arXiv subjects

Zhi Chen

Publications and source records attributed to Zhi Chen.

332 records · Page 19Linked to original sources

arXiv2010

Algebras associated with Pseudo Reflection Groups: A Generalization of Brauer Algebras

We present a way to associate an algebra $B_G (Υ) $ with every pseudo reflection group $G$. When $G$ is a Coxeter group of simply-laced type we show $B_G (Υ)$ is isomorphic to the generalized Brauer algebra of simply-laced type introduced by Cohen,Gijsbers and Wales[10]. We prove $B_G (Υ)$ has a cellular structure and be semisimple for generic parameters when $G$ is a rank 2 Coxeter group. In the process of construction we introduce a Cherednik type connection for BMW algebras and a generalization of Lawrence-Krammer representation to complex braid groups associated with all pseudo reflection groups.

math.RT↗

arXiv2009

The Riemannian manifolds with boundary and large symmetry

Sixty years ago, S. B. Myers and N. E. Steenrod ({\it Ann. of Math.} {\bf 40} (1939), 400-416) showed that the isometry group of a Riemannian manifold without boundary has a structure of Lie group. Recently A. V. Bagaev and N. I. Zhukova ({\it Siberian Math. J.} {\bf 48} (2007), 579-592) proved the same result for a Riemannian orbifold. In this paper, we firstly show that the isometry group of a Riemannian manifold $M$ with boundary has dimension at most ${1/2} \dim M (\dim M-1)$. Then we completely classify such Riemannian manifolds with boundary that their isometry groups attain the preceding maximal dimension.

math.DG↗

arXiv2008

Noise spectra of stochastic pulse sequences: application to large scale magnetization flips in the finite size 2D Ising model

We provide a general scheme to predict and derive the contribution to the noise spectrum of a stochastic sequence of pulses from the distribution of pulse parameters. An example is the magnetization noise spectra of a 2D Ising system near its phase transition. At $T\le T_c$, the low frequency spectra is dominated by magnetization flips of nearly the entire system. We find that both the predicted and the analytically derived spectra fit those produced from simulations. Subtracting this contribution leaves the high frequency spectra which follow a power law set by the critical exponents.

cond-mat.stat-mech↗

arXiv2006

Spurious detection of phase synchronization in coupled nonlinear oscillators

Coupled nonlinear systems under certain conditions exhibit phase synchronization, which may change for different frequency bands or with presence of additive system noise. In both cases, Fourier filtering is traditionally used to preprocess data. We investigate to what extent the phase synchronization of two coupled Rössler oscillators depends on (1) the broadness of their power spectrum, (2) the width of the band-pass filter, and (3) the level of added noise. We find that for identical coupling strengths, oscillators with broader power spectra exhibit weaker synchronization. Further, we find that within a broad band width range, band-pass filtering reduces the effect of noise but can lead to a spurious increase in the degree of synchronization with narrowing band width, even when the coupling between the two oscillators remains the same.

physics.data-an↗

arXiv2005

Cross-Correlation of Instantaneous Phase Increments in Pressure-Flow Fluctuations: Applications to Cerebral Autoregulation

We investigate the relationship between the blood flow velocities (BFV) in the middle cerebral arteries and beat-to-beat blood pressure (BP) recorded from a finger in healthy and post-stroke subjects during the quasi-steady state after perturbation for four different physiologic conditions: supine rest, head-up tilt, hyperventilation and CO_2 rebreathing in upright position. To evaluate whether instantaneous BP changes in the steady state are coupled with instantaneous changes in the BFV, we compare dynamical patterns in the instantaneous phases of these signals, obtained from the Hilbert transform, as a function of time. We find that in post-stroke subjects the instantaneous phase increments of BP and BFV exhibit well pronounced patterns that remain stable in time for all four conditions, while in healthy subjects these patterns are different, less pronounced and more variable. We propose a new approach based on the instantaneous phase increments cross-correlation to quantify the coupling between BP and BFV. We find that the maximum correlation strength is different for the two groups and for the different conditions. For healthy subjects the amplitude of the cross-correlation between the instantaneous phase increments of BP and BFV is small and attenuates within 3-5 heartbeats. In contrast, for post-stroke subjects, this amplitude is significantly larger and cross-correlations persist up to 20 heartbeats. We compare the results of our approach with three complementary methods: direct BP-BFV cross-correlation, transfer function analysis and phase synchronization analysis.

physics.bio-ph↗

arXiv2003

Scale Invariance and Nonlinear Patterns of Human Activity

We investigate if known extrinsic and intrinsic factors fully account for the complex features observed in recordings of human activity as measured from forearm motion in subjects undergoing their regular daily routine. We demonstrate that the apparently random forearm motion possesses previously unrecognized dynamic patterns characterized by fractal and nonlinear dynamics. These patterns are unaffected by changes in the average activity level, and persist when the same subjects undergo time-isolation laboratory experiments designed to account for the circadian phase and to control the known extrinsic factors. We attribute these patterns to a novel intrinsic multi-scale dynamic regulation of human activity.

physics.bio-ph↗

arXiv2002

Effect of nonstationarities on detrended fluctuation analysis

Detrended fluctuation analysis (DFA) is a scaling analysis method used to quantify long-range power-law correlations in signals. Many physical and biological signals are ``noisy'', heterogeneous and exhibit different types of nonstationarities, which can affect the correlation properties of these signals. We systematically study the effects of three types of nonstationarities often encountered in real data. Specifically, we consider nonstationary sequences formed in three ways: (i) stitching together segments of data obtained from discontinuous experimental recordings, or removing some noisy and unreliable parts from continuous recordings and stitching together the remaining parts -- a ``cutting'' procedure commonly used in preparing data prior to signal analysis; (ii) adding to a signal with known correlations a tunable concentration of random outliers or spikes with different amplitude, and (iii) generating a signal comprised of segments with different properties -- e.g. different standard deviations or different correlation exponents. We compare the difference between the scaling results obtained for stationary correlated signals and correlated signals with these three types of nonstationarities.

physics.data-an↗

arXiv2001

Effect of Trends on Detrended Fluctuation Analysis

Detrended fluctuation analysis (DFA) is a scaling analysis method used to estimate long-range power-law correlation exponents in noisy signals. Many noisy signals in real systems display trends, so that the scaling results obtained from the DFA method become difficult to analyze. We systematically study the effects of three types of trends -- linear, periodic, and power-law trends, and offer examples where these trends are likely to occur in real data. We compare the difference between the scaling results for artificially generated correlated noise and correlated noise with a trend, and study how trends lead to the appearance of crossovers in the scaling behavior. We find that crossovers result from the competition between the scaling of the noise and the ``apparent'' scaling of the trend. We study how the characteristics of these crossovers depend on (i) the slope of the linear trend; (ii) the amplitude and period of the periodic trend; (iii) the amplitude and power of the power-law trend and (iv) the length as well as the correlation properties of the noise. Surprisingly, we find that the crossovers in the scaling of noisy signals with trends also follow scaling laws -- i.e. long-range power-law dependence of the position of the crossover on the parameters of the trends. We show that the DFA result of noise with a trend can be exactly determined by the superposition of the separate results of the DFA on the noise and on the trend, assuming that the noise and the trend are not correlated. If this superposition rule is not followed, this is an indication that the noise and the superimposed trend are not independent, so that removing the trend could lead to changes in the correlation properties of the noise.

physics.data-an↗