Construction and implementation of asymptotic expansions for Jacobi-type orthogonal polynomials

We are interested in the asymptotic behavior of orthogonal polynomials of the generalized Jacobi type as their degree n goes to ∞. These are defined on the interval [−1, 1] with weight function: w(x)=(1−x)α(1+x)βh(x),α,β>−1 and h(x) a real, analytic and strictly positive function on [−1, 1]. This information is available in the work of Kuijlaars et al. (Adv. Math. 188, 337–398 2004), where the authors use the Riemann–Hilbert formulation and the Deift–Zhou non-linear steepest descent method. We show that computing higher-order terms can be simplified, leading to their efficient construction. The resulting asymptotic expansions in every region of the complex plane are implemented both symbolically and numerically, and the code is made publicly available. The main advantage of these expansions is that they lead to increasing accuracy for increasing degree of the polynomials, at a computational cost that is actually independent of the degree. In contrast, the typical use of the recurrence relation for orthogonal polynomials in computations leads to a cost that is at least linear in the degree. Furthermore, the expansions may be used to compute Gaussian quadrature rules in O(n) operations, rather than O(n2) based on the recurrence relation

Random Matrix Theory for the Hermitian Wilson Dirac Operator and the chGUE-GUE Transition

We introduce a random two-matrix model interpolating between a chiral Hermitian (2n+nu)x(2n+nu) matrix and a second Hermitian matrix without symmetries. These are taken from the chiral Gaussian Unitary Ensemble (chGUE) and Gaussian Unitary Ensemble (GUE), respectively. In the microscopic large-n limit in the vicinity of the chGUE (which we denote by weakly non-chiral limit) this theory is in one to one correspondence to the partition function of Wilson chiral perturbation theory in the epsilon regime, such as the related two matrix-model previously introduced in refs. [20,21]. For a generic number of flavours and rectangular block matrices in the chGUE part we derive an eigenvalue representation for the partition function displaying a Pfaffian structure. In the quenched case with nu=0,1 we derive all spectral correlations functions in our model for finite-n, given in terms of skew-orthogonal polynomials. The latter are expressed as Gaussian integrals over standard Laguerre polynomials. In the weakly non-chiral microscopic limit this yields all corresponding quenched eigenvalue correlation functions of the Hermitian Wilson operator.Comment: 27 pages, 4 figures; v2 typos corrected, published versio

Multimorbidity latent classes in relation to 11-year mortality, risk factors and health-related quality of life in Malaysia: a prospective health and demographic surveillance system study

\ua9 The Author(s) 2024.Background: We aimed to identify specific multimorbidity latent classes among multi-ethnic community-dwelling adults aged ≥ 18 years in Malaysia. We further explored the risk factors associated with these patterns and examined the relationships between the multimorbidity patterns and 11-year all-cause mortality risk, as well as health-related quality of life (HRQoL). Methods: Using data from 18,101 individuals (aged 18–97 years) from the baseline Census 2012, Health Round 2013, and Verbal Autopsies 2012–2023 of the South East Asia Community Observatory (SEACO) health and demographic surveillance system, latent class analysis was performed on 13 chronic health conditions to identify statistically and clinically meaningful groups. Multinomial logistic regression and Cox proportional hazards regression models were conducted to investigate the adjusted association of multimorbidity patterns with the risk factors and mortality, respectively. HRQoL was analyzed by linear contrasts in conjunction with ANCOVA adjusted for baseline confounders. Results: Four distinct multimorbidity latent classes were identified: (1) relatively healthy (n = 10,640); (2) cardiometabolic diseases (n = 2428); (3) musculoskeletal, mobility and sensory disorders (n = 2391); and (4) complex multimorbidity (a group with more severe multimorbidity with combined profiles of classes 2 and 3) (n = 699). Significant variations in associations between socio-demographic characteristics and multimorbidity patterns were discovered, including age, sex, ethnicity, education level, marital status, household monthly income and employment status. The complex multimorbidity group had the lowest HRQoL across all domains compared to other groups (p < 0.001), including physical health, psychological, social relationships and environment. This group also exhibited the highest mortality risk over 11 years even after adjustment of confounders (age, sex, ethnicity, education and employment status), with a hazard of death of 1.83 (95% CI 1.44–2.33), followed by the cardiometabolic group (HR 1.42, 95% CI 1.18–1.70) and the musculoskeletal, mobility and sensory disorders group (HR 1.29, 95% CI 1.04–1.59). Conclusions: Our study advances the understanding of the complexity of multimorbidity and its implications for health outcomes and healthcare delivery. The findings suggest the need for integrated healthcare approaches that account for the clusters of multiple conditions and prioritize the complex multimorbidity cohort. Further longitudinal studies are warranted to explore the underlying mechanisms and evolution of multimorbidity patterns

