Narrow Results

We present a new algorithm to estimate hemodynamic response function (HRF) and drift components of fMRI data in wavelet domain. The HRF is modeled by both parametric and nonparametric models. The functional Magnetic resonance Image (fMRI) noise is modeled as a fractional brownian motion (fBm). The HRF parameters are estimated in wavelet domain by exploiting the property that wavelet transforms with a sufficient number of vanishing moments decorrelates a fBm process. Using this property, the noise covariance matrix in wavelet domain can be assumed to be diagonal whose entries are estimated using the sample variance estimator at each scale. We study the influence of the sampling rate of fMRI time series and shape assumption of HRF on the estimation performance. Results are presented by adding synthetic HRFs on simulated and null fMRI data. We also compare these methods with an existing method,¹ where correlated fMRI noise is modeled by a second order polynomial functions.

AlGaN thin films and Schottky barrier Al_0.4Ga_0.6N diodes exhibit generation-recombination (GR) noise with activation energies of 0.8 - 1 eV. GR noise in AlGaN/GaN Heterostructure Field Effect transistors (HFETs) corresponds to activation energies in the range from 1 - 3 meV to 1 eV. No GR noise is observed in thin doped GaN films and GaN MESFETs. GR noise with the largest reported activation energy of 1.6 eV was measured in AlGaN/InGaN/GaN Double Heterostructure Field Effect Transistors (DHFETs). Local levels responsible for the GR noise in HFETs and DHFETs might be located in AlGaN barrier layers.

We report results of the experimental investigation of the low-frequency noise in graphene transistors. The graphene devices were measured in three-terminal configuration. The measurements revealed low flicker noise levels with the normalized noise spectral density close to 1/f (f is the frequency) and the Hooge parameter α_H ~10^-3. Both top-gate and back-gate devices were studied. The analysis of the noise spectral-density dependence on the gate biases helped us to elucidate the noise sources in these devices. We compared the noise performance of graphene devices with that of carbon nanotube devices. It was determined that graphene devices works better than carbon nanotube devices in terms of the low-frequency noise. The obtained results are important for graphene electronic, communication and sensor applications.

Several mathematical frameworks of phase-locking are developed. The classical Huyghens approach is generalized to include all harmonic and subharmonic resonances and is found to be connected to 1/f noise and prime number theory. Two types of quantum phase-locking operators are defined, one acting on the rational numbers, the other on the elements of a Galois field. In both cases we analyse in detail the phase properties and find that they are related to the Riemann zeta function and to incomplete Gauss sums, respectively.

The nodes with the largest degree are very susceptible to traffic congestion, thus an effective way to improve traffic and control congestion can be redistributing traffic load in hub nodes to others. We proposed an efficient routing strategy, which can remarkably enhance the network throughput. In addition, by using detrended fluctuation analysis, we found that the traffic rate fluctuation near the critical point exhibits the 1/f scaling in the power spectrum, which is in accordance with the empirical data.

We present a general formalism for the dissipative dynamics of an arbitrary quantum system in the presence of a classical stochastic process. It is applicable to a wide range of physical situations, and in particular it can be used for qubit arrays in the presence of classical two-level systems (TLS). In this formalism, all decoherence rates appear as eigenvalues of an evolution matrix. Thus the method is linear, and the close analogy to Hamiltonian systems opens up a toolbox of well-developed methods such as perturbation theory and mean-field theory. We apply the method to the problem of a single qubit in the presence of TLS that give rise to pure dephasing 1/f noise and solve this problem exactly.

A lower bound on the voltage noise power spectrum set by quantum indeterminacy exists in any conducting material. This bound is calculated explicitly for monolayer graphene taking into account graphene pseudospin/valley band structure. It is found to be of the form characteristic of the observed $1/f^{\gamma }$ noise. It is shown that the deviation of $\gamma$ from unity is a result of the piezoelectric interaction of charge carriers with acoustic phonons. A comparison with the measured $1/f$ noise in graphene and graphene-based heterostructures shows that the observed noise intensity is near the quantum bound. It is demonstrated that the recently observed sharp peak in $\gamma$ at small gate voltages in the field-effect transistors based on graphene/boron nitride heterostructure is well reproduced by the theory, and is to be attributed to the out-of-plane piezoelectric activity in this heterostructure. A simple kinetic model is proposed to describe the effect of the charge carrier trapping on $\gamma$.

