Polynomial Kernels for Weighted Problems

Kernelization is a formalization of efficient preprocessing for NP-hard problems using the framework of parameterized complexity. Among open problems in kernelization it has been asked many times whether there are deterministic polynomial kernelizations for Subset Sum and Knapsack when parameterized by the number $n$ of items. We answer both questions affirmatively by using an algorithm for compressing numbers due to Frank and Tardos (Combinatorica 1987). This result had been first used by Marx and V\'egh (ICALP 2013) in the context of kernelization. We further illustrate its applicability by giving polynomial kernels also for weighted versions of several well-studied parameterized problems. Furthermore, when parameterized by the different item sizes we obtain a polynomial kernelization for Subset Sum and an exponential kernelization for Knapsack. Finally, we also obtain kernelization results for polynomial integer programs

Advancing Workplace Diversity Through the Culturally Responsive Teamwork Framework.

Purpose Diversification of the profession is an important element of combating racism, bias, and prejudice in the speech-language pathology workforce at national and systemic levels. However, national and systemic change needs to be combined with equipping individual speech-language pathologists to adapt to the challenges that they face to engaging in culturally responsive practice. This paper presents four interacting levels of practice within the Culturally Responsive Teamwork Framework (CRTF): (a) intrapersonal practices, (b) interpersonal practices, (c) intraprofessional practices, and (d) the interprofessional practices. Conclusion CRTF is a practical, strengths-based framework that draws on international research and expertise to expand personal and professional practice and describe critical behaviors within the workplace that can be used to promote principles of evidence-based practice and social justice, especially when working with people from nondominant cultural or linguistic groups

Developing interventions to change recycling behaviors: A case study of applying behavioral science

The Theoretical Domains Framework (TDF) and the Behavior Change Wheel (BCW) are frameworks that can be used to develop recycling interventions. The aim of this study was to demonstrate the utility of these frameworks for developing recycling interventions. 20 semistructured interviews with university building users were analyzed using the TDF and BCW. Environmental context and resources, beliefs about consequences, knowledge, and intention were identified as the key theoretical domains influencing recycling behaviors. The BCW was used to develop recommendations for intervention. This research is the first case study to demonstrate how the TDF and the BCW can be used to develop recycling interventions

Frequency and duration of physical activity bouts in school-aged children: A comparison within and between days

Understanding how physical activity (PA) patterns vary within and between days may guide PA promotion in young people. We aimed to 1) describe and compare the frequency (bouts/day) and duration (min/bout) of bouts of moderate-to-vigorous intensity PA (MVPA) on weekdays vs. weekends and in-school vs. out-of-school, and 2) assess associations of bout frequency and duration in these time-segments with overall PA. We used cross-sectional accelerometer data from 2737 children (aged 6-19 years) in the United States National Health and Nutrition Examination Survey (NHANES) 2003-2006. A bout was defined as MVPA (≥ 2000 counts per minute [cpm]) lasting ≥ 3 min. Adjusted Wald tests were used to assess differences in bout characteristics between time-segments. Linear regression was used to examine the association of time-segment specific bout characteristics with daily minutes of MVPA and PA volume (average cpm). Bout frequency was higher on weekdays than weekends (median [IQR] 4.3 [2.2-7.2] vs. 3.0 [1.0-6.5] bouts/day, p < 0.001); however, bout duration did not differ (4.7 [4.0-5.7] vs. 4.5 [3.7-5.8] min/bout, p = 0.33). More bouts were accumulated out-of-school compared with in-school (2.2 [1.0-4.0] vs. 1.8 [0.8-3.2] bouts/day, p < 0.001), but bout duration was similar (4.7 [3.8-5.8] vs. 4.5 [3.8-5.7] min/bout, p = 0.158). For all time-segments, the frequency and duration of bouts of MVPA were independently and positively associated with overall MVPA and PA volume. In conclusion, the characteristics of children's PA vary within and between days; accounting for this in intervention design may improve future interventions. However, increasing bout frequency or duration in any time-segment may be beneficial for overall PA.This work was supported by the Medical Research Council [Unit Programme numbers MC_UU_12015/7 and MC_UU_12015/3] and the Centre for Diet and Activity Research (CEDAR), a UKCRC Public Health Research: Centre of Excellence. Funding from the British Heart Foundation, Economic and Social Research Council, Medical Research Council, the National Institute for Health Research, and the Wellcome Trust, under the auspices of the UK Clinical Research Collaboration (RES-590-28-0002), is gratefully acknowledged

