Maximum Entropy Spectral Analysis Research Articles

Image reconstruction: a unifying model for resolution enhancement and data extrapolation Tutorial

In reconstructing an object function F(r) from finitely many noisy linear-functional values integral of F(r)Gn(r)dr we face the problem that finite data, noisy or not, are insufficient to specify F(r) uniquely. Estimates based on the finite data may succeed in recovering broad features of F(r), but may fail to resolve important detail. Linear and nonlinear, model-based data extrapolation procedures can be used to improve resolution, but at the cost of sensitivity to noise. To estimate linear-functional values of F(r) that have not been measured from those that have been, we need to employ prior information about the object F(r), such as support information or, more generally, estimates of the overall profile of F(r). One way to do this is through minimum-weighted-norm (MWN) estimation, with the prior information used to determine the weights. The MWN approach extends the Gerchberg-Papoulis band-limited extrapolation method and is closely related to matched-filter linear detection, the approximation of the Wiener filter, and to iterative Shannon-entropy-maximization algorithms. Non-linear versions of the MWN method extend the noniterative, Burg, maximum-entropy spectral-estimation procedure.

Evidence and Ideology in Macroeconomics: The Case of Investment Cycles

The paper reports the principal findings of a long term research project on the description and explanation of business cycles. The research strongly confirmed the older view that business cycles have large systematic components that take the form of investment cycles. These quasi-periodic movements can be represented as low order, stochastic, dynamic processes with complex eigenvalues. Specifically, there is a fixed investment cycle of about 8 years and an inventory cycle of about 4 years. Maximum entropy spectral analysis was employed for the description of the cycles and continuous time econometrics for the explanatory models. The central explanatory mechanism is the second order accelerator, which incorporates adjustment costs both in relation to the capital stock and the rate of investment. By means of parametric resonance it was possible to show, both theoretically and empirically how cycles aggregate from the micro to the macro level. The same mathematical tool was also used to explain the international convergence of cycles. I argue that the theory of investment cycles was abandoned for ideological, not for evidential reasons. Methodological issues are also discussed.

Effects of temperature changes on the endogenous rhythm of oxygen consumption in the Japanese flounder Paralichthys olivaceus

The effects of temperature changes on the endogenous rhythm of oxygen consumption in the Japanese flounder Paralichthys olivaceus which were acclimated to 3, 14 or 20°C in advance were investigated. The oxygen consumption rate (OCR) of individuals (total length >28 cm) that were acclimated to 3°C, maintained a relatively low value of 6.9±2.3 mL (mean±SD) O2/kg ww (wet weight)/h till 5.8°C, which is considered a ‘minimum’ rate. Thereafter, the OCR gradually increased up to 18.7 mL O2/kg ww/h at the temperature of 10.6°C. The OCR of individuals acclimated to 14°C stabilized with 124.2±24.1 mL O2/kg ww/h, when tested at the relatively constant temperature of 14.4±0.17°C. Maximum entropy spectral analysis revealed that the peak OCR occurred at 23.9 h intervals, which could be a circadian rhythm. The mean OCR showed a peak at 06.00–08.00 hours. For the temperature above 25°C in which the fish were acclimated to 20°C, the rhythmic patterns of OCR were observed until the experimental temperature reached 26.4°C. For the temperature above 28.4°C, the metabolic activity rhythm of the OCR was dampened and then the OCR abruptly rose again. It is assumed that the oscillator of the endogenous rhythm lost the governing of normal metabolic activity in Japanese flounders above 28.4°C. These results suggest that the temperatures of around 5.8, 26.4 and 28.4°C are the ‘lower limit, temperature’, ‘upper incipient lethal temperature’, and the ‘critical thermal maximum’, respectively, for the endogenous rhythm of oxygen consumption in the Japanese flounder.

The Fast Fourier Transform for Experimentalists

In part one of this series, we discussed several basic properties of the fast Fourier transform (FFT). In addition to fundamental elements, we treated zero padding, aliasing, the relationship to a Fourier series, and ended with an introduction to windowing. In part II, we continue our discussion with a more general approach to spectrum estimation, including the periodogram, the autocorrelation function, autoregressive spectral estimation, and maximum entropy spectral estimation. In addition, we include brief descriptions of treating convolution, filtering, and detrending. In the final installment, as we treat several applications, we draw on a number of the ideas discussed in the first part dealing with concepts and then apply some of the methods. The particular applications we consider include the spectral analysis of a bat chirp, atmospheric sea-level pressure differences, and perhaps even take a look, at atmospheric CO/sub 2/.

