Asymmetric Window Research Articles

Full-sky correlation functions for CMB experiments with asymmetric window functions

We discuss full-sky convolution of the instrumental beam with the CMB sky signal in CMB single-dish and interferometry experiments using the method [A. Challinor et al., Phys. Rev. D 62, 123002 (2000); B. D. Wandelt and K. M. G\'orski, Phys. Rev. D 63, 123002 (2001).] that the measured temperature and polarization anisotropies are defined globally on the group manifold of the three-dimensional rotation by means of Wigner $D$ functions. We rederive the anisotropy and polarization correlation functions incorporated with asymmetric window functions, which are then explicitly calculated for a single-dish elliptical Gaussian beam and an interferometric Gaussian beam.

Numerical analysis of waveguide bandpass filters using singular integral equations and construction of simple design formulas

AbstractA powerful numerical solution is presented for bandpass filters in rectangular waveguides. The filters are composed of cascading of perfectly conducting inductive obstacles with zero thickness: asymmetrical windows, symmetrical windows, or symmetrical strips. The problem is reduced to a set of singular integral equations, which is solved by an extension of Lewin's quasi‐static procedure. After the accuracy of the classical formulas for the equivalent reactance is investigated, the simple inverse formulas are constructed to yield proper window widths for desired equivalent parameters. Their effectiveness is demonstrated by designing practical filters having maximally flat or equal‐ripple characteristics. © 2004 Wiley Periodicals, Inc. Electr Eng Jpn, 148(4): 17–25, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.10251

Linear stability analysis of retrieval state in associative memory neural networks of spiking neurons.

We study associative memory neural networks of the Hodgkin-Huxley type of spiking neurons in which multiple periodic spatiotemporal patterns of spike timing are memorized as limit-cycle-type attractors. In encoding the spatiotemporal patterns, we assume the spike-timing-dependent synaptic plasticity with the asymmetric time window. Analysis for periodic solution of retrieval state reveals that if the area of the negative part of the time window is equivalent to the positive part, then crosstalk among encoded patterns vanishes. Phase transition due to the loss of the stability of periodic solution is observed when we assume fast function for direct interaction among neurons. In order to evaluate the critical point of this phase transition, we employ Floquet theory in which the stability problem of the infinite number of spiking neurons interacting with function is reduced to the eigenvalue problem with the finite size of matrix. Numerical integration of the single-body dynamics yields the explicit value of the matrix, which enables us to determine the critical point of the phase transition with a high degree of precision.

Temporal asymmetry in spike timing-dependent synaptic plasticity

Activity-dependent synaptic modification is critical for the development and function of the nervous system. Recent experimental discoveries suggest that both the extent and the direction of modification may depend on the precise timing of pre- and postsynaptic action potentials (spikes). This phenomenon, termed spike timing-dependent plasticity (STDP), provides a new, quantitative interpretation of Hebb's rule and raises intriguing questions regarding the fundamental processes of cellular signaling. In this article, we summarize previous results obtained in a hippocampal culture system, where an asymmetric window of spike timing was found for paired pre- and postsynaptic spiking to induce STDP. We also discuss our recent studies using a “triplet-spiking” paradigm that reveals nonlinear, temporally asymmetric integration of STDP.

Time-varying MMSE modulated lapped transform and its applications to transform coding for speech and audio signals

The time-varying modulated lapped transform (MLT) is used in speech and audio coding schemes to adjust the time-frequency resolution, to eliminate pre-echoes in the reconstructed signal, and to improve the coding quality. In order to maintain the perfect-reconstruction property in transition periods, an asymmetrical window has to be used at cost of poorer frequency characteristics. We firstly generalize a window-design method for transition periods in the time-varying MLT with a rigorous proof of its PR property, then present a new window-design method, with which the prototype window is so designed that the total reconstruction distortion in presence of coefficient quantization is minimized. This leads to the time-varying minimum mean-square error (MMSE) MLT. Experiments have shown that the designed windows have better frequency characteristics than the sine window in both transition and regular periods. A general formulation of the quantization distortion for different quantization-error models and for all coding systems is given. A simplified optimal window-design algorithm without direct minimization of the distortion equation is suggested. As an example a transform-coding scheme with time-varying MMSE MLT for speech and audio signals is presented.

方形導波管帯域通過フィルタの特異積分方程式による数値解析と簡易設計公式の構成

A powerful numerical solution is presented for band-pass filters in rectangular waveguides. The filters are composed of cascading of perfectly conducting inductive obstacles with zero thickness: asymmetrical windows, symmetrical windows, or symmetrical strips. The problem is reduced to a set of singular integral equations, which is solved by an extension of Lewin’s quasi static procedure. After the accuracy of the classical formulae for the equivalent reactance is investigated, the simple inverse formulae are constructed to yield proper window widths for desired equivalent parameters. The effectiveness of them is demonstrated by designing practical filters having maximally flat or equal-ripple characteristics.

