AN EXTENSION OF SOME RESULTS DUE TO JARDEN

This paper defines some generalized Fibonacci and Lucas sequences which satisfy arbitrary order linear recurrence relations and which answer a problem posed by Jarden in 1966 about generalizing an elegant result for a connection between even and odd subscripted Fibonacci and Lucas numbers

Some aspects of Fibonacci polynomial congruences

This paper formulates a definition of Fibonacci polynomials which is slightly different from the traditional definitions, but which is related to the classical polynomials of Bernoulli, Euler and Hermite. Some related congruence properties are developed and some unanswered questions are outlined. Keywords: Congruences, recurrence relations, Fibonacci sequence, Lucas sequences, umbral calculus

ARBITRARY ORDER RECURSIVE SEQUENCES AND ASSOCIATED CONTINUED FRACTIONS

The essential idea in this paper it to generalize and synthesize some of the pioneering ideas of Bernstein, Lucas and Horadam on generalizations of basic and primordial Fibonacci numbers and their arbitrary order generalizations and their relation to generalized continued fractions with matrices as the unifying elements

“We can all just get on a bus and go” : Rethinking independent mobility in the context of the universal provision of free bus travel to young Londoners

This paper uses qualitative data from interviews with 118 young Londoners (age 12-18) to examine how the universal provision of free bus travel has affected young people’s independent mobility. Drawing on Sen’s ‘capabilities approach’, we argue that free bus travel enhanced young Londoners’ capability to shape their daily mobility, both directly by increasing financial access and indirectly by facilitating the acquisition of the necessary skills, travelling companions and confidence. These capabilities in turn extended both opportunity freedoms (e.g. facilitating non-“necessary” recreational and social trips) and process freedoms (e.g. feeling more independent by decreasing reliance on parents). Moreover, the universal nature of the entitlement rendered buses a socially inclusive way for groups to travel and spend time together, thereby enhancing group-level capabilities. We believe this attention to individual and group capabilities for self-determination provides the basis for a broader and more child-centred view of ‘independent mobility’ than the typical research focus upon ‘travelling without an adult’ and acquiring parental permissions.Peer reviewe

Post-COVID-19 assessment in a specialist clinical service: a 12-month, single-centre, prospective study in 1325 individuals

Introduction: Post-COVID-19 complications require simultaneous characterisation and management to plan policy and health system responses. We describe the 12-month experience of the first UK dedicated post-COVID-19 clinical service to include hospitalised and non-hospitalised patients. Methods: In a single-centre, observational analysis, we report the demographics, symptoms, comorbidities, investigations, treatments, functional recovery, specialist referral and rehabilitation of 1325 individuals assessed at the University College London Hospitals post-COVID-19 service between April 2020 and April 2021, comparing by referral route: posthospitalised (PH), non-hospitalised (NH) and post emergency department (PED). Symptoms associated with poor recovery or inability to return to work full time were assessed using multivariable logistic regression. Results: 1325 individuals were assessed (PH: 547, 41.3%; PED: 212, 16%; NH: 566, 42.7%). Compared with the PH and PED groups, the NH group were younger (median 44.6 (35.6–52.8) years vs 58.3 (47.0–67.7) years and 48.5 (39.4–55.7) years), more likely to be female (68.2%, 43.0% and 59.9%), less likely to be of ethnic minority (30.9%, 52.7% and 41.0%) or seen later after symptom onset (median (IQR): 194 (118–298) days, 69 (51–111) days and 76 (55–128) days; all p<0.0001). All groups had similar rates of onward specialist referral (NH 18.7%, PH 16.1% and PED 18.9%, p=0.452) and were more likely to require support for breathlessness (23.7%, 5.5% and 15.1%, p<0.001) and fatigue (17.8%, 4.8% and 8.0%, p<0.001). Hospitalised patients had higher rates of pulmonary emboli, persistent lung interstitial abnormalities and other organ impairment. 716 (54.0%) individuals reported <75% optimal health (median 70%, IQR 55%–85%). Less than half of employed individuals could return to work full time at first assessment. Conclusion: Post-COVID-19 symptoms were significant in PH and NH patients, with significant ongoing healthcare needs and utilisation. Trials of interventions and patient-centred pathways for diagnostic and treatment approaches are urgently required

A Survey of New Temperature-Sensitive, Embryonic-Lethal Mutations in C. elegans: 24 Alleles of Thirteen Genes

To study essential maternal gene requirements in the early C. elegans embryo, we have screened for temperature-sensitive, embryonic lethal mutations in an effort to bypass essential zygotic requirements for such genes during larval and adult germline development. With conditional alleles, multiple essential requirements can be examined by shifting at different times from the permissive temperature of 15°C to the restrictive temperature of 26°C. Here we describe 24 conditional mutations that affect 13 different loci and report the identity of the gene mutations responsible for the conditional lethality in 22 of the mutants. All but four are mis-sense mutations, with two mutations affecting splice sites, another creating an in-frame deletion, and one creating a premature stop codon. Almost all of the mis-sense mutations affect residues conserved in orthologs, and thus may be useful for engineering conditional mutations in other organisms. We find that 62% of the mutants display additional phenotypes when shifted to the restrictive temperature as L1 larvae, in addition to causing embryonic lethality after L4 upshifts. Remarkably, we also found that 13 out of the 24 mutations appear to be fast-acting, making them particularly useful for careful dissection of multiple essential requirements. Our findings highlight the value of C. elegans for identifying useful temperature-sensitive mutations in essential genes, and provide new insights into the requirements for some of the affected loci

