More Like this

1. 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} . 

   more » « less
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. 

   more » « less
3. Convergence science in the Anthropocene: Navigating the known and unknown

   https://doi.org/10.1002/pan3.10069  

   Angeler, David G.; Allen, Craig R.; Carnaval, Ana; Palmer, ed., Clare (February 2020, People and Nature)

   Abstract Rapidly changing ecological and social systems currently pose significant societal challenges. Navigating the complexity of social‐ecological change requires approaches able to cope with, and potentially solve, both foreseen and unforeseen societal challenges.The emergent field of convergence addresses the intricacies of such challenges, and is thus relevant to a broad range of interdisciplinary issues.This paper suggests a way to conceptualize convergence research. It discusses how it relates to two major societal challenges (adaptation, transformation), and to the generation of policy‐relevant science. It also points out limitations to the further development of convergence research. A freePlain Language Summarycan be found within the Supporting Information of this article. 

   more » « less
4. On the Determinant Problem for the Relativistic Boltzmann Equation

   https://doi.org/10.1007/s00220-021-04101-2  

   Chapman, James; Jang, Jin Woo; Strain, Robert M. (June 2021, Communications in Mathematical Physics)

   Abstract This article considers a long-outstanding open question regarding the Jacobian determinant for the relativistic Boltzmann equation in the center-of-momentum coordinates. For the Newtonian Boltzmann equation, the center-of-momentum coordinates have played a large role in the study of the Newtonian non-cutoff Boltzmann equation, in particular we mention the widely used cancellation lemma [1]. In this article we calculate specifically the very complicated Jacobian determinant, in ten variables, for the relativistic collision map from the momentum p to the post collisional momentum $$p'$$ p ′ ; specifically we calculate the determinant for $$p\mapsto u = \theta p'+\left( 1-\theta \right) p$$ p ↦ u = θ p ′ + 1 - θ p for $$\theta \in [0,1]$$ θ ∈ [ 0 , 1 ] . Afterwards we give an upper-bound for this determinant that has no singularity in both p and q variables. Next we give an example where we prove that the Jacobian goes to zero in a specific pointwise limit. We further explain the results of our numerical study which shows that the Jacobian determinant has a very large number of distinct points at which it is machine zero. This generalizes the work of Glassey-Strauss (1991) [8] and Guo-Strain (2012) [12]. These conclusions make it difficult to envision a direct relativistic analog of the Newtonian cancellation lemma in the center-of-momentum coordinates. 

   more » « less
5. Human cat borne rabies as the new epidemiology of the disease in the Andes mountains

   https://doi.org/10.1111/zph.13141  

   Meriño‐Olivella, Samir; del_Pilar Sánchez‐Bonilla, María; Escobar, Luis E; Correa‐Valencia, Nathalia M (August 2024, Zoonoses and Public Health)

   Abstract BackgroundRabies virus (RABV) is the etiologic agent of rabies, a fatal brain disease in mammals. Rabies circulation has historically involved the dog has the main source of human rabies worldwide. Nevertheless, in Colombia, cats (Felis catus) have become a relevant species in the epidemiology of rabies. AimsTo characterize rabies cases in humans in Colombia in the last three decades in the context of the epidemiology of the aggressor animal. Materials and MethodsWe conducted a retrospective longitudinal epidemiological study of human rabies caused by cats’ aggression, collecting primary and secondary information. Variables considered included the demography of the patient, symptoms, information about the aggressor animal as the source of infection and the viral variant identified. ResultsWe found that the distribution of rabies incidence over the years has been constant in Colombia. Nevertheless, between 2003 and 2012 a peak of cases occurred in rural Colombia where cats were the most frequent aggressor animal reported. Most cats involved in aggression were unvaccinated against rabies. Cat's clinical signs at the time of the report of the human cases included hypersalivation and changes in behaviour. Human patients were mostly children and female and the exposure primarily corresponded to bite and puncture lacerations in hands. The RABV lineage detected in most cases corresponded to variant 3, linked to the common vampire bat (Desmodus rotundus). The geographical presentation of cat borne RABV in humans occurred along the Andes mountains, epidemiologically known as the rabies red Andean corridor. DiscussionBy finding cats as the primary source of rabies spillover transmission in Colombia, this report highlights the importance of revising national rabies control and prevention protocol in countries in the Andes region. ConclusionOur results demonstrate that rabies vaccination for outdoor cats needs to prioritize to reduce the number of rabies‐related human deaths. 

   more » « less