A Special Homotopy Continuation Method For A Class of Polynomial Systems

A special homotopy continuation method, as a combination of the polyhedral homotopy and the linear product homotopy, is proposed for computing all the isolated solutions to a special class of polynomial systems. The root number bound of this method is between the total degree bound and the mixed volume bound and can be easily computed. The new algorithm has been implemented as a program called LPH using C++. Our experiments show its efficiency compared to the polyhedral or other homotopies on such systems. As an application, the algorithm can be used to find witness points on each connected component of a real variety

Protocol for a mixed-methods exploratory investigation of care following intensive care discharge: the REFLECT study

© Author(s) 2019. Re-use permitted under CC BY. Published by BMJ.INTRODUCTION: A substantial number of patients discharged from intensive care units (ICUs) subsequently die without leaving hospital. It is unclear how many of these deaths are preventable. Ward-based management following discharge from ICU is an area that patients and healthcare staff are concerned about. The primary aim of REFLECT (Recovery Following Intensive Care Treatment) is to develop an intervention plan to reduce in-hospital mortality rates in patients who have been discharged from ICU. METHODS AND ANALYSIS: REFLECT is a multicentre mixed-methods exploratory study examining ward care delivery to adult patients discharged from ICU. The study will be made up of four substudies. Medical notes of patients who were discharged from ICU and subsequently died will be examined using a retrospective case records review (RCRR) technique. Patients and their relatives will be interviewed about their post-ICU care, including relatives of patients who died in hospital following ICU discharge. Staff involved in the care of patients post-ICU discharge will be interviewed about the care of this patient group. The medical records of patients who survived their post-ICU stay will also be reviewed using the RCRR technique. The analyses of the substudies will be both descriptive and use a modified grounded theory approach to identify emerging themes. The evidence generated in these four substudies will form the basis of the intervention development, which will take place through stakeholder and clinical expert meetings. ETHICS AND DISSEMINATION: Ethical approval has been obtained through the Wales Research and Ethics Committee 4 (17/WA/0107). We aim to disseminate the findings through international conferences, international peer-reviewed journals and social media. TRIAL REGISTRATION NUMBER: ISRCTN14658054.Peer reviewedFinal Published versio

Nodal surfaces of helium atom eigenfunctions

Using a rapidly convergent composite basis of Frankowski-Pekeris and Frankowski functions, we have accurately calculated the nodal surfaces of low-lying excited states of the helium atom to investigate Bressanini and Reynolds\u2019 conjecture D. Bressanini and P. J. Reynolds, Phys. Rev. Lett. 95, 110201 2005 that these nodal surfaces are rigorously independent of the interelectronic angle 12. We find that in fact there is a slight dependence of the nodal surfaces on 12, but it is so small that the assumption of strict independence may well yield extremely useful approximations in fixed-node quantum Monte Carlo calculations. We explain how Kato\u2019s cusp conditions determine the qualitative features of these nodal surfaces, which can accurately be modeled using the familiar ansatz of a symmetric or antisymmetric linear combination of products of hydrogenic orbitals, with some adjustments of the parameters. We explain why a similar near independence of the nodal surfaces on the angular variables can be expected for the ground and singly excited states of the lithium atom, but generally not for larger atoms

Impact of wild-type and genetically modified Pseudomonas fluorescens on soil enzyme activities and microbial population structure in the rhizosphere of pea

The definitive version is available at www.blackwell-synergy.com. Copyright Blackwell Publishing DOI : 10.1046/j.1365-294x.1998.00367.xThe aim of this work was to determine the impact of wild type along with functionally and non-functionally modified Pseudomonas fluorescens strains in the rhizosphere. The wild type F113 strain carried a gene encoding the production of the antibiotic 2,4 diacetylphloroglucinol (DAPG) useful in plant disease control, and was marked with a lacZY gene cassette. The first modified strain was a functional modification of strain F113 with repressed production of DAPG, creating the DAPG negative strain F113 G22. The second paired comparison was a non-functional modification of wild type (unmarked) strain SBW25, constructed to carry marker genes only, creating strain SBW25 EeZY-6KX. Significant perturbations were found in the indigenous bacterial population structure, with the F113, (DAPG+) strain causing a shift towards slower growing colonies (K strategists) compared with the non-antibiotic producing derivative (F113 G22) and the SBW25 strains. The DAPG+ strain also significantly reduced, in comparison with the other inocula, the total Pseudomonas populations but did not affect the total microbial populations. The survival of F113 and F113 G22 were an order of magnitude lower than the SBW 25 strains. The DAPG+ strain caused a significant decrease in the shoot to root ratio in comparison to the control and other inoculants, indicating plant stress. F113 increased soil alkaline phosphatase, phosphodiesterase and aryl sulphatase activities compared to the other inocula, which themselves reduced the same enzyme activities compared to the control. In contrast to this, the -glucosidase, -galactosidase and N-acetyl glucosaminidase activities decreased with the inoculation of the DAPG+ strain. These results indicate that soil enzymes are sensitive to the impact of GMM inoculation.Peer reviewe

Certifying reality of projections

Computational tools in numerical algebraic geometry can be used to numerically approximate solutions to a system of polynomial equations. If the system is well-constrained (i.e., square), Newton's method is locally quadratically convergent near each nonsingular solution. In such cases, Smale's alpha theory can be used to certify that a given point is in the quadratic convergence basin of some solution. This was extended to certifiably determine the reality of the corresponding solution when the polynomial system is real. Using the theory of Newton-invariant sets, we certifiably decide the reality of projections of solutions. We apply this method to certifiably count the number of real and totally real tritangent planes for instances of curves of genus 4.Comment: 9 page

Corticobulbar tract changes as predictors of dysarthria in childhood brain injury.

