Discovering product and coproduct Rules for Bases of QSymF{\textsf {QSym}}_F through Supercharacters

In this paper, we establish product and coproduct rules for three bases of the Hopf algebra $\textsf{QSym}_F$ of quasisymmetric functions over $F$, with $F$ being either $\mathbb{C}(q,t)$ or $\mathbb{C}(q)$. These results are derived through the categorizations of $\textsf{QSym}_{\mathbb{C}}$ obtained by utilizing the normal lattice supercharacter theories. Firstly, we deal with a basis $\{\mathcal{D}_{\alpha}(q,t) \mid \alpha \in \textsf{Comp}\}$ of $\textsf{QSym}_{\mathbb{C}(q,t)}$, where $\textsf{Comp}$ denotes the set of all compositions. This basis is obtained from the direct sum of specific supercharacter function spaces and consists of superclass identifier functions. Upon appropriate specializations of $q$ and $t$, it yields notable bases of $\textsf{QSym}_{\mathbb{C}}$ and $\textsf{QSym}_{\mathbb{C}(q)}$, including enriched $q$-monomial quasisymmetric functions introduced by Grinberg and Vassilieva. Secondly, we deal with the basis $\{G_{\alpha}(q) \mid \alpha \in \textsf{Comp}\}$ of $\textsf{QSym}_{\mathbb{C}(q)}$, where $G_{\alpha}(q)$ represents the quasisymmetric Hall-Littlewood function introduced by Hivert. Our product rule is new, whereas our coproduct rule turns out to be equivalent to the existing coproduct rule of Hivert. Finally, we consider a basis $\{M_{\alpha}(q) \mid \alpha \in \textsf{Comp}\}$ of $\textsf{QSym}_{\mathbb{C}(q)}$, where $M_{\alpha}(q)$ is a $q$-analogue of the monomial quasisymmetric function.Comment: 51 pages. This paper is a revised version of arXiv:2207.11110, yet it is released independently due to substantial revisions and a significant shift in the research directio

Effective Field Theory of Dipolar Braiding Statistics in Two Dimensions

A rank-2 toric code (R2TC) Hamiltonian in two dimensions can be constructed as a Higgsed descendant of rank-2 U(1) lattice gauge theory. As noted by the authors recently, [Y.-T. Oh, J. Kim, E.-G. Moon, and J. H. Han, Phys. Rev. B {\bf 105}, 045128] the quasiparticles in that model showed braiding statistics that depends on the initial locations of the particles which participate in the braiding. We argue that this new kind of statistical phase captures the total dipole moment of quasiparticles encompassed in the braiding, whereas conventional anyonic braiding sees the total charge. An Aharonov-Bohm interpretation of such {\it dipolar braiding statistics} can be made in terms of emergent, rank-1 vector potentials built from the underlying rank-2 gauge fields. Pertinent field theories of the quasiparticle dynamics in the R2TC are developed, which turn out to be highly interacting theories predicting their constrained dynamics. The accompanying conservation laws are also of unusual types. A {\it dipolar BF theory} of the rank-2 gauge fields is constructed and shown to correctly capture the dipolar braiding statistics, in contrast to the conventional BF theory capturing the {\it monopolar braiding statistics} of anyons in the rank-1 toric code. A tight-binding model for the quasiparticle dynamics in the R2TC involves two-particle as well as the one-particle hopping, both of which are coupled to the tensor gauge fields.Comment: 6 pages, supplementary materials, 3 figure

Association of neuromuscular reversal by sugammadex and neostigmine with 90-day mortality after non-cardiac surgery