Increased permeability-oedema and atelectasis in pulmonary dysfunction after trauma and surgery: a prospective cohort study

<p>Abstract</p> <p>Background</p> <p>Trauma and surgery may be complicated by pulmonary dysfunction, acute lung injury (ALI) and acute respiratory distress syndrome (ARDS), but the mechanisms are incompletely understood.</p> <p>Methods</p> <p>We evaluated lung capillary protein permeability non-invasively with help of the ⁶⁷Ga-transferrin pulmonary leak index (PLI) technique and extravascular lung water (EVLW) by the transpulmonary thermal-dye dilution technique in consecutive, mechanically ventilated patients in the intensive care unit within 24 h of direct, blunt thoracic trauma (n = 5, 2 with ARDS), and within 12 h of indirect trauma by transhiatal oesophagectomy (n = 8), abdominal surgery for cancer (n = 6) and bone surgery (n = 4). We studied transfusion history, haemodynamics, oxygenation and mechanics of the lungs. The lung injury score (LIS, 0–4) was calculated. Plain radiography was also done to judge densities and atelectasis.</p> <p>Results</p> <p>The PLI and EVLW were elevated above normal in 61 and 30% of patients, respectively, and the PLI directly related to the number of red cell concentrates given (r_s= 0.69, P < 0.001), without group differences. Oxygenation, lung mechanics, radiographic densities and thus the LIS (1.0 [0.25–3.5]) did not relate to PLI and EVLW. However, groups differed in oxygenation and airway pressures and impaired oxygenation related to the number of radiographic quadrants with densities (r_s= 0.55, P = 0.007). Thoracic trauma patients had a worse oxygenation requiring higher airway pressures and thus higher LIS than the other patient groups, unrelated to PLI and EVLW but attributable to a higher cardiac output and thereby venous admixture. Finally, patients with radiographic signs of atelectasis had more impaired oxygenation and more densities than those without.</p> <p>Conclusion</p> <p>The oxygenation defect and radiographic densities in mechanically ventilated patients with pulmonary dysfunction and ALI/ARDS after trauma and surgery are likely caused by atelectasis rather than by increased permeability-oedema related to red cell transfusion.</p

Influence of Prototropic Reactions on the Absorption and Fluorescence Spectra of Methyl p-dimethylaminobenzoate and Its Two Ortho Derivatives

The influence of prototropic reactions on the spectral characteristics of methyl p-dimethylaminobenzoate (I) and its o-methoxy (II) and o-hydroxy (III) derivatives has been studied using steady-state spectroscopic technique and quantum-chemical calculations. This study concerns the solvent-induced shift of the absorption, locally excited (LE) and intramolecular charge transfer (ICT) fluorescence bands in the neat tetrahydrofuran (THF) and its hydrochloric acid solutions at different HCl concentrations. On the basis of the experimental results and quantum-chemical calculations, it was shown that in a hydrochloric acid solution the studied molecules exist as a mixture of neutral, mono-, and dicationic forms. Additionally, the results of spectroscopic measurements were used to calculate, according to the Benesi-Hildebrand method, the equilibrium constants of protopropic reactions in the ground, S0, and excited, S1, states. Our findings predestine molecules I and II to be used as acid fluorescence probes in a region of 0–2.5 M of [H+] concentrations

