Uniform Random Number Generator Research Articles

Depth-based vessel position fixing by means of a neural network

A depth-based vessel position fixing method on the basis of a neural network is proposed. The network takes as an input a sequence of depth values measured by an echo-sounder and predicts vessel latitude and longitude for the moment of the latest depth measurement. The neural network has a fully-connected feedforward architecture with several layers which satisfies conditions of the universal approximation in compliance with the Stone-Weierstrass theorem. The Adamax algorithm for the neural network training with controlling a maximum value of position error at each epoch is implemented. Modeling is conducted with the Python programming language and the Tensorflow library. The model surface of seabed is performed as a second-order polynomial. Training samples on the basis of virtual soundings at the coordinate net knots with the space resolution not worse than one cable are obtained. After samples obtaining the training of the neural network is conducted. A validation set is not used. Several neural networks are trained. They have different number of hidden layers and different number of neurons per each hidden layer. After training the test procedure is performed. Test samples are generated in the assumption that a vessel is moving along meridians which are not used at the stage of the preliminary soundings survey. The cases of mean and random test meridians are considered. The random meridians are obtained with a uniform random number generator. As the result, all the tested neural networks have shown approximately identical navigational accuracy which is close to the accuracy for the training set.

WALLAX: A memristor-based Gaussian random number generator

Generating Gaussian random numbers is essential in many applications such as cryptography, games, and computer simulations. Although software Gaussian Random Number Generators (GRNG) are widely used, hardware designs have been explored for their faster speed and lower computational cost. However, hardware GRNGs usually occupy large silicon areas when implemented in Complementary Metal Oxide Semiconductor (CMOS) technology, especially for their essential Uniform Random Number Generator (URNG) part. Here, we present a memristor-based GRNG, named WALLAX, conceived from the Wallace method to generate random numbers iteratively. This GRNG circuit benefits not only from the fully parallel analog-based Vector Matrix Multiplication (VMM) feature of memristive crossbars but also harness the intrinsic stochastic switching behaviour of the memristive devices to efficiently produce truly random numbers. The vector-matrix multiplication of WALLAX is implemented on the memristive crossbar, while its random fetching step is realized by a URNG based on the stochastic switching nature of memristors. WALLAX successfully passes all the tests in the NIST 800-22 randomness test suite with 105 numbers generated and five goodness-of-fit tests with various pool sizes and effectively reduces the power and area consumption by 68.78% and 70.0% compared to digital implementations of the same GRNG method. The impact brought by memristor non-idealities is investigated by simulating the proposed structure with 1000 pools under various scenarios. Wire resistance and the stuck of state, each result in a 2.2% and 12.3% reduction in test pass rate within the tested range, respectively.

Re-exploring the Penney-Ante Game

We propose a single loop diagram and use it to devise a single loop matrix method to computationally solve the Penney-Ante game. This method avoids the nuances of repeated use of conditional probability and Markov chain representations. We remove the limitations of Conway’s trick as applied to a fair coin and generalize the method where the coin is allowed to be biased. A uniform random number generator is used to simulate the game and formulate implicit mathematical relations to explore nontransitivity.

Difusi Bebas 1D dan 2D dengan Monte Carlo: Perbandingan Distribusi Bilangan Random Normal dan Seragam dengan Box-Müller

Many biological processes in the human body are based on the diffusion system. Diffusion is defined as a process of random movement of the particle whose the direction is from high concentrations to low concentrations. Many of various study of diffusion have been done both experimentally and computationally. Because the particle interaction is stochastic, the Monte Carlo (MC) method is used in performing particle simulations. The main of MC method is the use of random numbers. Many software have provided uniform random number generators. But based on the analytic results, the solution is normal distribution. Therefore, Box-Müller can be used as a transformation of particle distribution. The software used, MATLAB, has a normal random generator. Therefore, the aims of this study is comparing particle distribution of these two different random number generator with MATLAB and showing the impact of timestep parameter to these random number generator. This result can be used as based for the modelling of more complex biological systems.

Analytic simulator and image generator of multiple-scattering Compton camera for prompt gamma ray imaging.

