The US government imposes reporting requirements on healthcare providers as health metrics are important for assessing and improving the US healthcare system. However, proposed health metrics requirements can be unnecessarily burdensome if the preliminary analysis does not consider possible redundancies between the various metrics. Accordingly, if some subset of the proposed metrics could be demonstrated to contain nearly all the information of the full set of metrics, then the reporting burden could be substantially lightened with minimum impact. However, such an analysis is complicated by anomalies in the collected metrics. Accordingly, we propose a machine learning approach which simultaneously identifies redundancies in collected healthcare metrics and identifies anomalies in those collected metrics.

Although an extensive research literature on influence exists in fields like social psychology and communications, the advent of social media opens up new questions regarding how to define and measure influence online. In this paper, we present a new definition of influence that is tailored uniquely for online contexts and an associated methodology for gauging influence. According to our definition, influence entails the capacity to shift the patterns of emotion levels expressed by social media users. The source of influence may be the content of a user's message or the context of the relationship between exchanging users. Regardless of the source, measuring influence requires first identifying shifts in the patterns of emotion levels expressed by users and then studying the extent that these shifts can be associated with a user. This paper presents a new quantitative approach that combines the use of a text analysis program with a mathematical algorithm to derive trends in levels of emotions expressed in social media and, more importantly, detect breakpoints when those trends changed abruptly. First steps have also been taken to predict future trends in expressions (as well as quantify their accuracy). These methods constitute a new approach to quantifying influence in social media that focuses on detecting the impact of influence (e.g., shifts in levels of emotions expressed) as opposed to focusing on the dynamics of simple social media counts, e.g., retweets, followers, or likes.

Given transactional data consisting of service starting and finishing times in a queuing system with a Poisson arrival process and service in order of arrival, the distributions and moments of waiting times W1, …, WN, of customers within a busy period of length N are computed efficiently by exploiting an embedded Markov chain. All first moments E(Wk ∣ data from busy period of length N) are computed in O(N3) multiplications; finding the distributions of all Wk on a set of n prespecified times requires O(nN3) multiplications; finding all rth order moments needs O(rN4) multiplications. The algorithms described are all new, as fast or faster than all known algorithms, and address a broader range of performance measures than the extant literature.

Many telecommunication systems with time-critical requirements use a preempt-resume clocked schedule. An approximation to the ergodic distribution of the time to completion of a low-priority task is obtained by treating the priority service time distribution as the limit of compound Poisson distributions. Explicit formulas for the mean and variance that are highly accurate are given. For random clocked loads, a stochastic bound is provided for the discrepancy between the exact and approximate distributions. For deterministic clocked loads, sample path bounds are found. Simulation results are given to demonstrate the accuracy of the model.>

The Laplace Transform (and the first two moments) of the busy period of the recently introducedM/G/1vacation model with a Bernoulli schedule is completed exactly. This expression makes it possible to estimate the average waiting time of each queue for the Bernoulli schedule cyclic service queue. Consequently, the weighted average of the mean waiting time can be minimized over the class of Bernoulli schedules. The Bernoulli schedule has the advantage over exhaustive schedules (or classical priority schedules) in that the performance of one class of traffic is somewhat insulated from the adverse effects of high utilization in a different class of traffic. The analysis of cyclic service queues can be applied to processor schedules and token ring local area networks as well as components of other data communication systems.

In many data communication and telephone switching systems, one processor must perform more than one type of task. In some systems it is advantageous to place the different tasks in different queues and have the processor serve the queues in a cyclic manner. Moreover, the system design often imposes a (finite or infinite) limit on the number of entries that may be served per cycle from any given queue; this limit typically varies from queue to queue. This paper will derive the capacity estimation of such systems. We consider systems which, in addition to servingnqueues cyclically, must execute maintenance (or other low-priority jobs) without severely disrupting the queues' performance. For two alternative methods of scheduling the maintenance, we compute steady state values of i) the average cycle time, ii) the average number of entries of each queue served per cycle, iii) the average time spent at each queue per cycle, iv) the average amount of elapsed time necessary to complete a given amount of maintenance execution real time, and v) if the arrival rate to queuei,\lambda_{i}, is proportional toN, the number of customers in the system, i.e.,\lambda_{i} = N\alpha_{i}, then we a) compute the value ofNwhich saturates the system and b) predict which queue will first become saturated asNis increased towards this value.

A new approach is provided to facilitate the study of de-centalized resource allocation algorithms. Three algorithms are presented: the Arrow-Hurwicz algorithm, the center-free algorithm, and the Heal algorithm. For each algorithm, an associated network consisting of resistors, capacitors, and power supplies is found to exist. A one-to-one correspondence is proved between the equations describing these electrical networks and the equations governing the algorithms. With this correspondence, knowledge and intuition regarding electrical networks is demonstrated to facilitate the study of properties of these resource allocation algorithms.