Spike-Timing-Dependent Hebbian Plasticity as Temporal Difference Learning

A spike-timing-dependent Hebbian mechanism governs the plasticity of recurrent excitatory synapses in the neocortex: synapses that are activated a few milliseconds before a postsynaptic spike are potentiated, while those that are activated a few milliseconds after are depressed. We show that such a mechanism can implement a form of temporal difference learning for prediction of input sequences. Using a biophysical model of a cortical neuron, we show that a temporal difference rule used in conjunction with dendritic backpropagating action potentials reproduces the temporally asymmetric window of Hebbian plasticity observed physio-logically. Furthermore, the size and shape of the window vary with the distance of the synapse from the soma. Using a simple example, we show how a spike-timing-based temporal difference learning rule can allow a network of neocortical neurons to predict an input a few milliseconds before the input's expected arrival.

Self-organization model on receptive field of neuron with asymmetric time window of synaptic modification

The spatial-temporal response properties of some simple neurons in visual pathway arise basically prior to birth. In the absence of visual experience, how do these neurons develop in visual system? Based on Wimbauer network with delay, a four-layer feed-forward network model is proposed, which is characterized by modifying the Hebb learning rule through introducing the asymmetric time window of synaptic modification found recently in neurobiology. The model can not only generate by self-organization more diversified spatial-temporal response characteristics of neuronal receptive field than earlier models but also provide some explanations for the possible mechanism underlying the development of receptive fields of contrast polarity sensitive neurons found in visual system of vertebrate. Thus the proposed model may be more widely applicable than Linsker model and Wimbauer model.

Analytical calculations of cross-talk for dual-isotope SPECT projections

Simultaneous dual-isotope SPECT scans are clinically desirable because they require less acquisition time than sequential scans, and provide perfect spatial co-registration of the acquired images. However, they often suffer from extensive contamination caused by cross-talk, the detection of photons from one isotope in the energy window of the second. This contamination can make it difficult to distinguish between the detected distributions of the two isotopes, particularly when the emitted photons are of similar energies. The contamination can be reduced by using asymmetric windows but doing so does not completely remove the effect of cross-talk and there is a corresponding loss in sensitivity due to the reduction in size and/or the change in location of the energy-window. The authors propose to distinguish the source distributions of the two isotopes by fitting calculated projections of potential sites of activity to the acquired projection data. The initial estimates of the potential sites are assumed to be identified using a reconstruction of the uncorrected data. Once the activities of the sources have been determined, corrected projections, if desired, can be generated allowing for the reconstruction of cross-talk free images. The authors have performed an initial feasibility study of this approach using small /sup 123/I and /sup 99m/Tc sources in homogeneous and inhomogeneous media filled with /sup 99m/Tc. The results show good agreement between the true source activity and the authors' estimated activities.

Flat-specimen effect as a convolution in powder diffractometry with Bragg–Brentano geometry

The flat-specimen effect on the peak profile in powder diffractometry with Bragg–Brentano geometry can quantitatively be treated as a convolution with an asymmetric window function. The formula of the window function and a practical method for numerical calculation of the convolution are proposed. By applying the model function given by the convolution of the pseudo-Voigt function with asymmetric window functions based on vertical (axial) divergence and the flat-specimen effect, experimental profiles measured with a conventional diffractometer are fairly well reproduced with only a few parameters. When this function is applied to the analysis of experimental diffraction profiles of a lanthanum hexaboride (LaB6) standard sample measured with a conventional powder X-ray diffractometer, the lattice constant is estimated asa= 4.15685 (2)–4.15693 (2) Å at 299 (1) K, without the use of any other standard material or preceding correction of systematic instrumental errors, while the specified value isa= 4.15695 (6) Å.

Synaptic Modifications in Cultured Hippocampal Neurons: Dependence on Spike Timing, Synaptic Strength, and Postsynaptic Cell Type

In cultures of dissociated rat hippocampal neurons, persistent potentiation and depression of glutamatergic synapses were induced by correlated spiking of presynaptic and postsynaptic neurons. The relative timing between the presynaptic and postsynaptic spiking determined the direction and the extent of synaptic changes. Repetitive postsynaptic spiking within a time window of 20 msec after presynaptic activation resulted in long-term potentiation (LTP), whereas postsynaptic spiking within a window of 20 msec before the repetitive presynaptic activation led to long-term depression (LTD). Significant LTP occurred only at synapses with relatively low initial strength, whereas the extent of LTD did not show obvious dependence on the initial synaptic strength. Both LTP and LTD depended on the activation of NMDA receptors and were absent in cases in which the postsynaptic neurons were GABAergic in nature. Blockade of L-type calcium channels with nimodipine abolished the induction of LTD and reduced the extent of LTP. These results underscore the importance of precise spike timing, synaptic strength, and postsynaptic cell type in the activity-induced modification of central synapses and suggest that Hebb's rule may need to incorporate a quantitative consideration of spike timing that reflects the narrow and asymmetric window for the induction of synaptic modification.

