Let $\mathbb {F}$ be a field and $(s_0,\ldots ,s_{n-1})$ be a finite sequence of elements of $\mathbb {F}$. In an earlier paper [G. H. Norton, ‘On the annihilator ideal of an inverse form’, J. Appl. Algebra Engrg. Comm. Comput. 28 (2017), 31–78], we used the $\mathbb {F}[x,z]$ submodule $\mathbb {F}[x^{-1},z^{-1}]$ of Macaulay’s inverse system $\mathbb {F}[[x^{-1},z^{-1}]]$ (where z is our homogenising variable) to construct generating forms for the (homogeneous) annihilator ideal of $(s_0,\ldots ,s_{n-1})$. We also gave an $\mathcal {O}(n^2)$ algorithm to compute a special pair of generating forms of such an annihilator ideal. Here we apply this approach to the sequence r of the title. We obtain special forms generating the annihilator ideal for $(r_0,\ldots ,r_{n-1})$ without polynomial multiplication or division, so that the algorithm becomes linear. In particular, we obtain its linear complexities. We also give additional applications of this approach.

Stegenga (forthcoming) formulates and defends a novel account of scientific progress, according to which science makes progress just in case there is a change in scientific justification. Here, we present several problems for Stegenga’s account, concerning, respectively, (i) obtaining misleading evidence, (ii) losses or destruction of evidence, (iii) oscillations in scientific justification, and (iv) the possibility of scientific regress. We conclude by sketching a substantially different justification-based account of scientific progress that avoids these problems.

The UK population is living longer; therefore, promoting healthy ageing via positive nutrition could have widespread public health implications. Moreover, dietary fibre intake is associated with health benefits; however, intake is below UK recommendations (30 g/d). Utilising national dietary survey data can provide up-to-date information on a large representative cohort of UK older adults, so that tailored solutions can be developed in the future. This study used cross-sectional data from the National Diet and Nutrition Survey (years 2008–2009 to 2018–2019) for older adults’ (n 1863; 65–96 years) dietary fibre intake (three-to-four-day food diaries), top ten dietary fibre-rich foods, associated factors (demographics, dietary/lifestyle habits) and various health outcomes (anthropometric, blood and urine). Mean dietary fibre intake was 18·3 g/d (range: 2·9–55·1 g/d); therefore, below the UK dietary recommendations, with compliance at 5·7 %. In addition, there were five significant associations (P < 0·05) related to lower dietary fibre intake such as increasing age group, without own natural teeth, impaired chewing ability, lower education leaving age and poor general health. Older adults’ key foods containing dietary fibre were mainly based on convenience such as baked beans, bread and potatoes. Positively, higher dietary fibre consumption was significantly associated (P = 0·007) with reduced diastolic blood pressure. In summary, the benefits of dietary fibre consumption were identified in terms of health outcomes and oral health were key modulators of intake. Future work should focus on a life course approach and the role of food reformulation to help increase dietary fibre intake.

Background: Tethered cord syndrome, a condition in which the spinal cord stretches as a child grows, can cause various clinical symptoms. Occult TCS (OTCS) is a condition where a child displays some or many clinical symptoms of TCS, but no radiographic abnormality confirms the presence of a tethered cord (1-4). Diagnosis of OTCS in children is invasive and multi-factorial. The current diagnostic approach involves three main factors- clinical signs and symptoms, radiographic evidence, and motor evoked potentials (MEPs) tested under general anesthesia. Transcranial magnetic stimulation (TMS) is a non-invasive testing method for OTCS. It can replace MEPs, which are conducted under general anesthesia. Methods: We will conduct a case-control series of children at our center who have undergone TMS. We will characterize the children who have TCS and suspected OTCS and detail the children’s current diagnosis methods and outcomes in a technical note. We will then compare their pre-operative and post-operative data. Results: So far, we have conducted TMS on 10 children to help diagnose occult TCS. Conclusions: This approach is a novel and effective way to improve the accuracy of diagnosis in children, potentially preventing unnecessary surgery, or detecting patients who would otherwise suffer from the condition.