MAXENPER: a program for maximum entropy spectral estimation with assessment of statistical significance by the permutation test

The maximum entropy spectral estimator is widely used because of its high spectral resolution, but it lacks an easy procedure for evaluating the statistical significance of the spectral estimates. We implemented the non-parametric computer intensive permutation test in order to evaluate the statistical significance of the maximum entropy spectral estimates. There is the possibility of choosing between an underlying red or white noise in the permutation procedure. Two case studies, with a long and a short time series, illustrate the performance of the method.

Maximum-entropy spectral analysis of extended energy-loss fine structure and its application to time-resolved measurement

A maximum-entropy method (MEM) is applied to analysis of extended energy-loss fine structure (EXELFS). The present MEM–EXELFS analysis allows us to derive a radial distribution function (RDF) free from non-existing ghost peaks even when the original data set includes relatively a considerable amount of statistical noise. This markedly shortens the integration time for spectrum acquisition and simplifies the numerical procedures necessary for the RDF analysis, in contrast with the conventional fast Fourier transform method. The method can open the possibility of in-situ or time-resolved experiments of dynamic structural changes of materials. Its application to the recrystallization process of an amorphous Si film has suggested that the crystallization starts with the recovery of the coordination number and bond lengths, followed by the recovery of the stable bond angles in local tetrahedral configurations.

Prediction Analysis for Measles Epidemics

A newly devised procedure of prediction analysis, which is a linearized version of the nonlinear least squares method combined with the maximum entropy spectral analysis method, was proposed. This method was applied to time series data of measles case notification in several communities in the UK, USA and Denmark. The dominant spectral lines observed in each power spectral density (PSD) can be safely assigned as fundamental periods. The optimum least squares fitting (LSF) curve calculated using these fundamental periods can essentially reproduce the underlying variation of the measles data. An extension of the LSF curve can be used to predict measles case notification quantitatively. Some discussions including a predictability of chaotic time series are presented.

Fluctuations of surface air temperature in the Eastern Mediterranean

Changes in surface air temperature during the last century are widely discussed among researchers in the field of climatic change. Using various techniques, we investigate trends and periodicity of surface air temperature series from eight meteorological stations in the Eastern Mediterranean. For the analysis, we use the Mann-Kendall rank test, low-pass filtering, autocorrelation spectral analysis and maximum entropy spectral analysis. The latter two tests are compared. The study is based on series over one hundred years in length for four stations, and over fifty years in length for the other four. Increasing and decreasing surface temperature trends were found. These trends, however, are only significant for Malta, Jerusalem, and Tripoli at the 99% confidence level (positive trend) and for Amman at the 95% confidence level (negative trend). We also found inter-decadal variations in surface air temperature, including a fairly regular quasi 20-year oscillation, although its amplitude varied between different cycles. A period of warming began around 1910 at all stations. During the 1970s, the annual mean temperature series exhibit warming, but this warming was not uniform, continuous or of the same order at all the stations. The results of the Autocorrelation Spectral Analysis and the Maximum Entropy Spectral Analysis are similar, pointing to the reliability of the results. The quasi-biennial oscillation (QBO) exists at all stations during both increasing and decreasing trends. Similarly, a broad maximum from 3–8 years (related to El Nino) is found at Malta, Athens, Jerusalem, Beirut, and Latakia. An inverse relationship between El Nino and the North Atlantic Oscillation with surface air temperature over the Eastern Mediterranean is found at a highly significant confidence level.

Interannual variability of atmospheric Nitrous Oxide (N2O)

The 12-monthly running means of N2O measured at seven locations during 1977-91 were used for obtaining the yearly percentage growth rate series (4 values per year, centered 3 months apart), which were subjected to MESA (Maximum Entropy Spectral Analysis). The spectra revealed significant QBO and QTO (Quasi-biennial and Quasi-triennial oscillations) with QBO periods in the range (2.04-2.38) years and QTO periods near 4.0 years. These do not resemble the QBO of 2.58 years of the 50 hPa low latitude wnal wind but do resemble the QBO of 2.31 years and the 4.1 year periods of the Southern oscillation phenomenon, represented by Tahiti minus Darwin sea level atmospheric pressure difference (T-D).

