A network modelling approach to educational mapping leads to a scalable computational model that supports adaptive learning, intelligent tutors, intelligent teaching assistants, and data-driven continuous improvement. Current educational mapping processes are generally applied at a level of resolution that is too coarse to support adaptive learning and learning analytics systems at scale. This paper proposes a network modelling approach to structure extremely fine-grained statements of learning ability called Micro-outcomes, and a method to design sensors for inferring a learner’s knowledge state. These sensors take the form of high-resolution assessments and trackers that collect digital analytics. The sensors are linked to Micro-outcomes as part of the network model, enabling inference and pathway analysis. One example demonstrates the modelling approach applied to two community college subjects in College Algebra and Introductory Accounting. Application examples showcase how this modelling approach provides the design foundation for an intelligent tutoring system and intelligent teaching assistant system deployed at Arapahoe Community College and Quinsigamond Community College. A second example demonstrates the modelling approach deployed in an undergraduate aerospace engineering subject at the Massachusetts Institute of Technology to support course planning and teaching improvement.

Customer preference modeling provides quantitative assessment of the effects of engineering design attributes on customers’ choices. Utility-based approaches, such as discrete choice model (DCM), and network analysis approaches, such as exponential random graph model (ERGM), have been developed for customer preference modeling. However, no studies have compared these two approaches. Our objective is to identify the distinctions and connections between these two approaches based on both the theoretical foundation and the empirical evidence. Using the vehicle preference modeling as an example, our study shows that when network structure effects are not considered, results from ERGM are consistent with DCM in most of the test cases. However, in one case where customers have varying choice set with multiple alternatives, inconsistencies are observed, possibly due to the discrepancies of the two models in taking different information when calculating choice probabilities. The insights will lead to valuable guidance for choosing the technique for customer preference modeling and co- developing the two frameworks to support engineering design.

Magnetic-resonant wireless power transfer (MRWPT) has been typically realized by using systems of coupled resonators. In this paper, we introduce a rigorous network modeling of the wireless channel and we introduce several viable alternatives for achieving efficient MRWPT. Ideally, the wireless channel should realize a 1:n transformer; we implement such transformer by using immittance inverters. Examples illustrate the proposed network modeling of the magnetic-resonant wireless power channel.

Consider an infinite-source marked Poisson process to model end user inputs to a data network. At Poisson times, connections are initated. The connection is characterized by a triple (F, L, R) denoting the total quantity of transmitted data in a connection, the length or duration of the connection, and the transmission rate; the three quantities are related by F = LR. How critical is the dependence structure of the mark for network characteristics such as burstiness, distribution tails of cumulative input, and long-range dependence properties of traffic measured in consecutive time slots? In a previous publication (D'Auria and Resnick (2006)) we assumed that F and R were independent. Here we assume that L and R are independent. The change in dependence assumptions means that the model properties change dramatically: tails of cumulative input per time slot are dramatically heavier, traffic cannot be approximated by a Gaussian distribution, and the decay of dependence cannot be measured in the traditional way using correlation functions. Different network applications are likely to have different mark dependence structure. We argue that the present independence assumption on L and R is likely to be appropriate for network applications such as streaming media or peer-to-peer networks. Our conclusion is that it is desirable to separate network traffic by application and to model each application with its own appropriate dependence structure.

We review characteristics of data traffic which we term stylized facts: burstiness, long-range dependence, heavy tails, bursty behavior determined by high-bandwidth users, and dependence determined by users without high transmission rates. We propose an infinite-source Poisson input model which supplies traffic in adjacent time slots. We study properties of the model as slot width decreases and traffic intensity increases. This model has the ability to account for many of the stylized facts.

The usual concept of asymptotic independence, as discussed in the context of extreme value theory, requires the distribution of the coordinatewise sample maxima under suitable centering and scaling to converge to a product measure. However, this definition is too broad to conclude anything interesting about the tail behavior of the product of two random variables that are asymptotically independent. Here we introduce a new concept of asymptotic independence which allows us to study the tail behavior of products. We carefully discuss equivalent formulations of asymptotic independence. We then use the concept in the study of a network traffic model. The usual infinite source Poisson network model assumes that sources begin data transmissions at Poisson time points and continue for random lengths of time. It is assumed that the data transmissions proceed at a constant, nonrandom rate over the entire length of the transmission. However, analysis of network data suggests that the transmission rate is also random with a regularly varying tail. So, we modify the usual model to allow transmission sources to transmit at a random rate over the length of the transmission. We assume that the rate and the time have finite mean, infinite variance and possess asymptotic independence, as defined in the paper. We finally prove a limit theorem for the input process showing that the centered cumulative process under a suitable scaling converges to a totally skewed stable Lévy motion in the sense of finite-dimensional distributions.