We analyzed data from a community-based acute respiratory illness study involving K-12 students and their families in southcentral Wisconsin and assessed household transmission of two common seasonal respiratory viruses – human metapneumovirus (HMPV) and human coronaviruses OC43 and HKU1 (HCOV). We found secondary infection rates of 12.2% (95% CI: 8.1%–17.4%) and 19.2% (95% CI: 13.8%–25.7%) for HMPV and HCOV, respectively. We performed individual- and family-level regression models and found that HMPV transmission was positively associated age of the index case (individual model: p = .016; family model: p = .004) and HCOV transmission was positively associated with household density (family model: p = .048). We also found that the age of the non-index case was negatively associated with transmission of both HMPV (individual model: p = .049) and HCOV (individual model: p = .041), but we attributed this to selection bias from the original study design. Understanding household transmission of common respiratory viruses like HMPV and HCOV may help to broaden our understanding of the overall disease burden and establish methods to prevent the spread of disease from low- to high-risk populations.

Between October 1999 and October 2001, a total of 510 European eels Anguilla anguilla were captured in 13 different samples from the rivers Thames (five locations) and Test (one location) in southern England. The relationship between parasite component community species richness (CCR) and maximum infracommunity species richness (ICRmax) compared with that previously observed in bird and mammal hosts. Specifically, the maximum number of parasite species occurring in infracommunities equalled or exceeded half the number of parasite species in the component community at that time, across a wide range of CCR values (2–9 parasite species). Furthermore, the frequency distribution of infracommunity richness (ICR) suggested that the species composition of infracommunities is probably random. These findings suggest that intestinal macroparasite infracommunities in eels are unsaturated and potentially species rich assemblages and, in these respects, share a fundamental similarity with the infracommunities of birds and mammals.

OBJECTIVES/GOALS: Metabolic dysfunction-associated steatotic liver disease (MASLD) is a major public health concern due to its increasing prevalence and association with type 2 diabetes mellitus. Non-invasive magnetic resonance-based biomarkers can aid in the monitoring of disease progression and identification of patients at risk for chronic liver disease. METHODS/STUDY POPULATION: Over 600 subjects will be recruited from the San Antonio Mexican American Family Study and from a second study, which consists of (i) T2DM patients diagnosed with either MASLD or metabolic dysfunction-associated steatohepatitis (MASH) or (ii) metabolically healthy controls. Hydrogen-1 MRS and diffusion-weighted MRI (DW-MRI) will be used to measure liver fat fraction and liver stiffness biomarkers, respectively. Several potential biomarkers of liver stiffness will be evaluated in vivo using the intravoxel incoherent motion (IVIM) model for DW-MRI. To further improve the diagnostic accuracy of patients with liver fibrosis, we will integrate MRI/MRS data with relevant clinical indicators of hepatic metabolism. Results will be compared to biopsy samples to evaluate the model’s diagnostic accuracy. RESULTS/ANTICIPATED RESULTS: Based on preliminary data, we predict that IVIM will be able to accurately diagnose hepatic fibrosis in patients with MASLD, allowing it to be implemented in clinics with high-field MRI units easily. Previous studies have shown correlations between IVIM estimates and fibrosis stages, however, none included additional clinical indicators of liver disease in their models. We have already found significant differences in metabolic measurements such as fasting plasma glucose and HbA1c levels. Additionally, the use of machine learning in developing these models has shown improvements in the ability to extract features from the data. The aim is to achieve high accuracy and robustness in the staging of liver fibrosis. DISCUSSION/SIGNIFICANCE: Over 100 million people in the US are affected by MASLD. Without treatment, it progresses from hepatic steatosis to MASH, fibrosis (liver stiffening), and ultimately to hepatic cirrhosis and hepatocellular carcinoma (HCC). Continued research efforts and clinical implementation of MRI and MRS are vital in combating the growing burden of MASLD.

OBJECTIVES/GOALS: The objective is to assess the effect of pesticide exposure (individually and pesticide mixtures) on the immune response to COVID-19 in children. The goal is to improve scientific knowledge on factors affecting COVID-19 and identify a potentially modifiable factor to reduce disparities in COVID-19 morbidity. METHODS/STUDY POPULATION: Blood samples will be obtained from 50 children with asthma two time points; baseline and 12 months later. SARS-CoV-2 infection or vaccination will be determined with blood exposome RNA analyses.. Immunological response will be measured using neutralizing, phagocytizing, and NK-activating anti-body responses biomarkers. Pesticide exposure will be measured via urinary pesticide metabolites (UPMs). For individual metabolites multivariable analyses for each pesticide will be conducted using generalized estimating equation (GEE) models with compound symmetry correlation to account for the repeated measures design. To assess the pesticide mixture, weighted quantile sum regression (WQS) will be used. RESULTS/ANTICIPATED RESULTS: The main hypothesis is that increased pesticide exposure results in a reduction in the immunological response to SARS-CoV-2 infection and the COVID-19 vaccine. Therefore, we anticipate that increasing concentrations of individual UPMs as well as the increasing index will result in reductions in markers of the immune response to SARS-CoV-2 infection and the COVID-19 vaccine. DISCUSSION/SIGNIFICANCE: Exposure to pesticides is a modifiable environmental factor. If pesticides are found to alter the immune response to COVID-19 infection and vaccination, these data will provide an evidence base for efforts to reduce pesticide exposure in children.

