Counting Popular Matchings in House Allocation Problems

We study the problem of counting the number of popular matchings in a given instance. A popular matching instance consists of agents A and houses H, where each agent ranks a subset of houses according to their preferences. A matching is an assignment of agents to houses. A matching M is more popular than matching M' if the number of agents that prefer M to M' is more than the number of people that prefer M' to M. A matching M is called popular if there exists no matching more popular than M. McDermid and Irving gave a poly-time algorithm for counting the number of popular matchings when the preference lists are strictly ordered. We first consider the case of ties in preference lists. Nasre proved that the problem of counting the number of popular matching is #P-hard when there are ties. We give an FPRAS for this problem. We then consider the popular matching problem where preference lists are strictly ordered but each house has a capacity associated with it. We give a switching graph characterization of popular matchings in this case. Such characterizations were studied earlier for the case of strictly ordered preference lists (McDermid and Irving) and for preference lists with ties (Nasre). We use our characterization to prove that counting popular matchings in capacitated case is #P-hard

Learning with multiple representations: An example of a revision lesson in mechanics

We describe an example of learning with multiple representations in an A-level revision lesson on mechanics. The context of the problem involved the motion of a ball thrown vertically upwards in air and studying how the associated physical quantities changed during its flight. Different groups of students were assigned to look at the ball's motion using various representations: motion diagrams, vector diagrams, free-body diagrams, verbal description, equations and graphs, drawn against time as well as against displacement. Overall, feedback from students about the lesson was positive. We further discuss the benefits of using computer simulation to support and extend student learning.Comment: 10 pages, 5 figures, 2 tables http://iopscience.iop.org/0031-912

Popular matchings in the marriage and roommates problems

Popular matchings have recently been a subject of study in the context of the so-called House Allocation Problem, where the objective is to match applicants to houses over which the applicants have preferences. A matching M is called popular if there is no other matching M′ with the property that more applicants prefer their allocation in M′ to their allocation in M. In this paper we study popular matchings in the context of the Roommates Problem, including its special (bipartite) case, the Marriage Problem. We investigate the relationship between popularity and stability, and describe efficient algorithms to test a matching for popularity in these settings. We also show that, when ties are permitted in the preferences, it is NP-hard to determine whether a popular matching exists in both the Roommates and Marriage cases

Cancer History and Systemic Anti-Cancer Therapy Independently Predict COVID-19 Mortality: A UK Tertiary Hospital Experience

Background: The COVID-19 pandemic remains a pressing concern to patients with cancer as countries enter the second peak of the pandemic and beyond. It remains unclear whether cancer and its treatment contribute an independent risk for mortality in COVID-19. Methods: We included patients at a London tertiary hospital with laboratory confirmed SARS-CoV-2 infection. All patients with a history of solid cancer were included. Age- and sex-matched patients without cancer were randomly selected. Patients with hematological malignancies were excluded. Results: We identified 94 patients with cancer, matched to 226 patients without cancer. After adjusting for age, ethnicity, and co-morbidities, patients with cancer had increased mortality following COVID-19 (HR 1.57, 95% CI:1.04–2.4, p = 0.03). Increasing age (HR 1.49 every 10 years, 95% CI:1.25–1.8, p < 0.001), South Asian ethnicity (HR 2.92, 95% CI:1.73–4.9, p < 0.001), and cerebrovascular disease (HR 1.93, 95% CI:1.18–3.2, p = 0.008) also predicted mortality. Within the cancer cohort, systemic anti-cancer therapy (SACT) within 60 days of COVID-19 diagnosis was an independent risk factor for mortality (HR 2.30, 95% CI: 1.16–4.6, p = 0.02). Conclusions: Along with known risk factors, cancer and SACT confer an independent risk for mortality following COVID-19. Further studies are needed to understand the socioeconomic influences and pathophysiology of these associations

Systemic anti-cancer therapy and metastatic cancer are independent mortality risk factors during two uk waves of the covid-19 pandemic at university college london hospital

