings here show that the situation in QBF is slightly more complex: while CP+8red is again weaker than QBF Frege and stronger than the CDCL-based QBF resolution systems Q-Res and QU-Res, it turns out to be incomparable to even the weakest expansion-based QBF resolution system 8Exp+Res. Technically, our results establish the effectiveness of two lower boun

Are Short Proofs Narrow? QBF Resolution is not so Simple

The ground-breaking paper “Short Proofs Are Narrow -- Resolution Made Simple” by Ben-Sasson and Wigderson (J. ACM 2001) introduces what is today arguably the main technique to obtain resolution lower bounds: to show a lower bound for the width of proofs. Another important measure for resolution is space, and in their fundamental work, Atserias and Dalmau (J. Comput. Syst. Sci. 2008) show that lower bounds for space again can be obtained via lower bounds for width. In this article, we assess whether similar techniques are effective for resolution calculi for quantified Boolean formulas (QBFs). There are a number of different QBF resolution calculi like Q-resolution (the classical extension of propositional resolution to QBF) and the more recent calculi ∀Exp+Res and IR-calc. For these systems, a mixed picture emerges. Our main results show that the relations both between size and width and between space and width drastically fail in Q-resolution, even in its weaker tree-like version. On the other hand, we obtain positive results for the expansion-based resolution systems ∀Exp+Res and IR-calc, however, only in the weak tree-like models. Technically, our negative results rely on showing width lower bounds together with simultaneous upper bounds for size and space. For our positive results, we exhibit space and width-preserving simulations between QBF resolution calculi

The potential of general practice to support young people who self-harm: a narrative review

Background Self-harm in young people is a growing public health concern. Young people commonly present to their GP for help with self-harm, and thus general practice may be a key setting to support young people who have self-harmed. Aim To examine the potential of general practice to support young people aged 10–25 years who have harmed themselves. Design & setting A narrative review of published and grey literature. Method The Scale for the Assessment of Narrative Review Articles (SANRA) was used to guide a narrative review to examine the potential of general practice to support young people who have self-harmed. The evidence is presented textually. Results The included evidence showed that GPs have a key role in supporting young people, and they sometimes relied on gut feeling when handling uncertainty on how to help young people who had self-harmed. Young people described the importance of initial clinician responses after disclosing self-harm, and if they were perceived to be negative, the self-harm could become worse. Conclusion In context of the evidence included, this review found that general practice is a key setting for the identification and management of self-harm in young people; but improvements are needed to enhance general practice care for young people to fulfil its potential

A Galerkin boundary element method for high frequency scattering by convex polygons

In this paper we consider the problem of time-harmonic acoustic scattering in two dimensions by convex polygons. Standard boundary or finite element methods for acoustic scattering problems have a computational cost that grows at least linearly as a function of the frequency of the incident wave. Here we present a novel Galerkin boundary element method, which uses an approximation space consisting of the products of plane waves with piecewise polynomials supported on a graded mesh, with smaller elements closer to the corners of the polygon. We prove that the best approximation from the approximation space requires a number of degrees of freedom to achieve a prescribed level of accuracy that grows only logarithmically as a function of the frequency. Numerical results demonstrate the same logarithmic dependence on the frequency for the Galerkin method solution. Our boundary element method is a discretization of a well-known second kind combined-layer-potential integral equation. We provide a proof that this equation and its adjoint are well-posed and equivalent to the boundary value problem in a Sobolev space setting for general Lipschitz domains

Photocatalytic removal of cyclohexane on visible light-driven gallium oxide/carbon nitride composites prepared by impregnation

Carbon nitride is a material of interest for photocatalytic reactions due to its catalytic and visible light absorption properties. However, its photocatalytic activity is still low. Hence, modifications must be carried out to improve the photocatalytic activity of carbon nitride. In this work, a series of gallium oxide/carbon nitride composites with various gallium to carbon ratios (Ga/C = 1-50 mol%) was prepared by impregnation method for removal of cyclohexane under visible light irradiation for the first time. The successful preparation of gallium oxide/carbon nitride composites was supported by several characterization techniques. Xray diffraction (XRD) patterns and diffuse reflectance UV-visible (DR UV-vis) spectra revealed that the increased Ga/C ratio resulted in the increased formation of Ga2O3. Furthermore, all the prepared composite samples also showed visible light absorption up to about 430 nm. In the photocatalytic removal of cyclohexane under 6 h of visible light irradiation, sample with low loading of 1 mol% Ga/C improved the photocatalytic activity of carbon nitride for two times. The high activity obtained on the gallium oxide (1 mol%)/carbon nitride composite clearly suggested the presence of synergic effect between small amount of gallium oxide and carbon nitride when they were combined. This study showed that a visible light-driven gallium oxide/carbon nitride composite could be prepared by impregnating a small amount of gallium oxide on carbon nitride and the composite is a potential photocatalyst for removal of cyclohexane under visible light irradiation

Parallel Search with no Coordination

We consider a parallel version of a classical Bayesian search problem. $k$ agents are looking for a treasure that is placed in one of the boxes indexed by $\mathbb{N}^+$ according to a known distribution $p$. The aim is to minimize the expected time until the first agent finds it. Searchers run in parallel where at each time step each searcher can "peek" into a box. A basic family of algorithms which are inherently robust is \emph{non-coordinating} algorithms. Such algorithms act independently at each searcher, differing only by their probabilistic choices. We are interested in the price incurred by employing such algorithms when compared with the case of full coordination. We first show that there exists a non-coordination algorithm, that knowing only the relative likelihood of boxes according to $p$, has expected running time of at most $10+4(1+\frac{1}{k})^2 T$, where $T$ is the expected running time of the best fully coordinated algorithm. This result is obtained by applying a refined version of the main algorithm suggested by Fraigniaud, Korman and Rodeh in STOC'16, which was designed for the context of linear parallel search.We then describe an optimal non-coordinating algorithm for the case where the distribution $p$ is known. The running time of this algorithm is difficult to analyse in general, but we calculate it for several examples. In the case where $p$ is uniform over a finite set of boxes, then the algorithm just checks boxes uniformly at random among all non-checked boxes and is essentially $2$ times worse than the coordinating algorithm.We also show simple algorithms for Pareto distributions over $M$ boxes. That is, in the case where $p(x) \sim 1/x^b$ for $0< b < 1$, we suggest the following algorithm: at step $t$ choose uniformly from the boxes unchecked in ${1, . . . ,min(M, \lfloor t/\sigma\rfloor)}$, where $\sigma = b/(b + k - 1)$. It turns out this algorithm is asymptotically optimal, and runs about $2+b$ times worse than the case of full coordination