For prompt gamma ray imaging for biomedical applications and environmental radiation monitoring, we propose herein a multiple-scattering Compton camera (MSCC). MSCC consists of three or more semiconductor layers with good energy resolution, and has potential for simultaneous detection and differentiation of multiple radio-isotopes based on the measured energies, as well as three-dimensional (3D) imaging of the radio-isotope distribution. In this study, we developed an analytic simulator and a 3D image generator for a MSCC, including the physical models of the radiation source emission and detection processes that can be utilized for geometry and performance prediction prior to the construction of a real system. The analytic simulator for a MSCC records coincidence detections of successive interactions in multiple detector layers. In the successive interaction processes, the emission direction of the incident gamma ray, the scattering angle, and the changed traveling path after the Compton scattering interaction in each detector, were determined by a conical surface uniform random number generator (RNG), and by a Klein-Nishina RNG. The 3D image generator has two functions: the recovery of the initial source energy spectrum and the 3D spatial distribution of the source. We evaluated the analytic simulator and image generator with two different energetic point radiation sources (Cs-137 and Co-60) and with an MSCC comprising three detector layers. The recovered initial energies of the incident radiations were well differentiated from the generated MSCC events. Correspondingly, we could obtain a multi-tracer image that combined the two differentiated images. The developed analytic simulator in this study emulated the randomness of the detection process of a multiple-scattering Compton camera, including the inherent degradation factors of the detectors, such as the limited spatial and energy resolutions. The Doppler-broadening effect owing to the momentum distribution of electrons in Compton scattering was not considered in the detection process because most interested isotopes for biomedical and environmental applications have high energies that are less sensitive to Doppler broadening. The analytic simulator and image generator for MSCC can be utilized to determine the optimal geometrical parameters, such as the distances between detectors and detector size, thus affecting the imaging performance of the Compton camera prior to the development of a real system.

A Tutorial on Pharmacodynamic Scripting Facility inSimcyp.

The Simcyp Simulator provides a framework for mechanistic Physiologically‐Based Pharmacokinetic/Pharmacodynamic modeling of potentially interacting drugs. It also provides a scripting facility, using the Lua language, for developing customized pharmacodynamic and toxicity models driven by drug concentrations at the site of action. We present an overview of the scripting facility including the scripting language, the editor, and how scripts are embedded within the Simulator. Examples incorporating differential equations and including inter‐individual variability on parameters are presented.

Optimization of FPGA Architecture for Uniform Random Number Generator Using LUT-SR Family

Optimization of FPGA Architecture for Uniform Random Number Generator Using LUT-SR Family

Model to Increase the Number of Output States of a Random Variable Using a Histogram Based PDF

This paper is devoted to a pseudo-random number generator that generates numbers according to a known probability density function. This function has its origins in a histogram that contains the observed properties of a monitored random variable X. Using the recorded PDF and an ON/OFF model we are able to generate output states of a random variable Y, which is nearly alike distributed as the random variable X. Because the used PDF has its origins in a normed histogram function, the resulting number of all possible output states of variable Y is the same as the number of classes that are used to form the histogram. We propose this model that generates practically an unlimited set of possible output states of the random variable Y. At first a cumulative distribution function is formed from the input density function. Then the ON/OFF model driven by a random number generator in (0, 1) is applied to address classes that are defined in the distribution function. To address these classes a search function is applied. Then when a class is chosen, we propose to use a second uniform random number generator that generates numbers within the range of the selected class. The resulting output state of the variable Y is the output of the second random number generator. In this paper we apply this model on a packet generator that generates IPTV inter-departure times of an MPEG2-TS H.264 VBR based video source.

Fractional-order load-frequency control of interconnected power systems using chaotic multi-objective optimization

