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The approximate uniform sampling of graph realizations with a given degree sequence is an everyday task in several social science, computer science, engineering etc. projects. One approach is using Markov chains. The best available current result about the well-studied switch Markov chain is that it is rapidly mixing on P-stable degree sequences (see DOI:10.1016/j.ejc.2021.103421). The switch Markov chain does not change any degree sequence. However, there are cases where degree intervals are specified rather than a single degree sequence. (A natural scenario where this problem arises is in hypothesis testing on social networks that are only partially observed.) Rechner, Strowick, and M\"uller-Hannemann introduced in 2018 the notion of degree interval Markov chain which uses three (separately well-studied) local operations (switch, hinge-flip and toggle), and employing on degree sequence realizations where any two sequences under scrutiny have very small coordinate-wise distance. Recently Amanatidis and Kleer published a beautiful paper (arXiv:2110.09068), showing that the degree interval Markov chain is rapidly mixing if the sequences are coming from a system of very thin intervals which are centered not far from a regular degree sequence. In this paper we extend substantially their result, showing that the degree interval Markov chain is rapidly mixing if the intervals are centred at P-stable degree sequences.

The deep reinforcement learning-based energy management strategies (EMS) have become a promising solution for hybrid electric vehicles (HEVs). When driving cycles are changed, the neural network will be retrained, which is a time-consuming and laborious task. A more efficient way of choosing EMS is to combine deep reinforcement learning (DRL) with transfer learning, which can transfer knowledge of one domain to the other new domain, making the network of the new domain reach convergence values quickly. Different exploration methods of DRL, including adding action space noise and parameter space noise, are compared against each other in the transfer learning process in this work. Results indicate that the network added parameter space noise is more stable and faster convergent than the others. In conclusion, the best exploration method for transferable EMS is to add noise in the parameter space, while the combination of action space noise and parameter space noise generally performs poorly. Our code is available at //github.com/BIT-XJY/RL-based-Transferable-EMS.git.

Emerging distributed cloud architectures, e.g., fog and mobile edge computing, are playing an increasingly important role in the efficient delivery of real-time stream-processing applications such as augmented reality, multiplayer gaming, and industrial automation. While such applications require processed streams to be shared and simultaneously consumed by multiple users/devices, existing technologies lack efficient mechanisms to deal with their inherent multicast nature, leading to unnecessary traffic redundancy and network congestion. In this paper, we establish a unified framework for distributed cloud network control with generalized (mixed-cast) traffic flows that allows optimizing the distributed execution of the required packet processing, forwarding, and replication operations. We first characterize the enlarged multicast network stability region under the new control framework (with respect to its unicast counterpart). We then design a novel queuing system that allows scheduling data packets according to their current destination sets, and leverage Lyapunov drift-plus-penalty theory to develop the first fully decentralized, throughput- and cost-optimal algorithm for multicast cloud network flow control. Numerical experiments validate analytical results and demonstrate the performance gain of the proposed design over existing cloud network control techniques.

The fundamental tradeoff between transaction per second (TPS) and security in blockchain systems persists despite numerous prior attempts to boost TPS. To increase TPS without compromising security, we propose a bodyless block propagation (BBP) scheme for which the block body is not validated and transmitted during the block propagation process. Rather, the nodes in the blockchain network anticipate the transactions and their ordering in the next upcoming block so that these transactions can be pre-executed and pre-validated before the birth of the block. It is critical, however, all nodes have a consensus on the transaction content of the next block. This paper puts forth a transaction selection, ordering, and synchronization algorithm to drive the nodes to reach such a consensus. Yet, the coinbase address of the miner of the next block cannot be anticipated, and therefore transactions that depend on the coinbase address cannot be pre-executed and pre-validated. This paper further puts forth an algorithm to deal with such unresolvable transactions for an overall consistent and TPS-efficient scheme. With our scheme, most transactions do not need to be validated and transmitted during block propagation, ridding the dependence of propagation time on the number of transactions in the block, and making the system fully TPS scalable. Experimental results show that our protocol can reduce propagation time by 4x with respect to the current Ethereum blockchain, and its TPS performance is limited by the node hardware performance rather than block propagation.

Covariance estimation for matrix-valued data has received an increasing interest in applications. Unlike previous works that rely heavily on matrix normal distribution assumption and the requirement of fixed matrix size, we propose a class of distribution-free regularized covariance estimation methods for high-dimensional matrix data under a separability condition and a bandable covariance structure. Under these conditions, the original covariance matrix is decomposed into a Kronecker product of two bandable small covariance matrices representing the variability over row and column directions. We formulate a unified framework for estimating bandable covariance, and introduce an efficient algorithm based on rank one unconstrained Kronecker product approximation. The convergence rates of the proposed estimators are established, and the derived minimax lower bound shows our proposed estimator is rate-optimal under certain divergence regimes of matrix size. We further introduce a class of robust covariance estimators and provide theoretical guarantees to deal with heavy-tailed data. We demonstrate the superior finite-sample performance of our methods using simulations and real applications from a gridded temperature anomalies dataset and a S&P 500 stock data analysis.

