This brief addresses distributed continuous-time optimization problems with time-varying objective functions. The goal is for multiple agents to cooperatively minimize the sum of local time-varying objective functions with only local interaction and information while explicitly taking into account distributed adaptive gain design. Here, the optimal point is time varying and creates an optimal trajectory. First, for the unconstrained case, a distributed nonsmooth algorithm coupled with a state-dependent gain is proposed. It is shown that the interaction gain for each agent can be computed according to the variation of the Hessian and gradient information of the convex local objective functions so that the algorithm can solve the time-varying optimization problem without imposing a bound on any information about the local objective functions. Second, for the case where there exist common time-varying linear equality constraints, an extended algorithm is presented, where local Lagrangian functions are introduced to address the equality constraints. The asymptotic convergence of both algorithms to the optimal solution is proved. Numerical simulations are presented to illustrate the theoretical results. In addition, the one proposed algorithm is experimentally implemented and validated on a multi-Crazyflie platform.

Although vehicles are the most commonly used means of transportation in people's daily life, their computational power and memory resources are often ignored. The new paradigm, Internet of Vehicles, has turned on-road vehicles into intelligent service providers, making full use of on-board processing and storage capabilities. With the advent of 6G technology, e.g., millimeter wave and terahertz, fast and massive data transfers become possible between moving objects. In this paper, we consider a scenario where vehicles act as mobile edge caching nodes and form a local cloud, to provide popular contents for nearby users via 6G communication. To maximize the efficiency of content allocation under the limitation of short communication range, we first predict the driving trajectories of vehicles with a Markov chain model and estimate the popularity level of contents in each urban area. Next, we design a scoring system based on the above predictions to compare users' satisfaction and computational efficiency of different algorithms. Finally, we find a subset of vehicles with appropriate content to serve the demand in the area. The simulation experiments demonstrate that the proposed scheme outperforms the conventional methods by providing a cost-efficient content allocation solution with lower delay.

In spectrum sharing systems, a secondary user (SU) is permitted to share frequency bands with a primary user (PU) as long as its transmission does not interfere with the PU's communication. In this paper, the outage probability is investigated for the cognitive relay system over Nakagami-m fading channel. By applying the interference temperature constraints at the source nodes and relay nodes in secondary systems, we analyze the outage performance in two-hop underlay spectrum sharing with the best relay selection criterion. The probability density function (PDF) and cumulative distribution function (CDF) of the signal to noise ratio (SNR) at the SU's receiver are derived to obtain the closed-form upper bound of the outage probability of the secondary relay system. Simulations results demonstrate the validity and accuracy of the theoretical analysis.

With its rich history as a center for commerce, cultural interactions, and a tapestry of spiritual traditions, Singapore has evolved into a vibrant amalgamation of diverse ethnic and religious heritages. Various communities have harmoniously woven themselves into the fabric of Singaporean society, each enriching it with their distinct influences. Throughout history, the rich and varied tapestry of the Indian community has often been underestimated by external observers. In a parallel manner, the distinct identity of the Singaporean Indian community frequently remained in the shadows, eclipsed by the prevailing presence of the Tamil Hindu population. The Jain community in Singapore, though a small minority, has played a notable role in the nation’s growth and the enhancement of its diverse cultural landscape. This article draws upon ethnographic materials collected by the author through comprehensive fieldwork in Singapore. It unveils the multifaceted nature of identity within the Jain community, even though they represent a modest presence in Singapore. The Jains in Singapore exemplify the complex interactions of their multiple identities as they engage with the rich tapestry of Singapore’s diverse and multicultural landscape, where global viewpoints and local traditions intertwine. By engaging actively and adapting to diverse social contexts within Singaporean society, the Jain community has skillfully navigated the complexities of spatial dynamics, and vividly demonstrated the notion of “religious hybridity”.