NP-Completeness Results for Graph Burning on Geometric Graphs

Graph burning runs on discrete time steps. The aim is to burn all the vertices in a given graph in the least number of time steps. This number is known to be the burning number of the graph. The spread of social influence, an alarm, or a social contagion can be modeled using graph burning. The less the burning number, the faster the spread. Optimal burning of general graphs is NP-Hard. There is a 3-approximation algorithm to burn general graphs where as better approximation factors are there for many sub classes. Here we study burning of grids; provide a lower bound for burning arbitrary grids and a 2-approximation algorithm for burning square grids. On the other hand, burning path forests, spider graphs, and trees with maximum degree three is already known to be NP-Complete. In this article we show burning problem to be NP-Complete on connected interval graphs, permutation graphs and several other geometric graph classes as corollaries.Comment: 17 pages, 5 figure

Width Parameterizations for Knot-free Vertex Deletion on Digraphs

A knot in a directed graph $G$ is a strongly connected subgraph $Q$ of $G$ with at least two vertices, such that no vertex in $V(Q)$ is an in-neighbor of a vertex in $V(G)\setminus V(Q)$. Knots are important graph structures, because they characterize the existence of deadlocks in a classical distributed computation model, the so-called OR-model. Deadlock detection is correlated with the recognition of knot-free graphs as well as deadlock resolution is closely related to the {\sc Knot-Free Vertex Deletion (KFVD)} problem, which consists of determining whether an input graph $G$ has a subset $S \subseteq V(G)$ of size at most $k$ such that $G[V\setminus S]$ contains no knot. In this paper we focus on graph width measure parameterizations for {\sc KFVD}. First, we show that: (i) {\sc KFVD} parameterized by the size of the solution $k$ is W[1]-hard even when $p$, the length of a longest directed path of the input graph, as well as $\kappa$, its Kenny-width, are bounded by constants, and we remark that {\sc KFVD} is para-NP-hard even considering many directed width measures as parameters, but in FPT when parameterized by clique-width; (ii) {\sc KFVD} can be solved in time $2^{O(tw)}\times n$, but assuming ETH it cannot be solved in $2^{o(tw)}\times n^{O(1)}$, where $tw$ is the treewidth of the underlying undirected graph. Finally, since the size of a minimum directed feedback vertex set ($dfv$) is an upper bound for the size of a minimum knot-free vertex deletion set, we investigate parameterization by $dfv$ and we show that (iii) {\sc KFVD} can be solved in FPT-time parameterized by either $dfv+\kappa$ or $dfv+p$; and it admits a Turing kernel by the distance to a DAG having an Hamiltonian path.Comment: An extended abstract of this paper was published in IPEC 201

Human rights and ethical reasoning : capabilities, conventions and spheres of public action

This interdisciplinary article argues that human rights must be understood in terms of opportunities for social participation and that social and economic rights are integral to any discussion of the subject. We offer both a social constructionist and a normative framework for a sociology of human rights which reaches beyond liberal individualism, combining insights from the work of Amartya Sen and from French convention theory. Following Sen, we argue that human rights are founded on the promotion of human capabilities as ethical demands shaped by public reasoning. Using French convention theory, we show how the terms of such deliberation are shaped by different constructions of collectively held values and the compromises reached between them. We conclude by demonstrating how our approach offers a new perspective on spheres of public action and the role these should play in promoting social cohesion, individual capabilities and human rights

Parameterized Algorithms for Modular-Width

It is known that a number of natural graph problems which are FPT parameterized by treewidth become W-hard when parameterized by clique-width. It is therefore desirable to find a different structural graph parameter which is as general as possible, covers dense graphs but does not incur such a heavy algorithmic penalty. The main contribution of this paper is to consider a parameter called modular-width, defined using the well-known notion of modular decompositions. Using a combination of ILPs and dynamic programming we manage to design FPT algorithms for Coloring and Partitioning into paths (and hence Hamiltonian path and Hamiltonian cycle), which are W-hard for both clique-width and its recently introduced restriction, shrub-depth. We thus argue that modular-width occupies a sweet spot as a graph parameter, generalizing several simpler notions on dense graphs but still evading the "price of generality" paid by clique-width.Comment: to appear in IPEC 2013. arXiv admin note: text overlap with arXiv:1304.5479 by other author