CIRCADIAN RHYTHM IN TOTAL ARTIFICIAL HEART IMPLANTED CALF

Circadian rhythm (CR), which is a fundamental rhythm in life, may be disordered in a total artificial heart (TAH) recipient, through modified circulatory conditions with a TAH and physiological effects of the absence of the native heart. We investigated CR of mean aortic pressure (mAoP), mean pulmonary arterial pressure (mPAP), and core body temperature (cBT) in a calf implanted with an electrohydraulic artificial heart (EHTAH). The EHTAH was implanted and actuated at an adequate fixed rate (85bpm) postoperatively with a relatively stable pump output (6–7 L/minutes). The data were sampled every 15 minutes for 48 hours on the last day of the 4, 8, and 12 week after implantation (W4, W8, and W12, respectively), and were analyzed by the maximum entropy spectral analysis and the least squares method in respect of the period (Pr), acrophase (the phase of a peak point: Ac), mesor (Ms), and amplitude (Am) of CR. In the variation of mAoP and mPAP, CR was consistently observed during the course of experiment (mAoP, Pr: 21.5, 20.0, and 22.7 hours, Ac: 23.8, 2.0, and 1.3 o'clock, Ms: 92.8, 104.2 and 103.1 mmHg, Am: 0.6, 3.2, and 4.2 mmHg, mPAP, Pr: 20.5, 20.0, and 22.2 hours, Ac: 22.5, 3.0, and 22.2 o'clock, Ms: 33.6, 33.7 and 23.4 mmHg Am: 1.6, 0.8, and 2.0 mmHg, at W4, W8, and W12, respectively). In the variations of cBT, reflecting an intrinsic circadian clock, CR was also consistently observed during the course of experiment (Pr: 27.2, 20.2, and 22.1 hours, Ac: 19.4, 22.5, and 18.9 o'clock, Ms: 37.4, 37.6 and 37.7 degree, Am: 0.3, 0.1, and 0.2 degree, at W4, W8, and W12, respectively). In summary, CR of mAoP, mPAP, and cBT existed even in a calf with a TAH driven in a fixed condition.

A note on maximum entropy spectrum estimation

This article studies the maximum entropy spectrum estimation. After a bnei discussion on iiow co select ciic appropriate constraints and tiie objec¬tive functions, we decide to choose the constraints containing only the first four sample moments and, consequently, to employ the second order spectral entropy as the objective function. The resulting (maximum entropy) spectral estimate is the power spectral density of an ARMA sequence. Examples for comparing our proposal with the traditional maximum entropy spectral estimate follow at the end.

A new approach to spectral estimation: a tunable high-resolution spectral estimator

Traditional maximum entropy spectral estimation determines a power spectrum from covariance estimates. Here, we present a new approach to spectral estimation, which is based on the use of filter banks as a means of obtaining spectral interpolation data. Such data replaces standard covariance estimates. A computational procedure for obtaining suitable pole-zero (ARMA) models from such data is presented. The choice of the zeros (MA-part) of the model is completely arbitrary. By suitable choices of filter bank poles and spectral zeros, the estimator can be tuned to exhibit high resolution in targeted regions of the spectrum.

Solving for a quadratic programming with a quadratic constraint based on a neural network frame

In many applications, a class of optimization problems called quadratic programming with a special quadratic constraint (QPQC) often occurs, such as in the fields of maximum entropy spectral estimation, FIR filter design with time–frequency constraint and design of an FIR filter bank with perfect reconstruction property. In order to deal with this kind of optimization problems and be inspired by the computational virtue of analog or dynamic neural networks, a feedback neural network is proposed for solving for this class of QPQC computation problems in real time in this paper. The stability, convergence and computational performance of the proposed neural network have also been analyzed and proved in detail so as to theoretically guarantee the computational effectiveness and capability of the network. From the theoretical analyses it turns out that the solution of a QPQC problem is just the generalized minimum eigenvector of the objective matrix with respect to the constrained matrix. A number of simulation experiments have been given to further support our theoretical analysis and illustrate the computational performance of the proposed network.

Evolutionary maximum entropy spectral analysis of chirps in noise

In this manuscript, we analyze chirps in noise using the evolutionary maximum entropy spectral estimator (EMES). First, brief descriptions of evolutionary spectrum and its estimators, the evolutionary periodogram (EP), the smoothed evolutionary periodogram (SEP) and the EMES are given. Then, chirps in noise are analyzed with the EMES. It is shown that the EMES parameters are weighted functions of frequency components around the time of analysis. Later, the relation between bandwidth, SNR and number of basis functions is given for the case of a single pure sinusoid.

The autocorrelation function extrapolation and equivalence of determinant and entropy maximizations

This paper uses the theoretical properties of the autocorrelation matrices to approach the autocorrelation function extrapolation method based on maximizing the determinant of the autocorrelation matrix. Thus it arrives at the same results as appearing in the literature, while employing less complicated matrix algebra and considering the determinant calculus by matrix partitioning. Then the results obtained in this paper are compared with the maximum entropy spectral estimation method, and the equivalence of the maximum determinant and maximum entropy approaches is shown. Hence, a further understanding of the method is provided and it is deduced that the maximum determinant extrapolation algorithm, may also be used for direct spectral estimation in the maximum entropy method; i.e. without extrapolating the autocorrelation function.

