This paper considers the stationary distribution of the age of information (AoI) in information update systems. We first derive a general formula for the stationary distribution of the AoI, which holds for a wide class of information update systems. The formula indicates that the stationary distribution of the AoI is given in terms of the stationary distributions of the system delay and the peak AoI. To demonstrate its applicability and usefulness, we analyze the AoI in single-server queues with four different service disciplines: first-come first-served (FCFS), preemptive last-come first-served (LCFS), and two variants of non-preemptive LCFS service disciplines. For the FCFS and the preemptive LCFS service disciplines, the GI/GI/1, M/GI/1, and GI/M/1 queues are considered, and for the non-preemptive LCFS service disciplines, the M/GI/1 and GI/M/1 queues are considered. With these results, we further show comparison results for the mean AoI's in the M/GI/1 and GI/M/1 queues under those service disciplines.where η t (t ≥ 0) denotes the time-stamp of information being displayed on the monitor at time t. The mean AoI E[A] is defined asand under a fairly general setting, E[A] is given by [2]where E[G † ] and E[(G † ) 2 ] denote the mean and the second moment of interarrival times and E[G † n D n ] denotes the mean product of the interarrival time G † n of the (n − 1)st and the nth packets and the system delay D n of the nth packet. This formula has been the starting point in most previous work on the analysis of the AoI. As stated in [1, Page 170], however, the calculation of the mean AoI based on (2) is cumbersome because G † n and D n are dependent in general and their joint distribution can take a complicated form.The purpose of this paper is twofold. The first one is the derivation of a general formula for the stationary distribution A(x) (x ≥ 0) of the AoI in ergodic information update systems, which is defined as the long-run fraction of time in which the AoI is not greater than an arbitrarily fixed value x:where 1 {·} denotes an indicator function. Although the mean AoI E[A] is a primary performance metric, it alone is not sufficient to characterize the long-run behavior of the AoI and its related processes. First of all, if the stationary distribution A(x) of the AoI is available, we can evaluate the deviation of the AoI from its mean value. To support our claim further, we provide two examples, which show that the stationary distribution of the AoI plays a central role in the analysis of AoI-related processes. P-LCFS GI/GI/1/0 LST and E[A] (Theorem 26); Decomposition formula (Corollary 27) P-LCFS M/GI/1/0 LST, E[A], and E[A 2 ] (Corollary 28 (i)); ordering of E[A] (Corollary 31 (i)) P-LCFS GI/M/1/0 LST, E[A], and E[A 2 ] (Corollary 28 (ii)); ordering of dist. function (Corollary 31 (ii)) P-LCFS M/M/1/0 LST, dist. function, E[A] and E[A 2 ] (Appendix A.2) P-LCFS M/D/1/0 E[A] and E[A 2 ] (Appendix A.2) P-LCFS D/M/1/0 E[A] and E[A 2 ] (Appendix A.2)

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Background Eosinophilic myocarditis is a rare clinical entity characterized by eosinophilia and myocardial inflammation with infiltrating eosinophils. The prognosis of patients with eosinophilic myocarditis is difficult to determine due the disease's rarity and varied causes; consequently, standard treatment has not been established.

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Cardiac fibrosis is a hallmark of cardiovascular remodeling associated with hypertension. The purpose of this study was to explore the effect and mechanism of soluble guanylate cyclase (sGC) stimulator BAY 41-2272, leading to intracellular cyclic guanosine monophosphate (cGMP) elevation, on the remodeling process induced by pressure overload. Seven-week-old male Wistar rats with hypertension induced by suprarenal aortic constriction (AC) were treated orally with 2 mg kg À1 day À1 of BAY 41-2272 for 14 days. BAY 41-2272 had no effects on blood pressure, but decreased AC-induced collagen accumulation in the left ventricle (LV), inhibiting the number of myofibroblasts and gene expressions of transforming growth factor-b1 and type 1 collagen. In addition, the antifibrotic action of BAY 41-2272 was accompanied by reducing AC-induced angiotensin-converting enzyme (ACE) mRNA and its enzymatic activity, and angiotensin II concentration in LV. In cultured cardiac fibroblasts, BAY 41-2272 inhibited ACE synthesis and myofibroblast transformation, accompanied by elevating the intracellular cGMP concentration. These results suggest that sGC stimulator BAY 41-2272 might be effective to reduce fibrosis in hypertensive heart disease by attenuating angiotensin II generation through myofibroblast transformation.