An efficient method for calculating asymmetric diffraction peak profiles

An efficient method for evaluating asymmetric diffraction peak profile functions based on the convolution of the Lorentzian or Gaussian function with any asymmetric window function is proposed. When this method is applied to approximate the convolution with the Howard’s window function [J. Appl. Crystallogr. 15, 615 (1982)], only a few terms of numerical integration give satisfactory results, even if the asymmetry is very strong.

Detectability of simulated brain activation using dual radioisotope SPECT based on size and intensity of the focal hyperactivity

Simultaneous single-photon emission computed tomography (SPECT) neuroimaging with both technetium-99m (99mTc) hexamethylpropyleneamine oxime (HMPAO) and iodine-123 (123I) N-isopropyl-iodoamphetamine is a recently introduced method with potential for assessing activation phenomena in the brain. However, there is limited information on the accuracy of the technique for detecting focal cortical sites of neuroactivation. We determined, in vitro, what levels of activation could be detected as a function of the size of the activated region. A Lucite brain phantom was filled with both 123I and 99mTc so as to simulate both a nonactivated state (123I) along with focal sites of activation (99mTc). Simulated activations ranged from 0 to 18% in volumes of 7, 14, 20, and 27 cm3. Imaging was performed with a triple-detector gamma camera using a 10% symmetric window at 140 keV and 10% asymmetric window around 159 keV. No correction was made for gamma cross-talk. To determine whether a simulated activation was "detected," the 99mTc: 123I count ratios in the activated regions were compared by t test with ratios in nonactivated regions of similar volume. Detection sensitivities also were calculated as the fraction of the activated 99mTc: 123I ratios that were greater than the mean + 2 standard deviations of the corresponding nonactivated ratios. All sites of simulated activations of 10% or greater were detected. The detection sensitivity was 100% (95% confidence interval, 90-100%) for the two largest chambers with simulated activations of 13-18%. Activations in the 3-6% range, in the same-sized chambers, were detected with a limited sensitivity (67% with a confidence interval of 45-84%). In the 14-cm3 chamber, simulated activations in the 13-18% range were detected with 90% sensitivity (confidence interval, 74-98%). In general, the detection sensitivity was greater for larger chambers and higher levels of simulated activation. We conclude that the dual-radioisotope technique using triple-detector SPECT systems and low-energy all-purpose (LEAP) collimators should be highly reliable for identifying focal brain activations above 13% that cover at least 14 cm3 of brain cortex. Smaller, less intense sites of activation will be detected with reduced frequency. These conclusions are based on our assessment of only the physical parameters involved in this methodology and other factors (e.g., the possibility that the relation between cerebral radiotracer concentration and regional cerebral blood flow) may affect the results obtained with patients.

Effect of energy resolution on scatter fraction in scintigraphic imaging: Monte Carlo study.

The effect of energy resolution in detector systems on scatter fractions in scintigraphic imaging through Monte Carlo simulation is investigated. A 10-cm Tc-99m line source within a cylindrical water phantom 20 cm in diameter and 20 cm in length was modeled and energy spectra were calculated at three different line source positions. The energy resolution was changed from 8% to 16% FWHM at 140 keV and a symmetrical energy window width was varied from 8% to 23% on the photopeak of 140 keV in energy spectra corresponding to each energy resolution. The relationship between the scatter fraction and the symmetrical energy window width, and the relationship between the scatter fraction and the primary counts were presented for all energy resolutions investigated. Furthermore, the effect of the asymmetrical energy window on reducing the scatter fraction was also studied and compared with the narrow symmetrical energy window. The results quantitatively showed that improved energy resolution can considerably decrease the scatter fraction with a narrow symmetrical energy window or an asymmetrical energy window without significant primary count-loss compared to that obtained with lower quality energy resolution. The asymmetrical energy window could reduce scatter fraction as compared with the narrow symmetrical energy window when the same number of primary counts was required for both energy windows. Knowing the relationship between the scatter fraction and the primary counts is important in scintigraphic imaging to select the optimum energy window corresponding to the energy resolution.

