Quantum random number generation
Ma, Xiongfeng; Yuan, Xiao; Cao, Zhu; Zhang, Zhen; Qi, Bing
2016-06-28
Here, quantum physics can be exploited to generate true random numbers, which play important roles in many applications, especially in cryptography. Genuine randomness from the measurement of a quantum system reveals the inherent nature of quantumness -- coherence, an important feature that differentiates quantum mechanics from classical physics. The generation of genuine randomness is generally considered impossible with only classical means. Based on the degree of trustworthiness on devices, quantum random number generators (QRNGs) can be grouped into three categories. The first category, practical QRNG, is built on fully trusted and calibrated devices and typically can generate randomness at amore » high speed by properly modeling the devices. The second category is self-testing QRNG, where verifiable randomness can be generated without trusting the actual implementation. The third category, semi-self-testing QRNG, is an intermediate category which provides a tradeoff between the trustworthiness on the device and the random number generation speed.« less
Quantum random number generation
Ma, Xiongfeng; Yuan, Xiao; Cao, Zhu; Zhang, Zhen; Qi, Bing
2016-01-01
Here, quantum physics can be exploited to generate true random numbers, which play important roles in many applications, especially in cryptography. Genuine randomness from the measurement of a quantum system reveals the inherent nature of quantumness — coherence, an important feature that differentiates quantum mechanics from classical physics. The generation of genuine randomness is generally considered impossible with only classical means. Based on the degree of trustworthiness on devices, quantum random number generators (QRNGs) can be grouped into three categories. The first category, practical QRNG, is built on fully trusted and calibrated devices and typically can generate randomness at a high speed by properly modeling the devices. The second category is self-testing QRNG, where verifiable randomness can be generated without trusting the actual implementation. The third category, semi-self-testing QRNG, is an intermediate category which provides a tradeoff between the trustworthiness on the device and the random number generation speed.
Quantum random number generator
Pooser, Raphael C.
2016-05-10
A quantum random number generator (QRNG) and a photon generator for a QRNG are provided. The photon generator may be operated in a spontaneous mode below a lasing threshold to emit photons. Photons emitted from the photon generator may have at least one random characteristic, which may be monitored by the QRNG to generate a random number. In one embodiment, the photon generator may include a photon emitter and an amplifier coupled to the photon emitter. The amplifier may enable the photon generator to be used in the QRNG without introducing significant bias in the random number and may enable multiplexing of multiple random numbers. The amplifier may also desensitize the photon generator to fluctuations in power supplied thereto while operating in the spontaneous mode. In one embodiment, the photon emitter and amplifier may be a tapered diode amplifier.
Uniform random number generators
NASA Technical Reports Server (NTRS)
Farr, W. R.
1971-01-01
Methods are presented for the generation of random numbers with uniform and normal distributions. Subprogram listings of Fortran generators for the Univac 1108, SDS 930, and CDC 3200 digital computers are also included. The generators are of the mixed multiplicative type, and the mathematical method employed is that of Marsaglia and Bray.
Digital random-number generator
NASA Technical Reports Server (NTRS)
Brocker, D. H.
1973-01-01
For binary digit array of N bits, use N noise sources to feed N nonlinear operators; each flip-flop in digit array is set by nonlinear operator to reflect whether amplitude of generator which feeds it is above or below mean value of generated noise. Fixed-point uniform distribution random number generation method can also be used to generate random numbers with other than uniform distribution.
High speed optical quantum random number generation.
Fürst, Martin; Weier, Henning; Nauerth, Sebastian; Marangon, Davide G; Kurtsiefer, Christian; Weinfurter, Harald
2010-06-01
We present a fully integrated, ready-for-use quantum random number generator (QRNG) whose stochastic model is based on the randomness of detecting single photons in attenuated light. We show that often annoying deadtime effects associated with photomultiplier tubes (PMT) can be utilized to avoid postprocessing for bias or correlations. The random numbers directly delivered to a PC, generated at a rate of up to 50 Mbit/s, clearly pass all tests relevant for (physical) random number generators. PMID:20588431
Self-correcting random number generator
Humble, Travis S.; Pooser, Raphael C.
2016-09-06
A system and method for generating random numbers. The system may include a random number generator (RNG), such as a quantum random number generator (QRNG) configured to self-correct or adapt in order to substantially achieve randomness from the output of the RNG. By adapting, the RNG may generate a random number that may be considered random regardless of whether the random number itself is tested as such. As an example, the RNG may include components to monitor one or more characteristics of the RNG during operation, and may use the monitored characteristics as a basis for adapting, or self-correcting, to provide a random number according to one or more performance criteria.
Generation of pseudo-random numbers
NASA Technical Reports Server (NTRS)
Howell, L. W.; Rheinfurth, M. H.
1982-01-01
Practical methods for generating acceptable random numbers from a variety of probability distributions which are frequently encountered in engineering applications are described. The speed, accuracy, and guarantee of statistical randomness of the various methods are discussed.
The MCNP5 Random number generator
Brown, F. B.; Nagaya, Y.
2002-01-01
MCNP and other Monte Carlo particle transport codes use random number generators to produce random variates from a uniform distribution on the interval. These random variates are then used in subsequent sampling from probability distributions to simulate the physical behavior of particles during the transport process. This paper describes the new random number generator developed for MCNP Version 5. The new generator will optionally preserve the exact random sequence of previous versions and is entirely conformant to the Fortran-90 standard, hence completely portable. In addition, skip-ahead algorithms have been implemented to efficiently initialize the generator for new histories, a capability that greatly simplifies parallel algorithms. Further, the precision of the generator has been increased, extending the period by a factor of 10{sup 5}. Finally, the new generator has been subjected to 3 different sets of rigorous and extensive statistical tests to verify that it produces a sufficiently random sequence.
Self-Testing Quantum Random Number Generator
NASA Astrophysics Data System (ADS)
Lunghi, Tommaso; Brask, Jonatan Bohr; Lim, Charles Ci Wen; Lavigne, Quentin; Bowles, Joseph; Martin, Anthony; Zbinden, Hugo; Brunner, Nicolas
2015-04-01
The generation of random numbers is a task of paramount importance in modern science. A central problem for both classical and quantum randomness generation is to estimate the entropy of the data generated by a given device. Here we present a protocol for self-testing quantum random number generation, in which the user can monitor the entropy in real time. Based on a few general assumptions, our protocol guarantees continuous generation of high quality randomness, without the need for a detailed characterization of the devices. Using a fully optical setup, we implement our protocol and illustrate its self-testing capacity. Our work thus provides a practical approach to quantum randomness generation in a scenario of trusted but error-prone devices.
Self-testing quantum random number generator.