Nerve growth factor (NGF) pathway biomarkers in Down syndrome prior to and after the onset of clinical Alzheimer's disease : A paired CSF and plasma study

Altres ajuts: This work was also supported by the National Institutes of Health (R21AG056974 and R01AG061566 to JF); Departament de Salut de la Generalitat de Catalunya, Pla Estratègic de Recerca i Innovació en Salut (SLT002/16/00408 to AL); Fundació La Marató de TV3 (20141210 to JF, 044412 to RB). Fundació Catalana Síndrome de Down and Fundació Víctor Grífols i Lucas partially supported this work. This work was also supported by Generalitat de Catalunya (SLT006/17/00119 to JF) and a grant from the Fundació Bancaria La Caixa to RB.The discovery that nerve growth factor (NGF) metabolism is altered in Down syndrome (DS) and Alzheimer's disease (AD) brains offered a framework for the identification of novel biomarkers signalling NGF deregulation in AD pathology. We examined levels of NGF pathway proteins (proNGF, neuroserpin, tissue plasminogen activator [tPA], and metalloproteases [MMP]) in matched cerebrospinal fluid (CSF)/plasma samples from AD-symptomatic (DSAD) and AD-asymptomatic (aDS) individuals with DS, as well as controls (HC). ProNGF and MMP-3 were elevated while tPA was decreased in plasma from individuals with DS. CSF from individuals with DS showed elevated proNGF, neuroserpin, MMP-3, and MMP-9. ProNGF and MMP-9 in CSF differentiated DSAD from aDS (area under the curve = 0.86, 0.87). NGF pathway markers associated with CSF amyloid beta and tau and differed by sex. Brain NGF metabolism changes can be monitored in plasma and CSF, supporting relevance in AD pathology. These markers could assist staging, subtyping, or precision medicine for AD in DS

Age of Alzheimer’s disease diagnosis in people with Down syndrome and associated factors:Results from the Horizon 21 European Down syndrome consortium

IntroductionPeople with Down syndrome (DS) have high risk of developing Alzheimer's disease (AD). This study examined mean ages of AD diagnosis and associations with co-occurring conditions among adults with DS from five European countries.MethodsData from 1335 people with DS from the Horizon 21 European DS Consortium were used for the analysis.ResultsMean ages of AD diagnosis ranged between 51.4 (SD 7.0) years (United Kingdom) and 55.6 (SD 6.8) years (France). Sleep-related and mental health problems were associated with earlier age of AD diagnosis. The higher number of co-occurring conditions the more likely the person with DS is diagnosed with AD at an earlier age.DiscussionMean age of AD diagnosis in DS was relatively consistent across countries. However, co-occurring conditions varied and impacted on age of diagnosis, suggesting that improvements can be made in diagnosing and managing these conditions to delay onset of AD in DS.</p

Markers of early changes in cognition across cohorts of adults with Down syndrome at risk of Alzheimer's disease.

IntroductionDown syndrome (DS), a genetic variant of early onset Alzheimer's disease (AD), lacks a suitable outcome measure for prevention trials targeting pre-dementia stages.MethodsWe used cognitive test data collected in several longitudinal aging studies internationally from 312 participants with DS without dementia to identify composites that were sensitive to change over time. We then conducted additional analyses to provide support for the utility of the composites. The composites were presented to an expert panel to determine the most optimal cognitive battery based on predetermined criteria.ResultsThere were common cognitive domains across site composites, which were sensitive to early decline. The final composite consisted of memory, language/executive functioning, selective attention, orientation, and praxis tests.DiscussionWe have identified a composite that is sensitive to early decline and thus may have utility as an outcome measure in trials to prevent or delay symptoms of AD in DS

Markers of early changes in cognition across cohorts of adults with Down syndrome at risk of Alzheimer's disease.

