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

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

Cerebrospinal fluid profile of NPTX2 supports role of Alzheimer's disease-related inhibitory circuit dysfunction in adults with down syndrome

Alzheimer's disease (AD) is the major cause of death in adults with Down syndrome (DS). There is an urgent need for objective markers of AD in the DS population to improve early diagnosis and monitor disease progression. NPTX2 has recently emerged as a promising cerebrospinal fluid (CSF) biomarker of Alzheimer-related inhibitory circuit dysfunction in sporadic AD patients. The objective of this study was to evaluate NPTX2 in the CSF of adults with DS and to explore the relationship of NPTX2 to CSF levels of the PV interneuron receptor, GluA4, and existing AD biomarkers (CSF and neuroimaging). This is a cross-sectional, retrospective study of adults with DS with asymptomatic AD (aDS, n = 49), prodromal AD (pDS, n = 18) and AD dementia (dDS, n = 27). Non-trisomic controls (n = 34) and patients with sporadic AD dementia (sAD, n = 40) were included for comparison. We compared group differences in CSF NPTX2 according to clinical diagnosis and degree of intellectual disability. We determined the relationship of CSF NPTX2 levels to age, cognitive performance (CAMCOG, free and cued selective reminding, semantic verbal fluency), CSF levels of a PV-interneuron marker (GluA4) and core AD biomarkers; CSF Aβ1-42, CSF t-tau, cortical atrophy (magnetic resonance imaging) and glucose metabolism ([18F]-fluorodeoxyglucose positron emission tomography). Compared to controls, mean CSF NPTX2 levels were lower in DS at all AD stages; aDS (0.6-fold, adj.p 0.07). Low CSF NPTX2 levels were associated with low GluA4 in all clinical groups; controls (r 2 = 0.2, p = 0.003), adults with DS (r 2 = 0.4, p 0.3, p 0.3, p < 0.001), increased cortical atrophy (p < 0.05) and reduced glucose metabolism (p < 0.05). Low levels of CSF NPTX2, a protein implicated in inhibitory circuit function, is common to sporadic and genetic forms of AD. CSF NPTX2 represents a promising CSF surrogate marker of early AD-related changes in adults with 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

Clinical and biomarker changes of Alzheimer's disease in adults with Down syndrome : a cross-sectional study

Altres ajuts: Instituto de Salud Carlos III, Fundació Bancaria La Caixa, Fundació La Marató de TV3, Medical Research Council, and National Institutes of Health.Alzheimer's disease and its complications are the leading cause of death in adults with Down syndrome. Studies have assessed Alzheimer's disease in individuals with Down syndrome, but the natural history of biomarker changes in Down syndrome has not been established. We characterised the order and timing of changes in biomarkers of Alzheimer's disease in a population of adults with Down syndrome. We did a dual-centre cross-sectional study of adults with Down syndrome recruited through a population-based health plan in Barcelona (Spain) and through services for people with intellectual disabilities in Cambridge (UK). Cognitive impairment in participants with Down syndrome was classified with the Cambridge Cognitive Examination for Older Adults with Down Syndrome (CAMCOG-DS). Only participants with mild or moderate disability were included who had at least one of the following Alzheimer's disease measures: apolipoprotein E allele carrier status; plasma concentrations of amyloid β peptides 1-42 and 1-40 and their ratio (Aβ), total tau protein, and neurofilament light chain (NFL); tau phosphorylated at threonine 181 (p-tau), and NFL in cerebrospinal fluid (CSF); and one or more of PET with 18 F-fluorodeoxyglucose, PET with amyloid tracers, and MRI. Cognitively healthy euploid controls aged up to 75 years who had no biomarker abnormalities were recruited from the Sant Pau Initiative on Neurodegeneration. We used a first-order locally estimated scatterplot smoothing curve to determine the order and age at onset of the biomarker changes, and the lowest ages at the divergence with 95% CIs are also reported where appropriate. Between Feb 1, 2013, and June 28, 2019 (Barcelona), and between June 1, 2009, and Dec 31, 2014 (Cambridge), we included 388 participants with Down syndrome (257 [66%] asymptomatic, 48 [12%] with prodromal Alzheimer's disease, and 83 [21%] with Alzheimer's disease dementia) and 242 euploid controls. CSF Aβ and plasma NFL values changed in individuals with Down syndrome as early as the third decade of life, and amyloid PET uptake changed in the fourth decade. 18 F-fluorodeoxyglucose PET and CSF p-tau changes occurred later in the fourth decade of life, followed by hippocampal atrophy and changes in cognition in the fifth decade of life. Prodromal Alzheimer's disease was diagnosed at a median age of 50·2 years (IQR 47·5-54·1), and Alzheimer's disease dementia at 53·7 years (49·5-57·2). Symptomatic Alzheimer's disease prevalence increased with age in individuals with Down syndrome, reaching 90-100% in the seventh decade of life. Alzheimer's disease in individuals with Down syndrome has a long preclinical phase in which biomarkers follow a predictable order of changes over more than two decades. The similarities with sporadic and autosomal dominant Alzheimer's disease and the prevalence of Down syndrome make this population a suitable target for Alzheimer's disease preventive treatments. Instituto de Salud Carlos III, Fundació Bancaria La Caixa, Fundació La Marató de TV3, Medical Research Council, and National Institutes of Health

