On the construction of equivolume partitions of the d−d-dimensional unit cube

The aim of this note is to construct equivolume partitions of the $d$-dimensional unit cube with hyperplanes that are orthogonal to the main diagonal of the cube. Each such hyperplane $H_r \subset \mathbb{R}^d$ is defined via the equation $x_1 + \ldots + x_d + r=0$ for a parameter $r$ with $-d\leq r \leq 0$. For a given $N$, we characterise those real numbers $r_i$ with $1\leq i \leq N-1$ for which the corresponding hyperplanes $H_{r_i}$ partition the unit cube into $N$ sets of volume $1/N$. As a main result we derive an algebraic and a probabilistic characterisation of the $r_i$ for arbitrary $d\geq 2$ and $N \in \mathbb{N}$. Importantly, our results do not only work for equivolume partitions but also for arbitrary predefined distributions of volume among the $N$ sets of the partition generated from hyperplanes $H_r$.Comment: 10 pages, 4 figure

Development and Verification of the Charring, Ablating Thermal Protection Implicit System Simulator

The development and verification of the Charring Ablating Thermal Protection Implicit System Solver (CATPISS) is presented. This work concentrates on the derivation and verification of the stationary grid terms in the equations that govern three-dimensional heat and mass transfer for charring thermal protection systems including pyrolysis gas flow through the porous char layer. The governing equations are discretized according to the Galerkin finite element method (FEM) with first and second order fully implicit time integrators. The governing equations are fully coupled and are solved in parallel via Newton s method, while the linear system is solved via the Generalized Minimum Residual method (GMRES). Verification results from exact solutions and Method of Manufactured Solutions (MMS) are presented to show spatial and temporal orders of accuracy as well as nonlinear convergence rates

Development and Verification of the Charring Ablating Thermal Protection Implicit System Solver

The development and verification of the Charring Ablating Thermal Protection Implicit System Solver is presented. This work concentrates on the derivation and verification of the stationary grid terms in the equations that govern three-dimensional heat and mass transfer for charring thermal protection systems including pyrolysis gas flow through the porous char layer. The governing equations are discretized according to the Galerkin finite element method with first and second order implicit time integrators. The governing equations are fully coupled and are solved in parallel via Newton's method, while the fully implicit linear system is solved with the Generalized Minimal Residual method. Verification results from exact solutions and the Method of Manufactured Solutions are presented to show spatial and temporal orders of accuracy as well as nonlinear convergence rates

Genomic and transcriptomic signals of thermal tolerance in heat-tolerant corals (Platygyra daedalea) of the Arabian/Persian Gulf

© 2018 John Wiley & Sons Ltd Scleractinian corals occur in tropical regions near their upper thermal limits and are severely threatened by rising ocean temperatures. However, several recent studies have shown coral populations can harbour genetic variation in thermal tolerance. Here, we have extended these approaches to study heat tolerance of corals in the Persian/Arabian Gulf, where heat-tolerant local populations experience extreme summer temperatures (up to 36°C). To evaluate whether selection has depleted genetic variation in thermal tolerance, estimate potential future adaptive responses and understand the functional basis for these corals’ unusual heat tolerance, we conducted controlled crosses in the Gulf coral Platygyra daedalea. Heat tolerance is highly heritable in this population (h 2 = 0.487–0.748), suggesting substantial potential for adaptive responses to selection for elevated temperatures. To identify genetic markers associated with this variation, we conducted genomewide SNP genotyping in parental corals and tested for relationships between paternal genotype and offspring thermal tolerance. Resulting multilocus SNP genotypes explained a large fraction of variation in thermal tolerance in these crosses (69%). To investigate the functional basis of these differences in thermal tolerance, we profiled transcriptional responses in tolerant and susceptible families, revealing substantial sire effects on transcriptional responses to thermal stress. We also studied sequence variation in these expressed sequences, identifying alleles and functional groups of differentially expressed genes associated with thermal tolerance. Our findings demonstrate that corals in this population harbour extensive genetic variation in thermal tolerance, and heat-tolerant phenotypes differ in both gene sequences and transcriptional stress responses from their susceptible counterparts

When Less is More: Mindfulness Predicts Adaptive Affective Responding to Rejection Via Reduced Prefrontal Recruitment

Social rejection is a distressing and painful event that many people must cope with on a frequent basis. Mindfulness—defined here as a mental state of receptive attentiveness to internal and external stimuli as they arise, moment-to-moment—may buffer such social distress. However, little research indicates whether mindful individuals adaptively regulate the distress of rejection—or the neural mechanisms underlying this potential capacity. To fill these gaps in the literature, participants reported their trait mindfulness and then completed a social rejection paradigm (Cyberball) while undergoing functional magnetic resonance imaging. Approximately 1 hour after the rejection incident, participants reported their level of distress during rejection (i.e. social distress). Mindfulness was associated with less distress during rejection. This relation was mediated by lower activation in the left ventrolateral prefrontal cortex during the rejection incident, a brain region reliably associated with the inhibition of negative affect. Mindfulness was also correlated with less functional connectivity between the left ventrolateral prefrontal cortex and the bilateral amygdala and the dorsal anterior cingulate cortex, which play a critical role in the generation of social distress. Mindfulness may relate to effective coping with rejection by not over-activating top-down regulatory mechanisms, potentially resulting in more effective long-term emotion-regulation

Tracking Transmission of Apicomplexan Symbionts in Diverse Caribbean Corals

Symbionts in each generation are transmitted to new host individuals either vertically (parent to offspring), horizontally (from exogenous sources), or a combination of both. Scleractinian corals make an excellent study system for understanding patterns of symbiont transmission since they harbor diverse symbionts and possess distinct reproductive modes of either internal brooding or external broadcast spawning that generally correlate with vertical or horizontal transmission, respectively. Here, we focused on the under-recognized, but apparently widespread, coral-associated apicomplexans (Protista: Alveolata) to determine if symbiont transmission depends on host reproductive mode. Specifically, a PCR-based assay was utilized towards identifying whether planula larvae and reproductive adults from brooding and broadcast spawning scleractinian coral species in Florida and Belize harbored apicomplexan DNA. Nearly all (85.5%; n = 85/89) examined planulae of five brooding species (Porites astreoides, Agaricia tenuifolia, Agaricia agaricites, Favia fragum, Mycetophyllia ferox) and adults of P. astreoides were positive for apicomplexan DNA. In contrast, no (n = 0/10) apicomplexan DNA was detected from planulae of four broadcast spawning species (Acropora cervicornis, Acropora palmata, Pseudodiploria strigosa, and Orbicella faveolata) and rarely in gametes (8.9%; n = 5/56) of these species sampled from the same geographical range as the brooding species. In contrast, tissue samples from nearly all (92.0%; n = 81/88) adults of the broadcast spawning species A. cervicornis, A. palmata and O. faveolata harbored apicomplexan DNA, including colonies whose gametes and planulae tested negative for these symbionts. Taken together, these data suggest apicomplexans are transmitted vertically in these brooding scleractinian coral species while the broadcast spawning scleractinian species examined here acquire these symbionts horizontally. Notably, these transmission patterns are consistent with those of other scleractinian coral symbionts. While this study furthers knowledge regarding these symbionts, numerous questions remain to be addressed, particularly in regard to the specific interaction(s) between these apicomplexans and their hosts