On The Communication Complexity of Linear Algebraic Problems in the Message Passing Model

We study the communication complexity of linear algebraic problems over finite fields in the multi-player message passing model, proving a number of tight lower bounds. Specifically, for a matrix which is distributed among a number of players, we consider the problem of determining its rank, of computing entries in its inverse, and of solving linear equations. We also consider related problems such as computing the generalized inner product of vectors held on different servers. We give a general framework for reducing these multi-player problems to their two-player counterparts, showing that the randomized $s$-player communication complexity of these problems is at least $s$ times the randomized two-player communication complexity. Provided the problem has a certain amount of algebraic symmetry, which we formally define, we can show the hardest input distribution is a symmetric distribution, and therefore apply a recent multi-player lower bound technique of Phillips et al. Further, we give new two-player lower bounds for a number of these problems. In particular, our optimal lower bound for the two-player version of the matrix rank problem resolves an open question of Sun and Wang. A common feature of our lower bounds is that they apply even to the special "threshold promise" versions of these problems, wherein the underlying quantity, e.g., rank, is promised to be one of just two values, one on each side of some critical threshold. These kinds of promise problems are commonplace in the literature on data streaming as sources of hardness for reductions giving space lower bounds

Using internet search data to predict new HIV diagnoses in China: a modelling study.

ObjectivesInternet data are important sources of abundant information regarding HIV epidemics and risk factors. A number of case studies found an association between internet searches and outbreaks of infectious diseases, including HIV. In this research, we examined the feasibility of using search query data to predict the number of new HIV diagnoses in China.DesignWe identified a set of search queries that are associated with new HIV diagnoses in China. We developed statistical models (negative binomial generalised linear model and its Bayesian variants) to estimate the number of new HIV diagnoses by using data of search queries (Baidu) and official statistics (for the entire country and for Guangdong province) for 7 years (2010 to 2016).ResultsSearch query data were positively associated with the number of new HIV diagnoses in China and in Guangdong province. Experiments demonstrated that incorporating search query data could improve the prediction performance in nowcasting and forecasting tasks.ConclusionsBaidu data can be used to predict the number of new HIV diagnoses in China up to the province level. This study demonstrates the feasibility of using search query data to predict new HIV diagnoses. Results could potentially facilitate timely evidence-based decision making and complement conventional programmes for HIV prevention

Classification of Data Generated by Gaussian Mixture Models Using Deep ReLU Networks

This paper studies the binary classification of unbounded data from ${\mathbb R}^d$ generated under Gaussian Mixture Models (GMMs) using deep ReLU neural networks. We obtain \unicode{x2013} for the first time \unicode{x2013} non-asymptotic upper bounds and convergence rates of the excess risk (excess misclassification error) for the classification without restrictions on model parameters. The convergence rates we derive do not depend on dimension $d$, demonstrating that deep ReLU networks can overcome the curse of dimensionality in classification. While the majority of existing generalization analysis of classification algorithms relies on a bounded domain, we consider an unbounded domain by leveraging the analyticity and fast decay of Gaussian distributions. To facilitate our analysis, we give a novel approximation error bound for general analytic functions using ReLU networks, which may be of independent interest. Gaussian distributions can be adopted nicely to model data arising in applications, e.g., speeches, images, and texts; our results provide a theoretical verification of the observed efficiency of deep neural networks in practical classification problems

Learning Ability of Interpolating Deep Convolutional Neural Networks

It is frequently observed that overparameterized neural networks generalize well. Regarding such phenomena, existing theoretical work mainly devotes to linear settings or fully-connected neural networks. This paper studies the learning ability of an important family of deep neural networks, deep convolutional neural networks (DCNNs), under both underparameterized and overparameterized settings. We establish the first learning rates of underparameterized DCNNs without parameter or function variable structure restrictions presented in the literature. We also show that by adding well-defined layers to a non-interpolating DCNN, we can obtain some interpolating DCNNs that maintain the good learning rates of the non-interpolating DCNN. This result is achieved by a novel network deepening scheme designed for DCNNs. Our work provides theoretical verification of how overfitted DCNNs generalize well

A Study on Pulsed Power Supply based on Separate Excitation

© ASEE 2007Regular power supply cannot be used for some special applications such as discharging plasma generator, air purification system, medical discharging equipment, etc. Instead, a special low-power high-voltage pulsed power supply is required. In this paper, the design and simulation of a separate excited pulse power supply are proposed. The power supply can produce high-voltage small-current pulses adaptive to different loads. The working principle of the power supply is analyzed. A comparison between this power supply and other pulsed power supply based on capacitance energy storage is discussed. The circuit implementation of power supply is proposed. The key component for the power supply, pulse transformer, as well as other components is studied in detail. Based on the analysis, an optimized design of the power supply is proposed. Computer simulation is used to verify the performance of the designed power supply, such as the output characteristics under different load resistances, the pulse frequency and the duty ratio. Simulation results demonstrate the effectiveness of the designed power supply. Some possible performance improvements on the power supply are also suggested. The designed power supply can satisfy the requirements for commercial applications such as plasma generation and air purification system

Top Management Team Tenure Diversity and Performance: The Moderating Role of Behavioral Integration

Integrating insights from organizational information processing theory and social categorization theory, we examine how top management team (TMT) tenure diversity affects team performance. We propose a theoretical framework that examines how these two conflicting processes occur simultaneously within diverse TMTs by arguing that TMT tenure variety influences information processing while TMT tenure separation influences the social categorization process. We argue for the presence of nonlinear relationships between tenure variety, tenure separation, and team performance. Furthermore, we propose that these relationships are moderated by the level of TMT behavioral integration. Based on a sample of 357 senior managers from 126 firms in China, we find that both TMT tenure variety and TMT tenure separation have opposing and nonlinear relationships with TMT performance, and the relationship between TMT tenure separation and TMT performance is moderated by the level of TMT behavioral integration. Our results help clarify the conflicting conclusions of previous TMT tenure diversity research. Our findings suggest that the effect of diversity depends on the type of diversity as they affect different processes. Our findings also explain how the opposing effects of both information processing and social categorization can occur simultaneously in the TMT. Furthermore, the effects of both processes are not linear while the level of diversity variety and diversity separation can affect the marginal effects. Finally, TMT behavioral integration processes affect how tenure diversity plays its role in team performance