arXiv subjects

Ge Chen

Publications and source records attributed to Ge Chen.

84 records · Page 5Linked to original sources

arXiv2018

Linear Stochastic Approximation Algorithms and Group Consensus over Random Signed Networks: A Technical Report with All Proofs

This paper studies linear stochastic approximation (SA) algorithms and their application to multi-agent systems in engineering and sociology. As main contribution, we provide necessary and sufficient conditions for convergence of linear SA algorithms to a deterministic or random final vector. We also characterize the system convergence rate, when the system is convergent. Moreover, differing from non-negative gain functions in traditional SA algorithms, this paper considers also the case when the gain functions are allowed to take arbitrary real numbers. Using our general treatment, we provide necessary and sufficient conditions to reach consensus and group consensus for first-order discrete-time multi-agent system over random signed networks and with state-dependent noise. Finally, we extend our results to the setting of multi-dimensional linear SA algorithms and characterize the behavior of the multi-dimensional Friedkin-Johnsen model over random interaction networks.

math.OC↗

arXiv2018

An Improved Transit Measurement for a 2.4 R_{Earth} Planet Orbiting A Bright Mid-M Dwarf K2$-$28

We present a new {\em Spitzer} transit observation of K2$-$28b, a sub-Neptune ($R_{\rm p} = 2.45\pm0.28 R_{Earth}$) orbiting a relatively bright ($V_{\rm mag} = 16.06$, $K_{\rm mag} = 10.75$) metal-rich M4 dwarf (EPIC 206318379). This star is one of only seven with masses less than 0.2 M_{Sun} known to host transiting planets, and the planet appears to be a slightly smaller analogue of GJ 1214b ($2.85\pm0.20 R_{Earth}$; \citealt{2013A&A...549A..10H}). Our new {\em Spitzer} observations were taken two years after the original K2 discovery data and have a significantly higher cadence, allowing us to derive improved estimates for this planet's radius, semi-major axis, and orbital period, which greatly reduce the uncertainty in the prediction of near future transit times for the {\em James Webb Space Telescope} ({\em JWST}) observations. We also evaluate the system's suitability for atmospheric characterization with {\em JWST} and find that it is currently the only small (< 3 R_{Earth}) and cool ($< 600$ K) planet aside from GJ 1214b with a potentially detectable secondary eclipse. We also note that this system is a favorable target for near-infrared radial velocity instruments on larger telescopes (e.g., the Habitable Planet Finder on the Hobby-Eberly Telescope), making it one of only a handful of small, cool planets accessible with this technique. Finally, we compare our results with the simulated catalog of the Transiting Exoplanet Survey Satellite ({\em TESS}) and find K2$-$28b to be representative of the kind of mid-M systems that should be detectible in the {\em TESS} sample.

astro-ph.EP↗

arXiv2018

Programmable Switch as a Parallel Computing Device

Modern switches have packet processing capacity of up to multi-tera bits per second, and they are also becoming more and more programmable. We seek to understand whether the programmability can translate packet processing capacity to computational power for parallel computing applications. In this paper, we first develop a simple mathematical model to understand the costs and overheads of data plane computation. Then we validate the the performance benefits of offloading computation to network. Using experiments on real data center network, we finnd that offloading computation to the data plane results in up to 20x speed-up for a simple Map-Reduce application. Motivated by this, we propose a parallel programming framework, p4mr, to help users efficiently program multiple switches. We successfully build and test a prototype of p4mr on a simulated testbed.

cs.NI↗

arXiv2017

Robust Fragmentation Modeling of Hegselmann-Krause-Type Dynamics

In opinion dynamics, how to model the enduring fragmentation phenomenon (disagreement, cleavage, and polarization) of social opinions has long possessed a central position. It is widely known that the confidence-based opinion dynamics provide an acceptant mechanism to produce fragmentation phenomenon. In this study, taking the famous confidence-based Hegselmann-Krause (HK) model, we examine the robustness of the fragmentation coming from HK dynamics and its variations with prejudiced and stubborn agents against random noise. Prior to possible insightful explanations, the theoretical results in this paper explicitly reveal that the well-appearing fragmentation of HK dynamics and its homogeneous variations finally vanishes in the presence of arbitrarily tiny noise, while only the HK model with heterogenous prejudices displays a solid cleavage in noisy environment.