Multiorgan MRI findings after hospitalisation with COVID-19 in the UK (C-MORE): a prospective, multicentre, observational cohort study

Introduction: The multiorgan impact of moderate to severe coronavirus infections in the post-acute phase is still poorly understood. We aimed to evaluate the excess burden of multiorgan abnormalities after hospitalisation with COVID-19, evaluate their determinants, and explore associations with patient-related outcome measures. Methods: In a prospective, UK-wide, multicentre MRI follow-up study (C-MORE), adults (aged ≥18 years) discharged from hospital following COVID-19 who were included in Tier 2 of the Post-hospitalisation COVID-19 study (PHOSP-COVID) and contemporary controls with no evidence of previous COVID-19 (SARS-CoV-2 nucleocapsid antibody negative) underwent multiorgan MRI (lungs, heart, brain, liver, and kidneys) with quantitative and qualitative assessment of images and clinical adjudication when relevant. Individuals with end-stage renal failure or contraindications to MRI were excluded. Participants also underwent detailed recording of symptoms, and physiological and biochemical tests. The primary outcome was the excess burden of multiorgan abnormalities (two or more organs) relative to controls, with further adjustments for potential confounders. The C-MORE study is ongoing and is registered with ClinicalTrials.gov, NCT04510025. Findings: Of 2710 participants in Tier 2 of PHOSP-COVID, 531 were recruited across 13 UK-wide C-MORE sites. After exclusions, 259 C-MORE patients (mean age 57 years [SD 12]; 158 [61%] male and 101 [39%] female) who were discharged from hospital with PCR-confirmed or clinically diagnosed COVID-19 between March 1, 2020, and Nov 1, 2021, and 52 non-COVID-19 controls from the community (mean age 49 years [SD 14]; 30 [58%] male and 22 [42%] female) were included in the analysis. Patients were assessed at a median of 5·0 months (IQR 4·2–6·3) after hospital discharge. Compared with non-COVID-19 controls, patients were older, living with more obesity, and had more comorbidities. Multiorgan abnormalities on MRI were more frequent in patients than in controls (157 [61%] of 259 vs 14 [27%] of 52; p&lt;0·0001) and independently associated with COVID-19 status (odds ratio [OR] 2·9 [95% CI 1·5–5·8]; padjusted=0·0023) after adjusting for relevant confounders. Compared with controls, patients were more likely to have MRI evidence of lung abnormalities (p=0·0001; parenchymal abnormalities), brain abnormalities (p&lt;0·0001; more white matter hyperintensities and regional brain volume reduction), and kidney abnormalities (p=0·014; lower medullary T1 and loss of corticomedullary differentiation), whereas cardiac and liver MRI abnormalities were similar between patients and controls. Patients with multiorgan abnormalities were older (difference in mean age 7 years [95% CI 4–10]; mean age of 59·8 years [SD 11·7] with multiorgan abnormalities vs mean age of 52·8 years [11·9] without multiorgan abnormalities; p&lt;0·0001), more likely to have three or more comorbidities (OR 2·47 [1·32–4·82]; padjusted=0·0059), and more likely to have a more severe acute infection (acute CRP &gt;5mg/L, OR 3·55 [1·23–11·88]; padjusted=0·025) than those without multiorgan abnormalities. Presence of lung MRI abnormalities was associated with a two-fold higher risk of chest tightness, and multiorgan MRI abnormalities were associated with severe and very severe persistent physical and mental health impairment (PHOSP-COVID symptom clusters) after hospitalisation. Interpretation: After hospitalisation for COVID-19, people are at risk of multiorgan abnormalities in the medium term. Our findings emphasise the need for proactive multidisciplinary care pathways, with the potential for imaging to guide surveillance frequency and therapeutic stratification

The physiological stress response to high-intensity sprint exercise following the ingestion of sodium bicarbonate

The purpose of this study was to investigate the effects of pre-exercise alkalosis on the physiological stress response to high-intensity exercise. Seven physically active males (age 22 +/- A 3 years, height 1.82 +/- A 0.06 m, mass 81.3 +/- A 8.4 kg and peak power output 300 +/- A 22 W) performed a repeated sprint cycle exercise following a dose of 0.3 g kg(-1) body mass of sodium bicarbonate (NaHCO3) (BICARB), or a placebo of 0.045 g kg(-1) body mass of sodium chloride (PLAC). Monocyte-expressed heat shock protein 72 (HSP72) and plasma thiobarbituric acid reactive substances (TBARS) were significantly attenuated in BICARB compared to PLAC (p = 0.04 and p = 0.039, respectively), however total anti-oxidant capacity, the ratio of oxidised to total glutathione, cortisol, interleukin 6 and interleukin 8 were not significantly induced by the exercise. In conclusion, monocyte-expressed HSP72 is significantly increased following high-intensity anaerobic exercise, and its attenuation following such exercise with the ingestion of NaHCO3 is unlikely to be due to a decreased oxidative stress