Fractional-order proportional-integral-derivative (FOPID) controllers are designed for load-frequency control (LFC) of two interconnected power systems. Conflicting time-domain design objectives are considered in a multi-objective optimization (MOO)-based design framework to design the gains and the fractional differ-integral orders of the FOPID controllers in the two areas. Here, we explore the effect of augmenting two different chaotic maps along with the uniform random number generator (RNG) in the popular MOO algorithm—the Non-dominated Sorting Genetic Algorithm-II (NSGA-II). Different measures of quality for MOO, e.g. hypervolume indicator, moment of inertia-based diversity metric, total Pareto spread, spacing metric, are adopted to select the best set of controller parameters from multiple runs of all the NSGA-II variants (i.e. nominal and chaotic versions). The chaotic versions of the NSGA-II algorithm are compared with the standard NSGA-II in terms of solution quality and computational time. In addition, the Pareto optimal fronts showing the trade-off between the two conflicting time domain design objectives are compared to show the advantage of using the FOPID controller over that with simple PID controller. The nature of fast/slow and high/low noise amplification effects of the FOPID structure or the four quadrant operation in the two inter-connected areas of the power system is also explored. A fuzzy logic-based method has been adopted next to select the best compromise solution from the best Pareto fronts corresponding to each MOO comparison criteria. The time-domain system responses are shown for the fuzzy best compromise solutions under nominal operating conditions. Comparative analysis on the merits and de-merits of each controller structure is reported then. A robustness analysis is also done for the PID and the FOPID controllers.

Modelling Packet Departure Times using a Known PDF

This paper deals with IPTV traffic source modelling and describes a packet generator based on a known probability density function which is measured and formed from a histogram. Histogram based probability density functions destroy an amount of information, because classes used to form the histogram often cover significantly more events than one. In this work, we propose an algorithm to generate far more output states of random variable X than the input probability distribution function is made from. In this generator is assumed that all IPTV packets of the same video stream are the same length. Therefore, only packet times are generated. These times are generated using the measured normalized histogram that is converted to a cumulative distribution function which acts as a finite number of states that can be addressed. To address these states we use an ON/OFF model that is driven by an uniform random number generator in (0, 1). When a state is chosen then the resulting value is equal to a histogram class. To raise the number of possible output states of the random variable X, we propose to use an uniform random number generator that generates numbers within the range of the chosen histogram class. This second uniform random number generator assures that the number of output states is far more larger than the number of histogram classes.

SRAM Based Random Number Generator for Non-Repeating Pattern Generation

—Field-programmable gate array (FPGA) optimized random number generators (RNGs) are more resource-efficient than software-optimized RNGs because they can take advantage of bitwise operations and FPGA-specific features. A random number generator (RNG) is a computational or physical device designed to generate a sequence of numbers or symbols that lack any pattern, i.e. appear random. The many applications of randomness have led to the development of several different methods for generating random data. Several computational methods for random number generation exist, but often fall short of the goal of true randomness though they may meet, with varying success, some of the statistical tests for randomness intended to measure how unpredictable their results are (that is, to what degree their patterns are discernible).LUT-SR Family of Uniform Random Number Generators are able to handle randomness only based on seeds that is loaded in the look up table. To make random generation efficient, we propose new approach based on SRAM storage device. Keywords: RNG, LFSR, SRAM

Segmented Leap-Ahead LFSR Architecture for Uniform Random Number Generator

Random numbers are widely used in various applications. In the majority of cases, a pseudo-random number generator is used since true random number generators are slow and they are barely suitable for the hardware implementation. In this paper, we present new architecture of URNG (uniform random number generator) employing Leap-Ahead LFSR architecture for hardware implementation. In particular, the proposed URNG consists of two more segmented Leap-Ahead LFSRs to overcome the drawback of the conventional URNG employing Leap-Ahead architecture, that is, the sharp decrease of a maximum period of the generated random numbers. Thus, the proposed URNG with segmented LFSR architecture can generate multiple bits random number in a cycle without the frequent diminishing of maximum period of the generated random numbers. We prove the efficiency of the proposed segmented LFSR-architecture through the mathematical analysis. The simulation results show that the proposed URNG employing segmented Leap-Ahead LFSR architecture can be increased 2.5 times of the maximum period of generated random numbers compared to the URNG using the conventional Leap-Ahead architecture.

The LUT-SR Family of Uniform Random Number Generators for FPGA Architectures

Field-programmable gate array (FPGA) optimized random number generators (RNGs) are more resource-efficient than software-optimized RNGs because they can take advantage of bitwise operations and FPGA-specific features. However, it is difficult to concisely describe FPGA-optimized RNGs, so they are not commonly used in real-world designs. This paper describes a type of FPGA RNG called a LUT-SR RNG, which takes advantage of bitwise xor operations and the ability to turn lookup tables (LUTs) into shift registers of varying lengths. This provides a good resource-quality balance compared to previous FPGA-optimized generators, between the previous high-resource high-period LUT-FIFO RNGs and low-resource low-quality LUT-OPT RNGs, with quality comparable to the best software generators. The LUT-SR generators can also be expressed using a simple C++ algorithm contained within this paper, allowing 60 fully-specified LUT-SR RNGs with different characteristics to be embedded in this paper, backed up by an online set of very high speed integrated circuit hardware description language (VHDL) generators and test benches.

