8,863 research outputs found
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 , if its mapped state is EPR steerable, then the
state 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
-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 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
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