In this Brief Report we discuss entanglement of multiparticle quantum systems. We propose a potential measure of a type of entanglement of pure states of n qubits, the n-tangle. For a system of two qubits the n-tangle is equal to the square of the concurrence, and for systems of three qubits it is equal to the "residual entanglement". We show that the n-tangle, is also equal to the generalization of concurrence squared for even n, and use this fact to prove that the n-tangle is an entanglement monotone. However, the n-tangle is undefined for odd n > 3. Finally we propose a measure related to the n-tangle for mixed state systems of n qubits, and find an analytical formula for this measure for even n.

No abstract

The study of oxygen uptake (V̇o) dynamics during walking exercise transitions adds valuable information regarding fitness. However, direct V̇o measurements are not practical for general population under realistic settings. Devices to measure V̇o are associated with elevated cost, uncomfortable use of a mask, need of trained technicians, and impossibility of long-term data collection. The objective of this study was to predict the V̇o dynamics from heart rate and inputs from the treadmill ergometer by a novel artificial neural network approach. To accomplish this, 10 healthy young participants performed one incremental and three moderate constant work rate treadmill walking exercises. The speed and grade used for the moderate-intensity protocol was related to 80% of the V̇o response at the gas exchange threshold estimated during the incremental exercise. The measured V̇o was used to train an artificial neural network to create an algorithm able to predict the V̇o based on easy-to-obtain inputs. The dynamics of the V̇o response during exercise transition were evaluated by exponential modeling. Within each participant, the predicted V̇o was strongly correlated to the measured V̇o ( = 0.97 ± 0.0) and presented a low bias (~0.2%), enabling the characterization of the V̇o dynamics during treadmill walking exercise. The proposed algorithm could be incorporated into smart devices and fitness equipment, making them suitable for tracking changes in aerobic fitness and physical health beyond the infrequent monitoring of patients during clinical interventions and rehabilitation programs.

While significant research advances have been made in the field of deep reinforcement learning, there have been no concreteadversarial attack strategies in literature tailored for studying the vulnerability of deep reinforcement learning algorithms tomembership inference attacks. In such attacking systems, the adversary targets the set of collected input data on which thedeep reinforcement learning algorithm has been trained. To address this gap, we propose an adversarial attack frameworkdesigned for testing the vulnerability of a state-of-the-art deep reinforcement learning algorithm to a membership inferenceattack. In particular, we design a series of experiments to investigate the impact of temporal correlation, which naturally existsin reinforcement learning training data, on the probability of information leakage. Moreover, we compare the performance ofcollective and individual membership attacks against the deep reinforcement learning algorithm. Experimental results showthat the proposed adversarial attack framework is surprisingly effective at inferring data with an accuracy exceeding 84% inindividual and 97% in collective modes in three different continuous control Mujoco tasks, which raises serious privacy concernsin this regard. Finally, we show that the learning state of the reinforcement learning algorithm influences the level of privacybreaches significantly.