To identify corticobulbar tract changes that may predict chronic dysarthria in young people who have sustained a traumatic brain injury (TBI) in childhood using diffusion MRI tractography

Neuropsychological profile of patients with normal pressure hydrocephalus and Alzheimer's disease

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Anatomy and lateralization of the human corticobulbar tracts: an fMRI-guided tractography study

The left hemisphere lateralization bias for language functions, such as syntactic processing and semantic retrieval, is well known. Although several theories and clinical data indicate a link between speech motor execution and language, the functional and structural brain lateralization for these functions has never been examined concomitantly in the same individuals. Here we used functional MRI during rapid silent syllable repetition (/lalala/, /papapa/ and /pataka/, known as oral diadochokinesis or DDK) to map the cortical representation of the articulators in 17 healthy adults. In these same participants, functional lateralization for language production was assessed using the well established verb generation task. We then used DDK-related fMRI activation clusters to guide tractography of the corticobulbar tract from diffusion-weighted MRI. Functional MRI revealed a wide inter-individual variability of hemispheric asymmetry patterns (left and right dominant, as well as bilateral) for DDK in the motor cortex, despite predominantly left hemisphere dominance for language-related activity in Broca’s area. Tractography revealed no evidence for structural asymmetry (based on fractional anisotropy) within the corticobulbar tract. To our knowledge, this study is the first to reveal that motor brain activation for syllable repetition is unrelated to functional asymmetry for language production in adult humans. In addition, we found no evidence that the human corticobulbar tract is an asymmetric white matter pathway. We suggest that the predominance of dysarthria following left hemisphere infarct is probably a consequence of disrupted feedback or input from left hemisphere language and speech planning regions, rather than structural asymmetry of the corticobulbar tract itself

Adenosine metabolic signature in circulating CD4+ T cells predicts remission in rheumatoid arthritis

\ua9 Author(s) (or their employer(s)) 2024. Re-use permitted under CC BY-NC. No commercial re-use. See rights and permissions. Published by BMJ.Objectives Long-term outcomes in rheumatoid arthritis (RA) depend on early and effective disease control. Methotrexate (MTX) remains the first-line disease modifying therapy, however there are no biomarkers with which to identify those most likely to achieve remission. To address this unmet need we explored metabolic pathways involved in MTX mechanism of action within circulating CD4+T cells in a cohort of treatment naive patients with early RA. Methods Purified CD4+T cells were isolated from peripheral blood of 68 patients with early RA commencing MTX. The expression of a range of putative MTX metabolism and mechanism of action targets were explored by flow-cytometry and transcriptional analysis. From these data significant predictors of Disease Activity Score 28-C reactive protein (DAS28-CRP) remission (<2.4 at 6 months) were determined by logistic regression (clinical; flow-cytometry data) and linear modelling (gene expression data). Results Low baseline DAS28-CRP was associated with remission at 6 months (p=0.02). Expression of the ectonucleotidase CD39, involved in ATP-ADP conversion during adenosine synthesis, was higher on CD4+CD25 High regulatory T cells at baseline in those achieving remission (molecules of equivalent fluorescence 1264 vs 847; p=0.007). Expression of other adenosine signalling elements in CD4+T cells were also upregulated at baseline in patients achieving remission: AMPD1 (p<0.001), ADORA2b (p=0.039) and ADORA3 (p=0.047). When combined into a single predictive metric, a combination of these variables outperformed baseline DAS28-CRP in prediction of early remission (area under the curve 0.92 vs 0.67, p=0.001) Conclusions Adenosine signalling is important in the achievement of early remission with MTX in RA and biomarkers of adenosine activity may hold utility for the stratification of therapy in early disease

Detection of anti-drug antibodies using a bridging ELISA compared with radioimmunoassay in adalimumab-treated rheumatoid arthritis patients with random drug levels

Objective: To determine the concordance between RIA and bridging ELISA at detecting anti-drug antibodies (ADAbs) in the context of random adalimumab levels and investigate the additional clinical utility of detecting ADAbs in RA patients who test ADAb positive by RIA and negative by ELISA. Methods: ADAb levels were determined using RIA and bridging ELISA in 63 adalimumab treated RA patients (159 samples). Immunogenicity concordance was determined using receiver-operating characteristic (ROC) curves. To determine the additional clinical value provided by a positive RIA in the presence of negative ELISA, association between treatment response (ΔDAS28), adalimumab drug levels and ADAbs was evaluated longitudinally using generalised estimating equation. Results: Of the 60 RIA+ samples (n=31 patients), 19 (n=10 patients) were also ELISA+, corresponding to 31.7% of samples. Area under the curve (AUC) for detecting ADAbs using ELISA (compared with RIA) using ROC curves was 0.65 (95% CI: 0.59-0.71); this increased to 0.91 (95% CI: 0.81-0.99) if ADAbs were ≥100 AU/ml using RIA. In RIA+/ELISA- patients, adalimumab levels were associated with ΔDAS28 over 12 months [regression coefficient: 0.098 (0.043-0.15), p<0.0001] and whilst ADAbs were significantly associated with drug level, they were not directly associated with ΔDAS28 over 12 months [β coefficient: 0.00083 (-0.0038 to 0.0054), p=0.72]. Conclusion: ADAbs were detected using ELISA more frequently when present in high titres as measured by RIA. In RIA+/ELISA- patients, only drug levels were significantly associated with treatment response. Although ADAbs were not independently associated with treatment response, they may be helpful in determining the aetiology of low drug levels