Necrotizing fasciitis (NF) is a life-threatening soft tissue infection with limited epidemiological data from Latin America. This study aimed to characterize clinical outcomes, identify factors associated with in-hospital mortality, and develop a clinical prediction model in patients with NF at a tertiary care center in Medellín, Colombia. A retrospective cohort study was conducted including all adult patients (≥ 18 years) with surgically or histopathologically confirmed NF between January 2019 and December 2024. Demographic, clinical, microbiological, and therapeutic variables were collected. Bivariable analysis and multivariable logistic regression were performed to identify independent mortality predictors. A clinical risk score was developed and internally validated using bootstrap resampling and 10-fold cross-validation. Of 112 identified patients, 111 met inclusion criteria. Overall in-hospital mortality was 23.4
In this work, we propose a Stackelberg-like model for a resource allocation problem over an urban region. The model incorporates transportation costs, distribution costs, and utility functions. A social planner aims to minimize the total cost while maximizing the welfare of the population that receives the resource. The resulting formulation is a bilevel optimization problem—also known as a Stackelberg game in game theory. The existence of the best-response function is established by means of results from optimal transport theory.
Introduction Food insecurity is associated with cardiovascular mortality, but the processes involved are poorly characterized. This study examined whether that association can be statistically decomposed through depressive symptoms and systemic inflammation. Methods Secondary analysis of the five NHANES cycles between 2005 and 2018 in which high-sensitivity C-reactive protein (hs-CRP) was measured, linked to the National Death Index for mortality follow-up through December 31, 2019 (18,948 adults; 583 cardiovascular deaths). Food insecurity was assessed with the U.S. Department of Agriculture Food Security Survey Module and depressive symptoms with the 9-item Patient Health Questionnaire (PHQ-9). Both inflammatory markers were pre-specified. Paths were estimated by survey-weighted least squares and Cox regression, with bias-corrected percentile intervals from a design-based replicate bootstrap respecting survey strata and primary sampling units. Cause-specific hazards were the primary estimand and subdistribution hazards the secondary. Exposure, intermediates and covariates were measured at the same examination, so the ordering specified is one of several compatible with these data. Results The overall association between food insecurity and cardiovascular mortality was imprecisely estimated, with intervals including the null under minimal, moderate and extensive adjustment (hazard ratios 1.43, 1.35 and 1.30) and under the subdistribution estimand (1.24). Across the four severity categories, however, depressive symptoms rose monotonically while cardiovascular mortality did not: only very low food security carried a raised hazard (1.83, 95% CI 1.15–2.76). Food insecurity was associated with higher PHQ-9 scores (1.86 points, 95% CI 1.60–2.12) and depressive symptoms with cardiovascular mortality (1.045 per point, 95% CI 1.019–1.069). The component attributable to depressive symptoms was 0.082 on the log-hazard scale (95% CI 0.035–0.130) and excluded the null under all three adjustment sets, whereas the route continuing through systemic inflammation was two orders of magnitude smaller (0.0004 with hs-CRP, 0.0022 with the neutrophil-to-lymphocyte ratio [NLR]). NLR was associated with cardiovascular mortality (1.297 per unit, 95% CI 1.161–1.446) and hs-CRP was not (1.030, 95% CI 0.936–1.133), but that difference did not persist when participants excluded for acute inflammation were re-included. Conclusions Depressive symptoms accounted for part of the association between food insecurity and cardiovascular mortality; systemic inflammation did not. The overall association was imprecisely estimated and was concentrated in the most severe category of food insecurity, and concurrent measurement precludes causal inference. The apparent difference between the two inflammatory markers depended on a standard exclusion rule. Longitudinal measurement is required to establish ordering.
The concepts of derivations and antiderivations for Leibniz algebras naturally arise from the inner operators determined by their algebraic structure. In this paper, we introduce the corresponding analogues in the setting of dialgebras, which we call diderivations, and examine their structural properties in relation to classical derivations and multiplicative operators. Our approach is based on the study of left and right multiplication operators and on the construction of the Leibniz algebra generated by biderivations, thereby providing a systematic operator-theoretic framework that unifies several derivation-like structures. In addition to the general theory, we present a complete classification of the spaces of diderivations for dialgebras of dimensions two and three, obtained through explicit computations. These low-dimensional results not only illustrate the general constructions but also reveal structural patterns that inform possible extensions to higher dimensions and more intricate algebraic contexts.
We study cocommutative Hopf dialgebras through generalized digroups and rack combinatorics. We prove that the rack functor obtained from the adjoint rack bialgebra factorizes through the digroup of group-like elements. More precisely, for every cocommutative Hopf dialgebra $A$, the rack of set-like elements of its adjoint rack bialgebra is naturally isomorphic to the conjugation rack of the digroup $\Glike(A)$. For finite generalized digroups $D\simeq G\times E$, with $G$ acting on the halo $E$, we derive explicit formulas for the conjugation rack, its inner group, left-translation cycle index, fixed-point polynomial, orbit count and subrack structure. Finally, we construct the digroup algebra $K[D]$, prove that it is a cocommutative Hopf dialgebra, and show that $\Glike(K[D])=D\$.
