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The set of ultrametrics on [ n ] nodes that are l ∞ -nearest to a given dissimilarity map forms a ( max ⁡ , + ) tropical polytope. Previous work of Bernstein has given a superset of the set containing all the phylogenetic trees that are extreme rays of this polytope. In this paper, we show that Bernstein's necessary condition of tropical extreme rays is sufficient only for n = 3 but not for n ≥ 4 . Our proof relies on the exterior description of this tropical polytope, together with the tangent hypergraph techniques for extremality characterization. The sufficiency of the case n = 3 is proved by explicitly finding all extreme rays through the exterior description. Meanwhile, an inductive construction of counterexamples is given to show the insufficiency for n ≥ 4 .

The cotton textiles with superhydrophobic and flame-retardant properties used in this study were manufactured by combining nano APP@SiO2 with silicone oil. To generate nano APP@SiO2 particles, the APP is coated with nano SiO2. The nano APP@SiO2 improves the flame retardancy of cotton textiles while altering the surface roughness of cotton fabrics, making them superhydrophobic after being treated with silicone oil. Cotton fabrics’ surface topography, chemical components, crystalline structure, thermal stability, flame-retardant, and superhydrophobic properties were investigated. The modified cotton fabric demonstrated not only exceptional superhydrophobicity with a WCA of 151.28°, but also good flame-retardant property. This multifunctional cotton fabric offers a wide range of commercial applications.

Propylene glycol alginate sodium sulfate-loaded nanoparticles (PSS-NP) has been shown potential to prevent the microvascular endothelial injuries caused by diabetic cardiomyopathy (DCM). In this study, we aimed to investigate the effects of PSS-NP on the dysfunction of cardiac microvascular endothelia in streptozotocin (STZ)-induced DCM rat model. Echocardiographic measurements showed a significant improvement of cardiac function in the PSS-NP-treated group. Our results revealed that the abnormalities of cardiac systolic and diastolic functions were suppressed by the treatments of prostaglandin E1 (PGE1), low molecular weight heparin (LMWH), PSS and PSS-NP. Our comparison analysis indicated that PSS-NP showed the strongest inhibitory effects on microvascular endothelial injuries. Transmission electron microscopy analysis demonstrated that PSS-NP protected the cardiac microvascular endothelium and further improved endothelium dysfunction in DCM rats. ELISA and Western blot assays further showed a high efficiency of improving cardiac microvascular endothelial dysfunction with PSS-NP. Our results demonstrated that PSS-NP increased the protein expression of phosphatidylinositol 3-kinase (PI3K)-p85 and vascular endothelial growth factor (VEGF)-A, and the phosphorylation of protein kinase B (Akt) and endothelial nitric oxide synthase (eNOS), which were involved in the amelioration of cardiac microvascular endothelial dysfunction. These data suggest that PSS-NP may be a novel approach to the treatment the coronary microcirculation disorder diseases such as DCM.

Characterizing metastable neural dynamics in finite-size spiking networks remains a daunting challenge. We propose to address this challenge in the recently introduced replica-mean-field (RMF) limit. In this limit, networks are made of infinitely many replicas of the finite network of interest, but with randomized interactions across replicas. Such randomization renders certain excitatory networks fully tractable at the cost of neglecting activity correlations, but with explicit dependence on the finite size of the neural constituents. However, metastable dynamics typically unfold in networks with mixed inhibition and excitation. Here, we extend the RMF computational framework to point-process-based neural network models with exponential stochastic intensities, allowing for mixed excitation and inhibition. Within this setting, we show that metastable finite-size networks admit multistable RMF limits, which are fully characterized by stationary firing rates. Technically, these stationary rates are determined as the solutions of a set of delayed differential equations under certain regularity conditions that any physical solutions shall satisfy. We solve this original problem by combining the resolvent formalism and singular-perturbation theory. Importantly, we find that these rates specify probabilistic pseudo-equilibria which accurately capture the neural variability observed in the original finite-size network. We also discuss the emergence of metastability as a stochastic bifurcation, which can be interpreted as a static phase transition in the RMF limits. In turn, we expect to leverage the static picture of RMF limits to infer purely dynamical features of metastable finite-size networks, such as the transition rates between pseudo-equilibria., Comment: 40 pages, 14 figures

