Block-Structured Supermarket Models

Supermarket models are a class of parallel queueing networks with an adaptive control scheme that play a key role in the study of resource management of, such as, computer networks, manufacturing systems and transportation networks. When the arrival processes are non-Poisson and the service times are non-exponential, analysis of such a supermarket model is always limited, interesting, and challenging. This paper describes a supermarket model with non-Poisson inputs: Markovian Arrival Processes (MAPs) and with non-exponential service times: Phase-type (PH) distributions, and provides a generalized matrix-analytic method which is first combined with the operator semigroup and the mean-field limit. When discussing such a more general supermarket model, this paper makes some new results and advances as follows: (1) Providing a detailed probability analysis for setting up an infinite-dimensional system of differential vector equations satisfied by the expected fraction vector, where "the invariance of environment factors" is given as an important result. (2) Introducing the phase-type structure to the operator semigroup and to the mean-field limit, and a Lipschitz condition can be obtained by means of a unified matrix-differential algorithm. (3) The matrix-analytic method is used to compute the fixed point which leads to performance computation of this system. Finally, we use some numerical examples to illustrate how the performance measures of this supermarket model depend on the non-Poisson inputs and on the non-exponential service times. Thus the results of this paper give new highlight on understanding influence of non-Poisson inputs and of non-exponential service times on performance measures of more general supermarket models.Comment: 65 pages; 7 figure

Boosting Information Spread: An Algorithmic Approach

The majority of influence maximization (IM) studies focus on targeting influential seeders to trigger substantial information spread in social networks. In this paper, we consider a new and complementary problem of how to further increase the influence spread of given seeders. Our study is motivated by the observation that direct incentives could "boost" users so that they are more likely to be influenced by friends. We study the $k$-boosting problem which aims to find $k$ users to boost so that the final "boosted" influence spread is maximized. The $k$-boosting problem is different from the IM problem because boosted users behave differently from seeders: boosted users are initially uninfluenced and we only increase their probability to be influenced. Our work also complements the IM studies because we focus on triggering larger influence spread on the basis of given seeders. Both the NP-hardness of the problem and the non-submodularity of the objective function pose challenges to the $k$-boosting problem. To tackle the problem on general graphs, we devise two efficient algorithms with the data-dependent approximation ratio. For the $k$-boosting problem on bidirected trees, we present an efficient greedy algorithm and a rounded dynamic programming that is a fully polynomial-time approximation scheme. We conduct extensive experiments using real social networks and synthetic bidirected trees. We show that boosting solutions returned by our algorithms achieves boosts of influence that are up to several times higher than those achieved by boosting solutions returned by intuitive baselines, which have no guarantee of solution quality. We also explore the "budget allocation" problem in our experiments. Compared with targeting seeders with all budget, larger influence spread is achieved when we allocation the budget to both seeders and boosted users

A Matrix-Analytic Solution for Randomized Load Balancing Models with Phase-Type Service Times

In this paper, we provide a matrix-analytic solution for randomized load balancing models (also known as \emph{supermarket models}) with phase-type (PH) service times. Generalizing the service times to the phase-type distribution makes the analysis of the supermarket models more difficult and challenging than that of the exponential service time case which has been extensively discussed in the literature. We first describe the supermarket model as a system of differential vector equations, and provide a doubly exponential solution to the fixed point of the system of differential vector equations. Then we analyze the exponential convergence of the current location of the supermarket model to its fixed point. Finally, we present numerical examples to illustrate our approach and show its effectiveness in analyzing the randomized load balancing schemes with non-exponential service requirements.Comment: 24 page

Enriched Long-term Recurrent Convolutional Network for Facial Micro-Expression Recognition

Facial micro-expression (ME) recognition has posed a huge challenge to researchers for its subtlety in motion and limited databases. Recently, handcrafted techniques have achieved superior performance in micro-expression recognition but at the cost of domain specificity and cumbersome parametric tunings. In this paper, we propose an Enriched Long-term Recurrent Convolutional Network (ELRCN) that first encodes each micro-expression frame into a feature vector through CNN module(s), then predicts the micro-expression by passing the feature vector through a Long Short-term Memory (LSTM) module. The framework contains two different network variants: (1) Channel-wise stacking of input data for spatial enrichment, (2) Feature-wise stacking of features for temporal enrichment. We demonstrate that the proposed approach is able to achieve reasonably good performance, without data augmentation. In addition, we also present ablation studies conducted on the framework and visualizations of what CNN "sees" when predicting the micro-expression classes.Comment: Published in Micro-Expression Grand Challenge 2018, Workshop of 13th IEEE Facial & Gesture 201

Origin of large moments in Mnx_xSi1−x_{1-x} at small x

Recently, the magnetic moment/Mn, $M$, in Mn$_x$Si$_{1-x}$ was measured to be 5.0 $\mu_B$/Mn, at $x$ =0.1%. To understand this observed $M$, we investigate several Mn$_x$Si$_{1-x}$ models of alloys using first-principles density functional methods. The only model giving $M = 5.0$ was a 513-atom cell having the Mn at a substitutional site, and Si at a second-neighbor interstitial site. The observed large moment is a consequence of the weakened d-p hybridization between the Mn and one of its nearest neighbor Si atoms, resulting from the introduction of the second-neighbor interstitial Si. Our result suggests a way to tune the magnetic moments of transition metal doped semiconductors.Comment: 4 pages, 2 figure