Phase transition and landscape statistics of the number partitioning problem

The phase transition in the number partitioning problem (NPP), i.e., the transition from a region in the space of control parameters in which almost all instances have many solutions to a region in which almost all instances have no solution, is investigated by examining the energy landscape of this classic optimization problem. This is achieved by coding the information about the minimum energy paths connecting pairs of minima into a tree structure, termed a barrier tree, the leaves and internal nodes of which represent, respectively, the minima and the lowest energy saddles connecting those minima. Here we apply several measures of shape (balance and symmetry) as well as of branch lengths (barrier heights) to the barrier trees that result from the landscape of the NPP, aiming at identifying traces of the easy/hard transition. We find that it is not possible to tell the easy regime from the hard one by visual inspection of the trees or by measuring the barrier heights. Only the {\it difficulty} measure, given by the maximum value of the ratio between the barrier height and the energy surplus of local minima, succeeded in detecting traces of the phase transition in the tree. In adddition, we show that the barrier trees associated with the NPP are very similar to random trees, contrasting dramatically with trees associated with the $p$ spin-glass and random energy models. We also examine critically a recent conjecture on the equivalence between the NPP and a truncated random energy model

Integrated global assessment of the natural forest carbon potential

Forests are a substantial terrestrial carbon sink, but anthropogenic changes in land use and climate have considerably reduced the scale of this system 1. Remote-sensing estimates to quantify carbon losses from global forests 2–5 are characterized by considerable uncertainty and we lack a comprehensive ground-sourced evaluation to benchmark these estimates. Here we combine several ground-sourced 6 and satellite-derived approaches 2,7,8 to evaluate the scale of the global forest carbon potential outside agricultural and urban lands. Despite regional variation, the predictions demonstrated remarkable consistency at a global scale, with only a 12% difference between the ground-sourced and satellite-derived estimates. At present, global forest carbon storage is markedly under the natural potential, with a total deficit of 226 Gt (model range = 151–363 Gt) in areas with low human footprint. Most (61%, 139 Gt C) of this potential is in areas with existing forests, in which ecosystem protection can allow forests to recover to maturity. The remaining 39% (87 Gt C) of potential lies in regions in which forests have been removed or fragmented. Although forests cannot be a substitute for emissions reductions, our results support the idea 2,3,9 that the conservation, restoration and sustainable management of diverse forests offer valuable contributions to meeting global climate and biodiversity targets

Shapes of tree representations of spin-glass landscapes

Much of the information about the multi-valley structure of disordered spin systems can be convened in a simple tree structure – a barrier tree – the leaves and internal nodes of which represent, respectively, the local minima and the lowest energy saddles connecting those minima. Here we apply several statistics used in the study of phylogenetic trees to barrier trees that result from the energy landscapes of p-spin models. These statistics give information about the shape of these barrier trees, in particular about balance and symmetry. We then ask if they can be used to classify different types of landscapes, compare them with results obtained from random trees, and investigate the structure of subtrees of the barrier trees. We conclude that at least one of the used statistics is capable of distinguishing different types of landscapes, that the barrier trees from p-spin energy landscapes are quite different from random trees, and that subtrees of barrier trees do not reflect the overall tree structure, but their structure is correlated with their “depth ” in the tree. PACS numbers: 75.10.Nr, 87.23.Kg § To whom correspondence should be addressed. Tree representation of spin-glass landscapes 2 1

Neurocognitive functioning and health-related quality of life of children after pediatric intensive care admission: a systematic review

Objective : This study systematically reviewed recent findings on neurocognitive functioning and health-related quality of life (HRQoL) of children after pediatric intensive care unit admission (PICU). Data sources : Electronic databases searched included Embase, Medline Ovid, Web of Science, Cochrane CENTRAL, and Google Scholar. The search was limited to studies published in the last five years (2015–2019). Study selection : Original studies assessing neurocognitive functioning or HRQoL in children who were previously admitted to the PICU were included in this systematic review. Data extraction : Of the 3649 identified studies, 299 met the inclusion criteria based on title abstract screening. After full-text screening, 75 articles were included in the qualitative data reviewing: 38 on neurocognitive functioning, 33 on HRQoL, and 4 on both outcomes. Data synthesis : Studies examining neurocognitive functioning found overall worse scores for general intellectual functioning, attention, processing speed, memory, and executive functioning. Studies investigating HRQoL found overall worse scores for both physical and psychosocial HRQoL. On the short term (≤ 12 months), most studies reported HRQoL impairments, whereas in some long-term studies HRQoL normalized. The effectiveness of the few intervention studies during and after PICU admission on long-term outcomes varied. Conclusions : PICU survivors have lower scores for neurocognitive functioning and HRQoL than children from the general population. A structured follow-up program after a PICU admission is needed to identify those children and parents who are at risk. However, more research is needed into testing interventions in randomized controlled trials aiming on preventing or improving impairments in critically ill children during and after PICU admission

Role of age of critically ill children at time of exposure to early or late parenteral nutrition in determining the impact hereof on long-term neurocognitive development: A secondary analysis of the PEPaNIC-RCT.