In the storied Colonel Blotto game, two colonels allocate $a$ and $b$ troops, respectively, to $k$ distinct battlefields. A colonel wins a battle if they assign more troops to that particular battle, and each colonel seeks to maximize their total number of victories. Despite the problem's formulation in 1921, the first polynomial-time algorithm to compute Nash equilibrium (NE) strategies for this game was discovered only quite recently. In 2016, \citep{ahmadinejad_dehghani_hajiaghayi_lucier_mahini_seddighin_2019} formulated a breakthrough algorithm to compute NE strategies for the Colonel Blotto game\footnote{To the best of our knowledge, the algorithm from \citep{ahmadinejad_dehghani_hajiaghayi_lucier_mahini_seddighin_2019} has computational complexity $O(k^{14}\max\{a,b\}^{13})$}, receiving substantial media coverage (e.g. \citep{Insider}, \citep{NSF}, \citep{ScienceDaily}). In this work, we present the first known $\epsilon$-approximation algorithm to compute NE strategies in the two-player Colonel Blotto game in runtime $\widetilde{O}(\epsilon^{-4} k^8 \max\{a,b\}^2)$ for arbitrary settings of these parameters. Moreover, this algorithm computes approximate coarse correlated equilibrium strategies in the multiplayer (continuous and discrete) Colonel Blotto game (when there are $\ell > 2$ colonels) with runtime $\widetilde{O}(\ell \epsilon^{-4} k^8 n^2 + \ell^2 \epsilon^{-2} k^3 n (n+k))$, where $n$ is the maximum troop count. Before this work, no polynomial-time algorithm was known to compute exact or approximate equilibrium (in any sense) strategies for multiplayer Colonel Blotto with arbitrary parameters. Our algorithm computes these approximate equilibria by a novel (to the author's knowledge) sampling technique with which we implicitly perform multiplicative weights update over the exponentially many strategies available to each player.

To simulate noisy boson sampling approximating it by only the lower-order multi-boson interferences (e.g., by a smaller number of interfering bosons and classical particles) is very popular idea. I show that the output data from any such classical simulations can be efficiently distinguished from that of the quantum device they try to simulate, even with finite noise in the latter. The distinguishing datasets can be the experimental estimates of some large probabilities, a wide class of such is presented. This is a sequel of \textit{Quantum} \textbf{5}, 423 (2021), where I present more accessible account of the main result enhanced by additional insight on the contribution from the higher-order multi-boson interferences in presence of noise.

The outbreak of the COVID-19 pandemic has deeply influenced the lifestyle of the general public and the healthcare system of the society. As a promising approach to address the emerging challenges caused by the epidemic of infectious diseases like COVID-19, Internet of Medical Things (IoMT) deployed in hospitals, clinics, and healthcare centers can save the diagnosis time and improve the efficiency of medical resources though privacy and security concerns of IoMT stall the wide adoption. In order to tackle the privacy, security, and interoperability issues of IoMT, we propose a framework of blockchain-enabled IoMT by introducing blockchain to incumbent IoMT systems. In this paper, we review the benefits of this architecture and illustrate the opportunities brought by blockchain-enabled IoMT. We also provide use cases of blockchain-enabled IoMT on fighting against the COVID-19 pandemic, including the prevention of infectious diseases, location sharing and contact tracing, and the supply chain of injectable medicines. We also outline future work in this area.

The minimum energy path (MEP) describes the mechanism of reaction, and the energy barrier along the path can be used to calculate the reaction rate in thermal systems. The nudged elastic band (NEB) method is one of the most commonly used schemes to compute MEPs numerically. It approximates an MEP by a discrete set of configuration images, where the discretization size determines both computational cost and accuracy of the simulations. In this paper, we consider a discrete MEP to be a stationary state of the NEB method and prove an optimal convergence rate of the discrete MEP with respect to the number of images. Numerical simulations for the transitions of some several proto-typical model systems are performed to support the theory.

Reinforcement learning is one of the core components in designing an artificial intelligent system emphasizing real-time response. Reinforcement learning influences the system to take actions within an arbitrary environment either having previous knowledge about the environment model or not. In this paper, we present a comprehensive study on Reinforcement Learning focusing on various dimensions including challenges, the recent development of different state-of-the-art techniques, and future directions. The fundamental objective of this paper is to provide a framework for the presentation of available methods of reinforcement learning that is informative enough and simple to follow for the new researchers and academics in this domain considering the latest concerns. First, we illustrated the core techniques of reinforcement learning in an easily understandable and comparable way. Finally, we analyzed and depicted the recent developments in reinforcement learning approaches. My analysis pointed out that most of the models focused on tuning policy values rather than tuning other things in a particular state of reasoning.