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We study truncation-compatible families F=(Fm)m≥1 over Q[z] through an inverse-limit formalism, and we evaluate them at the punctured cyclotomic cosine points αk,n=cos(2πk/n) with the specialization z=n−1. For symmetric families of uniformly bounded total x-degree ≤d, we prove a stable-range rigidity theorem: for all n≥d+2, the cosine-point evaluation factors through the finitely many punctured cosine power sums P1(n),…,Pd(n). In the purely polynomial case, this implies eventual polynomiality in n. We then extend the framework to include fixed-product factors and package their cosine-point contribution in multiplicative invariants MQ(n). In the stable range, the bounded-degree symmetric part collapses as before; any remaining cyclotomic dependence occurs only through these explicit product terms. Finally, we show that coefficient extraction from such products produces further bounded-degree symmetric families, and we apply this to complete symmetric functions hr evaluated at cosine points.

Background Viruses are constantly changing as a result of mutations, and new viral variants are expected to appear over time. The virus that causes coronavirus disease 2019, severe acute respiratory syndrome coronavirus 2, is not excluded from this condition. Patients with some types of immunodeficiency have been reported to experience symptoms that vary from mild to severe, or even death, after being infected with severe acute respiratory syndrome coronavirus 2. We report a case of a woman with severe hypogammaglobulinemia who developed a prolonged and fatal severe acute respiratory syndrome coronavirus 2 infection. Case presentation A 60-year-old mestizo female with a previous history of severe hypogammaglobulinemia manifested by recurrent pulmonary infections and follicular bronchiolitis. She received a monthly treatment of intravenous immunoglobulins and was admitted after report of a neurological manifestation related to a left thalamic inflammatory lesion, for a duration of 2 weeks of hospitalization, indicated for the study of her neurological condition, including brain biopsy. Both on admission and 1 week later, nasopharyngeal polymerase chain reaction tests for severe acute respiratory syndrome coronavirus 2 were performed and reported negative. In the third week of hospitalization, she developed pulmonary symptoms, and a positive test result for severe acute respiratory syndrome coronavirus 2 was evidenced. On Day 3, the patients’ condition worsened as the infection progressed to respiratory failure and required mechanical ventilation. On Day 8 after the coronavirus disease 2019 diagnosis, the polymerase chain reaction test for severe acute respiratory syndrome coronavirus 2 showed persistent detection of the virus. Various bacterial coinfections, including Klebsiella pneumoniae and Enterobacter cloacae , were diagnosed and treated. On Day 35, her pulmonary symptoms worsened, and the results of the severe acute respiratory syndrome coronavirus 2 polymerase chain reaction test remained positive. On Day 36, despite all the respiratory support, the patient died. The severe acute respiratory syndrome coronavirus 2 virus was sequenced at the beginning and 8 days after the onset of the disease, and the strain, without obvious mutations in the gene that encodes spike protein, was identified. Conclusions This clinical case showed persistent severe acute respiratory syndrome coronavirus 2 detection after 35 days of infection in a patient with severe hypogammaglobulinemia. The sequencing of the virus showed no mutations on the spike protein at 8 days, indicating that, in this case, the persistence of the viral detection was associated with immunodeficiency instead of changes in the viral components.

We prove a general version of Bezout’s form of the Nullstellensatz for arbitrary fields. The corresponding sufficient and necessary condition only involves the local existence of multi-valued roots for each of the polynomials belonging to the ideal in consideration. Finally, this version implies the standard Nullstellensatz when the coefficient field is algebraically closed.