The influence of the built-in electric field on the low-frequency current fluctuations in n-type non-degenerate homogeneous semiconductors at presence of constant external electric and magnetic fields is examined. The problem is considered by means of Langevin-type Boltzmann transport equations for the electron and phonon systems at domination of electron–acoustic phonon scatterings. For the first time, it is shown that within the context of the introduced problem, the spectral density of the current noise contains 1/f component specified by the built-in electric field. By form it is similar to the empiric Hooge formula. On the basis of the computations, a model explaining the physical mechanism of the origin of the additional component of 1/f noise, conditioned by the presence of the built-in electric field in semiconductor, is proposed. For the Hooge parameter, a comparison with the experimental data of generally observed 1/f noise for Si samples is carried out. The comparison shows that at some "favorable" conditions, the level of this new component of the 1/f noise can reach the level of the generally observed 1/f noise.

The origin of the low-frequency noise with power spectrum $1/f^{\beta }$ (also known as $1/f$ fluctuations or flicker noise) remains a challenge. Recently, the nonlinear stochastic differential equations for modeling $1/f^{\beta }$ noise have been proposed and analyzed. Here, we use the self-similarity properties of this model with respect to the nonlinear transformations of the variables of these equations and show that $1/f^{\beta }$ noise of the observable may yield from the power-law transformations of well-known standard processes, like the Brownian motion, Bessel and similar stochastic processes. Analytical and numerical investigations of such techniques for modeling processes with $1/f^{\beta }$ fluctuations is presented.

In this paper, a very low 1/f noise integrated Wheatstone bridge magnetoresistive sensor ASIC based on magnetic tunnel junction (MTJ) technology is presented for high sensitivity measurements. The present CMOS instrumentation amplifier employs the gain-boost folded-cascode structure based on the capacitive-feedback chopper-stabilized technique. By chopping both the input and the output of the amplifier, combined with MTJ magnetoresistive sensitive elements, a noise equivalent magnetoresistance 1 nT/Hz${}^{1/2}$ at 2 Hz, the equivalent input noise spectral density 17 nV/Hz${}^{1/2}$(@2Hz) is achieved. The chip-scale package of the TMR sensor and the instrumentation amplifier is only about 5 mm × 5 mm × 1 mm, while the whole DC current dissipates only 2 mA.

Multiscale entropy (MSE) discloses the intrinsic multiple scales in the complexity of physical and physiological signals, which are usually featured by heavy-tailed distributions. Most of these research results are pure experimental search, till Costa et al. made the first attempt to the theoretical basis of MSE. However, the analysis only supports the Gaussian distribution [Phys. Rev. E71, 021906 (2005)]. In this paper, we present the theoretical basis of MSE under the inverse Gaussian distribution, which is a typical model for physiological, physical and financial data sets. The analysis is applicable to uncorrelated inverse Gaussian process and 1/f noise with the multivariate inverse Gaussian distribution, providing a reliable foundation for potential applications of MSE to explore complex physical and physiological time series.

This paper provides evidence of fractal, multifractal and chaotic behaviors in urban crime by computing key statistical attributes over a long data register of criminal activity. Fractal and multifractal analyses based on power spectrum, Hurst exponent computation, hierarchical power law detection and multifractal spectrum are considered ways to characterize and quantify the footprint of complexity of criminal activity. Moreover, observed chaos analysis is considered a second step to pinpoint the nature of the underlying crime dynamics. This approach is carried out on a long database of burglary activity reported by 10 police districts of San Francisco city. In general, interarrival time processes of criminal activity in San Francisco exhibit fractal and multifractal patterns. The behavior of some of these processes is close to $1/f$ noise. Therefore, a characterization as deterministic, high-dimensional, chaotic phenomena is viable. Thus, the nature of crime dynamics can be studied from geometric and chaotic perspectives. Our findings support that crime dynamics may be understood from complex systems theories like self-organized criticality or highly optimized tolerance.

Large-scale simulations and analysis of the original powers of 2 geometric source sum algorithm for simulating $1/f$ noise confirm that it provides a reasonably accurate approximation to an exact $1/f$ spectral density with a Gaussian amplitude distribution over any arbitrarily large frequency range. This incremental algorithm is computationally efficient with a computation time, after initialization, that varies linearly with the number of samples generated. A new variation allows non-integer and random ratios for the geometric sequence that reduces variations about the exact power-law spectral density and, by varying individual source amplitudes, produces generalized $1/f^{\beta }$ noises.