Lunghi, Tommaso; Brask, Jonatan Bohr; Lim, Charles Ci Wen; Lavigne, Quentin; Bowles, Joseph; Martin, Anthony; Zbinden, Hugo; Brunner, Nicolas
2015-04-17
The generation of random numbers is a task of paramount importance in modern science. A central problem for both classical and quantum randomness generation is to estimate the entropy of the data generated by a given device. Here we present a protocol for self-testing quantum random number generation, in which the user can monitor the entropy in real time. Based on a few general assumptions, our protocol guarantees continuous generation of high quality randomness, without the need for a detailed characterization of the devices. Using a fully optical setup, we implement our protocol and illustrate its self-testing capacity. Our work thus provides a practical approach to quantum randomness generation in a scenario of trusted but error-prone devices. PMID:25933297
Source-Independent Quantum Random Number Generation
NASA Astrophysics Data System (ADS)
Cao, Zhu; Zhou, Hongyi; Yuan, Xiao; Ma, Xiongfeng
2016-01-01
Quantum random number generators can provide genuine randomness by appealing to the fundamental principles of quantum mechanics. In general, a physical generator contains two parts—a randomness source and its readout. The source is essential to the quality of the resulting random numbers; hence, it needs to be carefully calibrated and modeled to achieve information-theoretical provable randomness. However, in practice, the source is a complicated physical system, such as a light source or an atomic ensemble, and any deviations in the real-life implementation from the theoretical model may affect the randomness of the output. To close this gap, we propose a source-independent scheme for quantum random number generation in which output randomness can be certified, even when the source is uncharacterized and untrusted. In our randomness analysis, we make no assumptions about the dimension of the source. For instance, multiphoton emissions are allowed in optical implementations. Our analysis takes into account the finite-key effect with the composable security definition. In the limit of large data size, the length of the input random seed is exponentially small compared to that of the output random bit. In addition, by modifying a quantum key distribution system, we experimentally demonstrate our scheme and achieve a randomness generation rate of over 5 ×103 bit /s .
Spatio-temporal optical random number generator.
Stipčević, M; Bowers, J E
2015-05-01
We present a first random number generator (RNG) which simultaneously uses independent spatial and temporal quantum randomness contained in an optical system. Availability of the two independent sources of entropy makes the RNG resilient to hardware failure and signal injection attacks. We show that the deviation from randomness of the generated numbers can be estimated quickly from simple measurements thus eliminating the need for usual time-consuming statistical testing of the output data. As a confirmation it is demonstrated that generated numbers pass NIST Statistical test suite. PMID:25969254
Generation of Random Numbers by Micromechanism
NASA Astrophysics Data System (ADS)
Mita, Makoto; Toshiyoshi, Hiroshi; Ataka, Manabu; Fujita, Hiroyuki
We have successfully developed a novel micromechanism of random number generator (RNG) by using the silicon micromachining technique. The MEM(Micro Electro Mechanical)RNG produce a series of random numbers by using the pull-in instability of electrostatic actuation operated with a typical dc 150 volt. The MEM RNG is made by the deep reactive ion etching of a silicon-on-insulator(SOI) wafer, and is very small compared with the conventional RNG hardware based on the randomness of thermal noise or isotope radiation. Quality of randomness has been experimentally confirmed by the self-correlation study of the generated series of numbers. The MEM RNG proposed here would be a true random number generation, which is needed for the highly secured encryption system of today’s information technology.
Truly random number generation: an example
NASA Astrophysics Data System (ADS)
Frauchiger, Daniela; Renner, Renato
2013-10-01
Randomness is crucial for a variety of applications, ranging from gambling to computer simulations, and from cryptography to statistics. However, many of the currently used methods for generating randomness do not meet the criteria that are necessary for these applications to work properly and safely. A common problem is that a sequence of numbers may look random but nevertheless not be truly random. In fact, the sequence may pass all standard statistical tests and yet be perfectly predictable. This renders it useless for many applications. For example, in cryptography, the predictability of a "andomly" chosen password is obviously undesirable. Here, we review a recently developed approach to generating true | and hence unpredictable | randomness.
Quantum random number generator using photon-number path entanglement.
Kwon, Osung; Cho, Young-Wook; Kim, Yoon-Ho
2009-03-20
We report a quantum random number generator based on the photon-number-path entangled state that is prepared by means of two-photon quantum interference at a beam splitter. The randomness in our scheme is truly quantum mechanical in origin since it results from the projection measurement of the entangled two-photon state. The generated bit sequences satisfy the standard randomness test. PMID:19305476
The RANDOM computer program: A linear congruential random number generator
NASA Technical Reports Server (NTRS)
Miles, R. F., Jr.
1986-01-01
The RANDOM Computer Program is a FORTRAN program for generating random number sequences and testing linear congruential random number generators (LCGs). The linear congruential form of random number generator is discussed, and the selection of parameters of an LCG for a microcomputer described. This document describes the following: (1) The RANDOM Computer Program; (2) RANDOM.MOD, the computer code needed to implement an LCG in a FORTRAN program; and (3) The RANCYCLE and the ARITH Computer Programs that provide computational assistance in the selection of parameters for an LCG. The RANDOM, RANCYCLE, and ARITH Computer Programs are written in Microsoft FORTRAN for the IBM PC microcomputer and its compatibles. With only minor modifications, the RANDOM Computer Program and its LCG can be run on most micromputers or mainframe computers.
Statistical Analysis of Random Number Generators
NASA Astrophysics Data System (ADS)
Accardi, Luigi; Gäbler, Markus
2011-01-01
In many applications, for example cryptography and Monte Carlo simulation, there is need for random numbers. Any procedure, algorithm or device which is intended to produce such is called a random number generator (RNG). What makes a good RNG? This paper gives an overview on empirical testing of the statistical properties of the sequences produced by RNGs and special software packages designed for that purpose. We also present the results of applying a particular test suite--TestU01-- to a family of RNGs currently being developed at the Centro Interdipartimentale Vito Volterra (CIVV), Roma, Italy.
How random are random numbers generated using photons?
NASA Astrophysics Data System (ADS)
Solis, Aldo; Angulo Martínez, Alí M.; Ramírez Alarcón, Roberto; Cruz Ramírez, Hector; U'Ren, Alfred B.; Hirsch, Jorge G.
2015-06-01
Randomness is fundamental in quantum theory, with many philosophical and practical implications. In this paper we discuss the concept of algorithmic randomness, which provides a quantitative method to assess the Borel normality of a given sequence of numbers, a necessary condition for it to be considered random. We use Borel normality as a tool to investigate the randomness of ten sequences of bits generated from the differences between detection times of photon pairs generated by spontaneous parametric downconversion. These sequences are shown to fulfil the randomness criteria without difficulties. As deviations from Borel normality for photon-generated random number sequences have been reported in previous work, a strategy to understand these diverging findings is outlined.
Operational conditions for random-number generation
NASA Astrophysics Data System (ADS)
Compagner, A.