Recipients of autologous haemopoietic stem-cell transplants (auto-HSCT) have an increased risk of herpes zoster and herpes zoster-related complications. The aim of this study was to establish the efficacy and safety of an inactivated varicella zoster vaccine for the prevention of herpes zoster after auto-HSCT. In this randomised, double-blind, placebo-controlled phase 3 trial, participants were recruited from 135 medical centres (ie, stem-cell transplant centres and hospitals) in North America, South America, Europe, and Asia. Patients were eligible if they were aged 18 years or older, scheduled to receive an auto-HSCT within 60 days of enrolment, and had a history of varicella infection or were seropositive for antibodies to varicella zoster virus, or both. Exclusion criteria included a history of herpes zoster within the previous year of enrolment, and intended antiviral prophylaxis for longer than 6 months after transplantation. Participants were randomly assigned according to a central randomisation schedule generated by the trial statistician, to receive either the inactivated-virus vaccine from one of three consistency lots, a high-antigen lot, or placebo, stratified by age (<50 vs ≥50 years) and intended duration of antiviral prophylaxis after transplantation (≤3 months vs >3 to ≤6 months). Participants, investigators, trial staff, and the funder's clinical and laboratory personnel were masked to group assignment. Participants were given four doses of inactivated vaccine or placebo, with the first dose 5–60 days before auto-HSCT, and the second, third, and fourth doses at about 30, 60, and 90 days after transplantation. The primary efficacy endpoint was the incidence of herpes zoster, confirmed by PCR or adjudication by a masked clinical committee, or both, assessed in all participants randomly assigned to the vaccine consistency lot group or placebo group who received at least one dose of vaccine and had auto-HSCT. Safety was assessed in all randomised participants who received at least one dose of vaccine and had follow-up data. A prespecified vaccine efficacy success criterion required the lower bound of the 95% CI be higher than 25% for the relative reduction of the hazard ratio of herpes zoster infection in participants given the vaccine from one of the consistency lots compared with those given placebo. This trial is registered on ClinicalTrials.gov (NCT01229267) and EudraCT (2010–020150–34). Between Dec 7, 2010, and April 25, 2013, 560 participants were randomly assigned to the vaccine consistency lot group, 106 to the high-antigen lot group, and 564 to the placebo group. 249 (44%) of patients in the vaccine consistency lot group, 35 (33%) in the high-antigen lot group, and 220 (39%) in the placebo group discontinued before study end, mostly because of death or withdrawal. 51 participants were excluded from the primary efficacy endpoint analyses because they did not undergo auto-HSCT or were not vaccinated, or both (22 [4%] in the vaccine consistency lot group, and 29 [5%] in the placebo group). Mean follow-up for efficacy was 2·4 years (SD 1·3) in the vaccine consistency lot group and 2·3 years (SD 1·3) in the placebo group. 42 (8%) of 538 participants in the vaccine consistency lot group (32·9 per 1000 person-years) and 113 (21%) of 535 in the placebo group (91·9 per 1000 person-years) had a confirmed case of herpes zoster. The estimated vaccine efficacy was 63·8% (95% CI 48·4–74·6), meeting the pre-specified success criterion. For the combined vaccine groups versus the placebo group, the proportion of patients with serious adverse events (216 [33%] of 657 vs 181 [33%] of 554; risk difference 0·2%, 95% CI −5·1 to 5·5) and serious vaccine-related adverse events (five [1%] vs five [1%]; risk difference 0·1%, −1·4 to 1·1) were similar. Vaccine-related injection-site adverse events occurred more frequently in participants given vaccine than those given placebo (191 [29%] vs 36 [7%]; risk difference 22·6%, 95% CI 18·5–26·6; p<0·0001). This study shows for the first time in a large phase 3 trial that early vaccination of auto-HSCT recipients during the peri-transplant period can be effective for the prevention of an opportunistic infection like herpes zoster and that the vaccine is well tolerated. Merck & Co., Inc.

We study truncation-compatible families F=(Fm)[sub.m≥1] over Q[z] through an inverse-limit formalism, and we evaluate them at the punctured cyclotomic cosine points α[sub.k,n]=cos(2πk/n) with the specialization z=n−1. For symmetric families of uniformly bounded total x-degree ≤d, we prove a stable-range rigidity theorem: for all n≥d+2, the cosine-point evaluation factors through the finitely many punctured cosine power sums P[sub.1](n),…,P[sub.d](n). In the purely polynomial case, this implies eventual polynomiality in n. We then extend the framework to include fixed-product factors and package their cosine-point contribution in multiplicative invariants M[sub.Q](n). In the stable range, the bounded-degree symmetric part collapses as before; any remaining cyclotomic dependence occurs only through these explicit product terms. Finally, we show that coefficient extraction from such products produces further bounded-degree symmetric families, and we apply this to complete symmetric functions h[sub.r] evaluated at cosine points.