BACKGROUND & AIMS: Early use of parenteral nutrition (early-PN), as compared with withholding it for one week (late-PN), in the PICU, has shown to slow down recovery from critical illness and impair long-term development of 6 neurocognitive/behavioural/emotional functions assessed 2 years later. Given that key steps in brain maturation occur at different times during childhood, we hypothesised that age at time of exposure determines long-term developmental impact of early-PN. METHODS: The 786 children who were neurocognitively tested 2 years after participation in the PEPaNIC-RCT were included in this study. First, for each studied long-term outcome, interaction between randomisation to early-PN versus late-PN and age was assessed with multivariable linear regression analysis. Subsequently, for outcomes with an interaction p ≤ 0.15, the impact of early-PN versus late-PN was analysed, after adjustment for risk factors, for 4 subgroups defined based on developmentally-relevant age at time of exposure [≤28 days (n = 121), 29 days to 11 months (n = 239), 11 months to <5 years (n = 223) and ≥5 years (n = 203)]. RESULTS: Interaction between randomisation and age was present for weight, and parent-reported inhibitory control, cognitive flexibility, working memory, planning/organisation, metacognition, total executive functioning, and internalising and total behavioural/emotional problems. Subgroup analyses revealed that none of the age-groups revealed benefit, whereas children aged 29 days to <11 months were most vulnerable to harm by early-PN for development of inhibitory control (p = 0.008), working memory (p = 0.009), planning/organisation (p = 0.004), metacognition (p = 0.008), and total executive functioning (p = 0.004), and for internalising (p = 0.005) and total behavioural/emotional problems (p = 0.01). Children aged 11 months to <5 years revealed harm by early-PN for development of inhibitory control (p = 0.003). In contrast, children aged ≥5 years and neonates aged ≤28 days appeared less vulnerable. CONCLUSIONS: Critically ill children aged 29 days to 11 months at time of exposure were identified as most vulnerable to developmental harm evoked by early-PN. CLINICAL TRIALS.GOV: NCT01536275.status: Published onlin

Role of age of critically ill children at time of exposure to early or late parenteral nutrition in determining the impact hereof on long-term neurocognitive development: A secondary analysis of the PEPaNIC-RCT

Background & aims: Early use of parenteral nutrition (early-PN), as compared with withholding it for one week (late-PN), in the PICU, has shown to slow down recovery from critical illness and impair long-term development of 6 neurocognitive/behavioural/emotional functions assessed 2 years later. Given that key steps in brain maturation occur at different times during childhood, we hypothesised that age at time of exposure determines long-term developmental impact of early-PN. Methods: The 786 children who were neurocognitively tested 2 years after participation in the PEPaNIC-RCT were included in this study. First, for each studied long-term outcome, interaction between randomisation to early-PN versus late-PN and age was assessed with multivariable linear regression analysis. Subsequently, for outcomes with an interaction p ≤ 0.15, the impact of early-PN versus late-PN was analysed, after adjustment for risk factors, for 4 subgroups defined based on developmentally-relevant age at time of exposure [≤28 days (n = 121), 29 days to 11 months (n = 239), 11 months to <5 years (n = 223) and ≥5 years (n = 203)]. Results: Interaction between randomisation and age was present for weight, and parent-reported inhibitory control, cognitive flexibility, working memory, planning/organisation, metacognition, total executive functioning, and internalising and total behavioural/emotional problems. Subgroup analyses revealed that none of the age-groups revealed benefit, whereas children aged 29 days to <11 months were most vulnerable to harm by early-PN for development of inhibitory control (p = 0.008), working memory (p = 0.009), planning/organisation (p = 0.004), metacognition (p = 0.008), and total executive functioning (p = 0.004), and for internalising (p = 0.005) and total behavioural/emotional problems (p = 0.01). Children aged 11 months to <5 years revealed harm by early-PN for development of inhibitory control (p = 0.003). In contrast, children aged ≥5 years and neonates aged ≤28 days appeared less vulnerable. Conclusions: Critically ill children aged 29 days to 11 months at time of exposure were identified as most vulnerable to developmental harm evoked by early-PN. Clinical trials.gov: NCT01536275

Role of age of critically ill children at time of exposure to early or late parenteral nutrition in determining the impact hereof on long-term neurocognitive development: A secondary analysis of the PEPaNIC-RCT