1995-11-01
Ensemble theory is used to describe arbitrary sequences of integers, whether formed by the decimals of π or produced by a roulette or by any other means. Correlation coefficients of any range and order are defined as Fourier transforms of the ensemble weights. Competing definitions of random sequences are considered. Special attention is given to sequences of random numbers needed for Monte Carlo calculations. Different recipes for those sequences lead to correlations that vary in range and order, but the total amount of correlation is the same for all sequences of a given length (without internal periodicities). For maximum-length sequences produced by linear algorithms, most correlation coefficients are zero, but the remaining ones are of absolute value 1. In well-tempered sequences, these complete correlations are of high order or of very long range. General conditions to be obeyed by random-number generators are discussed and a qualitative method for comparing different recipes is given.
Random number generation from spontaneous Raman scattering
NASA Astrophysics Data System (ADS)
Collins, M. J.; Clark, A. S.; Xiong, C.; Mägi, E.; Steel, M. J.; Eggleton, B. J.
2015-10-01
We investigate the generation of random numbers via the quantum process of spontaneous Raman scattering. Spontaneous Raman photons are produced by illuminating a highly nonlinear chalcogenide glass ( As 2 S 3 ) fiber with a CW laser at a power well below the stimulated Raman threshold. Single Raman photons are collected and separated into two discrete wavelength detuning bins of equal scattering probability. The sequence of photon detection clicks is converted into a random bit stream. Postprocessing is applied to remove detector bias, resulting in a final bit rate of ˜650 kb/s. The collected random bit-sequences pass the NIST statistical test suite for one hundred 1 Mb samples, with the significance level set to α = 0.01 . The fiber is stable, robust and the high nonlinearity (compared to silica) allows for a short fiber length and low pump power favourable for real world application.
Long period pseudo random number sequence generator
NASA Technical Reports Server (NTRS)
Wang, Charles C. (Inventor)
1989-01-01
A circuit for generating a sequence of pseudo random numbers, (A sub K). There is an exponentiator in GF(2 sup m) for the normal basis representation of elements in a finite field GF(2 sup m) each represented by m binary digits and having two inputs and an output from which the sequence (A sub K). Of pseudo random numbers is taken. One of the two inputs is connected to receive the outputs (E sub K) of maximal length shift register of n stages. There is a switch having a pair of inputs and an output. The switch outputs is connected to the other of the two inputs of the exponentiator. One of the switch inputs is connected for initially receiving a primitive element (A sub O) in GF(2 sup m). Finally, there is a delay circuit having an input and an output. The delay circuit output is connected to the other of the switch inputs and the delay circuit input is connected to the output of the exponentiator. Whereby after the exponentiator initially receives the primitive element (A sub O) in GF(2 sup m) through the switch, the switch can be switched to cause the exponentiator to receive as its input a delayed output A(K-1) from the exponentiator thereby generating (A sub K) continuously at the output of the exponentiator. The exponentiator in GF(2 sup m) is novel and comprises a cyclic-shift circuit; a Massey-Omura multiplier; and, a control logic circuit all operably connected together to perform the function U(sub i) = 92(sup i) (for n(sub i) = 1 or 1 (for n(subi) = 0).
A Pseudo-Random Number Generator Based on Normal Numbers
Bailey, David H.
2004-12-31
In a recent paper, Richard Crandall and the present author established that each of a certain class of explicitly given real constants, uncountably infinite in number, is b-normal, for an integer that appears in the formula defining the constant. A b-normal constant is one where every string of m digits appears in the base-b expansion of the constant with limiting frequency b{sup -m}. This paper shows how this result can be used to fashion an efficient and effective pseudo-random number generator, which generates successive strings of binary digits from one of the constants in this class. The resulting generator, which tests slightly faster than a conventional linear congruential generator, avoids difficulties with large power-of-two data access strides that may occur when using conventional generators. It is also well suited for parallel processing--each processor can quickly and independently compute its starting value, with the collective sequence generated by all processors being the same as that generated by a single processor.
A random number generator for continuous random variables
NASA Technical Reports Server (NTRS)
Guerra, V. M.; Tapia, R. A.; Thompson, J. R.
1972-01-01
A FORTRAN 4 routine is given which may be used to generate random observations of a continuous real valued random variable. Normal distribution of F(x), X, E(akimas), and E(linear) is presented in tabular form.
Statistical Evaluation of a Superconductive Physical Random Number Generator
NASA Astrophysics Data System (ADS)
Sugiura, Tatsuro; Yamanashi, Yuki; Yoshikawa, Nobuyuki
A physical random number generator, which generates truly random number trains by using the randomness of physical phenomena, is widely used in the field of cryptographic applications. We have developed an ultra high-speed superconductive physical random number generator that can generate random numbers at a frequency of more than 10GHz by utilizing the high-speed operation and high-sensitivity of superconductive integrated circuits. In this study, we have statistically evaluated the quality of the random number trains generated by the superconductive physical random number generator. The performances of the statistical tests were based on a test method provided by National Institute of Standards and Technology (NIST). These statistical tests comprised several fundamental tests that were performed to evaluate the random number trains for their utilization in practical cryptographic applications. We have generated 230 random number trains consisting of 20, 000-bits by using the superconductive physical random number generator fabricated by the SRL 2.5kA/cm2 Nb standard process. The generated random number trains passed all the fundamental statistical tests. This result indicates that the superconductive random number generator can be sufficiently utilized in practical applications.
Bias-free true random-number generator.
Wei, Wei; Guo, Hong
2009-06-15
We propose what we believe to be a new approach to nondeterministic random-number generation. The randomness originated from the uncorrelated nature of consecutive laser pulses with Poissonian photon statistics and that of photon number detections is used to generate random bit, and the von Neumann correction method is used to extract the final random bit. This method is proved to be bias free in randomness generation, provided that the single photon detections are mutually independent. Further, it has the advantage in fast random bit generation, since no postprocessing is needed. A true random-number generator based on this method is realized, and its randomness is tested and guaranteed using three statistical test batteries. PMID:19529733
Effects of regular switching between languages during random number generation.
Strenge, Hans; Böhm, Jessica
2005-04-01
Random number generation is a task that engages working memory and executive processes within the domain of number representation. In the present study we address the role of language in number processing by switching languages during random number generation (numbers 1-9), using German (L1) and English (L2), and alternating L1/L2. Results indicate large correspondence between performance in L1 and L2. In contrast to nonswitching performance, randomization with alternating languages showed a significant increase of omitted responses, whereas the random sequences were less stereotyped, showing significantly less repetition avoidance and cycling behavior. During an intentional switch between languages, errors in language sequence appeared in 23% of responses on the average, independently of the quality of randomization but associated with a clear persistence of L2. These results indicate that random number generation is more closely linked to auditory-phonological representation of numerals than to visual arabic notation. PMID:15974362
Quantum random number generation for loophole-free Bell tests
NASA Astrophysics Data System (ADS)
Mitchell, Morgan; Abellan, Carlos; Amaya, Waldimar
2015-05-01
We describe the generation of quantum random numbers at multi-Gbps rates, combined with real-time randomness extraction, to give very high purity random numbers based on quantum events at most tens of ns in the past. The system satisfies the stringent requirements of quantum non-locality tests that aim to close the timing loophole. We describe the generation mechanism using spontaneous-emission-driven phase diffusion in a semiconductor laser, digitization, and extraction by parity calculation using multi-GHz logic chips. We pay special attention to experimental proof of the quality of the random numbers and analysis of the randomness extraction. In contrast to widely-used models of randomness generators in the computer science literature, we argue that randomness generation by spontaneous emission can be extracted from a single source.