Doravirine and islatravir is an investigational, once-daily, single-tablet regimen containing two potent antiretrovirals with complementary mechanisms of action and resistance profiles. We aimed to evaluate the efficacy and safety of switching from stable, oral antiretroviral therapy (ART) to the fixed combination of doravirine (100 mg) and islatravir (0·25 mg) in virologically suppressed adults living with HIV-1. This phase 3, randomised, active-controlled, open-label, non-inferiority trial was conducted at 53 research, community, and hospital-based clinics in eight countries: Australia, Canada, Colombia, Japan, South Africa, Switzerland, the UK, and the USA. Adults (aged ≥18 years) with a viral load of fewer than 50 copies of HIV-1 RNA per mL on any oral, two-drug or three-drug ART regimen for at least 3 months, with no history of treatment failure, known resistance to doravirine, or active hepatitis B infection, were randomly assigned (2:1) according to a computer-generated randomisation schedule (block size three) to receive oral doravirine (100 mg) and islatravir (0·25 mg) once daily or to continue baseline ART for 48 weeks. Randomisation was stratified by the anchor antiretroviral drug class (integrase strand-transfer inhibitor [INSTI], non-nucleoside reverse transcriptase inhibitor, or protease inhibitor) in the baseline regimen. The primary endpoint (assessed in all treated participants) was the percentage of participants with a viral load of 50 copies per mL or higher at week 48 (analysed according to the US Food and Drug Administration snapshot approach); non-inferiority would be concluded if the upper bound of the multiplicity-adjusted 95% CI for the treatment difference was less than 4%. The safety analysis population included all randomly assigned participants who received at least one dose of study treatment. The trial is registered at ClinicalTrials.gov, NCT05631093, and is ongoing but closed to enrolment. Between Feb 20 and Oct 24, 2023, 614 individuals were screened for eligibility, of whom 553 were randomly assigned to receive doravirine and islatravir (n=368) or baseline ART (n=185). 551 participants received at least one dose of allocated medication: 366 in the doravirine and islatravir group and 185 in the baseline ART group. Of these 551 participants, 332 (60%) were assigned male and 219 (40%) were assigned female at birth, and the median age was 51 years (IQR 41–59); 250 (45%) identified as Black or African American and 80 (15%) identified as Hispanic, Latino, or Latina. Doravirine and islatravir showed non-inferiority at week 48, with viral loads of 50 copies per mL or higher in five (1·4%) of 366 participants versus nine (4·9%) of 185 participants on baseline ART (difference −3·6% [multiplicity-adjusted 95% CI −7·8 to −0·8]). Treatment-related adverse events were more common with doravirine and islatravir (44 [12·0%] of 366 participants) than with baseline ART (nine [4·9%] of 185 participants; difference 7·2 [95% CI 2·2 to 11·6]). Rates were similar in the doravirine and islatravir group and the baseline ART group for any adverse event (79·5% [291 of 366 participants] vs 83·8% [155 of 185 participants]; difference −4·3 [−10·7 to 2·8]), serious adverse events (6·3% [23] vs 4·9% [nine]; 1·4 [−3·2 to 5·2]), and discontinuation due to adverse events (0·5% [two] vs 2·2% [four]; −1·6 [−4·9 to 0·2]). One death occurred (in the baseline ART group) and was not considered treatment-related. No participants discontinued treatment as a result of protocol-specified declines in CD4 cell or total lymphocyte counts. Doravirine and islatravir is efficacious and well tolerated and would represent the first non-INSTI-based, two-drug regimen for HIV-1 treatment. With increasing concern over the potential development of widespread INSTI resistance, this once-daily, oral, single-tablet regimen could be a potential option for people living with HIV-1 requiring a change to their antiretroviral regimen. The safety and efficacy findings support the ongoing development of islatravir, a drug with long-acting potential. Merck Sharp & Dohme, a subsidiary of Merck & Co.

Streptococcus agalactiae or group B Streptococcus (GBS) has been recognized as a lethal pathogen in neonates worldwide. S. agalactiae infections also severely affect pregnant women and immunosuppressed adults with substantial attributable morbidity and mortality. However, in Latin America, studies on the epidemiology and behaviour of S. agalactiae infections remain limited. To better understand the behaviour of S. agalactiae infections in our region, we conducted a retrospective study to phenotypically describe S. agalactiae isolates collected in one of the largest hospitals in Colombia at two time periods: 1994-2001 and 2004-2012. The isolates were identified by biochemical analysis and tested for antimicrobial susceptibility. In 1994-2001 a total of 201 S. agalactiae isolates were found in urine 38.3%, vaginal exudates 27.8%, soft tissue 12.9%, and blood 8.5%. Susceptibility to ampicillin or penicillin was 94% whereas resistance to erythromycin and clindamycin were 2.8% and 5.2% respectively. In total 46 culture-positive cases of invasive infections were reported, 11 (24%) in neonates and 35 (76%) in adults. In 2004-2012 a total of 671 isolates were found in urine 47.8%, vaginal exudates 32.6%, soft tissue 2.7% and blood 9%. Susceptibility rates to ampicillin and penicillin were 98% whereas resistance to erythromycin and clindamycin were 12.5% and 9.4%. A total of 95 severe infections were reported: 12 (12.6%) were in neonates, 5 (5.3%) in children and 78 (82.1%) in adults. Over the 17-year study period the averaged prevalence of invasive S. agalactiae isolates was 17.4%. The estimated incidence for neonatal infections was 1.34 per 1000 livebirths (0.99 × 1000 livebirths for early- onset disease and 0.35 × 1000 livebirths for late- onset disease) whereas for non-pregnant adults the estimated incidence was 0.75 × 1000 admissions. A remarkable increase in bloodstream infections in immunosuppressed adults and a shift to early neonatal S. agalactiae infections were seen over time. We also found an increase in S. agalactiae resistance to erythromycin and clindamycin during the study period, and the emergence of penicillin-nonsusceptible isolates. Our findings are consistent with the global trends described elsewhere, reinforcing the need for S. agalactiae control measures in our region.

We study truncation compatible families F = (F_m)_m>=1 over Q[z] through an inverse limit formalism, and we evaluate them at the punctured cyclotomic cosine points alpha_k,n = cos(2 pi k/n) with the specialization z equals n-1. For symmetric families of uniformly bounded total degree in x <= d, we prove a stable range rigidity theorem: for all n >= d+2, the cosine point evaluation factors through the finitely many punctured cosine power sums the finitely many power sums P1(n) through Pd(n). In the purely polynomial case this implies eventual polynomiality in n. We then extend the framework to include fixed product factors and package their cosine point contribution in multiplicative invariants MQ(n). In the stable range, the bounded degree symmetric part collapses as before; any remaining cyclotomic dependence occurs only through these explicit product terms. Finally, we show that coefficient extraction from such products produces further bounded degree symmetric families, and we apply this to complete symmetric functions h_r evaluated at cosine points.