Digital remote assessment of speech acoustics in cognitively unimpaired adults: feasibility, reliability and associations with amyloid pathology

BACKGROUND: Digital speech assessment has potential relevance in the earliest, preclinical stages of Alzheimer's disease (AD). We evaluated the feasibility, test-retest reliability, and association with AD-related amyloid-beta (Aβ) pathology of speech acoustics measured over multiple assessments in a remote setting. METHODS: Fifty cognitively unimpaired adults (Age 68 ± 6.2 years, 58% female, 46% Aβ-positive) completed remote, tablet-based speech assessments (i.e., picture description, journal-prompt storytelling, verbal fluency tasks) for five days. The testing paradigm was repeated after 2-3 weeks. Acoustic speech features were automatically extracted from the voice recordings, and mean scores were calculated over the 5-day period. We assessed feasibility by adherence rates and usability ratings on the System Usability Scale (SUS) questionnaire. Test-retest reliability was examined with intraclass correlation coefficients (ICCs). We investigated the associations between acoustic features and Aβ-pathology, using linear regression models, adjusted for age, sex and education. RESULTS: The speech assessment was feasible, indicated by 91.6% adherence and usability scores of 86.0 ± 9.9. High reliability (ICC ≥ 0.75) was found across averaged speech samples. Aβ-positive individuals displayed a higher pause-to-word ratio in picture description (B = -0.05, p = 0.040) and journal-prompt storytelling (B = -0.07, p = 0.032) than Aβ-negative individuals, although this effect lost significance after correction for multiple testing. CONCLUSION: Our findings support the feasibility and reliability of multi-day remote assessment of speech acoustics in cognitively unimpaired individuals with and without Aβ-pathology, which lays the foundation for the use of speech biomarkers in the context of early AD

Free-standing supercapacitors from Kraft lignin nanofibers with remarkable volumetric energy density

We have discovered a very simple method to address the challenge associated with the low volumetric energy density of free-standing carbon nanofiber electrodes for supercapacitors by electrospinning Kraft lignin in the presence of an oxidizing salt (NaNO₃) and subsequent carbonization in a reducing atmosphere. The presence of the oxidative salt decreases the diameter of the resulting carbon nanofibers doubling their packing density from 0.51 to 1.03 mg cm⁻² and hence doubling the volumetric energy density. At the same time, the oxidative NaNO₃ salt eletrospun and carbonized together with lignin dissolved in NaOH acts as a template to increase the microporosity, thus contributing to a good gravimetric energy density. By simply adjusting the process parameters (amount of oxidizing/reducing agent), the gravimetric and volumetric energy density of the resulting lignin free-standing carbon nanofiber electrodes can be carefully tailored to fit specific power to energy demands. The areal capacitance increased from 147 mF cm⁻² in the absence of NaNO₃ to 350 mF cm⁻² with NaNO₃ translating into a volumetric energy density increase from 949 μW h cm⁻³ without NaNO₃ to 2245 μW h cm⁻³ with NaNO₃. Meanwhile, the gravimetric capacitance also increased from 151 F g⁻¹ without to 192 F g⁻¹ with NaNO

Mechanisms of pulmonary dysfunction after on-pump and off-pump cardiac surgery: a prospective cohort study

BACKGROUND: Pulmonary dysfunction following cardiac surgery is believed to be caused, at least in part, by a lung vascular injury and/or atelectasis following cardiopulmonary bypass (CPB) perfusion and collapse of non-ventilated lungs. METHODS: To test this hypothesis, we studied the postoperative pulmonary leak index (PLI) for (67)Ga-transferrin and (transpulmonary) extravascular lung water (EVLW) in consecutive patients undergoing on-pump (n = 31) and off-pump (n = 8) cardiac surgery. We also studied transfusion history, radiographs, ventilatory and gas exchange variables. RESULTS: The postoperative PLI and EVLW were elevated above normal in 42 and 29% after on-pump surgery and 63 and 37% after off-pump surgery, respectively (ns). Transfusion of red blood cell (RBC) concentrates, PLI, EVLW, occurrence of atelectasis, ventilatory variables and duration of mechanical ventilation did not differ between groups, whereas patients with atelectasis had higher venous admixture and airway pressures than patients without atelectasis (P = 0.037 and 0.049). The PLI related to number of RBC concentrates infused (P = 0.025). CONCLUSION: The lung vascular injury in about half of patients after cardiac surgery is not caused by CPB perfusion but by trauma necessitating RBC transfusion, so that off-pump surgery may not afford a benefit in this respect. However, atelectasis rather than lung vascular injury is a major determinant of postoperative pulmonary dysfunction, irrespective of CPB perfusion

