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1. 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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2. Behavioral fingerprinting of Internet‐of‐Things devices

   https://doi.org/10.1002/widm.1337  

   Bezawada, Bruhadeshwar; Ray, Indrakshi; Ray, Indrajit (September 2019, WIREs Data Mining and Knowledge Discovery)

   Abstract Rapid advances in the Internet‐of‐Things (IoT) domain have led to the development of several useful and interesting devices that have enhanced the quality of home living and industrial automation. The vulnerabilities in the IoT devices have rendered them susceptible to compromise and forgery. The problem of device authentication, that is, the question of whether a device's identity is what it claims to be, is still an open problem. Device fingerprinting seems to be a promising authentication mechanism. Device fingerprinting profiles a device based on information available about the device and generate a robust, verifiable and unique identity for the device. Existing approaches for device fingerprinting may not be feasible or cost‐effective for the IoT domain due to the resource constraints and heterogeneity of the IoT devices. Due to resource and cost constraints, behavioral fingerprinting provides promising directions for fingerprinting IoT devices. Behavioral fingerprinting allows security researchers to understand the behavioral profile of a device and to establish some guidelines regarding the device operations. In this article, we discuss existing approaches for behavioral fingerprinting of devices in general and evaluate their applicability for IoT devices. Furthermore, we discuss potential approaches for fingerprinting IoT devices and give an overview of some of the preliminary attempts to fingerprint IoT devices. We conclude by highlighting the future research directions for fingerprinting in the IoT domain. This article is categorized under:Application Areas > Science and TechnologyApplication Areas > InternetTechnologies > Machine LearningApplication Areas > Industry Specific Applications 

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3. The eigensplitting of the fiber of the cyclotomic trace for the sphere spectrum

   https://doi.org/10.1090/tran/8822  

   Blumberg, Andrew; Mandell, Michael (January 2022, Transactions of the American Mathematical Society)

   Let p ∈ Z p\in {\mathbb {Z}} be an odd prime. We show that the fiber sequence for the cyclotomic trace of the sphere spectrum S {\mathbb {S}} admits an “eigensplitting” that generalizes known splittings on K K -theory and T C TC . We identify the summands in the fiber as the covers of Z p {\mathbb {Z}}_{p} -Anderson duals of summands in the K ( 1 ) K(1) -localized algebraic K K -theory of Z {\mathbb {Z}} . Analogous results hold for the ring Z {\mathbb {Z}} where we prove that the K ( 1 ) K(1) -localized fiber sequence is self-dual for Z p {\mathbb {Z}}_{p} -Anderson duality, with the duality permuting the summands by i ↦ p − i i\mapsto p-i (indexed mod p − 1 p-1 ). We explain an intrinsic characterization of the summand we call Z Z in the splitting T C ( Z ) p ∧ ≃ j ∨ Σ j ′ ∨ Z TC({\mathbb {Z}})^{\wedge }_{p}\simeq j \vee \Sigma j’\vee Z in terms of units in the p p -cyclotomic tower of Q p {\mathbb {Q}}_{p} . 

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4. On the number of closed gaps of discrete periodic one-dimensional operators

   https://doi.org/10.1063/5.0175428  

   Arroyo, Andrew; Castro, Faye; Fillman, Jake (May 2024, Journal of Mathematical Physics)

   From the general inverse theory of periodic Jacobi matrices, it is known that a periodic Jacobi matrix of minimal period p≥2 may have at most p−2 closed spectral gaps. We discuss the maximal number of closed gaps for one-dimensional periodic discrete Schrödinger operators of period p. We prove nontrivial upper and lower bounds on this quantity for large p and compute it exactly for p≤6. Among our results, we show that a discrete Schrödinger operator of period four or five may have at most a single closed gap, and we characterize exactly which potentials may exhibit a closed gap. For period six, we show that at most two gaps may close. In all cases in which the maximal number of closed gaps is computed, it is seen to be strictly smaller than p−2, the bound guaranteed by the inverse theory. We also discuss similar results for purely off-diagonal Jacobi matrices. 

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5. 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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