Coronary microvascular dysfunction (CMD) is the pathological basis and pathogenesis of diabetic cardiomyopathy (DCM). Propylene glycol alginate sodium sulfate (PSS) as heparinoid drug has many biological activities. Here, a novel PSS-loaded nanoparticle (PSS-NP) was prepared to study its effect on the CMD of DCM. We used diabetes mellitus rat induced by STZ to establish the CMD model of DCM, and the study was detected by echocardiography, histological analysis, transmission electron microscopy, immunofluorescence staining, enzyme-linked immunosorbent assay, real time-PCR analysis, liquid-chip analysis, western blot analysis and so on. The experimental results suggested that PSS-NP could improve the survival state of rats, cardiac function, myocardial morphology and coronary microcirculation structure disorders, and increase the number of microvessels. In addition, we demonstrated that PSS-NP could alleviate the CMD by improving endothelial function, anticoagulation and antioxidative stress. The outcomes of this study provided new treatment thoughts for the therapy of coronary microcirculation dysfunction in DCM.

Objective To investigate the association between plasma levels of nucleotide-binding oligomerization domain-like (NOD)-like receptor protein 3 (NLRP3) and high mobility group box-1 (HMGB1) and their prognostic significance in neonatal patients with congenital heart disease (CHD). Methods This study enrolled neonatal patients with CHD and collected their demographic and clinical data. Plasma concentrations of NLRP3 and HMGB1 were measured using enzyme-linked immunosorbent assays. Spearman’s analysis was used to determine the correlation between NLRP3 and HMGB1 levels. The association between NLRP3 and HMGB1 levels and 2-year survival and mortality were evaluated using Kaplan–Meier curve and logistic regression analyses. Results A total of 84 neonatal patients with CHD were included in the study. Plasma NLRP3 and HMGB1 levels were significantly higher in deceased patients compared with those that survived. There was a positive correlation between NLRP3 and HMGB1 levels in neonatal patients with CHD. Patients with elevated levels of NLRP3 and HMGB1 showed significantly lower 2-year survival and higher mortality rates compared with those with lower NLRP3 and HMGB1 levels. Conclusion Neonatal patients with CHD and a poor prognosis had higher NLRP3 and HMGB1 levels, which suggests that these might be potential biomarkers of CHD prognosis.

Ferromagnetism in topological insulators (TIs) opens a topologically non-trivial exchange band gap, providing an exciting platform to manipulate the topological order through an external magnetic field. Here, we experimentally show that the surface of an antiferromagnetic thin film can independently control the topological order of the top and the bottom surface states of a TI thin film through proximity couplings. During the magnetization reversal in a field scan, two intermediate spin configurations stem from unsynchronized magnetic switchings of the top and the bottom AFM/TI interfaces. These magnetic configurations are shown to result in new topological phases with non-zero Chern numbers for each surface, introducing two counter-propagating chiral edge modes inside the exchange gap. This change in the number of transport channels, as the result of the topological transitions, induces antisymmetric magneto-resistance spikes during the magnetization reversal. With the high Neel ordering temperature provided by the antiferromagnetic layers, the signature of the induced topological transition persists in transport measurements up to a temperature of around 90 K, a factor of three over the Curie temperature in a typical magnetically doped TI thin film.

We systematically study the localization effect in discrete-time quantum walks on a honeycomb network and establish the mathematical framework. We focus on the Grover walk first and rigorously derive the limit form of the walker's state, showing it has a certain probability to be localized at the starting position. The relationship between localization and the initial coin state is concisely represented by a linear map. We also define and calculate the average probability of localization by generating random initial states. Further, coin operators varying with positions are considered and the sufficient condition for localization is discussed. We also similarly analyze another four-state Grover walk. Theoretical predictions are all in accord with numerical simulation results. Finally, our results are compared with previous works to demonstrate the unusual trapping effect of quantum walks on a honeycomb network, as well as the advantages of our method., 12 pages, 7 figures