Kirby and Thompson introduced a length of a trisection in Kirby and Thompson (PNAS 115(43):10857–10860, 2018). They also defined the length of a 4-manifold as the minimum of length among all lengths ...of trisection of a 4-manifold. In this paper, we consider trisections whose Kirby-Thompson length is 2. Kirby and Thompson conjectured that length 2 trisection is a trisection of 4-manifold with length 0. We shall prove this conjecture in this paper.
To understand how mantle dynamics exerts control over the history of magmatic activities and surface environment on Mars, I used a numerical model of magmatism in the convecting mantle that is ...nominally anhydrous and internally heated. Magmatism occurs as an upward permeable flow of basaltic magma generated by decompression melting through matrix. The mantle evolves in four stages in preferred models. In Stage I, high initial temperature in the uppermost mantle causes an extensive magmatism intensified by two types of positive feedback that operate between magmatism and mantle upwelling flow, the MMUb and MMUc feedbacks: the buoyancy and volume change of matrix, respectively, caused by migrating magma that a mantle upwelling flow generates intensify the flow itself to generate more magma. The stratification suppresses mantle convection and magmatism for the next tens to hundreds of millions of years, allowing heat to build up in the mantle by internal heating (Stage II). Eventually, magma is generated at depth, and the MMUb feedback operates to cause an episodic plume magmatism that releases water from the interior of Mars (Stage III). The plume magmatism also stirs the mantle to make it more homogeneous and extracts heat producing elements from the deep mantle to let the magmatism itself wane and cease. In the final stage IV, mantle convection becomes more akin to a thermal convection. The episodic magmatism and water outgassing in Stage III account for the volcanism and clement surface environment observed for early Mars.
Plain Language Summary
Upwelling flow in the convecting mantle of a rocky planet causes magmatism, that is, generates magma that migrates upward to the surface to cause volcanic activities, when its interior is sufficiently hot. The numerical experiments presented here suggest that magmatism has intensified the mantle upwelling flow that caused the magmatism itself in Mars, and that its mantle has evolved in four stages due to this positive feedback: in Stage I, an extensive magmatism formed the crust and compositionally differentiated the mantle; in Stage II, the resulting compositional stratification of the mantle suppressed magmatism and mantle convection for tens to hundreds of millions of years to allow heat to build up in the deep mantle; in Stage III, magma was generated at depth, and the buoyancy of generated magma induced plumes that ascend through the stratified mantle to cause an episodic volcanic activity and water outgassing from the interior of Mars; in Stage IV, the magmatism and outgassing subsided due to extraction of heat producing elements from the mantle by the magmatism itself. The episodic magmatism and water outgassing in Stage III account for the volcanism and clement surface environment observed for early Mars.
Key Points
Two types of positive feedback have operated between magmatism and mantle upwelling flow in Mars to let its mantle evolve in four stages
An initial extensive magmatism in the first stage compositionally stratified the mantle to make it dormant in the second stage
Episodic plume magmatism took place to stir the mantle and to release water from the interior of Mars in the third stage
About 10% of male infertile patients show abnormalities in spermatogenesis. The microdeletion of azoospermia factor a (AZFa) region of the Y chromosome is thought to be a cause of spermatogenic ...failure. However, candidate gene responsible for the spermatogenic failure in AZFa deleted patients has not been elucidated yet. Using mice, we explored the function of Ddx3y, a strong candidate gene in the Azfa region, and Ddx3x, a Ddx3y paralog on the X chromosome, in spermatogenesis. We first generated Ddx3y KO male mice using CRISPR/Cas9 and found that the Ddx3y KO male mice show normal spermatogenesis, produce morphologically normal spermatozoa, and sire healthy offspring. Because Ddx3x KO males were embryonic lethal, we next generated chimeric mice, which contain Ddx3x and Ddx3y double KO (dKO) germ cells, and found that the dKO germ cells can differentiate into spermatozoa and transmit their mutant alleles to offspring by normal mating. We conclude that Ddx3x and Ddx3y are dispensable for spermatogenesis at least in mice. Unlike human, mice have an additional Ddx3y paralog D1pas1, that has been reported to be essential for spermatogenesis. These findings suggest that human and mouse DDX3 related proteins have distinct differences in their functions.
