Modeling trend progression through an extension of the Polya Urn Process

Knowing how and when trends are formed is a frequently visited research goal. In our work, we focus on the progression of trends through (social) networks. We use a random graph (RG) model to mimic the progression of a trend through the network. The context of the trend is not included in our model. We show that every state of the RG model maps to a state of the Polya process. We find that the limit of the component size distribution of the RG model shows power-law behaviour. These results are also supported by simulations.Comment: 11 pages, 2 figures, NetSci-X Conference, Wroclaw, Poland, 11-13 January 2016. arXiv admin note: text overlap with arXiv:1502.0016

Optimal weighing schemes

We study the problem of determining the masses of a set of weights, given one standard weight, based on comparing two disjoint subsets of those weights with approximately equal mass. The question is how to choose a weighing scheme, i.e., different pairs of subsets, such that the masses can be determined as accurately as possible within a given number of measurements. In this paper we discuss a new way of using the so-called STS method of comparing two approximately equal masses, and we will give optimal weighing schemes which turn out to outperform schemes that are currently used by national metrology institutes

Dynamic routing policies for multi-skill call centers

We consider the problem of routing calls dynamically in a multiskill call center. Calls from different skill classes are offered to the call center according to a Poisson process. The agents in the center are grouped according to their heterogeneous skill sets that determine the classes of calls they can serve. Each agent group serves calls with independent exponentially distributed service times. We consider two scenarios. The first scenario deals with a call center with no buffers in the system, so that every arriving call either has to be routed immediately or has to be blocked and is lost. The objective in the system is to minimize the average number of blocked calls. The second scenario deals with call centers consisting of only agents that have one skill and fully cross-trained agents, where calls are pooled in common queues. The objective in this system is to minimize the average number of calls in the system. We obtain nearly optimal dynamic routing policies that are scalable with the problem instance and can be computed online. The algorithm is based on one-step policy improvement using the relative value functions of simpler queuing systems. Numerical experiments demonstrate the good performance of the routing policies. Finally, we discuss how the algorithm can be used to handle more general cases with the techniques described in this article. © 2009 Cambridge University Press

Personalized Stopping Rules in Bayesian Adaptive Mastery Assessment

We propose a new model to assess the mastery level of a given skill efficiently. The model, called Bayesian Adaptive Mastery Assessment (BAMA), uses information on the accuracy and the response time of the answers given and infers the mastery at every step of the assessment. BAMA balances the length of the assessment and the certainty of the mastery inference by employing a Bayesian decision-theoretic framework adapted to each student. All these properties contribute to a novel approach in assessment models for intelligent learning systems. The purpose of this research is to explore the properties of BAMA and evaluate its performance concerning the number of questions administered and the accuracy of the final mastery estimates across different students. We simulate student performances and establish that the model converges with low variance and high efficiency leading to shorter assessment duration for all students. Considering the experimental results, we expect our approach to avoid the issue of over-practicing and under-practicing and facilitate the development of Learning Analytics tools to support the tutors in the evaluation of learning effects and instructional decision making.Comment: 12 page