math.OC↗

arXiv2017

EddyNet: A Deep Neural Network For Pixel-Wise Classification of Oceanic Eddies

This work presents EddyNet, a deep learning based architecture for automated eddy detection and classification from Sea Surface Height (SSH) maps provided by the Copernicus Marine and Environment Monitoring Service (CMEMS). EddyNet is a U-Net like network that consists of a convolutional encoder-decoder followed by a pixel-wise classification layer. The output is a map with the same size of the input where pixels have the following labels \{'0': Non eddy, '1': anticyclonic eddy, '2': cyclonic eddy\}. We investigate the use of SELU activation function instead of the classical ReLU+BN and we use an overlap based loss function instead of the cross entropy loss. Keras Python code, the training datasets and EddyNet weights files are open-source and freely available on https://github.com/redouanelg/EddyNet.

cs.CV↗

arXiv2017

Critical Connectivity and Fastest Convergence Rates of Distributed Consensus with Switching Topologies and Additive Noises

Consensus conditions and convergence speeds are crucial for distributed consensus algorithms of networked systems. Based on a basic first-order average-consensus protocol with time-varying topologies and additive noises, this paper first investigates its critical consensus condition on network topology by stochastic approximation frameworks. A new joint-connectivity condition called extensible joint-connectivity that contains a parameter $δ$ (termed the extensible exponent) is proposed. With this and a balanced topology condition, we show that a critical value of $δ$ for consensus is $1/2$. Optimization on convergence rate of this protocol is further investigated. It is proved that the fastest convergence rate, which is the theoretic optimal rate among all controls, is of the order $1/t$ for the best topologies, and is of the order $1/t^{1-2δ}$ for the worst topologies which are balanced and satisfy the extensible joint-connectivity condition. For practical implementation, certain open-loop control strategies are introduced to achieve consensus with a convergence rate of the same order as the fastest convergence rate. Furthermore, a consensus condition is derived for non stationary and strongly correlated random topologies. The algorithms and consensus conditions are applied to distributed consensus computation of mobile ad-hoc networks; and their related critical exponents are derived from relative velocities of mobile agents for guaranteeing consensus.

math.OC↗

arXiv2016

Finite-Time Elimination of Disagreement of Opinion Dynamics via Covert Noise

Eliminating disagreement in a group is usually beneficial to the social stability. In this paper, using the well-known Hegselmann-Krause (HK) model, we design a quite simple strategy that could resolve the opinion difference of the system in finite time and induce the opinions synchronized to a targeted value. To be specific, we intentionally introduce weak random noise to only one agent to affect its opinion in the evolution and also a leader agent with fixed opinion in a divisive group, then strictly prove that the disagreement is finally eliminated and the opinions get synchronized to the leader's opinion in finite time. Other than that, we calculate the finite stopping time when the opinions synchronously reach the objective opinion value, which could provide further guide for designing more efficient noise intervention strategy.

math.OC↗

arXiv2016

Noise Leads to Quasi-Consensus of Hegselmann-Krause Opinion Dynamics

This paper aims at providing rigorous theoretical analysis to investigate the consensus behavior of opinion dynamics in noisy environments. It is known that the well-known Hegselmann-Krause (HK) opinion dynamics demonstrates various agreement or disagreement behaviors in the deterministic case. Here we strictly show how noises provide great help to "synchronize" the opinions of the HK model. In fact, we prove a "critical phenomena" of the noisy HK dynamics, that is, the opinions merge as a quasi-consensus in finite time in noisy environment when the noise strength is below a critical value, which implies the fragmentation phenomenon of the HK dynamics could eventually vanish in the presence of noise. On the other hand, the opinions almost surely diverge when the noise strength exceeds the critical value.