We aim to investigate the nature of time-variable X-ray sources detected in the XMM-Newton serendipitous survey. The X-ray light curves of objects in the XMM-Newton serendipitous survey were searched for variability, and coincident serendipitous sources observed by Chandra were also investigated. Subsequent infrared spectroscopy of the counterparts to the X-ray objects that were identified using UKIDSS was carried out using ISAAC on the VLT. We found that the object 4XMM J182531.5–144036 detected in the XMM-Newton serendipitous survey in 2008 April was also detected by Chandra as CXOU J182531.4–144036 in 2004 July. Both observations reveal a hard X-ray source displaying a coherent X-ray pulsation at a period of 781 s. The source position is coincident with a $K=14$ mag infrared object whose spectrum exhibits strong HeI and Br$\gamma$ emission lines and an infrared excess above that of early B-type dwarf or giant stars. We conclude that 4XMM J182531.5–144036 is a Be/X-ray binary pulsar exhibiting persistent X-ray emission and is likely in a long period, low eccentricity orbit, similar to X Per.

Background: Radiofrequency rhizotomy is a commonly used percutaneous technique for treatment of trigeminal neuralgia especially in cases not eligible for microvascular decompression. This technique is usually performed with the patient under conscious sedation. We devised a method for performance of this technique under general anesthetic with neurophysiology monitoring. Methods: The patient is put under general anaesthetic and EMG monitoring is set up. Needles are placed in temporalis muscle, masseter and mylohyoid or anterior belly of digastric. Resting activityis monitored. Rhizotomy is then performed under fluoroscopic guidance, with monitoring of EMG potentials pre- and post-lesioning, with specific attention paid to presence of an abnormal electrophysiologic reflex. Results: A total of 38 procedures were performed in 23 patients. Of these, 15 were revision procedures. Patients had improvement from BNI pain scale 3.8 ±0.8 to 1.3 ±1.5, and had a reduction in number of medications from 1.9 ±1.0 to 0.8 ±0.9. Survey results indicate greater practitioner satisfaction with this technique. Conclusions: Radiofrequency rhizotomy can be performed under GA with IONM guidance with good results. We present a novel method for EMG-based monitoring. Further study is required to validate this technique.

OBJECTIVES/GOALS: We adapted the Serious Illness Care Program (SICP), an evidence-based intervention designed to promote early serious illness conversation, to be delivered via telehealth for older patients with acute myeloid leukemia and myelodysplastic syndromes. The purpose of this study is to assess the feasibility and usability of the adapted intervention. METHODS/STUDY POPULATION: We are conducting a single-arm pilot study of an adapted SICP that is delivered via telehealth for older patients with AML or MDS (>=60 years) and their caregivers (if available). The adapted SICP includes: 1) Patient preparation pamphlet: sent to patient prior the visit with their clinician, 2) Geriatric assessment: completed by study team and provided to clinician prior to their visit with the patient, 3) A 30-60 minute telehealth visit with their primary oncologist or oncology advance practitioner, 4) Serious Illness Conversation Guide (SICG): used by the clinician during the visit to elicit patient values, 5) Family guide: provided to patient following their visit to help patient’s share their values with their family, 6) Electronic medical record note template for clinicians to document their visit the patient. RESULTS/ANTICIPATED RESULTS: We hypothesize that the adapted SICP intervention will be feasible and usable. We will assess feasibility based on retention rate (percent of patients who consent and complete the visit); >80% is considered feasible. Usability will be assessed using the telehealth usability questionnaire; an average score of >5 is considered usable. Other measures include psychological health, advance care planning engagement, quality of life, and disease understanding. We plan to enroll 20 patients in this study. To date, 11 patients have consented to participate, 10 patients have scheduled SICP visits, 9 patients have completed their visits, 7 patients have completed post-intervention qualitative interviews, and 4 patients have completed post-intervention surveys. DISCUSSION/SIGNIFICANCE: The adapted telehealth-based SICP may promote early serious illness conversation, patient-reported outcomes, and end-of-life experience for older patients with AML and MDS. Results from this study will be used to inform development of clinical trials testing the impact of the adapted SICP on patient- and caregiver-reported outcomes.