SPRNG Scalable Parallel Random Number Generator LIbrary
Energy Science and Technology Software Center (ESTSC)
2010-03-16
This revision corrects some errors in SPRNG 1. Users of newer SPRNG versions can obtain the corrected files and build their version with it. This version also improves the scalability of some of the application-based tests in the SPRNG test suite. It also includes an interface to a parallel Mersenne Twister, so that if users install the Mersenne Twister, then they can test this generator with the SPRNG test suite and also use some SPRNGmore » features with that generator.« less
Humans cannot consciously generate random numbers sequences: Polemic study.
Figurska, Małgorzata; Stańczyk, Maciej; Kulesza, Kamil
2008-01-01
It is widely believed, that randomness exists in Nature. In fact such an assumption underlies many scientific theories and is embedded in the foundations of quantum mechanics. Assuming that this hypothesis is valid one can use natural phenomena, like radioactive decay, to generate random numbers. Today, computers are capable of generating the so-called pseudorandom numbers. Such series of numbers are only seemingly random (bias in the randomness quality can be observed). Question whether people can produce random numbers, has been investigated by many scientists in the recent years. The paper "Humans can consciously generate random numbers sequences..." published recently in Medical Hypotheses made claims that were in many ways contrary to state of art; it also stated far-reaching hypotheses. So, we decided to repeat the experiments reported, with special care being taken of proper laboratory procedures. Here, we present the results and discuss possible implications in computer and other sciences. PMID:17888582
RNGAVXLIB: Program library for random number generation, AVX realization
NASA Astrophysics Data System (ADS)
Guskova, M. S.; Barash, L. Yu.; Shchur, L. N.
2016-03-01
We present the random number generator (RNG) library RNGAVXLIB, which contains fast AVX realizations of a number of modern random number generators, and also the abilities to jump ahead inside a RNG sequence and to initialize up to 1019 independent random number streams with block splitting method. Fast AVX implementations produce exactly the same output sequences as the original algorithms. Usage of AVX vectorization allows to substantially improve performance of the generators. The new realizations are up to 2 times faster than the SSE realizations implemented in the previous version of the library (Barash and Shchur, 2013), and up to 40 times faster compared to the original algorithms written in ANSI C.
Pseudo-random number generator for the Sigma 5 computer
NASA Technical Reports Server (NTRS)
Carroll, S. N.
1983-01-01
A technique is presented for developing a pseudo-random number generator based on the linear congruential form. The two numbers used for the generator are a prime number and a corresponding primitive root, where the prime is the largest prime number that can be accurately represented on a particular computer. The primitive root is selected by applying Marsaglia's lattice test. The technique presented was applied to write a random number program for the Sigma 5 computer. The new program, named S:RANDOM1, is judged to be superior to the older program named S:RANDOM. For applications requiring several independent random number generators, a table is included showing several acceptable primitive roots. The technique and programs described can be applied to any computer having word length different from that of the Sigma 5.
Quantum Random Number Generation Using a Quanta Image Sensor.
Amri, Emna; Felk, Yacine; Stucki, Damien; Ma, Jiaju; Fossum, Eric R
2016-01-01
A new quantum random number generation method is proposed. The method is based on the randomness of the photon emission process and the single photon counting capability of the Quanta Image Sensor (QIS). It has the potential to generate high-quality random numbers with remarkable data output rate. In this paper, the principle of photon statistics and theory of entropy are discussed. Sample data were collected with QIS jot device, and its randomness quality was analyzed. The randomness assessment method and results are discussed. PMID:27367698
Quantum Random Number Generation Using a Quanta Image Sensor
Amri, Emna; Felk, Yacine; Stucki, Damien; Ma, Jiaju; Fossum, Eric R.
2016-01-01
A new quantum random number generation method is proposed. The method is based on the randomness of the photon emission process and the single photon counting capability of the Quanta Image Sensor (QIS). It has the potential to generate high-quality random numbers with remarkable data output rate. In this paper, the principle of photon statistics and theory of entropy are discussed. Sample data were collected with QIS jot device, and its randomness quality was analyzed. The randomness assessment method and results are discussed. PMID:27367698
A hybrid-type quantum random number generator
NASA Astrophysics Data System (ADS)
Hai-Qiang, Ma; Wu, Zhu; Ke-Jin, Wei; Rui-Xue, Li; Hong-Wei, Liu
2016-05-01
This paper proposes a well-performing hybrid-type truly quantum random number generator based on the time interval between two independent single-photon detection signals, which is practical and intuitive, and generates the initial random number sources from a combination of multiple existing random number sources. A time-to-amplitude converter and multichannel analyzer are used for qualitative analysis to demonstrate that each and every step is random. Furthermore, a carefully designed data acquisition system is used to obtain a high-quality random sequence. Our scheme is simple and proves that the random number bit rate can be dramatically increased to satisfy practical requirements. Project supported by the National Natural Science Foundation of China (Grant Nos. 61178010 and 11374042), the Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications), China, and the Fundamental Research Funds for the Central Universities of China (Grant No. bupt2014TS01).
Quantum random number generator based on photonic emission in semiconductors.
Stipcević, M; Rogina, B Medved
2007-04-01
We report upon the realization of a novel fast nondeterministic random number generator whose randomness relies on the intrinsic randomness of the quantum physical processes of photonic emission in semiconductors and subsequent detection by the photoelectric effect. Timing information of detected photons is used to generate binary random digits-bits. The bit extraction method based on the restartable clock method theoretically eliminates both bias and autocorrelation while reaching efficiency of almost 0.5 bits per random event. A prototype has been built and statistically tested. PMID:17477690
NASA Astrophysics Data System (ADS)
Miszczak, Jarosław Adam
2013-01-01
The presented package for the Mathematica computing system allows the harnessing of quantum random number generators (QRNG) for investigating the statistical properties of quantum states. The described package implements a number of functions for generating random states. The new version of the package adds the ability to use the on-line quantum random number generator service and implements new functions for retrieving lists of random numbers. Thanks to the introduced improvements, the new version provides faster access to high-quality sources of random numbers and can be used in simulations requiring large amount of random data. New version program summaryProgram title: TRQS Catalogue identifier: AEKA_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEKA_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 18 134 No. of bytes in distributed program, including test data, etc.: 2 520 49 Distribution format: tar.gz Programming language: Mathematica, C. Computer: Any supporting Mathematica in version 7 or higher. Operating system: Any platform supporting Mathematica; tested with GNU/Linux (32 and 64 bit). RAM: Case-dependent Supplementary material: Fig. 1 mentioned below can be downloaded. Classification: 4.15. External routines: Quantis software library (http://www.idquantique.com/support/quantis-trng.html) Catalogue identifier of previous version: AEKA_v1_0 Journal reference of previous version: Comput. Phys. Comm. 183(2012)118 Does the new version supersede the previous version?: Yes Nature of problem: Generation of random density matrices and utilization of high-quality random numbers for the purpose of computer simulation. Solution method: Use of a physical quantum random number generator and an on-line service providing access to the source of true random
Social Noise: Generating Random Numbers from Twitter Streams
NASA Astrophysics Data System (ADS)
Fernández, Norberto; Quintas, Fernando; Sánchez, Luis; Arias, Jesús
2015-12-01
Due to the multiple applications of random numbers in computer systems (cryptography, online gambling, computer simulation, etc.) it is important to have mechanisms to generate these numbers. True Random Number Generators (TRNGs) are commonly used for this purpose. TRNGs rely on non-deterministic sources to generate randomness. Physical processes (like noise in semiconductors, quantum phenomenon, etc.) play this role in state of the art TRNGs. In this paper, we depart from previous work and explore the possibility of defining social TRNGs using the stream of public messages of the microblogging service Twitter as randomness source. Thus, we define two TRNGs based on Twitter stream information and evaluate them using the National Institute of Standards and Technology (NIST) statistical test suite. The results of the evaluation confirm the feasibility of the proposed approach.
