Collisions and Mergers of Disk Galaxies: Hydrodynamics of Star Forming Gas

We summarize the results of numerical simulations of colliding gas-rich disk galaxies in which the impact velocity is set parallel to the spin axes of the two galaxies. The effects of varying the impact speed are studied with particular attention to the resulting gaseous structures and shockwave patterns, and the time needed to produce these structures. The simulations employ an N-body treatment of the stars and dark matter, together with an SPH treatment of the gas, in which all components of the models are gravitationally active. The results indicate that for such impact geometries, collisions can lead to the very rapid formation of a central, rapidly rotating, dense gas disk, and that in all cases extensive star formation is predicted by the very high gas densities and prevalence of shocks, both in the nucleus and out in the galactic disks. As the dense nucleus is forming, gas and stars are dispersed over very large volumes, and only fall back towards the nucleus over long times. In the case of low impact velocities, this takes an order of magnitude more time than that needed for the formation of a dense nucleus.Comment: To be published in Proceedings of 'The Evolution of Galaxies III- From simple approaches to self-consistent models,' held in Kiel, Germany, July 2002, Astrophysics and Space Science (Kluwer), vol. 284, p. 479, 200

Push-Pull Block Puzzles are Hard

This paper proves that push-pull block puzzles in 3D are PSPACE-complete to solve, and push-pull block puzzles in 2D with thin walls are NP-hard to solve, settling an open question by Zubaran and Ritt. Push-pull block puzzles are a type of recreational motion planning problem, similar to Sokoban, that involve moving a `robot' on a square grid with $1 \times 1$ obstacles. The obstacles cannot be traversed by the robot, but some can be pushed and pulled by the robot into adjacent squares. Thin walls prevent movement between two adjacent squares. This work follows in a long line of algorithms and complexity work on similar problems. The 2D push-pull block puzzle shows up in the video games Pukoban as well as The Legend of Zelda: A Link to the Past, giving another proof of hardness for the latter. This variant of block-pushing puzzles is of particular interest because of its connections to reversibility, since any action (e.g., push or pull) can be inverted by another valid action (e.g., pull or push).Comment: Full version of CIAC 2017 paper. 17 page

On the Complexity of an Unregulated Traffic Crossing

The steady development of motor vehicle technology will enable cars of the near future to assume an ever increasing role in the decision making and control of the vehicle itself. In the foreseeable future, cars will have the ability to communicate with one another in order to better coordinate their motion. This motivates a number of interesting algorithmic problems. One of the most challenging aspects of traffic coordination involves traffic intersections. In this paper we consider two formulations of a simple and fundamental geometric optimization problem involving coordinating the motion of vehicles through an intersection. We are given a set of $n$ vehicles in the plane, each modeled as a unit length line segment that moves monotonically, either horizontally or vertically, subject to a maximum speed limit. Each vehicle is described by a start and goal position and a start time and deadline. The question is whether, subject to the speed limit, there exists a collision-free motion plan so that each vehicle travels from its start position to its goal position prior to its deadline. We present three results. We begin by showing that this problem is NP-complete with a reduction from 3-SAT. Second, we consider a constrained version in which cars traveling horizontally can alter their speeds while cars traveling vertically cannot. We present a simple algorithm that solves this problem in $O(n \log n)$ time. Finally, we provide a solution to the discrete version of the problem and prove its asymptotic optimality in terms of the maximum delay of a vehicle

The complexity of dominating set reconfiguration

Suppose that we are given two dominating sets $D_s$ and $D_t$ of a graph $G$ whose cardinalities are at most a given threshold $k$. Then, we are asked whether there exists a sequence of dominating sets of $G$ between $D_s$ and $D_t$ such that each dominating set in the sequence is of cardinality at most $k$ and can be obtained from the previous one by either adding or deleting exactly one vertex. This problem is known to be PSPACE-complete in general. In this paper, we study the complexity of this decision problem from the viewpoint of graph classes. We first prove that the problem remains PSPACE-complete even for planar graphs, bounded bandwidth graphs, split graphs, and bipartite graphs. We then give a general scheme to construct linear-time algorithms and show that the problem can be solved in linear time for cographs, trees, and interval graphs. Furthermore, for these tractable cases, we can obtain a desired sequence such that the number of additions and deletions is bounded by $O(n)$, where $n$ is the number of vertices in the input graph

Efficient Multi-Robot Motion Planning for Unlabeled Discs in Simple Polygons

We consider the following motion-planning problem: we are given $m$ unit discs in a simple polygon with $n$ vertices, each at their own start position, and we want to move the discs to a given set of $m$ target positions. Contrary to the standard (labeled) version of the problem, each disc is allowed to be moved to any target position, as long as in the end every target position is occupied. We show that this unlabeled version of the problem can be solved in $O(n\log n+mn+m^2)$ time, assuming that the start and target positions are at least some minimal distance from each other. This is in sharp contrast to the standard (labeled) and more general multi-robot motion-planning problem for discs moving in a simple polygon, which is known to be strongly NP-hard

Fixed-Parameter Tractability of Token Jumping on Planar Graphs

Suppose that we are given two independent sets $I_0$ and $I_r$ of a graph such that $|I_0| = |I_r|$, and imagine that a token is placed on each vertex in $I_0$. The token jumping problem is to determine whether there exists a sequence of independent sets which transforms $I_0$ into $I_r$ so that each independent set in the sequence results from the previous one by moving exactly one token to another vertex. This problem is known to be PSPACE-complete even for planar graphs of maximum degree three, and W[1]-hard for general graphs when parameterized by the number of tokens. In this paper, we present a fixed-parameter algorithm for the token jumping problem on planar graphs, where the parameter is only the number of tokens. Furthermore, the algorithm can be modified so that it finds a shortest sequence for a yes-instance. The same scheme of the algorithms can be applied to a wider class of graphs, $K_{3,t}$-free graphs for any fixed integer $t \ge 3$, and it yields fixed-parameter algorithms

