Semi-regular sequences and other random systems of equations

The security of multivariate cryptosystems and digital signature schemes relies on the hardness of solving a system of polynomial equations over a finite field. Polynomial system solving is also currently a bottleneck of index-calculus algorithms to solve the elliptic and hyperelliptic curve discrete logarithm problem. The complexity of solving a system of polynomial equations is closely related to the cost of computing Groebner bases, since computing the solutions of a polynomial system can be reduced to finding a lexicographic Groebner basis for the ideal generated by the equations. Several algorithms for computing such bases exist: We consider those based on repeated Gaussian elimination of Macaulay matrices. In this paper, we analyze the case of random systems, where random systems means either semi-regular systems, or quadratic systems in n variables which contain a regular sequence of n polynomials. We provide explicit formulae for bounds on the solving degree of semi-regular systems with m > n equations in n variables, for equations of arbitrary degrees for m = n+1, and for any m for systems of quadratic or cubic polynomials. In the appendix, we provide a table of bounds for the solving degree of semi-regular systems of m = n + k quadratic equations in n variables for 2 <= k; n <= 100 and online we provide the values of the bounds for 2 <= k; n <= 500. For quadratic systems which contain a regular sequence of n polynomials, we argue that the Eisenbud-Green-Harris Conjecture, if true, provides a sharp bound for their solving degree, which we compute explicitly.Comment: 27 pages, 4 table

PET brain imaging in HIV-associated neurocognitive disorders (HAND) in the era of combination antiretroviral therapy

Effective combination antiretroviral therapy (cART) has lead to a significant reduction in the prevalence and incidence of central nervous system (CNS) HIV-associated brain disease, particularly CNS opportunistic infections and HIV encephalitis. Despite this, cognitive deficits in people living with HIV, also known as HIV-associated neurocognitive disorders (HAND) have become more prevalent in recent years. The pathogenesis of HAND is likely to be multifactorial, however recent evidence suggests that brain microglial activation is the most likely pathogenic mechanism. Recent developments in positron emission tomography (PET) brain neuroimaging using novel brain radioligands targeting a variety of physiological changes in the brains of HIV-positive individuals have improved our understanding of the mechanisms associated with the development of HAND. This review will highlight recent PET brain neuroimaging studies in the cART era, focusing on physiological and neurochemical changes associated with HAND in people living with HIV

Dynamic contrast-enhanced CT compared with positron emission tomography CT to characterise solitary pulmonary nodules: the SPUtNIk diagnostic accuracy study and economic modelling

BACKGROUND: Current pathways recommend positron emission tomography-computerised tomography for the characterisation of solitary pulmonary nodules. Dynamic contrast-enhanced computerised tomography may be a more cost-effective approach. OBJECTIVES: To determine the diagnostic performances of dynamic contrast-enhanced computerised tomography and positron emission tomography-computerised tomography in the NHS for solitary pulmonary nodules. Systematic reviews and a health economic evaluation contributed to the decision-analytic modelling to assess the likely costs and health outcomes resulting from incorporation of dynamic contrast-enhanced computerised tomography into management strategies. DESIGN: Multicentre comparative accuracy trial. SETTING: Secondary or tertiary outpatient settings at 16 hospitals in the UK. PARTICIPANTS: Participants with solitary pulmonary nodules of ≥ 8 mm and of ≤ 30 mm in size with no malignancy in the previous 2 years were included. INTERVENTIONS: Baseline positron emission tomography-computerised tomography and dynamic contrast-enhanced computer tomography with 2 years' follow-up. MAIN OUTCOME MEASURES: Primary outcome measures were sensitivity, specificity and diagnostic accuracy for positron emission tomography-computerised tomography and dynamic contrast-enhanced computerised tomography. Incremental cost-effectiveness ratios compared management strategies that used dynamic contrast-enhanced computerised tomography with management strategies that did not use dynamic contrast-enhanced computerised tomography. RESULTS: A total of 380 patients were recruited (median age 69 years). Of 312 patients with matched dynamic contrast-enhanced computer tomography and positron emission tomography-computerised tomography examinations, 191 (61%) were cancer patients. The sensitivity, specificity and diagnostic accuracy for positron emission tomography-computerised tomography and dynamic contrast-enhanced computer tomography were 72.8% (95% confidence interval 66.1% to 78.6%), 81.8% (95% confidence interval 74.0% to 87.7%), 76.3% (95% confidence interval 71.3% to 80.7%) and 95.3% (95% confidence interval 91.3% to 97.5%), 29.8% (95% confidence interval 22.3% to 38.4%) and 69.9% (95% confidence interval 64.6% to 74.7%), respectively. Exploratory modelling showed that maximum standardised uptake values had the best diagnostic accuracy, with an area under the curve of 0.87, which increased to 0.90 if combined with dynamic contrast-enhanced computerised tomography peak enhancement. The economic analysis showed that, over 24 months, dynamic contrast-enhanced computerised tomography was less costly (£3305, 95% confidence interval £2952 to £3746) than positron emission tomography-computerised tomography (£4013, 95% confidence interval £3673 to £4498) or a strategy combining the two tests (£4058, 95% confidence interval £3702 to £4547). Positron emission tomography-computerised tomography led to more patients with malignant nodules being correctly managed, 0.44 on average (95% confidence interval 0.39 to 0.49), compared with 0.40 (95% confidence interval 0.35 to 0.45); using both tests further increased this (0.47, 95% confidence interval 0.42 to 0.51). LIMITATIONS: The high prevalence of malignancy in nodules observed in this trial, compared with that observed in nodules identified within screening programmes, limits the generalisation of the current results to nodules identified by screening. CONCLUSIONS: Findings from this research indicate that positron emission tomography-computerised tomography is more accurate than dynamic contrast-enhanced computerised tomography for the characterisation of solitary pulmonary nodules. A combination of maximum standardised uptake value and peak enhancement had the highest accuracy with a small increase in costs. Findings from this research also indicate that a combined positron emission tomography-dynamic contrast-enhanced computerised tomography approach with a slightly higher willingness to pay to avoid missing small cancers or to avoid a 'watch and wait' policy may be an approach to consider. FUTURE WORK: Integration of the dynamic contrast-enhanced component into the positron emission tomography-computerised tomography examination and the feasibility of dynamic contrast-enhanced computerised tomography at lung screening for the characterisation of solitary pulmonary nodules should be explored, together with a lower radiation dose protocol