Skewed contributions of individual trees to indirect nature experiences

This is the author accepted manuscript. Final version available from Elsevier via the DOI in this record.Exposure to nature is associated with a broad range of benefits to human health. Whilst there has been exploration of how these experiences vary amongst people, the converse – how different individual organisms contribute to human nature experiences – has largely been overlooked. The most common way that people experience nature occurs indirectly, when they are in a room with a natural view. Here, we estimate variation in how individual trees provide indirect nature experiences in an urban human population. As a proxy for its contribution towards indirect nature experiences, within an extended urban area in southern England, UK (n = 612,920) we calculated the number of buildings with line of sight to each tree. We then modelled each tree’s contribution towards these experiences against potential predictors, namely tree height, land ownership, social deprivation, while controlling for human population density. We demonstrate that a small number of trees contribute disproportionately towards indirect nature experiences, with individual trees in socio-economically deprived high density housing falling within the viewscape of significantly more buildings. Further, trees in private gardens were generally more important for providing indirect nature experiences than those in public green spaces. This novel study demonstrates the skewed contribution of different organisms to human population indirect nature experiences. This approach can be applied more broadly to understand how individual organisms provide indirect, incidental and intentional nature experiences. Understanding the ecology behind human nature experiences is an important step towards linking urban design and policy for maximising the health benefits from nature.Natural Environment Research Council (NERC

General graviton exchange graph for four point functions in the AdS/CFT correspondence

In this note we explicitly compute the graviton exchange graph for scalar fields with arbitrary conformal dimension \Delta in arbitrary spacetime dimension d. This results in an analytical function in \Delta as well as in d.Comment: 14 pages, 2 figure

Compact Labelings For Efficient First-Order Model-Checking

We consider graph properties that can be checked from labels, i.e., bit sequences, of logarithmic length attached to vertices. We prove that there exists such a labeling for checking a first-order formula with free set variables in the graphs of every class that is \emph{nicely locally cwd-decomposable}. This notion generalizes that of a \emph{nicely locally tree-decomposable} class. The graphs of such classes can be covered by graphs of bounded \emph{clique-width} with limited overlaps. We also consider such labelings for \emph{bounded} first-order formulas on graph classes of \emph{bounded expansion}. Some of these results are extended to counting queries

Crossing Paths with Hans Bodlaender:A Personal View on Cross-Composition for Sparsification Lower Bounds

On the occasion of Hans Bodlaender’s 60th birthday, I give a personal account of our history and work together on the technique of cross-composition for kernelization lower bounds. I present several simple new proofs for polynomial kernelization lower bounds using cross-composition, interlaced with personal anecdotes about my time as Hans’ PhD student at Utrecht University. Concretely, I will prove that Vertex Cover, Feedback Vertex Set, and the H-Factor problem for every graph H that has a connected component of at least three vertices, do not admit kernels of (formula presented) bits when parameterized by the number of vertices n for any (formula presented), unless (formula presented). These lower bounds are obtained by elementary gadget constructions, in particular avoiding the use of the Packing Lemma by Dell and van Melkebeek.</p

The Minimum Shared Edges Problem on Grid-like Graphs

We study the NP-hard Minimum Shared Edges (MSE) problem on graphs: decide whether it is possible to route $p$ paths from a start vertex to a target vertex in a given graph while using at most $k$ edges more than once. We show that MSE can be decided on bounded (i.e. finite) grids in linear time when both dimensions are either small or large compared to the number $p$ of paths. On the contrary, we show that MSE remains NP-hard on subgraphs of bounded grids. Finally, we study MSE from a parametrised complexity point of view. It is known that MSE is fixed-parameter tractable with respect to the number $p$ of paths. We show that, under standard complexity-theoretical assumptions, the problem parametrised by the combined parameter $k$, $p$, maximum degree, diameter, and treewidth does not admit a polynomial-size problem kernel, even when restricted to planar graphs