Correction of scattered photons in Tc-99m imaging by means of a photopeak dual-energy window acquisition

We are proposing a new method for correcting of scattered photons in technetium-99m (99mTc) imaging by means of photopeak dual-energy window acquisition. This method consists of the simultaneous acquisition of two images and estimation of a scatter image included in the symmetric energy window (SW) image by the difference between these images. The scatter corrected image is obtained by subtracting the scatter image from the SW image. In order to evaluate this method, we imaged a planar and a SPECT phantom with cold lesions and calculated the contrast value with and without the scatter correction. In addition, we performed asymmetric energy window (ASW) imaging to compare with this scatter correction method for planar images. In the planar image with the tissue-equivalent material of 10 cm, the scatter correction method removed 32% of the counting rate of the SW image and improved from 0.81 to 0.94 of the contrast value for a 4 cm-diameter cold lesion, while the contrast value with the ASW was 0.87 for such a cold lesion. The scatter corrected SPECT image had a reduction of 18% of the counting rate of the SW SPECT image and improvement of approximately 11% in contrast for cold spot sizes larger than a 3 cm-diameter, compared with the SW SPECT image. In addition, a perfusion defect could be well visualized by this scatter correction method on 99mTc-HMPAO regional cerebral blood flow SPECT of a patient. Our proposed scatter correction method can improve both planar and SPECT images qualitatively and quantitatively.

Spectral analysis in linear process identification—a new look at an old problem

The problem of estimating the transfer function (frequency response) of a linear process by means of a modified spectral analysis method is treated. A method of determining the maximum time lags of the correlation functions which makes use of the available a priori physical knowledge about the process and the input signal is proposed. This leads, in a natural way, to the use of an asymmetrical window technique. Some simulation results are used to illustrate the method. Based on the asymptotic properties of the estimate, the input design is studied. Finally it will be shown that this work can be used for the estimation of an upper bound of the model uncertainty in the frequency domain.

Count‐based monitoring of Anger‐camera spectra—local energy shifts due to rotation

This study reports on a spectral monitoring method in which (1) a small source fixed to the camera is used, (2) a narrow, offset window is set on the side of the photopeak, and (3) variations in count rate are measured to assess energy shifts in the vicinity of the source. For one camera model, the count rate drops from 100% to 76% over a rotation of 180 degrees, implying a local energy shift of 1.4 keV. Also looked for are local count-rate variations with rotation for (1) wide-symmetric, (2) 20%-symmetric, and (3) 10%-asymmetric windows. The last is in limited use to partially compensate for Compton scattering. The effects of background and time stability are assessed.

Improving emission-computed-tomography quantification by Compton-scatter rejection through offset windows

Historically in nuclear medicine the acceptance window for total-energy pulse-height has been set to maximize contrast and resolution in the image. Recently, there has been increased emphasis on quantification of digital images to calculate, for example, left ventricular volume or tumor radiation absorbed dose. In this paper, we consider specifically what improvements can be made in emission computed tomography simply by employing a window which is offset to the high-energy side of the photopeak in order to reduce the contribution of Compton scattered gamma-rays. The window is offset so as to reduce the count rate for a source in air by 20%. Two lucite phantoms were measured. One was a short cylinder filled with a uniformly-distributed solution of 99mTc in water. The other was a head phantom with a 0.6 cm 3 “tumor” containing 99mTc. Water surrounding the tumor could be nonradioactive or contain a dilute background activity. Absolute calibration was accomplished by imaging the simulated tumor in the air-filled phantom. With the offset window, calculated tumor activity is only 3% and 7% high without and with background respectively compared to 20% and 26% high with the symmetric window. However, total activity of the entire slice is still 37% high even without background. For the cylinder containing uniform activity, the error in specific activity drops from 30% to 18% with the offset window. Therefore, an asymmetric window significantly improves quantification, and for certain cases such as an isolated tumor, may be sufficiently accurate without further correction.

Gamma camera energy windows for Tc-99m bone scintigraphy: effect of asymmetry on contrast resolution. Work in progress.

By raising the lower threshold of the Tc-99m energy window, rejection of scattered photons can be made more efficient. Unfortunately, with most gamma cameras significant nonuniformities are produced when the window is changed to an asymmetric setting. Recently introduced designs with gain stabilization of the photomultiplier tubes and improved energy correction maintain field uniformity even for an asymmetric window. To assess the impact of an asymmetric energy window on clinical images, 33 Tc-99m-MDP scintigrams of the lumbar spine were taken with symmetrical (126-154 keV) and asymmetric windows (135-154 keV). Bone:soft tissue ratios improved with the asymmetric window, and the resulting images were preferred by the physicians questioned.

Lesion detectability as a function of pulse-height selection for dynamic imaging with 99mTc.

Previous studies on pulse-height selection for scintillation cameras have been concerned with static imaging or asymmetric window settings around the photo peak. For count densities typical of those encountered in flow studies and for the customary symmetric window it is shown here, both computationally and experimentally, that a window setting in the range of 25-35% provides the maximum lesion detectability rate for lesions of 0.5- to 2.0-cm diameter.