Vasopressors and Inotropes in the Treatment of Human Septic Shock: Effect on Innate Immunity?

Catecholamines have been suggested to modulate innate immune responses in experimental settings. The significance hereof in the treatment of human septic shock is unknown. We therefore sought if and how vasopressor/inotropic doses relate to pro-inflammatory mediators during treatment of septic shock. We prospectively studied 20 consecutive septic shock patients. For 3 days after admission, hemodynamic variables, lactate and plasma levels of interleukins (IL)-6 and 8, tumor necrosis factor (TNF)-α, and elastase-α1-antitrypsin were measured six hourly. Doses of vasoactive drugs were recorded. Of the 20 patients, nine died in the intensive care unit. Dobutamine doses were positively associated and related to TNF-α plasma levels, independently of disease severity, hemodynamics, and outcome, in multivariable models. Dopamine doses were positively associated with IL-6, and norepinephrine was inversely associated with IL-8 and TNF-α levels. Our observations suggest that catecholamines used in the treatment of human septic shock differ in their potential modulation of the innate immune response to sepsis in vivo. Dobutamine treatment may contribute to circulating TNF-α and dopamine to IL-6, independently of activated neutrophils. Conversely, norepinephrine may lack pro-inflammatory actions

Comparative genomics in cyprinids: common carp ESTs help the annotation of the zebrafish genome

BACKGROUND: Automatic annotation of sequenced eukaryotic genomes integrates a combination of methodologies such as ab-initio methods and alignment of homologous genes and/or proteins. For example, annotation of the zebrafish genome within Ensembl relies heavily on available cDNA and protein sequences from two distantly related fish species and other vertebrates that have diverged several hundred million years ago. The scarcity of genomic information from other cyprinids provides the impetus to leverage EST collections to understand gene structures in this diverse teleost group. RESULTS: We have generated 6,050 ESTs from the differentiating testis of common carp (Cyprinus carpio) and clustered them with 9,303 non-gonadal ESTs from CarpBase as well as 1,317 ESTs and 652 common carp mRNAs from GenBank. Over 28% of the resulting 8,663 unique transcripts are exclusively testis-derived ESTs. Moreover, 974 of these transcripts did not match any sequence in the zebrafish or fathead minnow EST collection. A total of 1,843 unique common carp sequences could be stringently mapped to the zebrafish genome (version 5), of which 1,752 matched coding sequences of zebrafish genes with or without potential splice variants. We show that 91 common carp transcripts map to intergenic and intronic regions on the zebrafish genome assembly and regions annotated with non-teleost sequences. Interestingly, an additional 42 common carp transcripts indicate the potential presence of new splicing variants not found in zebrafish databases so far. The fact that common carp transcripts help the identification or confirmation of these coding regions in zebrafish exemplifies the usefulness of sequences from closely related species for the annotation of model genomes. We also demonstrate that 5' UTR sequences of common carp and zebrafish orthologs share a significant level of similarity based on preservation of motif arrangements for as many as 10 ab-initio motifs. CONCLUSION: Our data show that there is sufficient homology between the transcribed sequences of common carp and zebrafish to warrant an even deeper cyprinid transcriptome comparison. On the other hand, the comparative analysis illustrates the value in utilizing partially sequenced transcriptomes to understand gene structure in this diverse teleost group. We highlight the need for integrated resources to leverage the wealth of fragmented genomic data