Brain potentials index executive functions during random number generation.
Joppich, Gregor; Däuper, Jan; Dengler, Reinhard; Johannes, Sönke; Rodriguez-Fornells, Antoni; Münte, Thomas F
2004-06-01
The generation of random sequences is considered to tax different executive functions. To explore the involvement of these functions further, brain potentials were recorded in 16 healthy young adults while either engaging in random number generation (RNG) by pressing the number keys on a computer keyboard in a random sequence or in ordered number generation (ONG) necessitating key presses in the canonical order. Key presses were paced by an external auditory stimulus to yield either fast (1 press/800 ms) or slow (1 press/1300 ms) sequences in separate runs. Attentional demands of random and ordered tasks were assessed by the introduction of a secondary task (key-press to a target tone). The P3 amplitude to the target tone of this secondary task was reduced during RNG, reflecting the greater consumption of attentional resources during RNG. Moreover, RNG led to a left frontal negativity peaking 140 ms after the onset of the pacing stimulus, whenever the subjects produced a true random response. This negativity could be attributed to the left dorsolateral prefrontal cortex and was absent when numbers were repeated. This negativity was interpreted as an index for the inhibition of habitual responses. Finally, in response locked ERPs a negative component was apparent peaking about 50 ms after the key-press that was more prominent during RNG. Source localization suggested a medial frontal source. This effect was tentatively interpreted as a reflection of the greater monitoring demands during random sequence generation. PMID:15140558
Two-bit quantum random number generator based on photon-number-resolving detection.
Jian, Yi; Ren, Min; Wu, E; Wu, Guang; Zeng, Heping
2011-07-01
Here we present a new fast two-bit quantum random number generator based on the intrinsic randomness of the quantum physical phenomenon of photon statistics of coherent light source. Two-bit random numbers were generated according to the number of detected photons in each light pulse by a photon-number-resolving detector. Poissonian photon statistics of the coherent light source guaranteed the complete randomness of the bit sequences. Multi-bit true random numbers were generated for the first time based on the multi-photon events from a coherent light source. PMID:21806174
Accelerating Pseudo-Random Number Generator for MCNP on GPU
NASA Astrophysics Data System (ADS)
Gong, Chunye; Liu, Jie; Chi, Lihua; Hu, Qingfeng; Deng, Li; Gong, Zhenghu
2010-09-01
Pseudo-random number generators (PRNG) are intensively used in many stochastic algorithms in particle simulations, artificial neural networks and other scientific computation. The PRNG in Monte Carlo N-Particle Transport Code (MCNP) requires long period, high quality, flexible jump and fast enough. In this paper, we implement such a PRNG for MCNP on NVIDIA's GTX200 Graphics Processor Units (GPU) using CUDA programming model. Results shows that 3.80 to 8.10 times speedup are achieved compared with 4 to 6 cores CPUs and more than 679.18 million double precision random numbers can be generated per second on GPU.
Ultrafast quantum random number generation based on quantum phase fluctuations.
Xu, Feihu; Qi, Bing; Ma, Xiongfeng; Xu, He; Zheng, Haoxuan; Lo, Hoi-Kwong
2012-05-21
A quantum random number generator (QRNG) can generate true randomness by exploiting the fundamental indeterminism of quantum mechanics. Most approaches to QRNG employ single-photon detection technologies and are limited in speed. Here, we experimentally demonstrate an ultrafast QRNG at a rate over 6 Gbits/s based on the quantum phase fluctuations of a laser operating near threshold. Moreover, we consider a potential adversary who has partial knowledge on the raw data and discuss how one can rigorously remove such partial knowledge with postprocessing. We quantify the quantum randomness through min-entropy by modeling our system and employ two randomness extractors--Trevisan's extractor and Toeplitz-hashing--to distill the randomness, which is information-theoretically provable. The simplicity and high-speed of our experimental setup show the feasibility of a robust, low-cost, high-speed QRNG. PMID:22714224
GASPRNG: GPU accelerated scalable parallel random number generator library
NASA Astrophysics Data System (ADS)
Gao, Shuang; Peterson, Gregory D.
2013-04-01
Graphics processors represent a promising technology for accelerating computational science applications. Many computational science applications require fast and scalable random number generation with good statistical properties, so they use the Scalable Parallel Random Number Generators library (SPRNG). We present the GPU Accelerated SPRNG library (GASPRNG) to accelerate SPRNG in GPU-based high performance computing systems. GASPRNG includes code for a host CPU and CUDA code for execution on NVIDIA graphics processing units (GPUs) along with a programming interface to support various usage models for pseudorandom numbers and computational science applications executing on the CPU, GPU, or both. This paper describes the implementation approach used to produce high performance and also describes how to use the programming interface. The programming interface allows a user to be able to use GASPRNG the same way as SPRNG on traditional serial or parallel computers as well as to develop tightly coupled programs executing primarily on the GPU. We also describe how to install GASPRNG and use it. To help illustrate linking with GASPRNG, various demonstration codes are included for the different usage models. GASPRNG on a single GPU shows up to 280x speedup over SPRNG on a single CPU core and is able to scale for larger systems in the same manner as SPRNG. Because GASPRNG generates identical streams of pseudorandom numbers as SPRNG, users can be confident about the quality of GASPRNG for scalable computational science applications. Catalogue identifier: AEOI_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEOI_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: UTK license. No. of lines in distributed program, including test data, etc.: 167900 No. of bytes in distributed program, including test data, etc.: 1422058 Distribution format: tar.gz Programming language: C and CUDA. Computer: Any PC or
Random number generation in native and foreign languages.
