We consider a large-scale cyber network with N components (e.g., paths, servers, subnets). Each component is either in a healthy state (0) or an abnormal state (1). Due to random intrusions, the state of each component transits from 0 to 1 over time according to certain stochastic process. At each time, a subset of K (K < N) components are checked and those observed in abnormal states are fixed. The objective is to design the optimal scheduling for intrusion detection such that the long-term network cost incurred by all abnormal components is minimized. We formulate the problem as a special class of Restless Multi-Armed Bandit (RMAB) process. A general RMAB suffers from the curse of dimensionality (PSPACE-hard) and numerical methods are often inapplicable. We show that, for this class of RMAB, Whittle index exists and can be obtained in closed form, leading to a low-complexity implementation of Whittle index policy with a strong performance. For homogeneous components, Whittle index policy is shown to have a simple structure that does not require any prior knowledge on the intrusion processes. Based on this structure, Whittle index policy is further shown to be optimal over a finite time horizon with an arbitrary length. Beyond intrusion detection, these results also find applications in queuing networks with finite-size buffers.

We consider the multi-armed bandit problems in which a player aims to accrue reward by sequentially playing a given set of arms with unknown reward statistics. In the classic work, policies were proposed to achieve the optimal logarithmic regret order for some special classes of light-tailed reward distributions, e.g., Auer et al.'s UCB1 index policy for reward distributions with finite support. In this paper, we extend Auer et al.'s UCB1 index policy to achieve the optimal logarithmic regret order for all light-tailed (or equivalently, locally sub-Gaussian) reward distributions defined by the (local) existence of the moment-generating function.

We consider the restless multi-armed bandit (RMAB) problem with unknown dynamics in which a player chooses M out of N arms to play at each time. The reward state of each arm transits according to an unknown Markovian rule when it is played and evolves according to an arbitrary unknown random process when it is passive. The performance of an arm selection policy is measured by regret, defined as the reward loss with respect to the case where the player knows which M arms are the most rewarding and always plays the M best arms. We construct a policy with an interleaving exploration and exploitation epoch structure that achieves a regret with logarithmic order when arbitrary (but nontrivial) bounds on certain system parameters are known. When no knowledge about the system is available, we show that the proposed policy achieves a regret arbitrarily close to the logarithmic order. We further extend the problem to a decentralized setting where multiple distributed players share the arms without information exchange. Under both an exogenous restless model and an endogenous restless model, we show that a decentralized extension of the proposed policy preserves the logarithmic regret order as in the centralized setting. The results apply to adaptive learning in various dynamic systems and communication networks, as well as financial investment.

We aim to investigate whether the phenomenon of "sudden drop" in blood pressure (BP) within the first 2 hours is associated with vessel recanalization.We retrospectively examined clinical and imaging data from a consecutive series of patients with stroke with large vessel occlusion treated with intravenous thrombolysis (IVT). BP was monitored every 15 minutes during the first 2 hours, then every 30 minutes for 6 hours, and then every hour for 16 hours.We observed the phenomenon of "sudden drop" in systolic BP (≥20 mm Hg) in 82 (50.9%) patients in the first 2 hours and vessel recanalization in 87 (54.0%) patients 24 hours after treatment. This phenomenon was independently associated with recanalization (odds ratio 2.100; 95% confidence interval: 1.085-4.062; P = 0.028) after adjusting for the history of atrial fibrillation, coronary heart disease, and hypertension.The phenomenon of "sudden drop" in systolic BP with 20 mm Hg or greater between 2 continuous measurements within the first 2 hours is associated with recanalization after IVT in patients with large vessel occlusion, especially for middle cerebral artery occlusion.

Background and purpose

We aim to investigate whether lower admission serum calcium levels are associated with hemorrhagic transformation (HT) after intravenous thrombolysis (IVT).

Methods

A total of 362 patients treated with IVT was divided into 4 quartiles based on admission serum calcium levels (Q1[<2.16], Q2[2.16, 2.23], Q3[2.24, 2.31], and Q4[>2.31] mmol/L). HT was classified as hemorrhagic infarction and parenchymal hemorrhage. Logistic regression was applied to assess the association between serum calcium levels and the incidence of HT.

Results

Compared with Q4, HT was more common in Q1 (odds ratio, 2.580; 95% CI, [1.258-5.292]; P=0.010), Q2 (odds ratio, 2.382; 95% CI, [1.163-4.877]; P=0.018), and Q3 (odds ratio, 2.293; 95% CI, [1.133-4.637]; P=0.021). Hemorrhagic infarction was more common in Q1 (P=0.037), and Q2 (P=0.018), compared with Q4, and parenchymal hemorrhage was more common in Q1 (P=0.029) than Q4.

Conclusions

Lower admission serum calcium level is independently associated with HT after IVT, and this hypothesis needs larger confirmatory trials.