Dynamics of social contagions with limited contact capacity

Individuals are always limited by some inelastic resources, such as time and energy, which restrict them to dedicate to social interaction and limit their contact capacity. Contact capacity plays an important role in dynamics of social contagions, which so far has eluded theoretical analysis. In this paper, we first propose a non-Markovian model to understand the effects of contact capacity on social contagions, in which each individual can only contact and transmit the information to a finite number of neighbors. We then develop a heterogeneous edge-based compartmental theory for this model, and a remarkable agreement with simulations is obtained. Through theory and simulations, we find that enlarging the contact capacity makes the network more fragile to behavior spreading. Interestingly, we find that both the continuous and discontinuous dependence of the final adoption size on the information transmission probability can arise. And there is a crossover phenomenon between the two types of dependence. More specifically, the crossover phenomenon can be induced by enlarging the contact capacity only when the degree exponent is above a critical degree exponent, while the the final behavior adoption size always grows continuously for any contact capacity when degree exponent is below the critical degree exponent.

Dynamic Power Control for Delay-Aware Device-to-Device Communications

In this paper, we consider the dynamic power control for delay-aware D2D communications. The stochastic optimization problem is formulated as an infinite horizon average cost Markov decision process. To deal with the curse of dimensionality, we utilize the interference filtering property of the CSMA-like MAC protocol and derive a closed-form approximate priority function and the associated error bound using perturbation analysis. Based on the closed-form approximate priority function, we propose a low-complexity power control algorithm solving the per-stage optimization problem. The proposed solution is further shown to be asymptotically optimal for a sufficiently large carrier sensing distance. Finally, the proposed power control scheme is compared with various baselines through simulations, and it is shown that significant performance gain can be achieved.

Delay-Aware Uplink Fronthaul Allocation in Cloud Radio Access Networks

In cloud radio access networks (C-RANs), the baseband units and radio units of base stations are separated, which requires high-capacity fronthaul links connecting both parts. In this paper, we consider the delay-aware fronthaul allocation problem for C-RANs. The stochastic optimization problem is formulated as an infinite horizon average cost Markov decision process. To deal with the curse of dimensionality, we derive a closed-form approximate priority function and the associated error bound using perturbation analysis. Based on the closed-form approximate priority function, we propose a low-complexity delay-aware fronthaul allocation algorithm solving the per-stage optimization problem. The proposed solution is further shown to be asymptotically optimal for sufficiently small cross link path gains. Finally, the proposed fronthaul allocation algorithm is compared with various baselines through simulations, and it is shown that significant performance gain can be achieved.

Neutrino mass hierarchy determination and other physics potential of medium-baseline reactor neutrino oscillation experiments

Medium-baseline reactor neutrino oscillation experiments (MBRO) have been proposed to determine the neutrino mass hierarchy (MH) and to make precise measurements of the neutrino oscillation parameters. With sufficient statistics, better than ~3%/sqrt{E} energy resolution and well understood energy non-linearity, MH can be determined by analyzing oscillation signals driven by the atmospheric mass-squared difference in the survival spectrum of reactor antineutrinos. With such high performance MBRO detectors, oscillation parameters, such as sin^22theta_{12}, Delta m^2_{21}, and Delta m^2_{32}, can be measured to sub-percent level, which enables a future test of the PMNS matrix unitarity to ~1% level and helps the forthcoming neutrinoless double beta decay experiments to constrain the allowed <m_{beta beta}> values. Combined with results from the next generation long-baseline beam neutrino and atmospheric neutrino oscillation experiments, the MH determination sensitivity can reach higher levels. In addition to the neutrino oscillation physics, MBRO detectors can also be utilized to study geoneutrinos, astrophysical neutrinos and proton decay. We propose to start a U.S. R&D program to identify, quantify and fulfill the key challenges essential for the success of MBRO experiments.

Macroscopic discrete modelling of stochastic reaction-diffusion equations on a periodic domain

Dynamical systems theory provides powerful methods to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. Here we derive and theoretically support a macroscopic, spatially discrete, model for a class of stochastic reaction-diffusion partial differential equations with cubic nonlinearity. Dividing space into overlapping finite elements, a special coupling condition between neighbouring elements preserves the self-adjoint dynamics and controls interelement interactions. When the interelement coupling parameter is small, an averaging method and an asymptotic expansion of the slow modes show that the macroscopic discrete model will be a family of coupled stochastic ordinary differential equations which describe the evolution of the grid values. This modelling shows the importance of subgrid scale interaction between noise and spatial diffusion and provides a new rigourous approach to constructing semi-discrete approximations to stochastic reaction-diffusion partial differential equations.

Large deviations for slow-fast stochastic partial differential equations

A large deviation principle is derived for stochastic partial differential equations with slow-fast components. The result shows that the rate function is exactly that of the averaged equation plus the fluctuating deviation which is a stochastic partial differential equation with small Gaussian perturbation. This also confirms the effectiveness of the approximation of the averaged equation plus the fluctuating deviation to the slow-fast stochastic partial differential equations.

Average and deviation for slow-fast stochastic partial differential equations

Averaging is an important method to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. This article derives an averaged equation for a class of stochastic partial differential equations without any Lipschitz assumption on the slow modes. The rate of convergence in probability is obtained as a byproduct. Importantly, the deviation between the original equation and the averaged equation is also studied. A martingale approach proves that the deviation is described by a Gaussian process. This gives an approximation to errors of $mathcal{O}(e)$ instead of $mathcal{O}(sqrt{e})$ attained in previous averaging.

Macroscopic reduction for stochastic reaction-diffusion equations

The macroscopic behavior of dissipative stochastic partial differential equations usually can be described by a finite dimensional system. This article proves that a macroscopic reduced model may be constructed for stochastic reaction-diffusion equations with cubic nonlinearity by artificial separating the system into two distinct slow-fast time parts. An averaging method and a deviation estimate show that the macroscopic reduced model should be a stochastic ordinary equation which includes the random effect transmitted from the microscopic timescale due to the nonlinear interaction. Numerical simulations of an example stochastic heat equation confirms the predictions of this stochastic modelling theory. This theory empowers us to better model the long time dynamics of complex stochastic systems.

SPI observations of the diffuse 60Fe emission in the Galaxy

Gamma-ray line emission from radioactive decay of 60Fe provides constraints on nucleosynthesis in massive stars and supernovae. The spectrometer SPI on board INTEGRAL has accumulated nearly three years of data on gamma-ray emission from the Galactic plane. We have analyzed these data with suitable instrumental-background models and sky distributions to produce high-resolution spectra of Galactic emission. We detect the gamma-ray lines from 60Fe decay at 1173 and 1333 keV, obtaining an improvement over our earlier measurement of both lines with now 4.9 sigma significance for the combination of the two lines. The average flux per line is (4.4 pm 0.9) times 10^{-5} ph cm^{-2} s^{-1} rad^{-1} for the inner Galaxy region. Deriving the Galactic 26Al gamma-ray line flux with using the same set of observations and analysis method, we determine the flux ratio of 60Fe/26Al gamma-rays as 0.148 pm 0.06. The current theoretical predictions are still consistent with our result.