Nonisomorphic curves that become isomorphic over extensions of coprime degrees

We show that one can find two nonisomorphic curves over a field K that become isomorphic to one another over two finite extensions of K whose degrees over K are coprime to one another. More specifically, let K_0 be an arbitrary prime field and let r and s be integers greater than 1 that are coprime to one another. We show that one can find a finite extension K of K_0, a degree-r extension L of K, a degree-s extension M of K, and two curves C and D over K such that C and D become isomorphic to one another over L and over M, but not over any proper subextensions of L/K or M/K. We show that such C and D can never have genus 0, and that if K is finite, C and D can have genus 1 if and only if {r,s} = {2,3} and K is an odd-degree extension of F_3. On the other hand, when {r,s}={2,3} we show that genus-2 examples occur in every characteristic other than 3. Our detailed analysis of the case {r,s} = {2,3} shows that over every finite field K there exist nonisomorphic curves C and D that become isomorphic to one another over the quadratic and cubic extensions of K. Most of our proofs rely on Galois cohomology. Without using Galois cohomology, we show that two nonisomorphic genus-0 curves over an arbitrary field remain nonisomorphic over every odd-degree extension of the base field.Comment: LaTeX, 32 pages. Further references added to the discussion in Section 1

Kcne4 deletion sex- and age-specifically impairs cardiac repolarization in mice.

Myocardial repolarization capacity varies with sex, age, and pathology; the molecular basis for this variation is incompletely understood. Here, we show that the transcript for KCNE4, a voltage-gated potassium (Kv) channel β subunit associated with human atrial fibrillation, was 8-fold more highly expressed in the male left ventricle compared with females in young adult C57BL/6 mice (P < 0.05). Similarly, Kv current density was 25% greater in ventricular myocytes from young adult males (P < 0.05). Germ-line Kcne4 deletion eliminated the sex-specific Kv current disparity by diminishing ventricular fast transient outward current (Ito,f) and slowly activating K(+) current (IK,slow1). Kcne4 deletion also reduced Kv currents in male mouse atrial myocytes, by >45% (P < 0.001). As we previously found for Kv4.2 (which generates mouse Ito,f), heterologously expressed KCNE4 functionally regulated Kv1.5 (the Kv α subunit that generates IKslow1 in mice). Of note, in postmenopausal female mice, ventricular repolarization was impaired by Kcne4 deletion, and ventricular Kcne4 expression increased to match that of males. Moreover, castration diminished male ventricular Kcne4 expression 2.8-fold, whereas 5α-dihydrotestosterone (DHT) implants in castrated mice increased Kcne4 expression >3-fold (P = 0.01) to match noncastrated levels. KCNE4 is thereby shown to be a DHT-regulated determinant of cardiac excitability and a molecular substrate for sex- and age-dependent cardiac arrhythmogenesis

Semiparametric inference of effective reproduction number dynamics from wastewater pathogen surveillance data

Concentrations of pathogen genomes measured in wastewater have recently become available as a new data source to use when modeling the spread of infectious diseases. One promising use for this data source is inference of the effective reproduction number, the average number of individuals a newly infected person will infect. We propose a model where new infections arrive according to a time-varying immigration rate which can be interpreted as a compound parameter equal to the product of the proportion of susceptibles in the population and the transmission rate. This model allows us to estimate the effective reproduction number from concentrations of pathogen genomes while avoiding difficult to verify assumptions about the dynamics of the susceptible population. As a byproduct of our primary goal, we also produce a new model for estimating the effective reproduction number from case data using the same framework. We test this modeling framework in an agent-based simulation study with a realistic data generating mechanism which accounts for the time-varying dynamics of pathogen shedding. Finally, we apply our new model to estimating the effective reproduction number of SARS-CoV-2 in Los Angeles, California, using pathogen RNA concentrations collected from a large wastewater treatment facility.Comment: 23 pages, 6 figures in main te

Middle and posterior cardiac veins: An underused option for ventricular pacing

Tarrasó, Olga;Fuente Fuente, Carlos;Reventós, Manue