This paper presents an extended mathematical base for the interpretation of cluster processes in introducing an intermittent stochastic process; this is characterized by clusters of events being separated by distinct breaks so-called intermissions. The spectral features of such an intermittent process are investigated for the case that either intermission δ or duration of cluster τ_c is power-law distributed like t^z. Correspondingly, a spectral shape like 1/f^b(z) is found; a pure 1/f shape (b=1) is obtained for z = -2. The most striking result is the dependence of exponent b(z) on quotient δ/τ_c: we obtain b≤2 for δ > τ_c and b≤ 1 for δ < τ_c. This behavior is explained by mutual time relations between clusters which cannot be neglected in case intermissions are small in comparison to duration of clusters (δ < τ_c). The conditions under which superimposed intermittent processes converge to the clustering Poisson process exhibiting 1/f noise are investigated. Possible applications are discussed for 1/f noise in neuronal spike trains, ionic channels, on-off intermittency and semiconductors.

1/4 scaling of various biological variables in relation to body mass is universal in biology. Recent models provided evidence that such a scaling is a result of optimization of the processes in the system. We present evidence for 1/4 scaling in dynamical processes from two different types of experiments: fluctuation of the erythrocyte diameter and a task of random generation of series of numbers by human subjects. The time series obtained for different cells and human subjects respectively were analyzed by detrended fluctuation analysis. The exponents from different individuals presented a gaussian distribution centered at a scaling exponent equivalent to 1/4 for both types of experiments. While this proves the existence of 1/4 scaling in dynamics, it also shows that processes do not proceed equally efficient in various individuals. Consequently the deviation from the 1/4 scaling individuals can be used as a universal tool of investigation for the efficiency, or the optimization of various biological, psychological or other types of variables.

In this paper, we propose an original statistical explanation to interpret 1/f noise consistently. It is shown that a sequence of noise signals is necessarily non-stationary if it is generated by stationary random walks at random time points. The variance of the signal distribution is random and the probability of the appearance of random increments in the k'th time interval (k > 1) is based on the intensities of a family of Poisson processes in the current time interval and on conditional probabilities generated in all previous time intervals. This leads to increasing expectations of the random variances in consecutive time intervals. As a consequence, the correlation of signals is random with time dependent expectations. The noise process is non-stationary and not first-order Markovian. Common estimation yields biased frequency spectra with increasing error variances appearing as 1/f error spectra. Families of Poisson processes with jump probabilities characterized by a priori Beta distributions are investigated and the second moments of the resulting noise processes are conisdered. Simulated process yield spectral estimates with linearly increasing error variances.

Atomic diffusion of impurity centers is investigated as a possible origin of 1/f noise in semiconductors. Following the trace of an individual impurity center, the noise produced at a certain site is calculated; due to diffusion of centers this is an intermittent process. Besides generation-recombination (= g-r) noise, an excess noise is obtained which is attributed to diffusion of impurity centers. This excess noise exhibits 1/f noise and g-r burst noise. 1/f noise is attributed to the return time of a center to the origin; g-r burst noise is the noise produced by centers residing at a certain site. For a n-type strongly extrinsic semiconductor, the Hooge coefficient α of the present model is derived and impact of compensating acceptors or additional doping by shallow centers is investigated. Increasing the concentration of additional shallow centers α is decreased; an increase of concentration of compensating acceptors results in an increase of α. The temperature dependence of the Hooge coefficient α(T) is calculated and is compared with empirical findings.

Experimental studies on low frequency noise in bipolar junction transistors (BJT) including polysilicon emitter, hetero-junction bipolar transistors (HBTs) and silicon-germanium hetero-junction transistors (SiGe HBTs) are reviewed. The 1/f noise is treated in terms of mobility fluctuations. The validity of a new empirical relation between the 1/f noise corner frequency f_c (the frequency where the 1/f noise and shot noise are equal) and the peak cutoff frequency fr_peak is investigated. The experimental procedure to investigate the most dominant low-frequency noise source in the equivalent circuit is described. At medium frequencies, the white noise becomes dominant and the noise figure is calculated taking into account the emitter and base series resistance.

The dependence of the 1/f noise on 2D electron concentration in the channel n_Ch of AlGaN/GaN Heterostructure Field Effect Transistors and Metal Oxide Semiconductor Heterostructure Field Effect Transistors has been studied and compared. The dependencies of Hooge parameter α_Ch for the noise sources located in the channel of the transistors on sheet electron concentration are found identical for both types of devices. The increase of the Hooge parameter α_Ch with the decrease of the channel concentration observed in both types of devices confirms that the noise sources are located in the region under the gate in the AlGaN/GaN heterostructure and that electron tunneling from the 2D electron gas into the traps in GaN or AlGaN layers is a probable noise mechanism.

In this work, we experimentally investigate fundamental aspects of 1/f noise in silicon CMOS transistors, considering a broad group of technological families. We bring out some device down-scaling issues. A direct comparison between our experimental data and the noise dominant theories in MOS-FETs is dealt with.