An Iterative Minimization Formulation for Saddle-Point Search

This paper proposes and analyzes an iterative minimization formulation for search- ing index-1 saddle points of an energy function. This formulation differs from other eigenvector-following methods by constructing a new objective function near the guess at each iteration step. This leads to a quadratic convergence rate, in comparison to the linear case of the gentlest ascent dynamics (E and Zhou, nonlinearity, vol 24, p1831, 2011) and many other existing methods. We also propose the generalization of the new methodology for saddle points of higher index and for constrained energy functions on manifold

Evolving nature of human contact networks with its impact on epidemic processes

Human contact networks are constituted by a multitude of individuals and pairwise contacts among them. However, the dynamic nature, which generates the evolution of human contact networks, of contact patterns is not known yet. Here, we analyse three empirical datasets and identify two crucial mechanisms of the evolution of temporal human contact networks, i.e. the activity state transition laws for an individual to be socially active, and the contact establishment mechanism that active individuals adopt. We consider both of the two mechanisms to propose a temporal network model, named the memory driven (MD) model, of human contact networks. Then we study the susceptible-infected (SI) spreading processes on empirical human contact networks and four corresponding temporal network models, and compare the full prevalence time of SI processes with various infection rates on the networks. The full prevalence time of SI processes in the MD model is the same as that in real-world human contact networks. Moreover, we find that the individual activity state transition promotes the spreading process, while, the contact establishment of active individuals suppress the prevalence. Apart from this, we observe that even a small percentage of individuals to explore new social ties is able to induce an explosive spreading on networks. The proposed temporal network framework could help the further study of dynamic processes in temporal human contact networks, and offer new insights to predict and control the diffusion processes on networks

RLS-Based Adaptive Dereverberation Tracing Abrupt Position Change of Target Speaker

Adaptive algorithm based on multi-channel linear prediction is an effective dereverberation method balancing well between the attenuation of the long-term reverberation and the dereverberated speech quality. However, the abrupt change of the speech source position, usually caused by the shift of the speakers, forms an obstacle to the adaptive algorithm and makes it difficult to guarantee both the fast convergence speed and the optimal steady-state behavior. In this paper, the RLS-based adaptive multi-channel linear prediction method is investigated and a time-varying forgetting factor based on the relative weighted change of the adaptive filter coefficients is proposed to effectively tracing the abrupt change of the target speaker position. The advantages of the proposed scheme are demonstrated in the simulations and experiments.Comment: Accepted by 2018 IEEE Sensor Array and Multichannel Signal Processing Workshop (SAM

Bell's Nonlocality Can be Tested through Einstein-Podolsky-Rosen Steering

Quantum nonlocality has recently been classified into three distinct types: quantum entanglement, Einstein-Podolsky-Rosen (EPR) steering, and Bell's nonlocality. Experimentally Bell's nonlocality is usually tested by quantum violation of the Clause-Horne-Shimony-Holt (CHSH) inequality in the two-qubit system. Bell's nonlocality is the strongest type of nonlocality, also due this reason Bell-test experiments have encountered both the locality loophole and the detection loophole for a very long time. As a weaker nonlocality, EPR steering naturally escapes from the locality loophole and is correspondingly easier to be demonstrated without the detection loophole. In this work, we trigger an extraordinary approach to investigate Bell's nonlocality, which is strongly based on the EPR steering. We present a theorem, showing that for any two-qubit state $\tau$, if its mapped state $\rho$ is EPR steerable, then the state $\tau$ must be Bell nonlocal. The result not only pinpoints a deep connection between EPR steering and Bell's nonlocality, but also sheds a new light to realize a loophole-free Bell-test experiment (without the CHSH inequality) through the violation of steering inequality.Comment: 4 pages, 2 figures. Supplementary Materials, 4 page

A Simple Channel Independent Beamforming Scheme with Circular Array

In this letter, we consider a uniform circular array (UCA) based line-of-sight (LOS) multiple-input-multiple-output (MIMO) system, where the transmit and receive UCAs are aligned with each other. We propose a simple channel independent beamforming scheme with fast symbol-wise maximum likelihood (ML) detection