Strenge, Hans; Bohm, Jessica
2004-06-01
The effects of different levels of language proficiency on random number generation were examined in this study. 16 healthy right-handed students (7 women, 9 men; aged 22 to 25 years, M=23.8, SD=.83) attempted to generate a random sequence of the digits 1 to 9 at pacing frequencies of 1, 1.5, and 2 Hz. Randomization was done in German (native language L1), English (first foreign language L2), and French (second foreign language L3). There was a pattern of redundancy and seriation tendencies, increasing with speed of generation for all languages (L1-L3). While using L2 and L3, responses slowed and the number of errors committed increased. Further, there was a peculiar pattern of dissociation in nonrandom performance with an increase of habitual counting in ones and a strong reduction of counting in twos. All effects were most pronounced when subjects used L3 and 2-Hz pacing rates. Slowing and nonrandomness was not correlated with self-assessment parameters regarding language proficiency. We suggest that in a task involving number activation in a nonnative language, lack of proficiency will interfere with random number generation, leading to interruptions and rule breaking, at least when reaching the limits of attentional capacity at higher pacing rates. PMID:15291201
Analysis of entropy extraction efficiencies in random number generation systems
NASA Astrophysics Data System (ADS)
Wang, Chao; Wang, Shuang; Chen, Wei; Yin, Zhen-Qiang; Han, Zheng-Fu
2016-05-01
Random numbers (RNs) have applications in many areas: lottery games, gambling, computer simulation, and, most importantly, cryptography [N. Gisin et al., Rev. Mod. Phys. 74 (2002) 145]. In cryptography theory, the theoretical security of the system calls for high quality RNs. Therefore, developing methods for producing unpredictable RNs with adequate speed is an attractive topic. Early on, despite the lack of theoretical support, pseudo RNs generated by algorithmic methods performed well and satisfied reasonable statistical requirements. However, as implemented, those pseudorandom sequences were completely determined by mathematical formulas and initial seeds, which cannot introduce extra entropy or information. In these cases, “random” bits are generated that are not at all random. Physical random number generators (RNGs), which, in contrast to algorithmic methods, are based on unpredictable physical random phenomena, have attracted considerable research interest. However, the way that we extract random bits from those physical entropy sources has a large influence on the efficiency and performance of the system. In this manuscript, we will review and discuss several randomness extraction schemes that are based on radiation or photon arrival times. We analyze the robustness, post-processing requirements and, in particular, the extraction efficiency of those methods to aid in the construction of efficient, compact and robust physical RNG systems.
Strong experimental guarantees in ultrafast quantum random number generation
NASA Astrophysics Data System (ADS)
Mitchell, Morgan W.; Abellan, Carlos; Amaya, Waldimar
2015-01-01
We describe a methodology and standard of proof for experimental claims of quantum random-number generation (QRNG), analogous to well-established methods from precision measurement. For appropriately constructed physical implementations, lower bounds on the quantum contribution to the average min-entropy can be derived from measurements on the QRNG output. Given these bounds, randomness extractors allow generation of nearly perfect "ɛ -random" bit streams. An analysis of experimental uncertainties then gives experimentally derived confidence levels on the ɛ randomness of these sequences. We demonstrate the methodology by application to phase-diffusion QRNG, driven by spontaneous emission as a trusted randomness source. All other factors, including classical phase noise, amplitude fluctuations, digitization errors, and correlations due to finite detection bandwidth, are treated with paranoid caution, i.e., assuming the worst possible behaviors consistent with observations. A data-constrained numerical optimization of the distribution of untrusted parameters is used to lower bound the average min-entropy. Under this paranoid analysis, the QRNG remains efficient, generating at least 2.3 quantum random bits per symbol with 8-bit digitization and at least 0.83 quantum random bits per symbol with binary digitization at a confidence level of 0.999 93. The result demonstrates ultrafast QRNG with strong experimental guarantees.
Quantum random number generators and their applications in cryptography
NASA Astrophysics Data System (ADS)
Stipcevic, Mario
2012-06-01
Random number generators (RNG) are an important resource in many areas: cryptography (both quantum and classical), probabilistic computation (Monte Carlo methods), numerical simulations, industrial testing and labeling, hazard games, scientific research etc. Because today's computers are deterministic, they can not create random numbers unless complemented with a physical RNG. Randomness of a RNG can be defined and scientifically characterized and measured. Especially valuable is the information-theoretic provable RNG which, at state of the art, seem to be possible only by harvest of randomness inherent to certain (simple) quantum systems and such a generator we call Quantum RNG (QRNG). On the other hand, current industry standards dictate use of RNGs based on free running oscillators (FRO) whose randomness is derived from electronics noise present in logic circuits and which, although quantum in nature, cannot be strictly proven. This approach is currently used in FPGA and ASIC chips. We compare weak and strong aspects of the two approaches for use in cryptography and in general. We also give an alternative definition of randomness, discuss usage of single photon detectors in realization of QRNGs and give several examples where QRNG can significantly improve security of a cryptographic system.
Postprocessing for quantum random-number generators: Entropy evaluation and randomness extraction
NASA Astrophysics Data System (ADS)
Ma, Xiongfeng; Xu, Feihu; Xu, He; Tan, Xiaoqing; Qi, Bing; Lo, Hoi-Kwong
2013-06-01
Quantum random-number generators (QRNGs) can offer a means to generate information-theoretically provable random numbers, in principle. In practice, unfortunately, the quantum randomness is inevitably mixed with classical randomness due to classical noises. To distill this quantum randomness, one needs to quantify the randomness of the source and apply a randomness extractor. Here, we propose a generic framework for evaluating quantum randomness of real-life QRNGs by min-entropy, and apply it to two different existing quantum random-number systems in the literature. Moreover, we provide a guideline of QRNG data postprocessing for which we implement two information-theoretically provable randomness extractors: Toeplitz-hashing extractor and Trevisan's extractor.
NASA Astrophysics Data System (ADS)
Barash, L. Yu.; Shchur, L. N.
2013-10-01
In this update, we present the new version of the random number generator (RNG) library RNGSSELIB, which, in particular, contains fast SSE realizations of a number of modern and most reliable generators [1]. The new features are: (i) Fortran compatibility and examples of using the library in Fortran; (ii) new modern and reliable generators; (iii) the abilities to jump ahead inside a RNG sequence and to initialize up to 1019 independent random number streams with block splitting method. Summary of revisions: We added Fortran compatibility and examples of using the library in Fortran for each of the generators. New modern and reliable generators GM29, GM55.4, GQ58.1, GQ58.3, and GQ58.4, which were introduced in [5] were added to the library. The ability to jump ahead inside a RNG sequence and to initialize independent random number streams with block splitting method are added for each of the RNGs. Restrictions: For SSE realizations of the generators, the Intel or AMD CPU supporting SSE2 command set is required. In order to use the SSE realization for the lfsr113 generator, the CPU must support the SSE4.1 command set. Additional comments: The function call interface has been slightly modified compared to the previous version in order to support Fortran compatibility. For each of the generators, RNGSSELIB supports the following functions, where rng should be replaced by the particular name of the RNG: void rng_skipahead_(rng_state* state, unsigned long long offset); void rng_init_(rng_state* state); void rng_init_sequence_(rng_state* state,unsigned long long SequenceNumber); unsigned int rng_generate_(rng_state* state); float rng_generate_uniform_float_(rng_state* state); unsigned int rng_sse_generate_(rng_sse_state* state); void rng_get_sse_state_(rng_state* state,rng_sse_state* sse_state); void rng_print_state_(rng_state* state); void rng_print_sse_state_(rng_sse_state* state); There are a few peculiarities for some of the RNGs. For example, the function void mt
Implementing Quality Control on a Random Number Stream to Improve a Stochastic Weather Generator
Technology Transfer Automated Retrieval System (TEKTRAN)
For decades stochastic modelers have used computerized random number generators to produce random numeric sequences fitting a specified statistical distribution. Unfortunately, none of the random number generators we tested satisfactorily produced the target distribution. The result is generated d...