Independent Set Reconfiguration in Cographs

We study the following independent set reconfiguration problem, called TAR-Reachability: given two independent sets $I$ and $J$ of a graph $G$, both of size at least $k$, is it possible to transform $I$ into $J$ by adding and removing vertices one-by-one, while maintaining an independent set of size at least $k$ throughout? This problem is known to be PSPACE-hard in general. For the case that $G$ is a cograph (i.e. $P_4$-free graph) on $n$ vertices, we show that it can be solved in time $O(n^2)$, and that the length of a shortest reconfiguration sequence from $I$ to $J$ is bounded by $4n-2k$, if such a sequence exists. More generally, we show that if $X$ is a graph class for which (i) TAR-Reachability can be solved efficiently, (ii) maximum independent sets can be computed efficiently, and which satisfies a certain additional property, then the problem can be solved efficiently for any graph that can be obtained from a collection of graphs in $X$ using disjoint union and complete join operations. Chordal graphs are given as an example of such a class $X$

Trials we cannot trust: investigating their impact on systematic reviews and clinical guidelines in spinal pain

Data Sharing Statement: The full data underpinning the analysis of the impact of studies on published meta-analyses is available via Figshare: 10.17633/rd.brunel.21427995 .Supplementary material is available online at https://www.jpain.org/article/S1526-5900(23)00467-4/fulltext#supplementaryMaterial .Copyright © 2023 The Author(s). We previously conducted an exploration of the trustworthiness of a group of clinical trials of cognitive behavioural therapy (CBT) and exercise in spinal pain. We identified multiple concerns in eight trials, judging them untrustworthy. In this study, we systematically explored the impact of these trials (“index trials”) on results, conclusions and recommendations of systematic reviews and clinical practice guidelines (CPGs). We conducted forward citation tracking using Google Scholar and the citationchaser tool, searched the Guidelines International Network (GIN) library and National Institute of Health and Care Excellence (NICE) archive to June 2022 to identify systematic reviews and CPGs. We explored how index trials impacted their findings. Where reviews presented meta-analyses, we extracted or conducted sensitivity analyses for the outcomes pain and disability, to explore how exclusion of index trials affected effect estimates. We developed and applied an ’Impact Index’ to categorise the extent to which index studies impacted their results. We included 32 unique reviews and 10 CPGs. None directly raised concerns regarding the veracity of the trials. Across meta-analyses (55 comparisons), removal of index trials reduced effect sizes by a median 58% (IQR 40 to 74). 85% of comparisons were classified as highly, 3% as moderately, and 11% as minimally impacted. Nine out 10 reviews conducting narrative synthesis drew positive conclusions regarding the intervention tested. Nine out of 10 CPGs made positive recommendations for the intervention(s) evaluated. This cohort of trials, with concerns regarding trustworthiness, has substantially impacted the results of systematic reviews and guideline recommendations. Perspective: We found that a group of trials of CBT for spinal pain with concerns relating to their trustworthiness have had substantial impacts on the analyses and conclusions of systematic reviews and clinical practice guidelines. This highlights the need for a greater focus on the trustworthiness of studies in evidence appraisal. Pre-registration: Our protocol was pre-registered on the Open Science Framework: https://osf.io/m92ax/This study was not supported by any external funding

Reconfiguration of Cliques in a Graph

We study reconfiguration problems for cliques in a graph, which determine whether there exists a sequence of cliques that transforms a given clique into another one in a step-by-step fashion. As one step of a transformation, we consider three different types of rules, which are defined and studied in reconfiguration problems for independent sets. We first prove that all the three rules are equivalent in cliques. We then show that the problems are PSPACE-complete for perfect graphs, while we give polynomial-time algorithms for several classes of graphs, such as even-hole-free graphs and cographs. In particular, the shortest variant, which computes the shortest length of a desired sequence, can be solved in polynomial time for chordal graphs, bipartite graphs, planar graphs, and bounded treewidth graphs

Maternal psychological distress in primary care and association with child behavioural outcomes at age three

Observational studies indicate children whose mothers have poor mental health are at increased risk of socio-emotional behavioural difficulties, but it is unknown whether these outcomes vary by the mothers’ mental health recognition and treatment status. To examine this question, we analysed linked longitudinal primary care and research data from 1078 women enrolled in the Born in Bradford cohort. A latent class analysis of treatment status and self-reported distress broadly categorised women as (a) not having a common mental disorder (CMD) that persisted through pregnancy and the first 2 years after delivery (N = 756, 70.1 %), (b) treated for CMD (N = 67, 6.2 %), or (c) untreated (N = 255, 23.7 %). Compared to children of mothers without CMD, 3-year-old children with mothers classified as having untreated CMD had higher standardised factor scores on the Strengths and Difficulties Questionnaire (d = 0.32), as did children with mothers classified as having treated CMD (d = 0.27). Results were only slightly attenuated in adjusted analyses. Children of mothers with CMD may be at risk for socio-emotional and behavioural difficulties. The development of effective treatments for CMD needs to be balanced by greater attempts to identify and treat women. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1007/s00787-015-0777-2) contains supplementary material, which is available to authorized users