Association of biological sex with clinical outcomes and biomarkers of Alzheimer's disease in adults with Down syndrome

The study of sex differences in Alzheimer's disease is increasingly recognized as a key priority in research and clinical development. People with Down syndrome represent the largest population with a genetic link to Alzheimer's disease (>90% in the 7th decade). Yet, sex differences in Alzheimer's disease manifestations have not been fully investigated in these individuals, who are key candidates for preventive clinical trials. In this double-centre, cross-sectional study of 628 adults with Down syndrome [46% female, 44.4 (34.6; 50.7) years], we compared Alzheimer's disease prevalence, as well as cognitive outcomes and AT(N) biomarkers across age and sex. Participants were recruited from a population-based health plan in Barcelona, Spain, and from a convenience sample recruited via services for people with intellectual disabilities in England and Scotland. They underwent assessment with the Cambridge Cognitive Examination for Older Adults with Down Syndrome, modified cued recall test and determinations of brain amyloidosis (CSF amyloid-β 42 / 40 and amyloid-PET), tau pathology (CSF and plasma phosphorylated-tau181) and neurodegeneration biomarkers (CSF and plasma neurofilament light, total-tau, fluorodeoxyglucose-PET and MRI). We used within-group locally estimated scatterplot smoothing models to compare the trajectory of biomarker changes with age in females versus males, as well as by apolipoprotein ɛ4 carriership. Our work revealed similar prevalence, age at diagnosis and Cambridge Cognitive Examination for Older Adults with Down Syndrome scores by sex, but males showed lower modified cued recall test scores from age 45 compared with females. AT(N) biomarkers were comparable in males and females. When considering apolipoprotein ɛ4, female ɛ4 carriers showed a 3-year earlier age at diagnosis compared with female non-carriers (50.5 versus 53.2 years, P = 0.01). This difference was not seen in males (52.2 versus 52.5 years, P = 0.76). Our exploratory analyses considering sex, apolipoprotein ɛ4 and biomarkers showed that female ɛ4 carriers tended to exhibit lower CSF amyloid-β 42/amyloid-β 40 ratios and lower hippocampal volume compared with females without this allele, in line with the clinical difference. This work showed that biological sex did not influence clinical and biomarker profiles of Alzheimer's disease in adults with Down syndrome. Consideration of apolipoprotein ɛ4 haplotype, particularly in females, may be important for clinical research and clinical trials that consider this population. Accounting for, reporting and publishing sex-stratified data, even when no sex differences are found, is central to helping advance precision medicine

Association of biological sex with clinical outcomes and biomarkers of Alzheimer’s disease in adults with Down syndrome

The study of sex differences in Alzheimer's disease is increasingly recognized as a key priority in research and clinical development. People with Down syndrome represent the largest population with a genetic link to Alzheimer's disease (>90% in the 7th decade). Yet, sex differences in Alzheimer's disease manifestations have not been fully investigated in these individuals, who are key candidates for preventive clinical trials. In this double-centre, cross-sectional study of 628 adults with Down syndrome [46% female, 44.4 (34.6; 50.7) years], we compared Alzheimer's disease prevalence, as well as cognitive outcomes and AT(N) biomarkers across age and sex. Participants were recruited from a population-based health plan in Barcelona, Spain, and from a convenience sample recruited via services for people with intellectual disabilities in England and Scotland. They underwent assessment with the Cambridge Cognitive Examination for Older Adults with Down Syndrome, modified cued recall test and determinations of brain amyloidosis (CSF amyloid-beta 42 / 40 and amyloid-PET), tau pathology (CSF and plasma phosphorylated-tau181) and neurodegeneration biomarkers (CSF and plasma neurofilament light, total-tau, fluorodeoxyglucose-PET and MRI). We used within-group locally estimated scatterplot smoothing models to compare the trajectory of biomarker changes with age in females versus males, as well as by apolipoprotein.4 carriership. Our work revealed similar prevalence, age at diagnosis and Cambridge Cognitive Examination for Older Adults with Down Syndrome scores by sex, but males showed lower modified cued recall test scores from age 45 compared with females. AT(N) biomarkers were comparable in males and females. When considering apolipoprotein.4, female.4 carriers showed a 3-year earlier age at diagnosis compared with female non-carriers (50.5 versus 53.2 years, P = 0.01). This difference was not seen in males (52.2 versus 52.5 years, P = 0.76). Our exploratory analyses considering sex, apolipoprotein.4 and biomarkers showed that female.4 carriers tended to exhibit lower CSF amyloid-beta 42/amyloid-beta 40 ratios and lower hippocampal volume compared with females without this allele, in line with the clinical difference. This work showed that biological sex did not influence clinical and biomarker profiles of Alzheimer's disease in adults with Down syndrome. Consideration of apolipoprotein.4 haplotype, particularly in females, may be important for clinical research and clinical trials that consider this population. Accounting for, reporting and publishing sex-stratified data, even when no sex differences are found, is central to helping advance precision medicine