Impact of solitary pulmonary nodule size on qualitative and quantitative assessment using 18F-fluorodeoxyglucose PET/CT: the SPUTNIK trial

Purpose: To compare qualitative and semi-quantitative PET/CT criteria, and the impact of nodule size on the diagnosis of solitary pulmonary nodules in a prospective multicentre trial. / Methods: Patients with an SPN on CT ≥ 8 and ≤ 30 mm were recruited to the SPUTNIK trial at 16 sites accredited by the UK PET Core Lab. Qualitative assessment used a five-point ordinal PET-grade compared to the mediastinal blood pool, and a combined PET/CT grade using the CT features. Semi-quantitative measures included SUVmax of the nodule, and as an uptake ratio to the mediastinal blood pool (SURBLOOD) or liver (SURLIVER). The endpoints were diagnosis of lung cancer via biopsy/histology or completion of 2-year follow-up. Impact of nodule size was analysed by comparison between nodule size tertiles. / Results: Three hundred fifty-five participants completed PET/CT and 2-year follow-up, with 59% (209/355) malignant nodules. The AUCs of the three techniques were SUVmax 0.87 (95% CI 0.83;0.91); SURBLOOD 0.87 (95% CI 0.83; 0.91, p = 0.30 versus SUVmax); and SURLIVER 0.87 (95% CI 0.83; 0.91, p = 0.09 vs. SUVmax). The AUCs for all techniques remained stable across size tertiles (p > 0.1 for difference), although the optimal diagnostic threshold varied by size. For nodules  16 mm, an SUVmax ≥ 3.6 or visual PET uptake greater than the mediastinum was the most accurate. / Conclusion: In this multicentre trial, SUVmax was the most accurate technique for the diagnosis of solitary pulmonary nodules. Diagnostic thresholds should be altered according to nodule size. / Trial registration: ISRCTN - ISRCTN30784948. ClinicalTrials.gov - NCT0201306

Collaborative European NeuroTrauma Effectiveness Research in Traumatic Brain Injury (CENTER-TBI): A Prospective Longitudinal Observational Study

BACKGROUND: Current classification of traumatic brain injury (TBI) is suboptimal, and management is based on weak evidence, with little attempt to personalize treatment. A need exists for new precision medicine and stratified management approaches that incorporate emerging technologies. OBJECTIVE: To improve characterization and classification of TBI and to identify best clinical care, using comparative effectiveness research approaches. METHODS: This multicenter, longitudinal, prospective, observational study in 22 countries across Europe and Israel will collect detailed data from 5400 consenting patients, presenting within 24 hours of injury, with a clinical diagnosis of TBI and an indication for computed tomography. Broader registry-level data collection in approximately 20 000 patients will assess generalizability. Cross sectional comprehensive outcome assessments, including quality of life and neuropsychological testing, will be performed at 6 months. Longitudinal assessments will continue up to 24 months post TBI in patient subsets. Advanced neuroimaging and genomic and biomarker data will be used to improve characterization, and analyses will include neuroinformatics approaches to address variations in process and clinical care. Results will be integrated with living systematic reviews in a process of knowledge transfer. The study initiation was from October to December 2014, and the recruitment period was for 18 to 24 months. EXPECTED OUTCOMES: Collaborative European NeuroTrauma Effectiveness Research in TBI should provide novel multidimensional approaches to TBI characterization and classification, evidence to support treatment recommendations, and benchmarks for quality of care. Data and sample repositories will ensure opportunities for legacy research. DISCUSSION: Comparative effectiveness research provides an alternative to reductionistic clinical trials in restricted patient populations by exploiting differences in biology, care, and outcome to support optimal personalized patient management