Formulation and implementation of the non-stationary evolutionary Wiener filtering

In this paper we consider solutions to the non-stationary Wiener filtering problem using the evolutionary spectral theory. Two cases of interest result from the uncorrelation between the desired signal and the noise. One constrains the support of the generating kernels of the signals and the other imposes orthogonality on their innovation processes. The latter condition is more general and our solution coincides with the one presented previously by Abdrabbo and Priestley. For the first case, we develop a new solution that depends directly on the Wold–Cramer models of the desired and noisy processes. Implementation is achieved in both cases by estimating the kernels for the Wold–Cramer representations from the spectra using the evolutionary maximum entropy spectral estimation. The connections of the Wiener filter with the Wiener–Hopf equations and with the special case of stationary processes are discussed. Although the developed Wiener filter is non-recursive, an approximate recursive filter is obtained using a nonlinear Kalman system identification method. Examples illustrating the filtering are given.

Cardiac autonomic nervous function during long-term nonpulsatile left heart bypass.

We investigated the changes in cardiac autonomic nervous activities during long-term nonpulsatile left heart bypass (NLHB) by analyzing heart rate variability. A pulsatile ventricular assist device was installed in 3 goats, and pulsatile left heart bypass (PLHB) was conducted for 2 weeks. Then, NLHB was maintained for the following 4 weeks. The segmental data of the R-R intervals (R-Rs) was analyzed by maximum entropy spectral analysis. Changes in evaluated parameters from the last week of PLHB to the 4th week of NLHB were as follows: the mean R-Rs increased from 511 ms to 692 ms; the coefficient of variation of R-R increased from 10.2 to 14.1%; the power of the low frequency band (LF) increased from 747 ms2 to 2,855 ms2; the power of the high frequency band (HF) increased from 512 ms2 to 1,270 ms2; and the ratio of LF to HF increased from 2.6 to 6.5. These results indicated that the cardiac autonomic nervous activity, both sympathetic and parasympathetic, increased during long-term NLHB.

Endogenous rhythms of locomotor activity in the high-shore limpet,Helcion pectunculus(Patellogastropoda)

Helcion pectunculus, a high-shore, crevice-dwelling limpet, is active during nocturnal low tides and during daytime low tides whilst in the shade. We examined whether this activity is controlled by an internal clock or purely by exogenous stimuli, such as light levels and tidal phase. Maximum entropy spectral analysis (MESA) revealed that the limpets possess a free-running endogenous rhythm of locomotor activity with both circadian (period 28.1h) and circatidal (period 13.8h) components. We suggest that this rhythm plays a role in allowing individuals to avoid unfavourable environmental conditions. The exogenous entrainment factor of the endogenous circatidal rhythm inH.pectunculusis the time of exposure to air, whilst the zeitgeber for the circadian component is not yet known.

A Persistent Circhoral Ultradian Rhythm is Identified in Human Core Temperature

There have been inconclusive reports of intermittent rhythmic fluctuations in human core temperature, with the fluctuations having a period of about an hour. However, there has been no definitive demonstration of the phenomenon. This is likely due to the intermittency and seeming instability of the events. They have been assumed to be secondary rather than autonomous phenomena, putatively arising from the oscillation between rapid eye movement (REM) and non-REM (NREM) sleep. In this study, we report identification of a clear, persistent circhoral ultradian rhythm in core temperature with a period for this study sample of 64 ± 8 minutes. It appeared simultaneously with an intact circadian core temperature rhythm, persisted despite complex perturbations in core temperature brought about by the sequelae of 40h of sleep deprivation, and could not be attributed to sleep stage alternation or other endogenous or exogenous factors. Analysis of power spectra using the maximum entropy spectral analysis (MESA) method, which can uncover hidden rhythmicities, demonstrated that the apparent intermittency of the rhythm is due to periodic interference of this rhythm by other rhythmic events. The persistence of this oscillation suggests that, in this system as in the endocrine system, circhoral regulation is an integral component of thermoregulatory control. Identifying the source and functional role of this novel rhythm warrants further work.

Multidimensional Nonstationary Maximum Entropy Spectral Analysis by Using Neural Net

A multidimensional version of the nonstationary maximum entropy spectral estimation method has been developed. By applying the neural net technique, the estimated maximum entropy spectral density function has more resolution power than the conventional nonstationary periodogram spectral density function. The application of spectral density functions to simulate multidimensional nonstationary random fields is also investigated.