math.OC↗

arXiv2016

Small noise may diversify collective motion in Vicsek model

Natural systems are inextricably affected by noise. Within recent decades, the manner in which noise affects the collective behavior of self-organized systems, specifically, has garnered considerable interest from researchers and developers in various fields. To describe the collective motion of multiple interacting particles, Vicsek et al. proposed a well-known self-propelled particle (SPP) system, which exhibits a second-order phase transition from disordered to ordered motion in simulation; due to its non-equilibrium, randomness, and strong coupling nonlinear dynamics, however, there has been no rigorous analysis of such a system to date. To decouple systems consisting of deterministic laws and randomness, we propose a general method which transfers the analysis of these systems to the design of cooperative control algorithms. In this study, we rigorously analyzed the original Vicsek model under both open and periodic boundary conditions for the first time, and developed extensions to heterogeneous SPP systems (including leaderfollower models) using the proposed method. Theoretical results show that SPP systems switch an infinite number of times between ordered and disordered states for any noise intensity and population density, which implies that the phase transition indeed takes a nontraditional form. We also investigated the robust consensus and connectivity of these systems. Moreover, the findings presented in this paper suggest that our method can be used to predict possible configurations during the evolution of complex systems, including turn, vortex, bifurcation and flock merger phenomena as they appear in SPP systems.

math.OC↗

arXiv2015

NuSTAR observations of the young, energetic radio pulsar PSR B1509-58

We report on Nuclear Spectroscopic Telescope Array (NuSTAR) hard X-ray observations of the young rotation-powered radio pulsar PSR B1509$-$58 in the supernova remnant MSH 15$-$52. We confirm the previously reported curvature in the hard X-ray spectrum, showing that a log parabolic model provides a statistically superior fit to the spectrum compared with the standard power law. The log parabolic model describes the NuSTAR data, as well as previously published gamma-ray data obtained with COMPTEL and AGILE, all together spanning 3 keV through 500 MeV. Our spectral modelling allows us to constrain the peak of the broadband high energy spectrum to be at 2.6$\pm$0.8 MeV, an improvement of nearly an order of magnitude in precision over previous measurements. In addition, we calculate NuSTAR spectra in 26 pulse phase bins and confirm previously reported variations of photon indices with phase. Finally, we measure the pulsed fraction of PSR B1509$-$58 in the hard X-ray energy band for the first time. Using the energy resolved pulsed fraction results, we estimate that the pulsar's off-pulse emission has a photon index value between 1.26 and 1.96. Our results support a model in which the pulsar's lack of GeV emission is due to viewing geometry, with the X-rays originating from synchrotron emission from secondary pairs in the magnetosphere.

astro-ph.HE↗

arXiv2014

M Times Photon Subtraction-Addition Coherent Superposition Operated Odd-Schrődinger-cat State: Nonclassicality and Decoherence

We introduce a new non-Gaussian state, generated by m times coherent superposition operation $a\cos θ+a^{\dagger }e^{iφ}\sin θ$ (MCSO) on odd-Schrodinger-cat state (OSCS). Its normalized constant is turned out to be related with the Hermite polynomial. We further investigate the nonclassical properties of the MCSO-OSCS through Mandel's Q-parameter, quadrature squeezing, the photocount distribution and Wigner function (WF). It is shown that the nonclassicality of the MCSO-OSCS is influenced by the number of times (m) of coherent superpositon operation, the angle $θ$ and the amplitude of the coherent state (|$α_{0}$|). Especially the volume of negative region of WF increases with the increment of parameters m, $θ$ and $α_{0}$. We also investigate the decoherence of the MCSO-OSCS in terms of the fadeaway of the negativity of WF in a thermal environment.

quant-ph↗

arXiv2013

The asymptotic size of the largest component in random geometric graphs with some applications

For the size of the largest component in a supercritical random geometric graph, this paper estimates its expectation which tends to a polynomial on a rate of exponential decay, and sharpens its asymptotic result with a central limit theory. Similar results can be obtained for the size of biggest open cluster, and for the number of open clusters of percolation on a box, and so on.

math.PR↗