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1. Size of nodal domains of the eigenvectors of a graph

   https://doi.org/10.1002/rsa.20925  

   Huang, Han; Rudelson, Mark (April 2020, Random Structures & Algorithms)

   Consider an eigenvector of the adjacency matrix of aG(n,p) graph. A nodal domain is a connected component of the set of vertices where this eigenvector has a constant sign. It is known that with high probability, there are exactly two nodal domains for each eigenvector corresponding to a nonleading eigenvalue. We prove that with high probability, the sizes of these nodal domains are approximately equal to each other. 

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2. THE BOUNDARY OF THE p -RANK STRATUM OF THE MODULI SPACE OF CYCLIC COVERS OF THE PROJECTIVE LINE

   https://doi.org/10.1017/nmj.2022.12  

   OZMAN, EKIN; PRIES, RACHEL; WEIR, COLIN (December 2022, Nagoya Mathematical Journal)

   Abstract. We study the p-rank stratification of the moduli space of cyclic degree ! covers of the projective line in characteristic p for distinct primes p and !. The main result is about the intersection of the p-rank 0 stratum with the boundary of the moduli space of curves. When ! = 3 and p ≡ 2 mod 3 is an odd prime, we prove that there exists a smooth trielliptic curve in characteristic p, for every genus g, signature type (r,s), and p-rank f satisfying the clear necessary conditions. 

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3. Impact of Obesity on Timing of Tracheotomy: A Multi‐institutional Retrospective Study

   https://doi.org/10.1002/lary.31586  

   Yousef, Andrew; Soliman, Shady I; Solomon, Isaac; Panuganti, Bharat A; Francis, David O; Pang, John; Klebaner, Dasha; Asturias, Alicia; Alattar, Ali; Wood, Samuel; et al (November 2024, The Laryngoscope)

   ObjectiveTo examine the impact of increased body mass index (BMI) on (1) tracheotomy timing and (2) short‐term surgical complications requiring a return to the operating room and 30‐day mortality utilizing data from the Multi‐Institutional Study on Tracheotomy (MIST). MethodsA retrospective analysis of patients from the MIST database who underwent surgical or percutaneous tracheotomy between 2013 and 2016 at eight institutions was completed. Unadjusted and adjusted logistic regression analyses were used to assess the impact of obesity on tracheotomy timing and complications. ResultsAmong the 3369 patients who underwent tracheotomy, 41.0% were obese and 21.6% were morbidly obese. BMI was associated with higher rates of prolonged intubation prior to tracheotomy accounting for comorbidities, indication for tracheotomy, institution, and type of tracheostomy (p = 0.001). Morbidly obese patients (BMI ≥35 kg/m²) experienced a longer duration of intubation compared with patients with a normal BMI (median days intubated [IQR 25%–75%]: 11.0 days [7–17 days] versus 9.0 days [5–14 days];p < 0.001) but did not have statistically higher rates of return to the operating room within 30 days (p = 0.12) or mortality (p = 0.90) on multivariable analysis. This same finding of prolonged intubation was not seen in overweight, nonobese patients when compared with normal BMI patients (median days intubated [IQR 25%–75%]: 10.0 days [6–15 days] versus 10.0 days [6–15 days];p = 0.36). ConclusionBMI was associated with increased duration of intubation prior to tracheotomy. Although morbidly obese patients had a longer duration of intubation, there were no differences in return to the operating room or mortality within 30 days. Level of Evidence3Laryngoscope, 134:4674–4681, 2024 

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4. Spatial phylogenetics of Fagales: Investigating drivers of temperate forest distributions

   https://doi.org/10.1111/jbi.14840  

   Folk, R_A; Siniscalchi, C_M; Doby, J.; Kates, H_R; Manchester, S_R; Soltis, P_S; Soltis, D_E; Guralnick, R_P; Belitz, M. (April 2024, Journal of Biogeography)

   Abstract AimQuantifying the phylogenetic diversity of temperate trees is essential for understanding the processes that have shaped the modern distribution of temperate broadleaf forest and other major forest biomes. Here, we focus on Fagales, an iconic member of forests worldwide, to uncover global diversity and endemism patterns and investigate the distribution of root nodule symbiosis (RNS), an important morphological specialisation in this clade, as a key factor behind these patterns. LocationGlobal. TaxonFagales. MethodsWe combined phylogenetic data covering 60.2% of living species, fine‐scale distribution models covering 90% of species, and nodulation data covering all species to investigate the distribution of species richness and phylogenetic diversity at fine spatial scales compared to the distribution of RNS. We identify abiotic environmental factors associated with RNS and with Fagales diversity in general. ResultsWe find the highest species richness in temperate east Asia, eastern North America, and equatorial montane regions of Asia and Central America. By contrast, relative phylogenetic diversity (RPD) is highest at higher latitudes, where RNS also predominates. We found a strong spatial structuring of regionalisations of Fagales floras, reflecting distinct Northern and Southern Hemisphere floras (except a unique Afro‐Boreal region), each with distinct RNS‐environment relationships. Main ConclusionsAlthough species richness and phylogenetic regionalisation for Fagales accord well with traditional biogeographic concepts for temperate forests, this is not the case for RPD. RNS is almost universal in the highest RPD regions, which may reflect ecological filtering promoting RNS in these regions. Our results highlight the utility of global‐scale, clade‐specific spatial phylogenetics and its utility for understanding drivers of diversity in species‐rich clades. 

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5. Impact of salt and fillers on the rheological properties of polymer composites

   https://doi.org/10.1002/pc.29409  

   Teymoory, Parya; Driscoll, Stephen_Burke; Zhao, Jingzhou; Shen, Caiwei (December 2024, Polymer Composites)

   Abstract Polymer composites with salts or conductive fillers are promising for various solid‐state energy storage applications, where processability is often determined by their rheological properties. This study investigates the effect of lithium salts and conductive fillers on the rheological behavior of polylactic acid (PLA)‐based composites. We specifically examine how these additives influence complex viscosity and the interactions between the salt, fillers, and polymer. Our findings reveal that adding salt to the polymer reduces its viscosity, whereas adding conductive fillers imparts a shear‐thinning property, which is advantageous for thermal processing methods like thermal drawing, injection molding, or 3D printing. The combination of salt and conductive fillers results in multifunctional electrode‐electrolyte composites with enhanced shear‐thinning behavior and improved storage modulus. Characterizations through x‐ray diffraction, electrical measurements, and transmission electron microscopy link the electrical properties and morphology with rheological behavior. The formation of a robust filler network in these composites ensures stable viscoelastic behavior across a range of temperatures and frequencies, indicating their suitability for efficient manufacturing of polymer‐based solid‐state electrode‐electrolyte composites via thermal processing. HighlightsShear‐thinning behavior enhanced by conductive fillers.Viscosity increased with CB and CNT fillers, forming robust networks.Salt reduced viscosity but filler networks dominated flow behavior.Filler combinations led to stable viscoelastic properties across temperatures.Polymer electrolyte–electrode composites improved processability and storage modulus. 

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