Measuring Contextual Relationships in Temporal Social Networks by Circle Link

Network science has released its talents in social network analysis based on the information of static topologies. In reality social contacts are dynamic and evolve concurrently in time. Nowadays they can be recorded by ubiquitous information technologies, and generated into temporal social networks to provide new sights in social reality mining. Here, we define \emph{circle link} to measure contextual relationships in three empirical social temporal networks, and find that the tendency of friends having frequent continuous interactions with their common friend prefer to be close, which can be considered as the extension of Granovetter's hypothesis in temporal social networks. Finally, we present a heuristic method based on circle link to predict relationships and acquire acceptable results.Comment: 5 pages, 3 figure

Learning with Differential Privacy: Stability, Learnability and the Sufficiency and Necessity of ERM Principle

While machine learning has proven to be a powerful data-driven solution to many real-life problems, its use in sensitive domains has been limited due to privacy concerns. A popular approach known as **differential privacy** offers provable privacy guarantees, but it is often observed in practice that it could substantially hamper learning accuracy. In this paper we study the learnability (whether a problem can be learned by any algorithm) under Vapnik's general learning setting with differential privacy constraint, and reveal some intricate relationships between privacy, stability and learnability. In particular, we show that a problem is privately learnable **if an only if** there is a private algorithm that asymptotically minimizes the empirical risk (AERM). In contrast, for non-private learning AERM alone is not sufficient for learnability. This result suggests that when searching for private learning algorithms, we can restrict the search to algorithms that are AERM. In light of this, we propose a conceptual procedure that always finds a universally consistent algorithm whenever the problem is learnable under privacy constraint. We also propose a generic and practical algorithm and show that under very general conditions it privately learns a wide class of learning problems. Lastly, we extend some of the results to the more practical $(\epsilon,\delta)$-differential privacy and establish the existence of a phase-transition on the class of problems that are approximately privately learnable with respect to how small $\delta$ needs to be.Comment: to appear, Journal of Machine Learning Research, 201

Culturomics meets random fractal theory: Insights into long-range correlations of social and natural phenomena over the past two centuries

Culturomics was recently introduced as the application of high-throughput data collection and analysis to the study of human culture. Here we make use of this data by investigating fluctuations in yearly usage frequencies of specific words that describe social and natural phenomena, as derived from books that were published over the course of the past two centuries. We show that the determination of the Hurst parameter by means of fractal analysis provides fundamental insights into the nature of long-range correlations contained in the culturomic trajectories, and by doing so, offers new interpretations as to what might be the main driving forces behind the examined phenomena. Quite remarkably, we find that social and natural phenomena are governed by fundamentally different processes. While natural phenomena have properties that are typical for processes with persistent long-range correlations, social phenomena are better described as nonstationary, on-off intermittent, or Levy walk processes.Comment: 8 two-column pages, 5 figures; accepted for publication in Journal of the Royal Society Interface [data available at http://books.google.com/ngrams

Inverse mean curvature flow inside a cone in warped products

Given a convex cone in the \emph{prescribed} warped product, we consider hypersurfaces with boundary which are star-shaped with respect to the center of the cone and which meet the cone perpendicularly. If those hypersurfaces inside the cone evolve along the inverse mean curvature flow, then, by using the convexity of the cone, we can prove that this evolution exists for all the time and the evolving hypersurfaces converge smoothly to a piece of round sphere as time tends to infinity.Comment: 12 pages. Several minor revisions (including typos) have been made to v

On-Average KL-Privacy and its equivalence to Generalization for Max-Entropy Mechanisms

We define On-Average KL-Privacy and present its properties and connections to differential privacy, generalization and information-theoretic quantities including max-information and mutual information. The new definition significantly weakens differential privacy, while preserving its minimalistic design features such as composition over small group and multiple queries as well as closeness to post-processing. Moreover, we show that On-Average KL-Privacy is **equivalent** to generalization for a large class of commonly-used tools in statistics and machine learning that samples from Gibbs distributions---a class of distributions that arises naturally from the maximum entropy principle. In addition, a byproduct of our analysis yields a lower bound for generalization error in terms of mutual information which reveals an interesting interplay with known upper bounds that use the same quantity