An augmented moment method for stochastic ensembles with delayed couplings: I. Langevin model

By employing a semi-analytical dynamical mean-field approximation theory previously proposed by the author [H. Hasegawa, Phys. Rev. E {\bf 67}, 041903 (2003)], we have developed an augmented moment method (AMM) in order to discuss dynamics of an $N$-unit ensemble described by linear and nonlinear Langevin equations with delays. In AMM, original $N$-dimensional {\it stochastic} delay differential equations (SDDEs) are transformed to infinite-dimensional {\it deterministic} DEs for means and correlations of local as well as global variables. Infinite-order DEs arising from the non-Markovian property of SDDE, are terminated at the finite level $m$ in the level-$m$ AMM (AMM$m$), which yields $(3+m)$-dimensional deterministic DEs. Model calculations have been made for linear and nonlinear Langevin models. The stationary solution of AMM for the linear Langevin model with N=1 is nicely compared to the exact result. The synchronization induced by an applied single spike is shown to be enhanced in the nonlinear Langevin ensemble with model parameters locating at the transition between oscillating and non-oscillating states. Results calculated by AMM6 are in good agreement with those obtained by direct simulations.Comment: 18 pages, 3 figures, changed the title with re-arranged figures, accepted in Phys. Rev. E with some change

35 Transient Multiexponential Data Selection Using Cramer Rao Lower Bound

Previously, analysis of transient multiexponential data using a combination of Gardner transform and parametric methods was shown to yield good results. However, one problem that remains unsolved is that of the nonstationarity of the data resulting from the associated deconvolution. Hitherto, trial and error methods have been used to select the qualitative length of the deconvolved data. In this paper, Cramer Rao Lower Bound (CRLB) is used to select the data truncation points for use with the MUSIC (Multiple Signal Classification), minimum norm and ARMA (autoregressive moving average) methods. Several simulations are made based on which truncation points are recommended for each of the three parametric methods

Parameter Estimation of Transient Multiexponential Signals Using SVD-ARMA and Multiparameter Deconvolution Techniques

Much has been reported about the analysis of transient multiexponentials data. In a previous paper, for example, this analysis was done using autoregressive moving average model which was applied to the deconvolved data arising from the application of Gardner transform followed by optimal compensation deconvolution to the original signal. Optimal compensation deconvolution uses a single parameter noise-reduction parameter. In this paper, a deconvolution parameter incorporating multiple noise-reduction parameters is used instead. Simulations and experimental results show that the proposed combination, despite its limitations supersedes several existing methods

Analysis of transient multiexponential signals using exponential compensation deconvolution

A three-step procedure for the parameter estimation of transient multiexponential signals is proposed. The first step involves the use of the classical Gardner transform to convert the data signal into a convolution model which is deconvolved using exponential compensation deconvolution technique in the second step. In the third step, eigenvector algorithms are used to process the resulting complex exponentials to obtain better estimates of decay rates and number of components. Simulation and experimental results show that this method outperforms previous approaches if a number of preprocessing parameters are correctly selected

Performance evaluation of music and minimum norm eigenvector algorithms in resolving noisy multiexponential signals

Eigenvector methods are gaining increasing acceptance in the area of spectrum estimation. This paper presents a successful attempt at testing and evaluating the performance of two of the most popular types of subspace techniques in determining the parameters of multiexponential signals with real decay constants buried in noise. In particular, MUSIC (Multiple Signal Classification) and minimum-norm techniques are examined. It is shown that these methods perform almost equally well on multiexponential signals with MUSIC displaying better defined peaks

Performance evaluation of music and minimum norm eigenvector algorithms in resolving noisy multiexponential signals

Eigenvector methods are gaining increasing acceptance in the area of spectrum estimation. This paper presents a successful attempt at testing and evaluating the performance of two of the most popular types of subspace techniques in determining the parameters of multiexponential signals with real decay constants buried in noise. In particular, MUSIC (Multiple Signal Classification) and minimum-norm techniques are examined. It is shown that these methods perform almost equally well on multiexponential signals with MUSIC displaying better defined peaks

Performance evaluation of music and minimum norm eigenvector algorithms in resolving noisy multiexponential signals

Eigenvector methods are gaining increasing acceptance in the area of spectrum estimation. This paper presents a successful attempt at testing and evaluating the performance of two of the most popular types of subspace techniques in determining the parameters of multiexponential signals with real decay constants buried in noise. In particular, MUSIC (Multiple Signal Classification) and minimum-norm techniques are examined. It is shown that these methods perform almost equally well on multiexponential signals with MUSIC displaying better defined peaks

Performance evaluation of music and minimum norm eigenvector algorithms in resolving noisy multiexponential signals

Eigenvector methods are gaining increasing acceptance in the area of spectrum estimation. This paper presents a successful attempt at testing and evaluating the performance of two of the most popular types of subspace techniques in determining the parameters of multiexponential signals with real decay constants buried in noise. In particular, MUSIC (Multiple Signal Classification) and minimum-norm techniques are examined. It is shown that these methods perform almost equally well on multiexponential signals with MUSIC displaying better defined peaks

Effect of sampling on the parameter estimates of multicomponent transients

The need to estimate the parameters of transient multiexponential signals frequently arises in different areas of applied science. A classical technique that has been frequently used with different modifications is the Gardner transform. Gardner transform is used to convert the original data signal into a convolution model. Converting this model into a discrete type for further analysis depends on the selection of correct sampling conditions. Previously, a relationship between the sampling frequency and the weighting factor in the modified Gardner transform was derived. In this paper, the effect of this relationship on the accuracy of parameter estimates is investigated

The burden of erectile dysfunction in hypertensive men attending a general out patient unit in a rural Nigerian hospital

Background: Hypertension is often cited as a cause of erectile dysfuntion (ED) which is currently known to be a risk factor for coronary artery disease (CAD). Both ED and CAD lower the quality of life of affected men.Objectives: To study the characteristics of men with hypertension-associated ED and to determine the ED burden in hypertension in this rural community.Design: Questionnaire based cohort study.Setting: The General Out Patient unit of Irrua Teaching Hospital, Nigeria.Subjects: Men attending the General Out Patient Unit during the study period for diagnosis and treatment of hypertension and who consented to the study.Outcome Measure: The burden of ED in hypertensive men and the characteristics of such men.Result: Two hundred and forty two respondents correctly filled and submitted the questionnaire. Fifty four (22.41%) were newly diagnosed, un treated while 188(77.59%) had been on treatment. In the untreated group, 40(74.07%) and in the treated group, 166(86.20%) had some degree of ED compared to 57.4% in the general population. Age(p=0.000), BMI(P=0.010)in the newly diagnosed group and age(p=0.001), duration of treatment(p=0.009) and co-morbidities(p=0.010) in the treated group were risk factors for ED. Majority of the men(80.30%) were on combination therapy.Conclusion: ED is common among hypertensive men, treated or untreated. Considering the socio-economic and clinical effects of CAD for which ED is a fore runner, physicians should endeavour to obtain a sexual history when evaluating these men as a preventive measure against feature cardiovascular event