Background & aims: Early use of parenteral nutrition (early-PN), as compared with withholding it for one week (late-PN), in the PICU, has shown to slow down recovery from critical illness and impair long-term development of 6 neurocognitive/behavioural/emotional functions assessed 2 years later. Given that key steps in brain maturation occur at different times during childhood, we hypothesised that age at time of exposure determines long-term developmental impact of early-PN. Methods: The 786 children who were neurocognitively tested 2 years after participation in the PEPaNIC-RCT were included in this study. First, for each studied long-term outcome, interaction between randomisation to early-PN versus late-PN and age was assessed with multivariable linear regression analysis. Subsequently, for outcomes with an interaction p ≤ 0.15, the impact of early-PN versus late-PN was analysed, after adjustment for risk factors, for 4 subgroups defined based on developmentally-relevant age at time of exposure [≤28 days (n = 121), 29 days to 11 months (n = 239), 11 months to <5 years (n = 223) and ≥5 years (n = 203)]. Results: Interaction between randomisation and age was present for weight, and parent-reported inhibitory control, cognitive flexibility, working memory, planning/organisation, metacognition, total executive functioning, and internalising and total behavioural/emotional problems. Subgroup analyses revealed that none of the age-groups revealed benefit, whereas children aged 29 days to <11 months were most vulnerable to harm by early-PN for development of inhibitory control (p = 0.008), working memory (p = 0.009), planning/organisation (p = 0.004), metacognition (p = 0.008), and total executive functioning (p = 0.004), and for internalising (p = 0.005) and total behavioural/emotional problems (p = 0.01). Children aged 11 months to <5 years revealed harm by early-PN for development of inhibitory control (p = 0.003). In contrast, children aged ≥5 years and neonates aged ≤28 days appeared less vulnerable. Conclusions: Critically ill children aged 29 days to 11 months at time of exposure were identified as most vulnerable to developmental harm evoked by early-PN. Clinical trials.gov: NCT01536275

Long-term developmental effects of withholding parenteral nutrition for 1 week in the paediatric intensive care unit: a 2-year follow-up of the PEPaNIC international, randomised, controlled trial.

BACKGROUND: The paediatric early versus late parenteral nutrition in critical illness (PEPaNIC) multicentre, randomised, controlled trial showed that, compared with early parenteral nutrition, withholding supplemental parenteral nutrition for 1 week in the paediatric intensive care unit (PICU; late parenteral nutrition) reduced infections and accelerated recovery from critical illness in children. We aimed to investigate the long-term impact on physical and neurocognitive development of early versus late parenteral nutrition. METHODS: In this preplanned 2-year follow-up study, all patients included in the PEPaNIC trial (which was done in University Hospitals Leuven, Belgium; Erasmus Medical Centre-Sophia Children's Hospital, Rotterdam, Netherlands; and Stollery Children's Hospital, Edmonton, AB, Canada) were approached for possible assessment of physical and neurocognitive development compared with healthy children who were matched for age and sex, and who had never been admitted to a neonatal ICU or a PICU. Assessed outcomes comprised anthropometric data; health status; parent-reported or caregiver-reported executive functions and emotional and behavioural problems; and tests for intelligence, visual-motor integration, alertness, motor coordination, inhibitory control, cognitive flexibility, and memory. To address partial responses among the children tested, we did multiple data imputation by chained equations before univariable and multivariable linear and logistic regression analyses adjusted for risk factors. This trial is registered with ClinicalTrials.gov, number NCT01536275. FINDINGS: At the 2-year follow-up, 60 (8%) of 717 children who received late parenteral nutrition and 63 (9%) of 723 children who received early parenteral nutrition had died (p=0·81). 68 (9%) of 717 children who received late and 91 (13%) of 723 children who received early parenteral nutrition were too disabled for neurocognitive assessment (p=0·059), and 786 patients (395 assigned to late and 391 assigned to early parenteral nutrition) consented for testing. 786 patients and 405 healthy control children underwent long-term outcome testing between Aug 4, 2014, and Jan 19, 2018, and were included in the imputation model for subsequent multivariable analyses. Late parenteral nutrition did not adversely affect anthropometric data, health status, or neurological functioning, and improved parent-reported or caregiver-reported executive functioning (late vs early parenteral nutrition β estimate -2·258, 95% CI -4·012 to -0·504; p=0·011), more specifically inhibition (-3·422, -5·171 to -1·673; p=0·0001), working memory (-2·016, -3·761 to -0·270; p=0·023), and meta-cognition (-1·957, -3·694 to -0·220; p=0·027). Externalising behavioural problems (β estimate -1·715, 95% CI -3·325 to -0·106; p=0·036) and visual-motor integration (0·468, 0·087 to 0·850; p=0·016) were also improved in the late parenteral nutrition group compared with the early parenteral nutrition group. After Bonferroni correction for multiple comparisons, the effect on inhibitory control remained significant (p=0·0001). INTERPRETATION: Withholding early parenteral nutrition for 1 week in the PICU did not negatively affect survival, anthropometrics, health status, and neurocognitive development, and improved inhibitory control 2 years after PICU admission. FUNDING: European Research Council Advanced Grant, Methusalem programme provided by the Flemish Government, Flemish Agency for Innovation by Science and Technology (IWT), Research Foundation Flanders (FWO), Sophia Children's Hospital Foundation (SSWO), Stichting Agis Zorginnovatie, Erasmus Trustfonds, and European Society for Parenteral and Enteral Nutrition (ESPEN) research grant.status: publishe