Comparison of random number generators via Fourier transform

In this paper, we investigate simple yet practical schemes to generate random variates from the characteristic function of any continuous distribution. We discuss the generation of non-uniform random variates from a uniform random number generator. The inverse of the cumulative distribution function is derived from its characteristic function via the fast Fourier transform. We conduct several numerical experiments to assess the accuracy and efficiency of the schemes.

Hardware Architecture of a Gaussian Noise Generator Based on the Inversion Method

In this brief, we present a hardware-based Gaussian noise generator (GNG) with low hardware cost, high generation rate, and high Gaussian tail accuracy. The proposed generator is based on a piecewise polynomial approximation of the inverse cumulative distribution function (ICDF). We propose to avoid the area-demanding barrel-shifter of the ICDF approximation by means of creating a new uniform random sequence from the uniform random number generator output. The GNG architecture has been implemented in field-programmable gate array devices, and the implementation results are compared with other published designs, achieving a higher deviation with fewer hardware resources. Our GNG generates 242 Msps of random noise and achieves a tail of 13.1 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX"> $\sigma$</tex></formula> with 442 slices, two multipliers, and two Block-RAM of a Virtex-II device. The generator output successfully passed commonly used statistical tests.

High Performance FPGA-oriented Mersenne Twister Uniform Random Number Generator

Mersenne Twister (MT) uniform random number generators are key cores for hardware acceleration of Monte Carlo simulations. In this work, two different architectures are studied: besides the classical table-based architecture, a different architecture based on a circular buffer and especially targeting FPGAs is proposed. A 30% performance improvement has been obtained when compared to the fastest previous work. The applicability of the proposed MT architectures has been proven in a high performance Gaussian RNG.

Fine-Grained Parallel and Distributed Spatial Stochastic Simulation of Biological Reactions

Fine-Grained Parallel and Distributed Spatial Stochastic Simulation of Biological Reactions

Algorithm and software for defining the distribution of eigenvalues of random symmetric matrices via simulation

A simulation algorithm for defining the distribution of eigenvalues of a random symmetric matrix with arbitrary continuous joint probability density function of its entries is presented. The algorithm requires only a uniform random number generator. As a numerical example, the probability that eigenvalues of a certain random symmetric matrix satisfy a given condition is calculated using software implementing the algorithm.

Numerical representation of quantum states in the positive- P and Wigner representations

Numerical stochastic integration is a powerful tool for the investigation of quantum dynamics in interacting many-body systems. As with all numerical integration of differential equations, the initial conditions of the system being investigated must be specified. With application to quantum optics in mind, we show how various commonly considered quantum states can be numerically simulated by the use of widely available Gaussian and uniform random number generators. We note that the same methods can also be applied to computational studies of Bose–Einstein condensates, and give some examples of how this can be done.

An FPGA Implementation of a Parallelized MT19937 Uniform Random Number Generator

Recent times have witnessed an increase in use of high-performance reconfigurable computing for accelerating large-scale simulations. A characteristic of such simulations, like infrared (IR) scene simulation, is the use of large quantities of uncorrelated random numbers. It is therefore of interest to have a fast uniform random number generator implemented in reconfigurable hardware. While there have been previous attempts to accelerate the MT19937 pseudouniform random number generator using FPGAs we believe that we can substantially improve the previous implementations to develop a higher throughput and more areatime efficient design. Due to the potential for parallel implementation of random numbers generators, designs that have both a small area footprint and high throughput are to be preferred to ones that have the high throughput but with significant extra area requirements. In this paper, we first present a single port design and then present an enhanced 624 port hardware implementation of the MT19937 algorithm. The 624 port hardware implementation when implemented on a Xilinx XC2VP70-6 FPGA chip has a throughput of 119.6 × 109 32 bit random numbers per second which is more than 17x that of the previously best published uniform random number generator. Furthermore it has the lowest area time metric of all the currently published FPGA-based pseudouniform random number generators.