Scaled Brownian motion: a paradoxical process with a time dependent diffusivity for the description of anomalous diffusion

Anomalous diffusion is frequently described by scaled Brownian motion (SBM), a Gaussian process with a power-law time dependent diffusion coefficient. Its mean squared displacement is $\langle x^2(t)\rangle\simeq\mathscr{K}(t)t$ with $\mathscr{K}(t)\simeq t^{\alpha-1}$ for $0<\alpha<2$. SBM may provide a seemingly adequate description in the case of unbounded diffusion, for which its probability density function coincides with that of fractional Brownian motion. Here we show that free SBM is weakly non-ergodic but does not exhibit a significant amplitude scatter of the time averaged mean squared displacement. More severely, we demonstrate that under confinement, the dynamics encoded by SBM is fundamentally different from both fractional Brownian motion and continuous time random walks. SBM is highly non-stationary and cannot provide a physical description for particles in a thermalised stationary system. Our findings have direct impact on the modelling of single particle tracking experiments, in particular, under confinement inside cellular compartments or when optical tweezers tracking methods are used.Comment: 7 pages, 5 figure

Radiative Feedback from high mass X-ray binaries on the formation of the first galaxies and early reionization

Recent work suggests that the first generation of stars, the so-called Population III (Pop III), could have formed primarily in binaries or as members of small multiple systems. Here we investigate the impact of X-ray feedback from High-Mass X-ray Binaries (HMXBs) left behind in stellar binary systems after the primary forms a black hole (BH), accreting gas at a high rate from the companion, a process that is thought to be favored at the low metallicities characteristic of high-redshift gas. Thanks to their large mean free path, X-rays are capable of preionizing and preheating the gas in the intergalactic medium (IGM) and in haloes long before the reionization of the Universe is complete, and thus could have strongly affected the formation of subsequent generations of stars as well as reionization. We have carried out zoomed hydrodynamical cosmological simulations of minihaloes, accounting for the formation of Pop III stars and their collapse into BHs and HMXBs, and the associated radiation-hydrodynamic feedback from UV and X-ray photons. We find no strong net feedback from HMXBs on the simulated star formation history. On the other hand, the preheating of the IGM by HMXBs leads to a strong suppression of small-scale structures and significantly lowers the recombination rate in the IGM, thus yielding a net positive feedback on reionization. We further show that X-ray feedback from HMXBs can augment the ionizing feedback from the Pop III progenitor stars to suppress gas accretion onto the first BHs, limiting their growth into supermassive BHs. Finally, we show that X-ray ionization by HMXBs leaves distinct signatures in the properties of the high-redshift hydrogen that may be probed in upcoming observations of the redshifted 21cm spin-flip line.Comment: 20 pages, 12 figures. Accepted for publication in MNRA

The first galaxies: simulating their feedback-regulated assembly

We investigate the formation of a galaxy reaching a virial mass of $~ 10^8$ solar mass at $z=10$ by carrying out a zoomed radiation-hydrodynamical cosmological simulation. This simulation traces Population~III (Pop~III) star formation, characterized by a modestly top-heavy initial mass function (IMF), and considers stellar feedback such as photoionization heating from Pop III and Population~II (Pop~II) stars, mechanical and chemical feedback from supernovae (SNe), and X-ray feedback from accreting black holes (BHs) and high-mass X-ray binaries (HMXBs). We self-consistently impose a transition in star formation mode from top-heavy Pop III to low-mass Pop~II, and find that the star formation rate in the computational box is dominated by Pop~III until $z=13$, and by Pop~II thereafter. The simulated galaxy experiences bursty star formation, with a substantially reduced gas content due to photoionization heating from Pop~III and Pop~II stars, together with SN feedback. All the gas within the simulated galaxy is metal-enriched above $10^{-5}$ solar, such that there are no remaining pockets of primordial gas. The simulated galaxy has an estimated observed flux of $~10^{-3} nJy$, which is too low to be detected by the James Webb Space Telescope (JWST) without strong lensing amplification. We also show that our simulated galaxy is similar in terms of stellar mass to Segue 2, the least luminous dwarf known in the Local Group.Comment: 18 pages 14 figures, Accepted for publication in MNRA

Formulating the Net Gain of MISO-SFN in the Presence of Self-Interferences

In this study, an analytical formula for multiple-input single-output single frequency network gain (MISO-SFNG) is investigated. To formulate the net MISO-SFNG, we derived the average signal to interference plus noise ratio (SINR) where the gain achieved by the distributed MISO diversity as a function of power imbalance is curve-fitted. Further, we analyzed the losses owing to self-interferences resulting from the delay spread and imperfect channel estimation. We verified the accuracy and effectiveness of the derived formula by comparing the measurement results with the analytical results. The derived formula helps to understand how various system factors affect the gain under a given condition. The formula can be used to evaluate the MISO-SFNG and to predict the MISO-SFN coverage in various system configurations

FOXO1 Differentially Regulates Both Normal and Diabetic Gingival Wound Healing

We have previously demonstrated that keratinocyte-specific forkhead box O1 (FOXO1) deletion interferes with keratinocyte migration in normal skin wounds. However it has an opposite effect in diabetic skin wounds, significantly improving the healing response. In addition we found that skin epithelium regulates connective tissue healing mediated by FOXO1, which is strongly associated with wound angiogenesis in our microarray results. However, a role for keratinocytes in this complex process has yet to be investigated. To this end, we investigated possible involvement of gingival keratinocytes in connective tissue healing under both normal and diabetic conditions. We found that keratinocyte-specific FOXO1 deletion interfered with normal gingival connective tissue healing by decreasing granulation tissue formation and angiogenesis, which were mediated by vascular endothelial growth factor A (VEGF-A). In particular this is the first evidence that avascular epithelium regulates angiogenesis involving the VEGF-A secretion mediated by FOXO1. Furthermore, we investigated the possible role of epithelial to mesenchymal transition (EMT) during wound healing using the lineage tracing in transgenic mice. But we did not find any keratinocyte-specific reporter activity in the connective tissue indicating that there was no apparent trans-differentiation of keratinocytes into typical fibroblasts or myofibroblasts during wound healing. These results establish an important role of epithelial cells in accelerating wound angiogenesis and connective tissue healing through a FOXO1-dependent mechanism