A systematic review of cerebral microdialysis and outcomes in TBI: relationships to patient functional outcome, neurophysiologic measures, and tissue outcome

OBJECTIVE: To perform a systematic review on commonly measured cerebral microdialysis (CMD) analytes and their association to: (A) patient functional outcome, (B) neurophysiologic measures, and (C) tissue outcome; after moderate/severe TBI. The aim was to provide a foundation for next-generation CMD studies and build on existing pragmatic expert guidelines for CMD. METHODS: We searched MEDLINE, BIOSIS, EMBASE, Global Health, Scopus, Cochrane Library (inception to October 2016). Strength of evidence was adjudicated using GRADE. RESULTS: (A) Functional Outcome: 55 articles were included, assessing outcome as mortality or Glasgow Outcome Scale (GOS) at 3-6 months post-injury. Overall, there is GRADE C evidence to support an association between CMD glucose, glutamate, glycerol, lactate, and LPR to patient outcome at 3-6 months. (B) Neurophysiologic Measures: 59 articles were included. Overall, there currently exists GRADE C level of evidence supporting an association between elevated CMD measured mean LPR, glutamate and glycerol with elevated ICP and/or decreased CPP. In addition, there currently exists GRADE C evidence to support an association between elevated mean lactate:pyruvate ratio (LPR) and low PbtO2. Remaining CMD measures and physiologic outcomes displayed GRADE D or no evidence to support a relationship. (C) Tissue Outcome: four studies were included. Given the conflicting literature, the only conclusion that can be drawn is acute/subacute phase elevation of CMD measured LPR is associated with frontal lobe atrophy at 6 months. CONCLUSIONS: This systematic review replicates previously documented relationships between CMD and various outcome, which have driven clinical application of the technique. Evidence assessments do not address the application of CMD for exploring pathophysiology or titrating therapy in individual patients, and do not account for the modulatory effect of therapy on outcome, triggered at different CMD thresholds in individual centers. Our findings support clinical application of CMD and refinement of existing guidelines

Variation in Structure and Process of Care in Traumatic Brain Injury: Provider Profiles of European Neurotrauma Centers Participating in the CENTER-TBI Study.

INTRODUCTION: The strength of evidence underpinning care and treatment recommendations in traumatic brain injury (TBI) is low. Comparative effectiveness research (CER) has been proposed as a framework to provide evidence for optimal care for TBI patients. The first step in CER is to map the existing variation. The aim of current study is to quantify variation in general structural and process characteristics among centers participating in the Collaborative European NeuroTrauma Effectiveness Research in Traumatic Brain Injury (CENTER-TBI) study. METHODS: We designed a set of 11 provider profiling questionnaires with 321 questions about various aspects of TBI care, chosen based on literature and expert opinion. After pilot testing, questionnaires were disseminated to 71 centers from 20 countries participating in the CENTER-TBI study. Reliability of questionnaires was estimated by calculating a concordance rate among 5% duplicate questions. RESULTS: All 71 centers completed the questionnaires. Median concordance rate among duplicate questions was 0.85. The majority of centers were academic hospitals (n = 65, 92%), designated as a level I trauma center (n = 48, 68%) and situated in an urban location (n = 70, 99%). The availability of facilities for neuro-trauma care varied across centers; e.g. 40 (57%) had a dedicated neuro-intensive care unit (ICU), 36 (51%) had an in-hospital rehabilitation unit and the organization of the ICU was closed in 64% (n = 45) of the centers. In addition, we found wide variation in processes of care, such as the ICU admission policy and intracranial pressure monitoring policy among centers. CONCLUSION: Even among high-volume, specialized neurotrauma centers there is substantial variation in structures and processes of TBI care. This variation provides an opportunity to study effectiveness of specific aspects of TBI care and to identify best practices with CER approaches

Traumatic brain injury: integrated approaches to improve prevention, clinical care, and research

No abstract available