Variance-Reduction Methods for Monte Carlo Simulation of Radiation Transport

After a brief description of the essentials of Monte Carlo simulation methods and the definition of simulation efficiency, the rationale for variance-reduction techniques is presented. Popular variance-reduction techniques applicable to Monte Carlo simulations of radiation transport are described and motivated. The focus is on those techniques that can be used with any transport code, irrespective of the strategies used to track charged particles; they operate by manipulating either the number and weights of the transported particles or the mean free paths of the various interaction mechanisms. The considered techniques are 1) splitting and Russian roulette, with the ant colony method as builder of importance maps, 2) exponential transform and interaction-forcing biasing, 3) Woodcock or delta-scattering method, 4) interaction forcing, and 5) proper use of symmetries and combinations of different techniques. Illustrative results from analog simulations (without recourse to variance-reduction) and from variance-reduced simulations of various transport problems are presented.

Geometrically Invariant NSCT–GPCET-Based Image Watermarking with Accurate Moment Calculation

Generic polar complex exponential transform (GPCET), as continuous orthogonal moment, has the advantages of computational simplicity, numerical stability, and resistance to geometric transforms, which make it suitable for watermarking. However, errors in kernel function discretization can degrade these advantages. To maximize the GPCET utilization in robust watermarking, this paper proposes a secondary grid-division (SGD)-based moment calculation method that divides each grid corresponding to one pixel into nonoverlapping subgrids and increases the number of sampling points. Using the accurate moment calculation method, a nonsubsampled contourlet transform (NSCT)–GPCET-based watermarking scheme with resistance to image processing and geometrical attacks is proposed. In this scheme, the accurate moment calculation can reduce the numerical error and geometrical error of the traditional methods, which is verified by an image reconstruction comparison. Additionally, NSCT and accurate GPCET are utilized to achieve watermark stability. Subsequent experiments test the proposed watermarking scheme for its invisibility and robustness, and verify that the robustness of the proposed scheme outperforms that of other schemes when its level of invisibility is significantly higher.

A Polar Complex Exponential Transform-Based Zero-Watermarking for Multiple Medical Images with High Discrimination

Zero-watermarking is one of the solutions for image copyright protection without tampering with images, and thus it is suitable for medical images, which commonly do not allow any distortion. Moment-based zero-watermarking is robust against both image processing and geometric attacks, but the discrimination of watermarks is often ignored by researchers, resulting in the high possibility that host images and fake host images cannot be distinguished by verifier. To this end, this paper proposes a PCET- (polar complex exponential transform-) based zero-watermarking scheme based on the stability of the relationships between moment magnitudes of the same order and stability of the relationships between moment magnitudes of the same repetition, which can handle multiple medical images simultaneously. The scheme first calculates the PCET moment magnitudes for each image in an image group. Then, the magnitudes of the same order and the magnitudes of the same repetition are compared to obtain the content-related features. All the image features are added together to obtain the features for the image group. Finally, the scheme extracts a robust feature vector with the chaos system and takes the bitwise XOR of the robust feature and a scrambled watermark to generate a zero-watermark. The scheme produces robust features with both resistance to various attacks and low similarity among different images. In addition, the one-to-many mapping between magnitudes and robust feature bits reduces the number of moments involved, which not only reduces the computation time but also further improves the robustness. The experimental results show that the proposed scheme meets the performance requirements of zero-watermarking on the robustness, discrimination, and capacity, and it outperforms the state-of-the-art methods in terms of robustness, discrimination, and computational time under the same payloads.

On an upper bound for the spreading speed

<p style='text-indent:20px;'>In this paper, we use the exponential transform to give a unified formal upper bound for the asymptotic rate of spread of a population propagating in a one dimensional habitat. We show through examples how this upper bound can be obtained directly for discrete and continuous time models. This upper bound has the form <inline-formula><tex-math id="M1">\begin{document}$ \min_{s&gt;0} \ln (\rho(s))/s $\end{document}</tex-math></inline-formula> and coincides with the speeds of several models found in the literature.</p>

A Real Time QRS Detection Algorithm Based on ET and PD Controlled Threshold Strategy

As one of the important components of electrocardiogram (ECG) signals, QRS signal represents the basic characteristics of ECG signals. The detection of QRS waves is also an essential step for ECG signal analysis. In order to further meet the clinical needs for the accuracy and real-time detection of QRS waves, a simple, fast, reliable, and hardware-friendly algorithm for real-time QRS detection is proposed. The exponential transform (ET) and proportional-derivative (PD) control-based adaptive threshold are designed to detect QRS-complex. The proposed ET can effectively narrow the magnitude difference of QRS peaks, and the PD control-based method can adaptively adjust the current threshold for QRS detection according to thresholds of previous two windows and predefined minimal threshold. The ECG signals from MIT-BIH databases are used to evaluate the performance of the proposed algorithm. The overall sensitivity, positive predictivity, and accuracy for QRS detection are 99.90%, 99.92%, and 99.82%, respectively. It is also implemented on Altera Cyclone V 5CSEMA5F31C6 Field Programmable Gate Array (FPGA). The time consumed for a 30-min ECG record is approximately 1.3 s. It indicates that the proposed algorithm can be used for wearable heart rate monitoring and automatic ECG analysis.