An increased mortality risk was observed in patients with cancer during the first wave of COVID-19. Here, we describe determinants of mortality in patients with solid cancer comparing the first and second waves of COVID-19. A retrospective analysis encompassing two waves of COVID-19 (March–May 2020; December 2020–February 2021) was performed. 207 patients with cancer were matched to 452 patients without cancer. Patient demographics and oncological variables such as cancer subtype, staging and anti-cancer treatment were evaluated for association with COVID-19 mortality. Overall mortality was lower in wave two compared to wave one, HR 0.41 (95% CI: 0.30–0.56). In patients with cancer, mortality was 43.6% in wave one and 15.9% in wave two. In hospitalized patients, after adjusting for age, ethnicity and co-morbidities, a history of cancer was associated with increased mortality in wave one but not wave two. In summary, the second UK wave of COVID-19 is associated with lower mortality in hospitalized patients. A history of solid cancer was not associated with increased mortality despite the dominance of the more transmissible B.1.1.7 SARS-CoV-2 variant. In both waves, metastatic disease and systemic anti-cancer treatment appeared to be independent risk factors for death within the combined cancer cohort

Preconditioning of mesenchymal stromal cells with low-intensity ultrasound: influence on chondrogenesis and directed SOX9 signaling pathways

Background: Continuous low-intensity ultrasound (cLIUS) facilitates the chondrogenic differentiation of human mesenchymal stromal cells (MSCs) in the absence of exogenously added transforming growth factor-beta (TGFβ) by upregulating the expression of transcription factor SOX9, a master regulator of chondrogenesis. The present study evaluated the molecular events associated with the signaling pathways impacting SOX9 gene and protein expression under cLIUS. Methods: Human bone marrow-derived MSCs were exposed to cLIUS stimulation at 14 kPa (5 MHz, 2.5 Vpp) for 5 min. The gene and protein expression of SOX9 was evaluated. The specificity of SOX9 upregulation under cLIUS was determined by treating the MSCs with small molecule inhibitors of select signaling molecules, followed by cLIUS treatment. Signaling events regulating SOX9 expression under cLIUS were analyzed by gene expression, immunofluorescence staining, and western blotting. Results: cLIUS upregulated the gene expression of SOX9 and enhanced the nuclear localization of SOX9 protein when compared to non-cLIUS-stimulated control. cLIUS was noted to enhance the phosphorylation of the signaling molecule ERK1/2. Inhibition of MEK/ERK1/2 by PD98059 resulted in the effective abrogation of cLIUS-induced SOX9 expression, indicating that cLIUS-induced SOX9 upregulation was dependent on the phosphorylation of ERK1/2. Inhibition of integrin and TRPV4, the upstream cell-surface effectors of ERK1/2, did not inhibit the phosphorylation of ERK1/2 and therefore did not abrogate cLIUS-induced SOX9 expression, thereby suggesting the involvement of other mechanoreceptors. Consequently, the effect of cLIUS on the actin cytoskeleton, a mechanosensitive receptor regulating SOX9, was evaluated. Diffused and disrupted actin fibers observed in MSCs under cLIUS closely resembled actin disruption by treatment with cytoskeletal drug Y27632, which is known to increase the gene expression of SOX9. The upregulation of SOX9 under cLIUS was, therefore, related to cLIUS-induced actin reorganization. SOX9 upregulation induced by actin reorganization was also found to be dependent on the phosphorylation of ERK1/2. Conclusions: Collectively, preconditioning of MSCs by cLIUS resulted in the nuclear localization of SOX9, phosphorylation of ERK1/2 and disruption of actin filaments, and the expression of SOX9 was dependent on the phosphorylation of ERK1/2 under cLIUS

Ancestral SARS-CoV-2, but not Omicron, replicates less efficiently in primary pediatric nasal epithelial cells