Abstract Background Reversing a neuromuscular blockade agent with sugammadex is known to lessen postoperative complications by reducing postoperative residual curarization. However, its effects on 90-day mortality are unknown. Therefore, this study aimed to compare the effects of sugammadex and neostigmine in terms of 90-day mortality after non-cardiac surgery. Methods This retrospective cohort study analyzed the medical records of adult patients aged 18 years or older who underwent non-cardiac surgery at a single tertiary care hospital between 2011 and 2016. Propensity score matching and Cox regression analysis were used to investigate the effectiveness of sugammadex and neostigmine in lowering 90-day mortality after non-cardiac surgery. Results A total of 65,702 patients were included in the analysis (mean age: 52.3 years, standard deviation: 15.7), and 23,532 of these patients (35.8%) received general surgery. After propensity score matching, 14,179 patients (3906 patients from the sugammadex group and 10,273 patients from the neostigmine group) were included in the final analysis. Cox regression analysis in the propensity score-matched cohort showed that the risk of 90-day mortality was 40% lower in the sugammadex group than in the neostigmine group (hazard ratio: 0.60, 95% confidence interval: 0.37, 0.98; P = 0.042). These results were similar in the multivariable Cox regression analysis of the entire cohort (hazard ratio: 0.62, 95% confidence interval: 0.39, 0.96; P = 0.036). Conclusions This retrospective cohort study suggested that reversing rocuronium with sugammadex might be associated with lower 90-day mortality after non-cardiac surgery compared to neostigmine. However, since this study did not evaluate quantitative neuromuscular function in the postoperative period due to its retrospective design, the results should be interpreted carefully. Future prospective studies with quantitative neuromuscular monitoring in the postoperative period should be performed to confirm these results

Good Glycemic Control Is Associated with Better Survival in Diabetic Patients on Peritoneal Dialysis: A Prospective Observational Study

BACKGROUND: The effect of glycemic control after starting peritoneal dialysis (PD) on the survival of diabetic PD patients has largely been unexplored, especially in Asian population. METHODS: We conducted a prospective observational study, in which 140 incident PD patients with diabetes were recruited. Patients were divided into tertiles according to the means of quarterly HbA1C levels measured during the first year after starting PD. We examined the association between HbA1C and all-cause mortality using Cox proportional hazards models. RESULTS: The mean age was 58.7 years, 59.3% were male, and the mean follow-up duration was 3.5 years (range 0.4-9.5 years). The mean HbA1C levels were 6.3%, 7.1%, and 8.5% in the 1(st), 2(nd), and 3(rd) tertiles, respectively. Compared to the 1(st) tertile, the all-cause mortality rates were higher in the 2(nd) [hazard ratio (HR), 4.16; 95% confidence interval (CI), 0.91-18.94; p = 0.065] and significantly higher in the 3(rd) (HR, 13.16; 95% CI, 2.67-64.92; p = 0.002) tertiles (p for trend = 0.005), after adjusting for confounding factors. Cardiovascular mortality, however, did not differ significantly among the tertiles (p for trend = 0.682). In contrast, non-cardiovascular deaths, most of which were caused by infection, were more frequent in the 2(nd) (HR, 7.67; 95% CI, 0.68-86.37; p = 0.099) and the 3(rd) (HR, 51.24; 95% CI, 3.85-681.35; p = 0.003) tertiles than the 1(st) tertile (p for trend = 0.007). CONCLUSIONS: Poor glycemic control is associated with high mortality rates in diabetic PD patients, suggesting that better glycemic control may improve the outcomes of these patients

A Case of Acrodermatitis Enteropathica Localized on the Hands and Feet with a Normal Serum Zinc Level

Acrodermatitis enteropathica is classified as a congenital autosomal recessive type and an acquired transient type. This disease manifests as acral and periorificial dermatitis, alopecia, intractable diarrhea, and failure to thrive. Whereas the autosomal hereditary type is caused by malabsorption of zinc in the intestine, the acquired type is caused by low nutritional support or decreased peripheral release of zinc from blood. We experienced a case of a 5-month old, breast feeding, full-term female presenting with only acral bullous dermatitis without diarrhea, periorificial dermatitis and an abnormal serum zinc level