Quantum Statistical Testing of a Quantum Random Number Generator
Humble, Travis S
2014-01-01
The unobservable elements in a quantum technology, e.g., the quantum state, complicate system verification against promised behavior. Using model-based system engineering, we present methods for verifying the opera- tion of a prototypical quantum random number generator. We begin with the algorithmic design of the QRNG followed by the synthesis of its physical design requirements. We next discuss how quantum statistical testing can be used to verify device behavior as well as detect device bias. We conclude by highlighting how system design and verification methods must influence effort to certify future quantum technologies.
Strenge, Hans; Rogge, Carolin
2010-04-01
The effects of different instructions on verbal random number generation were examined in 40 healthy students who attempted to generate random sequences of the digits 1 to 6. Two groups of 20 received different instructions with alternative numerical representations. The Symbolic group (Arabic digits) was instructed to randomize while continuously using the analogy of selecting and replacing numbered balls from a hat, whereas the Nonsymbolic group (arrays of dots) was instructed to imagine repeatedly throwing a die. Participants asked for self-reports on their strategies reported spontaneously occurring visuospatial imagination of a mental number line (42%), or imagining throwing a die (23%). Individual number representation was not affected by the initial instruction. There were no differences in randomization performance by group. Comprehensive understanding of the nature of the randomization task requires considering individual differences in construction of mental models. PMID:20499555
Statistical Tests of the Apple IIe Random Number Generator Yield Suggestions from Generator Seeding.
ERIC Educational Resources Information Center
Gleason, John M.
1988-01-01
Discusses flaws in the Apple IIe Applesoft random number generator, RND, and reports results of frequency and serial correlation tests of the generator. Suggestions of seeds that yield sequences of numbers which pass fundamental screening tests for randomness are presented. (Author/LRW)
FPGA Implementation of Metastability-Based True Random Number Generator
NASA Astrophysics Data System (ADS)
Hata, Hisashi; Ichikawa, Shuichi
True random number generators (TRNGs) are important as a basis for computer security. Though there are some TRNGs composed of analog circuit, the use of digital circuits is desired for the application of TRNGs to logic LSIs. Some of the digital TRNGs utilize jitter in free-running ring oscillators as a source of entropy, which consume large power. Another type of TRNG exploits the metastability of a latch to generate entropy. Although this kind of TRNG has been mostly implemented with full-custom LSI technology, this study presents an implementation based on common FPGA technology. Our TRNG is comprised of logic gates only, and can be integrated in any kind of logic LSI. The RS latch in our TRNG is implemented as a hard-macro to guarantee the quality of randomness by minimizing the signal skew and load imbalance of internal nodes. To improve the quality and throughput, the output of 64-256 latches are XOR'ed. The derived design was verified on a Xilinx Virtex-4 FPGA (XC4VFX20), and passed NIST statistical test suite without post-processing. Our TRNG with 256 latches occupies 580 slices, while achieving 12.5Mbps throughput.
Maximization of Extractable Randomness in a Quantum Random-Number Generator
NASA Astrophysics Data System (ADS)
Haw, J. Y.; Assad, S. M.; Lance, A. M.; Ng, N. H. Y.; Sharma, V.; Lam, P. K.; Symul, T.
2015-05-01
The generation of random numbers via quantum processes is an efficient and reliable method to obtain true indeterministic random numbers that are of vital importance to cryptographic communication and large-scale computer modeling. However, in realistic scenarios, the raw output of a quantum random-number generator is inevitably tainted by classical technical noise. The integrity of the device can be compromised if this noise is tampered with or even controlled by some malicious party. To safeguard against this, we propose and experimentally demonstrate an approach that produces side-information-independent randomness that is quantified by min-entropy conditioned on this classical noise. We present a method for maximizing the conditional min entropy of the number sequence generated from a given quantum-to-classical-noise ratio. The detected photocurrent in our experiment is shown to have a real-time random-number generation rate of 14 (Mb i t /s )/MHz . The spectral response of the detection system shows the potential to deliver more than 70 Gbit /s of random numbers in our experimental setup.
Statistical evaluation of PACSTAT random number generation capabilities
Piepel, G.F.; Toland, M.R.; Harty, H.; Budden, M.J.; Bartley, C.L.
1988-05-01
This report summarizes the work performed in verifying the general purpose Monte Carlo driver-program PACSTAT. The main objective of the work was to verify the performance of PACSTAT's random number generation capabilities. Secondary objectives were to document (using controlled configuration management procedures) changes made in PACSTAT at Pacific Northwest Laboratory, and to assure that PACSTAT input and output files satisfy quality assurance traceability constraints. Upon receipt of the PRIME version of the PACSTAT code from the Basalt Waste Isolation Project, Pacific Northwest Laboratory staff converted the code to run on Digital Equipment Corporation (DEC) VAXs. The modifications to PACSTAT were implemented using the WITNESS configuration management system, with the modifications themselves intended to make the code as portable as possible. Certain modifications were made to make the PACSTAT input and output files conform to quality assurance traceability constraints. 10 refs., 17 figs., 6 tabs.
Manipulating attentional load in sequence learning through random number generation
Wierzchoń, Michał; Gaillard, Vinciane; Asanowicz, Dariusz; Cleeremans, Axel
2012-01-01
Implicit learning is often assumed to be an effortless process. However, some artificial grammar learning and sequence learning studies using dual tasks seem to suggest that attention is essential for implicit learning to occur. This discrepancy probably results from the specific type of secondary task that is used. Different secondary tasks may engage attentional resources differently and therefore may bias performance on the primary task in different ways. Here, we used a random number generation (RNG) task, which may allow for a closer monitoring of a participant’s engagement in a secondary task than the popular secondary task in sequence learning studies: tone counting (TC). In the first two experiments, we investigated the interference associated with performing RNG concurrently with a serial reaction time (SRT) task. In a third experiment, we compared the effects of RNG and TC. In all three experiments, we directly evaluated participants’ knowledge of the sequence with a subsequent sequence generation task. Sequence learning was consistently observed in all experiments, but was impaired under dual-task conditions. Most importantly, our data suggest that RNG is more demanding and impairs learning to a greater extent than TC. Nevertheless, we failed to observe effects of the secondary task in subsequent sequence generation. Our studies indicate that RNG is a promising task to explore the involvement of attention in the SRT task. PMID:22723816
Efficient Raman generation in a waveguide: A route to ultrafast quantum random number generation
England, D. G.; Bustard, P. J.; Moffatt, D. J.; Nunn, J.; Lausten, R.; Sussman, B. J.