A schoolteacher’s job is considered one of the most stressful occupations globally. The coronavirus disease 2019 pandemic has posed further challenges for schoolteachers. This study aimed to examine ...the effects of the pandemic on primary school teachers’ stress responses in Japan. We analyzed the data from a nationwide survey of public-school teachers conducted between June 2019 and December 2021. The total numbers of participants were 65,968 in 2019, 72,248 in 2020, and 75,435 in 2021. Working hours and perceived main stressors as well as stress response scores were assessed. Contrary to expectations, the results showed that the stress response scores among primary school teachers did not increase in the first year of the pandemic. Rather, the stress response scores and the proportion of high-stress teachers significantly decreased from the pre-pandemic year (2019) to the first year of the pandemic (2020). However, the stress response scores showed a rising trend in the second year of the pandemic (2021). Participants’ working hours decreased from 2019 to 2021. The findings in relation to teachers’ main stressors matched these trends. Continuous monitoring of teachers’ stress levels is required both during and after the pandemic.
Two‐dimensional numerical models are systematically presented for magmatism in a convecting mantle internally heated by incompatible radioactive elements. Plate tectonics is self‐consistently modeled ...as a part of convection of Newtonian fluid with temperature‐ and stress‐history‐dependent viscosity driven by thermal and compositional buoyancy, while magmatism is modeled as an upward migration of basaltic magma generated by decompression melting. Ridge magmatism actively takes place to chemically differentiate the mantle, and a superplume is well developed in the lowermost mantle as a broad hot region enriched in basaltic component, provided that the lithosphere is mechanically strong enough to inhibit spontaneous initiation of subduction by its own weight and that the internal heating rate is sufficiently high. Hot narrow plumes frequently rise up from the superplume to induce deep magma generation and hot spot magmatism, which in turn frequently induces new plate margins. The frequent plate margin formation keeps the activity of plate tectonics rather steady. The thermal and chemical state of the mantle remains rather steady, too. As the internal heating rate becomes lower, however, the narrow plumes from superplume become sporadic and significantly colder, deep magma generation becomes rare; and new plate margin formation becomes less frequent. As a consequence, the activity of plate tectonics and the thermal and chemical state of the mantle become fluctuating much with time. The mantle structure and plume behavior modeled here match with many observations for those of the Earth from the Archean to the present.
To discuss mantle evolution in Mercury, I present two‐dimensional numerical models of magmatism in a convecting mantle. Thermal, compositional, and magmatic buoyancy drives convection of ...temperature‐dependent viscosity fluid in a rectangular box placed on the top of the core that is modeled as a heat bath of uniform temperature. Magmatism occurs as a permeable flow of basaltic magma generated by decompression melting through a matrix. Widespread magmatism caused by high initial temperature of the mantle and the core makes the mantle compositionally stratified within the first several hundred million years of the 4.5 Gyr calculated history. The stratified structure persists for 4.5 Gyr, when the reference mantle viscosity at 1573 K is higher than around 1020 Pa s. The planet thermally contracts by an amount comparable to the one suggested for Mercury over the past 4 Gyr. Mantle upwelling, however, generates magma only for the first 0.1–0.3 Gyr. At lower mantle viscosity, in contrast, a positive feedback between magmatism and mantle upwelling operates to cause episodic magmatism that continues for the first 0.3–0.8 Gyr. Convective current stirs the mantle and eventually dissolves its stratified structure to enhance heat flow from the core and temporarily resurrect magmatism depending on the core size. These models, however, predict larger contraction of the planet. Coupling between magmatism and mantle convection plays key roles in mantle evolution, and the difficulty in numerically reproducing the history of magmatism of Mercury without causing too large radial contraction of the planet warrants further exploration of this coupling.
