Detectability of gravitational waves from a population of inspiralling black holes in Milky Way-mass galaxies

ABSTRACT We estimate the rate of inspiral for a population of stellar mass black holes in the star cluster around the supermassive black hole (SMBHs) at the centre of Milky Way mass galaxies. Our approach is based on an orbit averaged Fokker Planck approach. This is then followed by a post-processing approach, which incorporates the impact of the angular momentum diffusion and the GW dissipation in the evolution of system. We make a sample of 104 BHs with different initial semimajor and eccentricities with the distribution of fc(a)/a and e, respectively, where fc(a) refers to the phase–space distribution function for cth species. Angular momentum diffusion leads to an enhancement in the eccentricity of every system in the above sample and so increases the rate of inspiral. We compute the fraction of time that every system spends in the LISA band with the signal-to-noise ratio $\rm {S/N} \ge 8$. Every system eventually approaches the loss-cone with a replenishment rate given by the diffusion rate of the cluster, $\mu / \rm {Gyr}^{-1} \lesssim 1$. This small rate reduces the total rate of the inspiral for individual MW mass galaxies with an estimate Robs ≲ 10−6−10−5 yr−1. A large collection of galaxies (Ngal > 104 MW) may lead to an observable GW signal in the LISA band.

Optimal pricing and deteriorating inventory control when inventory stimulates stochastic demand with reference price effect

We study the joint dynamic pricing and deteriorating inventory management problem in the presence of reference price and stock display effects. In a random potential market setting with convex replenishment/ordering and holding/shortage cost functions, the retailer replenishes/orders and sells a single deteriorating product over a continuous-time infinite horizon to maximize its profit. The demand rate depends negatively on the sales price and positively on the consumers' reference price and displayed stock quantity. The inventories deteriorate physically at a constant fraction of the on-hand stocks. A stochastic optimal control model is established to characterize the optimal policy in a linear feedback form of the state variables when the observed inventory level is either positive or negative. We also investigate the asymptotic behavior of the system and provide sufficient conditions for the stability and monotone convergence of the expected long-run behavior. Finally, we perform numerical examples to illustrate the theoretical results and sensitivity analysis to derive insights into deteriorating inventory management under reference price and stock display effects. The findings suggest that current reference price level has a positive effect while inventory level has a negative on the optimal replenishment rate and price. We characterize the sample paths of optimal strategies and find that the initial consumer reference price has an important impact on the firm's optimal operations management. On the expected long-run behavior, it is beneficial for the firm to reduce demand uncertainty and deteriorating rate. We also observe that a large factor of displayed stock effect brings a positive effect on the total expected profit. Additionally, the firm needs to reduce (increase) the price and increase (reduce) the replenishment rate with high reference price effect intensity (memory factor).

Active presynaptic ribosomes in the mammalian brain, and altered transmitter release after protein synthesis inhibition

Presynaptic neuronal activity requires the localization of thousands of proteins that are typically synthesized in the soma and transported to nerve terminals. Local translation for some dendritic proteins occurs, but local translation in mammalian presynaptic nerve terminals is difficult to demonstrate. Here, we show an essential ribosomal component, 5.8S rRNA, at a glutamatergic nerve terminal in the mammalian brain. We also show active translation in nerve terminals, in situ, in brain slices demonstrating ongoing presynaptic protein synthesis in the mammalian brain. Shortly after inhibiting translation, the presynaptic terminal exhibits increased spontaneous release, an increased paired pulse ratio, an increased vesicle replenishment rate during stimulation trains, and a reduced initial probability of release. The rise and decay rates of postsynaptic responses were not affected. We conclude that ongoing protein synthesis can limit excessive vesicle release which reduces the vesicle replenishment rate, thus conserving the energy required for maintaining synaptic transmission.

Tissue-resident macrophages in the intestine are long lived and defined by Tim-4 and CD4 expression

A defining feature of resident gut macrophages is their high replenishment rate from blood monocytes attributed to tonic commensal stimulation of this site. In contrast, almost all other tissues contain locally maintained macrophage populations, which coexist with monocyte-replenished cells at homeostasis. In this study, we identified three transcriptionally distinct mouse gut macrophage subsets that segregate based on expression of Tim-4 and CD4. Challenging current understanding, Tim-4+CD4+ gut macrophages were found to be locally maintained, while Tim-4–CD4+ macrophages had a slow turnover from blood monocytes; indeed, Tim-4–CD4– macrophages were the only subset with the high monocyte-replenishment rate currently attributed to gut macrophages. Moreover, all macrophage subpopulations required live microbiota to sustain their numbers, not only those derived from blood monocytes. These findings oppose the prevailing paradigm that all macrophages in the adult mouse gut rapidly turn over from monocytes in a microbiome-dependent manner; instead, these findings supplant it with a model of ontogenetic diversity where locally maintained subsets coexist with rapidly replaced monocyte-derived populations.

Sediment Transport and Characteristics in Perak River and Kurau River

Particle size is the most important parameter to deal in sediment transport processes. This parameter is important to determine the class of sediment transport in river. It is also important for the selection of site for sand mining operation through the determination of the size of sediment, sediment capacity and sediment replenishment rate. Data were obtained through observations made from two rivers namely Sungai Perak and Sungai Kurau in Malaysia. The rivers were categorized as wide river for Sungai Perak and small river for Sungai Kurau. For Sungai Perak, the width of river ranges from 248.18 to 338.53 meter whilst the width of Sungai Kurau ranges from 9 to 11 meter. Data covers flow discharges from 130.988 m3/s to 435.915 m3/s for Sungai Perak and from 2.52 m3/s to 4.723 m3/s for Sungai Kurau. Based on the results, the bed load of two rivers are found to be mostly uniform mixture. The results indicate that these two Malaysian rivers mostly have uniform bed load The bed material for the two rivers are poorly graded mixture and the median size of bed loads mostly ranges from 0.62 to 2.94 mm.

Physical determinants of vesicle mobility and supply at a central synapse

Encoding continuous sensory variables requires sustained synaptic signalling. At several sensory synapses, rapid vesicle supply is achieved via highly mobile vesicles and specialized ribbon structures, but how this is achieved at central synapses without ribbons is unclear. Here we examine vesicle mobility at excitatory cerebellar mossy fibre synapses which sustain transmission over a broad frequency bandwidth. Fluorescent recovery after photobleaching in slices from VGLUT1Venus knock-in mice reveal 75% of VGLUT1-containing vesicles have a high mobility, comparable to that at ribbon synapses. Experimentally constrained models establish hydrodynamic interactions and vesicle collisions are major determinants of vesicle mobility in crowded presynaptic terminals. Moreover, models incorporating 3D reconstructions of vesicle clouds near active zones (AZs) predict the measured releasable pool size and replenishment rate from the reserve pool. They also show that while vesicle reloading at AZs is not diffusion-limited at the onset of release, diffusion limits vesicle reloading during sustained high-frequency signalling.