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Neutrinos at the Main Injector (NuMI) is a project at Fermilab that provides an intense beam of neutrinos used by a number of experiments. NuMI creates a beam of pions that decay into neutrinos, muons, and other particles. Muons are registered by the muon monitors. Magnetic horns are the key elements of the NuMI beam line. This paper uses the muon beam profile observed at the muon monitors to study the NuMI horn focusing mechanism. It is found that the horn magnet generates dipole and quadrupole fields to focus pions. This suggests that the optics of the horn magnet are predominantly linear. Our study shows that the muon beam profile accurately detects the horn current within 0.05%.

We propose a simple and fast method for providing a high quality solution for the sum-interference minimization problem. As future networks are deployed in high density urban areas, improved clustering methods are needed to provide low interference network connectivity. The proposed algorithm applies straightforward similarity based clustering and optionally stable matchings to outperform state of the art algorithms. The running times of our algorithms are dominated by one matrix multiplication.

In this document, we give the optimal network throughput when the DR-DLMA node (see our paper for definition) coexists with the nodes using other protocol (e.g., TDMA and/or ALOHA). Then we use the optimal network throughput as the benchmark for our paper. The simulation results in our paper demonstrated that the DR-DLMA node can achieve performance similar to that of the model-aware node.

This paper investigates a futuristic spectrum sharing paradigm for heterogeneous wireless networks with imperfect channels. In the heterogeneous networks, multiple wireless networks adopt different medium access control (MAC) protocols to share a common wireless spectrum and each network is unaware of the MACs of others. This paper aims to design a distributed deep reinforcement learning (DRL) based MAC protocol for a particular network, and the objective of this network is to achieve a global $\alpha$-fairness objective. In the conventional DRL framework, feedback/reward given to the agent is always correctly received, so that the agent can optimize its strategy based on the received reward. In our wireless application where the channels are noisy, the feedback/reward (i.e., the ACK packet) may be lost due to channel noise and interference. Without correct feedback, the agent (i.e., the network user) may fail to find a good solution. Moreover, in the distributed protocol, each agent makes decisions on its own. It is a challenge to guarantee that the multiple agents will make coherent decisions and work together to achieve the same objective, particularly in the face of imperfect feedback channels. To tackle the challenge, we put forth (i) a feedback recovery mechanism to recover missing feedback information, and (ii) a two-stage action selection mechanism to aid coherent decision making to reduce transmission collisions among the agents. Extensive simulation results demonstrate the effectiveness of these two mechanisms. Last but not least, we believe that the feedback recovery mechanism and the two-stage action selection mechanism can also be used in general distributed multi-agent reinforcement learning problems in which feedback information on rewards can be corrupted.

This paper investigates a new class of carrier-sense multiple access (CSMA) protocols that employ deep reinforcement learning (DRL) techniques, referred to as carrier-sense deep-reinforcement learning multiple access (CS-DLMA). The goal of CS-DLMA is to enable efficient and equitable spectrum sharing among a group of co-located heterogeneous wireless networks. Existing CSMA protocols, such as the medium access control (MAC) of WiFi, are designed for a homogeneous network in which all nodes adopt the same protocol. Such protocols suffer from severe performance degradation in a heterogeneous environment where there are nodes adopting other MAC protocols. CS-DLMA aims to circumvent this problem by making use of DRL. In particular, this paper adopts alpha-fairness as the general objective of CS-DLMA. With alpha-fairness, CS-DLMA can achieve a range of different objectives when coexisting with other MACs by changing the value of alpha. A salient feature of CS-DLMA is that it can achieve these objectives without knowing the coexisting MACs through a learning process based on DRL. The underpinning DRL technique in CS-DLMA is deep Q-network (DQN). However, the conventional DQN algorithms are not suitable for CS-DLMA due to their uniform time-step assumption. In CSMA protocols, time steps are non-uniform in that the time duration required for carrier sensing is smaller than the duration of data transmission. This paper introduces a non-uniform time-step formulation of DQN to address this issue. Our simulation results show that CS-DLMA can achieve the general alpha-fairness objective when coexisting with TDMA, ALOHA, and WiFi protocols by adjusting its own transmission strategy. Interestingly, we also find that CS-DLMA is more Pareto efficient than other CSMA protocols when coexisting with WiFi., Comment: 14 pages, 11 figures

This paper investigates a new class of carrier-sense multiple access (CSMA) protocols that employ deep reinforcement learning (DRL) techniques for heterogeneous wireless networking, referred to as carrier-sense deep-reinforcement learning multiple access (CS-DLMA). Existing CSMA protocols, such as the medium access control (MAC) of WiFi, are designed for a homogeneous network environment in which all nodes adopt the same protocol. Such protocols suffer from severe performance degradation in a heterogeneous environment where there are nodes adopting other MAC protocols. This paper shows that DRL techniques can be used to design efficient MAC protocols for heterogeneous networking. In particular, in a heterogeneous environment with nodes adopting different MAC protocols (e.g., CS-DLMA, TDMA, and ALOHA), a CS-DLMA node can learn to maximize the sum throughput of all nodes. Furthermore, compared with WiFi's CSMA, CS-DLMA can achieve both higher sum throughput and individual throughputs when coexisting with other MAC protocols. Last but not least, a salient feature of CS-DLMA is that it does not need to know the operating mechanisms of the co-existing MACs. Neither does it need to know the number of nodes using these other MACs., Comment: 8 pages

This paper investigates the use of deep reinforcement learning (DRL) in a MAC protocol for heterogeneous wireless networking referred to as Deep-reinforcement Learning Multiple Access (DLMA). The thrust of this work is partially inspired by the vision of DARPA SC2, a 3-year competition whereby competitors are to come up with a clean-slate design that "best share spectrum with any network(s), in any environment, without prior knowledge, leveraging on machine-learning technique". Specifically, this paper considers the problem of sharing time slots among a multiple of time-slotted networks that adopt different MAC protocols. One of the MAC protocols is DLMA. The other two are TDMA and ALOHA. The nodes operating DLMA do not know that the other two MAC protocols are TDMA and ALOHA. Yet, by a series of observations of the environment, its own actions, and the resulting rewards, a DLMA node can learn an optimal MAC strategy to coexist harmoniously with the TDMA and ALOHA nodes according to a specified objective (e.g., the objective could be the sum throughput of all networks, or a general alpha-fairness objective).