Key Points
Coupling between magmatism and mantle upwelling in Mercury is simulated
The mantle structurally evolves owing to magmatism and convective stirring
The coupling causes episodic magmatism when mantle viscosity is sufficiently low
Plate tectonics is a key feature of the dynamics of the Earth’s mantle. By taking into account the stress-history-dependent rheology of mantle materials, we succeeded in realistically producing ...tectonic plates in our numerical model of mantle convection in a three-dimensional rectangular box. The calculated lithosphere is separated into several pieces (tectonic plates) that rigidly move. Deformation of the lithosphere caused by the relative motion of adjacent plates is concentrated in narrow bands (plate margins) where the viscosity is substantially reduced. The plate margins develop when the stress exceeds a threshold and the lithosphere is ruptured. Once formed, the plate margins persist, even after the stress is reduced below the threshold, allowing the plates to stably move over geologic time. The vertical component of vorticity takes a large value in the narrow plate margins. Secondary convection occurs beneath old tectonic plates as two-dimensional rolls with their axes aligned to the direction of plate motion. The surface heat flow decreases with increasing distance from divergent plate margins (ridges) in their vicinity in the way the cooling half-space model predicts, but it tends towards a constant value away from ridges as observed for the Earth because of the heat transport by the secondary convection.
Geological and geodetic observations of the Moon from spacecraft revealed that it expanded by a few km for the first several hundred million years and then contracted later. The period when the ...planet expanded most coincides with that when the mare volcanism of the Moon was active. Given the high initial temperature of the deep mantle inferred from the giant impact and mantle overturn hypotheses of the Moon, the observed early expansion is difficult to account for by thermal expansion only. To understand the observed radial change of the Moon, we numerically calculated the thermal evolution of a one-dimensional spherically symmetric mantle caused by transport of heat, mass, and incompatible heat-producing elements (HPEs) by migration of magma that is generated by internal heating. The mantle is assumed to be enriched in HPEs at its base in the initial condition. The calculated mantle expands for the first several hundred million years by melting of the deep mantle and upward migration of the generated magma to the uppermost mantle; the top of the partially molten region rises to the depth level of around 300 km, which is shallow enough to generate mare basalts of the Moon. The migrating magma, however, extracts HPEs from the deep interior, and the planet then contracts gradually by cooling and solidification of the partially molten mantle. We obtained a thermal history model that is consistent with the observed history of radial change of the Moon when the initial mid-mantle temperature
T
M
≈
1600
K
and the initial ratio of the concentration of HPEs in the crust to that of the mantle
F
crst
∗
≤
12
. This model suggests that melting of the deep mantle and upward migration of the generated magma strongly affect the thermal history of the Moon. The model we developed here is a good starting point for constructing more realistic models of the thermal history of the Moon where the effects of heat and mass transport by mantle convection are also considered.
Graphical Abstract
A school teacher's job is considered one of the most stressful occupations worldwide. To maintain the mental health of teachers, it is crucial to clarify the factors affecting work-related stress ...among teachers. The present study thus aimed to examine the main stressors among primary school teachers considering the difference in job positions by using data from a large-scale nationwide survey.
We analyzed the data from a nationwide survey of public school teachers conducted between June and December 2021. The total number of participants was 138,651. The information of perceived main stressors, working hours per day, job workloads, job control, workplace support, and stress response scores were assessed by job position.
Among all teachers' job positions, the working hours of vice-principals were the longest, but their stress response scores were the second lowest. In contrast, the stress response scores among diet and nutrition teachers and health education teachers were the highest; their supervisors' and co-workers' support scores were the lowest among all teachers. Quantitative and qualitative workloads, job control, workplace support from supervisors and co-workers are significantly associated with teachers' stress responses in all job positions. Perceived main stressors among teachers were different depending on job positions. However, regardless of job positions, relationships with supervisors and co-workers were significantly associated with stress response scores among teachers. Dealing with difficult students and parents as well as workloads of clerical tasks were also associated with teachers' stress responses depending on job positions.
Perceived main stressors among teachers were different depending on job positions. However, relationships with supervisors and co-workers were significantly associated with stress response levels among teachers regardless of job positions. This study highlighted the importance of interpersonal relationships at the workplace in terms of teachers' mental health. The results suggest that providing interpersonal skills training targeting co-workers' relationships and harassment prevention measures would be crucial to maintain teachers' mental health. The results also suggest that increasing school staff and providing sufficient organizational support for teachers will be required to prevent teachers' burnout.
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