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We derive and implement a new way to find lower bounds on the smallest limiting trace-to-degree ratio of totally positive algebraic integers and improve the previously best known bound to 1.80203. Our method adds new constraints to Smyth’s linear programming method to decrease the number of variables required in the new problem of interest. This allows for faster convergence recovering Schur’s bound in the simplest case and Siegel’s bound in the second simplest case of our new family of bounds. We also prove the existence of a unique optimal solution to our newly phrased problem and express the optimal solution in terms of polynomials. Lastly, we solve this new problem numerically with a gradient descent algorithm to attain the new bound 1.80203. 

Abstract Given a prime powerqand$$n \gg 1$$ $n\gg 1$, we prove that every integer in a large subinterval of the Hasse–Weil interval$$[(\sqrt{q}-1)^{2n},(\sqrt{q}+1)^{2n}]$$ $[{(\sqrt{q}-1)}^{2n},{(\sqrt{q}+1)}^{2n}]$is$$\#A({\mathbb {F}}_q)$$ $\#A\left(F_q\right)$for some ordinary geometrically simple principally polarized abelian varietyAof dimensionnover$${\mathbb {F}}_q$$ $F_q$. As a consequence, we generalize a result of Howe and Kedlaya for$${\mathbb {F}}_2$$ $F_2$to show that for each prime powerq, every sufficiently large positive integer is realizable, i.e.,$$\#A({\mathbb {F}}_q)$$ $\#A\left(F_q\right)$for some abelian varietyAover$${\mathbb {F}}_q$$ $F_q$. Our result also improves upon the best known constructions of sequences of simple abelian varieties with point counts towards the extremes of the Hasse–Weil interval. A separate argument determines, for fixedn, the largest subinterval of the Hasse–Weil interval consisting of realizable integers, asymptotically as$$q \rightarrow \infty $$ $q\to \infty$; this gives an asymptotically optimal improvement of a 1998 theorem of DiPippo and Howe. Our methods are effective: We prove that if$$q \le 5$$ $q\le 5$, then every positive integer is realizable, and for arbitraryq, every positive integer$$\ge q^{3 \sqrt{q} \log q}$$ $\ge q^{3\sqrt{q}logq}$is realizable. 

Nepal’s forest cover nearly doubled over the last three decades. While Community Forest (CF) management and agricultural abandonment are primary drivers of forest cover expansion, the contribution of afforestation on privately managed land is not well documented. We mapped forest cover change from 1988 through 2016 in 40 privately managed sites that transitioned from agriculture to forest and assessed how agricultural abandonment influenced private land management and afforestation. We used a mixed method analysis to integrate our 29- year Landsat satellite image-based record of annual forest cover with interview data on historical land cover and land use dynamics from 65 land managers in Bagmati Province. We find that privately managed land accounted for 37% of local forest cover gain, with mean forest area within private forests growing from 9% to 59%. Land managers identified two factors driving these gains on private land: implementation of CF man- agement in adjacent government forests and out-migration. These previously undocumented linkages between forest cover gain on private land and CF management merits further research in community forests and calls for greater policy and technical support for small-scale timber growers and rural households who rely on private forests for income generation. 

Abstract Zinc (Zn) is a major soil contaminant and high Zn levels can disrupt growth, survival, and reproduction of fungi. Some fungal species evolved Zn tolerance through cell processes mitigating Zn toxicity, although the genes and detailed mechanisms underlying mycorrhizal fungal Zn tolerance remain unexplored. To fill this gap in knowledge, we investigated the gene expression of Zn tolerance in the ectomycorrhizal fungus Suillus luteus. We found that Zn tolerance in this species is mainly a constitutive trait that can also be environmentally dependent. Zinc tolerance in S. luteus is associated with differences in the expression of genes involved in metal exclusion and immobilization, as well as recognition and mitigation of metal-induced oxidative stress. Differentially expressed genes were predicted to be involved in transmembrane transport, metal chelation, oxidoreductase activity, and signal transduction. Some of these genes were previously reported as candidates for S. luteus Zn tolerance, while others are reported here for the first time. Our results contribute to understanding the mechanisms of fungal metal tolerance and pave the way for further research on the role of fungal metal tolerance in mycorrhizal associations.