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The age of information (AoI) metric was proposed to measure the freshness of messages obtained at the terminal node of a status updating system. In this paper, the AoI of a discrete time status updating system with probabilistic packet preemption is investigated by analyzing the steady state of a three-dimensional discrete stochastic process. We assume that the queue used in the system is Ber/Geo/1/2*/η, which represents that the system size is 2 and the packet in the buffer can be preempted by a fresher packet with probability η. Instead of considering the system's AoI separately, we use a three-dimensional state vector (n,m,l) to simultaneously track the real-time changes of the AoI, the age of a packet in the server, and the age of a packet waiting in the buffer. We give the explicit expression of the system's average AoI and show that the average AoI of the system without packet preemption is obtained by letting η=0. When η is set to 1, the mean of the AoI of the system with a Ber/Geo/1/2* queue is obtained as well. Combining the results we have obtained and comparing them with corresponding average continuous AoIs, we propose a possible relationship between the average discrete AoI with the Ber/Geo/1/c queue and the average continuous AoI with the M/M/1/c queue. For each of two extreme cases where η=0 and η=1, we also determine the stationary distribution of AoI using the probability generation function (PGF) method. The relations between the average AoI and the packet preemption probability η, as well as the AoI's distribution curves in two extreme cases, are illustrated by numerical simulations. Notice that the probabilistic packet preemption may occur, for example, in an energy harvest (EH) node of a wireless sensor network, where the packet in the buffer can be replaced only when the node collects enough energy. In particular, to exhibit the usefulness of our idea and methods and highlight the merits of considering discrete time systems, in this paper, we provide detailed discussions showing how the results about continuous AoI are derived by analyzing the corresponding discrete time system and how the discrete age analysis is generalized to the system with multiple sources. In terms of packet service process, we also propose an idea to analyze the AoI of a system when the service time distribution is arbitrary.

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Nonalcoholic fatty liver disease (NAFLD) has become the most common cause of chronic liver disease and threatens human health worldwide. As shown in our previous study, co-supplementation with phytosterol ester (PSE) (3.3 g day-1) and n-3 polyunsaturated fatty acids (PUFAs) (450 mg eicosapentaenoic acid (EPA) + 1500 mg docosahexaenoic acid (DHA) per day) was more effective at ameliorating hepatic steatosis than treatment with PSE or n-3 PUFAs alone. In the present study, we further investigated the changes in the serum metabolic profiles of subjects with NAFLD in response to n-3 PUFAs and PSE. Thirty-one differentially altered serum metabolites were annotated using the nontargeted ultra-performance liquid chromatography-quadrupole/time-of-flight mass spectrometry (UPLC-Q-TOF-MSE) analysis technique. Multivariable statistical and clustering analyses showed that co-supplementation of n-3 PUFAs and PSE was more effective at improving metabolic disorders in patients with NAFLD than treatment with n-3 PUFAs or PSE alone. The regulated metabolic pathways included metabolism of retinol, linoleic acid, arachidonic acid, glycerophospholipid, sphingolipid, and steroid hormone biosynthesis. Overall, the co-supplementation of n-3 PUFAs and PSE significantly increased the serum levels of PUFA-containing phosphatidylcholine (PC), lysophosphatidylcholine (LysoPC), perillyl alcohol and retinyl ester in patients with NAFLD after 12 weeks of intervention, and the levels of PC (14:0/20:5, 15:0/20:5), LysoPC (20:5, 22:6) and retinyl ester correlated negatively with the degree of hepatic steatosis. The regulatory effect of co-supplementation of n-3 PUFAs and PSE on metabolomic profiles may explain their potential role in alleviating hepatic steatosis in patients with NAFLD.

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This paper investigates the optimal inter-organization control of collaborative advertising considering the myopic and far-sighted behaviors. Taking a two-echelon supply chain as an example, four kinds of differential game models including myopic Stackelberg game, far-sighted Stackelberg game, myopic cooperative game and far-sighted cooperative game are studied. The results show that the optimal advertising efforts of both manufacturer and retailer in the myopic situation decrease with time. But they remain constant in the far-sighted situation. The Pareto improvement applies to both game players from the non-cooperative game to the cooperative game. The numerical analyses are conducted to further investigate the theoretical results and to guide the inter-organization control of collaborative advertising in practice.

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PURPOSE: To evaluate the use of TNF-alpha inhibitors for non-infectious, non-necrotizing scleritis. METHODS: We conducted a retrospective chart review of patients with non-infectious, non-necrotizing scleritis treated at our institutions from 2002 to 2012. RESULTS: Seventeen patients (26 eyes) were included. Ten patients were started on infliximab and seven on adalimumab; five patients were treated with both TNF-alpha inhibitors on separate occasions. All patients had an associated autoimmune disease. Control of active inflammation for at least 2 months was achieved in 15 (88%) of 17 patients. Seven out of eight patients successfully tapered concurrent corticosteroid use. Only one patient discontinued TNF-alpha inhibitor use due to an allergic reaction. CONCLUSIONS: TNF-alpha inhibitors appear to have a role in managing non-infectious, non-necrotizing scleritis refractory to initial therapy, mainly by reducing inflammation and decreasing concurrent CS use.

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We present the case of an Alport syndrome patient whose anterior lenticonus was detected by wavefront analysis and Scheimpflug imaging technology. The patient's lenticular abnormalities were too subtle to be detected by the initial slitlamp examination. Normal corneal topography and elevation maps with high total-eye aberrations pointed to internal optics as the source of aberrations, and predominant negative spherical aberrations suggested anterior lenticonus, a diagnosis confirmed by Scheimpflug images that showed central bulging of the anterior lens surface. Following diagnosis, uneventful phacoemulsification and intraocular lens implantation were performed. We recommend wavefront analysis and Scheimpflug imaging technology as effective tools in the detection of lens disorders, especially those that are too subtle to be observed by other examination methods.

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