Children typically experience more mild symptoms of Coronavirus Disease 2019 (COVID-19) when compared to adults. There is a strong body of evidence that children are also less susceptible to Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) infection with the ancestral viral isolate. However, the emergence of SARS-CoV-2 variants of concern (VOCs) has been associated with an increased number of pediatric infections. Whether this is the result of widespread adult vaccination or fundamental changes in the biology of SARS-CoV-2 remain to be determined. Here, we use primary nasal epithelial cells (NECs) from children and adults, differentiated at an air-liquid interface to show that the ancestral SARS-CoV-2 replicates to significantly lower titers in the NECs of children compared to those of adults. This was associated with a heightened antiviral response to SARS-CoV-2 in the NECs of children. Importantly, the Delta variant also replicated to significantly lower titers in the NECs of children. This trend was markedly less pronounced in the case of Omicron. It is also striking to note that, at least in terms of viral RNA, Omicron replicated better in pediatric NECs compared to both Delta and the ancestral virus. Taken together, these data show that the nasal epithelium of children supports lower infection and replication of ancestral SARS-CoV-2, although this may be changing as the virus evolves.Peer reviewe

Ancestral SARS-CoV-2, but not Omicron, replicates less efficiently in primary pediatric nasal epithelial cells

Children typically experience more mild symptoms of Coronavirus Disease 2019 (COVID-19) when compared to adults. There is a strong body of evidence that children are also less susceptible to Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) infection with the ancestral viral isolate. However, the emergence of SARS-CoV-2 variants of concern (VOCs) has been associated with an increased number of pediatric infections. Whether this is the result of widespread adult vaccination or fundamental changes in the biology of SARS-CoV-2 remain to be determined. Here, we use primary nasal epithelial cells (NECs) from children and adults, differentiated at an air-liquid interface to show that the ancestral SARS-CoV-2 replicates to significantly lower titers in the NECs of children compared to those of adults. This was associated with a heightened antiviral response to SARS-CoV-2 in the NECs of children. Importantly, the Delta variant also replicated to significantly lower titers in the NECs of children. This trend was markedly less pronounced in the case of Omicron. It is also striking to note that, at least in terms of viral RNA, Omicron replicated better in pediatric NECs compared to both Delta and the ancestral virus. Taken together, these data show that the nasal epithelium of children supports lower infection and replication of ancestral SARS-CoV-2, although this may be changing as the virus evolves

A type III complement factor D deficiency: Structural insights for inhibition of the alternative pathway.

Abstract Background: Complement factor D (FD) is the rate-limiting enzyme of the alternative complement pathway. Previous reports of FD deficiency featured absent plasma FD (type I deficiency) and susceptibility to meningococcal infection. A new FD mutant, which is non-functional but fully expressed, was identified in a patient with invasive meningococcal disease. Objectives: We sought to investigate the molecular features of this novel FD mutant. Methods: We performed complement haemolytic assays, western blot analysis of serum FD and Sanger sequencing of the CFD gene. Recombinant mutant FD was assessed by in vitro catalytic assays, circular dichroism, thermal shift assays, esterolytic assays and surface plasmon resonance. Molecular dynamics simulation was used to visualise the structural changes in mutant FD. Results: A homozygous single-nucleotide variation of the CFD gene in the patient and their sibling resulted in an arginine to proline (R176P) substitution in FD. While R176P FD was stable and fully expressed in blood, it had minimal catalytic activity. Mutation R176P caused key FD-C3bB binding exosite loop 156-162 to lose its binding-competent conformation and stabilised the inactive conformation of FD. Consequently, R176P FD was unable to bind its natural substrate, C3bB. Neither patient nor sibling demonstrated the glucose homeostasis impairment that occurs in FD-null mice. Conclusions: Here, we report the first genetically confirmed functional, or type III, deficiency of an activating complement serine protease. This novel mechanism of FD inhibition can inform further development of alternative pathway inhibitors to treat common inflammatory diseases such as age-related macular degeneration