Introduction: Down syndrome (DS), a genetic variant of early onset Alzheimer's disease (AD), lacks a suitable outcome measure for prevention trials targeting pre-dementia stages. Methods: We used cognitive test data collected in several longitudinal aging studies internationally from 312 participants with DS without dementia to identify composites that were sensitive to change over time. We then conducted additional analyses to provide support for the utility of the composites. The composites were presented to an expert panel to determine the most optimal cognitive battery based on predetermined criteria. Results: There were common cognitive domains across site composites, which were sensitive to early decline. The final composite consisted of memory, language/executive functioning, selective attention, orientation, and praxis tests. Discussion: We have identified a composite that is sensitive to early decline and thus may have utility as an outcome measure in trials to prevent or delay symptoms of AD in DS

Prevalence of sleep disorders in adults with down syndrome: a comparative study of subjective, actigraphic and polygraphic findings

STUDY OBJECTIVES:Sleep problems are often undetected in adults with Down syndrome (DS). Our objective was to determine the prevalence of sleep disorders in adults with DS through self-reported and objective sleep measures. METHODS:We performed a community-based cross-sectional study of 54 adults with DS not referred for sleep disorders. Two polysomnography (PSG) sleep studies were performed. Sleep quality was evaluated using the Pittsburgh Sleep Quality Index (PSQI); daytime sleepiness was evaluated using the Epworth Sleepiness Scale (ESS) and the risk for the sleep apnea syndrome (OSA) was identified using the Berlin Questionnaire (BQ). Participants' sleep/wake pattern was assessed from sleep diaries and by wrist actigraphy. PSQI, ESS, and PSG measures were compared with 35 sex-, age-, and body mass index-matched patients in the control groups. RESULTS:In PSG measures, adults with DS showed lower sleep efficiency (69 ± 17.7 versus 81.6 ± 11; P < .001), less rapid eye movement sleep (9.4 ± 5.8 versus 19.4 ± 5.1; P < .001), a higher prevalence of OSA (78% versus 14%; P < .001), and a higher apnea-hypopnea index (23.5 ± 24.5 versus 3.8 ± 10.5; P < .001) than patients in the control group. In the DS group, the questionnaires (mean PSQI 3.7 ± 2.9; mean ESS 6.3 ± 4.5 and mean BQ 1 ± 0) did not reflect the sleep disturbances detected on the PSG. Actigraphy data recorded daytime sleep that was not self-reported (118.2 ± 104.2 minutes). CONCLUSIONS:Adults with DS show severe sleep disruption and a high prevalence of OSA, undetected by self-reported sleep measures. Actigraphy, PSG, and validated simplified devices for screening OSA should be routinely recommended for this population because treatment of sleep disorders can contribute to healthy aging

Cerebral Amyloid Angiopathy in Down Syndrome and Sporadic and Autosomal-Dominant Alzheimer\u27s Disease

Introduction—We aimed to investigate if cerebral amyloid angiopathy (CAA) is more frequent in genetically determined than in sporadic early-onset forms of Alzheimer\u27s disease (AD) (early-onset AD [EOAD]). Methods—Neuroimaging features of CAA, APOE, and cerebrospinal fluid-Aβ40 levels were studied in subjects with Down syndrome (DS, n = 117), autosomal-dominant AD (ADAD, n = 29), sporadic EOAD (n = 42), and healthy controls (n = 68). Results—CAA was present in 31%, 38%, and 12% of cognitively impaired DS, symptomatic ADAD, and sporadic EOAD subjects and in 13% and 4% of cognitively unimpaired DS individuals and healthy controls, respectively. APOE-ε4 genotype was borderline significantly associated with CAA in sporadic EOAD (p = .06) but not with DS or ADAD. There were no differences in Aβ040 levels between groups or between subjects with and without CAA. Discussion—CAA is more frequently found in genetically determined AD than in sporadic EOAD. Cerebrospinal fluid-Aβ40 levels are not a useful biomarker for CAA in AD