2014-02-03
The inherent uncertainty in quantum mechanics offers a source of true randomness which can be used to produce unbreakable cryptographic keys. We discuss the development of a high-speed random number generator based on the quantum phase fluctuations in spontaneously initiated stimulated Raman scattering (SISRS). We utilize the tight confinement and long interaction length available in a Potassium Titanyl Phosphate waveguide to generate highly efficient SISRS using nanojoule pulse energies, reducing the high pump power requirements of the previous approaches. We measure the random phase of the Stokes output using a simple interferometric setup to yield quantum random numbers at 145 Mbps.
Stipčević, Mario
2016-03-01
In this work, a new type of elementary logic circuit, named random flip-flop (RFF), is proposed, experimentally realized, and studied. Unlike conventional Boolean logic circuits whose action is deterministic and highly reproducible, the action of a RFF is intentionally made maximally unpredictable and, in the proposed realization, derived from a fundamentally random process of emission and detection of light quanta. We demonstrate novel applications of RFF in randomness preserving frequency division, random frequency synthesis, and random number generation. Possible usages of these applications in the information and communication technology, cryptographic hardware, and testing equipment are discussed. PMID:27036825
NASA Astrophysics Data System (ADS)
Stipčević, Mario
2016-03-01
In this work, a new type of elementary logic circuit, named random flip-flop (RFF), is proposed, experimentally realized, and studied. Unlike conventional Boolean logic circuits whose action is deterministic and highly reproducible, the action of a RFF is intentionally made maximally unpredictable and, in the proposed realization, derived from a fundamentally random process of emission and detection of light quanta. We demonstrate novel applications of RFF in randomness preserving frequency division, random frequency synthesis, and random number generation. Possible usages of these applications in the information and communication technology, cryptographic hardware, and testing equipment are discussed.
Efficient and robust quantum random number generation by photon number detection
Applegate, M. J.; Thomas, O.; Dynes, J. F.; Yuan, Z. L.; Shields, A. J.; Ritchie, D. A.
2015-08-17
We present an efficient and robust quantum random number generator based upon high-rate room temperature photon number detection. We employ an electric field-modulated silicon avalanche photodiode, a type of device particularly suited to high-rate photon number detection with excellent photon number resolution to detect, without an applied dead-time, up to 4 photons from the optical pulses emitted by a laser. By both measuring and modeling the response of the detector to the incident photons, we are able to determine the illumination conditions that achieve an optimal bit rate that we show is robust against variation in the photon flux. We extract random bits from the detected photon numbers with an efficiency of 99% corresponding to 1.97 bits per detected photon number yielding a bit rate of 143 Mbit/s, and verify that the extracted bits pass stringent statistical tests for randomness. Our scheme is highly scalable and has the potential of multi-Gbit/s bit rates.
Using Computer-Generated Random Numbers to Calculate the Lifetime of a Comet.
ERIC Educational Resources Information Center
Danesh, Iraj
1991-01-01
An educational technique to calculate the lifetime of a comet using software-generated random numbers is introduced to undergraduate physiques and astronomy students. Discussed are the generation and eligibility of the required random numbers, background literature related to the problem, and the solution to the problem using random numbers.…
Bias-free true random number generation using superconducting nanowire single-photon detectors
NASA Astrophysics Data System (ADS)
He, Yuhao; Zhang, Weijun; Zhou, Hui; You, Lixing; Lv, Chaolin; Zhang, Lu; Liu, Xiaoyu; Wu, Junjie; Chen, Sijing; Ren, Min; Wang, Zhen; Xie, Xiaoming
2016-08-01
We demonstrate a bias-free true random number generator (TRNG) based on single photon detection using superconducting nanowire single photon detectors (SNSPDs). By comparing the photon detection signals of two consecutive laser pulses and extracting the random bits by the von Neumann correction method, we achieved a random number generation efficiency of 25% (a generation rate of 3.75 Mbit s‑1 at a system clock rate of 15 MHz). Using a multi-channel superconducting nanowire single photon detector system with controllable pulse signal amplitudes, we detected the single photons with photon number resolution and positional sensitivity, which could further increase the random number generation efficiency. In a three-channel SNSPD system, the random number bit generation efficiency was improved to 75%, corresponding to a generation rate of 7.5 Mbit s‑1 with a 10 MHz system clock rate. All of the generated random numbers successfully passed the statistical test suite.
Multi-bit quantum random number generation by measuring positions of arrival photons
NASA Astrophysics Data System (ADS)
Yan, Qiurong; Zhao, Baosheng; Liao, Qinghong; Zhou, Nanrun
2014-10-01
We report upon the realization of a novel multi-bit optical quantum random number generator by continuously measuring the arrival positions of photon emitted from a LED using MCP-based WSA photon counting imaging detector. A spatial encoding method is proposed to extract multi-bits random number from the position coordinates of each detected photon. The randomness of bits sequence relies on the intrinsic randomness of the quantum physical processes of photonic emission and subsequent photoelectric conversion. A prototype has been built and the random bit generation rate could reach 8 Mbit/s, with random bit generation efficiency of 16 bits per detected photon. FPGA implementation of Huffman coding is proposed to reduce the bias of raw extracted random bits. The random numbers passed all tests for physical random number generator.
Multi-bit quantum random number generation by measuring positions of arrival photons.
Yan, Qiurong; Zhao, Baosheng; Liao, Qinghong; Zhou, Nanrun
2014-10-01
We report upon the realization of a novel multi-bit optical quantum random number generator by continuously measuring the arrival positions of photon emitted from a LED using MCP-based WSA photon counting imaging detector. A spatial encoding method is proposed to extract multi-bits random number from the position coordinates of each detected photon. The randomness of bits sequence relies on the intrinsic randomness of the quantum physical processes of photonic emission and subsequent photoelectric conversion. A prototype has been built and the random bit generation rate could reach 8 Mbit/s, with random bit generation efficiency of 16 bits per detected photon. FPGA implementation of Huffman coding is proposed to reduce the bias of raw extracted random bits. The random numbers passed all tests for physical random number generator. PMID:25362380
Multi-bit quantum random number generation by measuring positions of arrival photons
Yan, Qiurong; Zhao, Baosheng; Liao, Qinghong; Zhou, Nanrun
2014-10-15
We report upon the realization of a novel multi-bit optical quantum random number generator by continuously measuring the arrival positions of photon emitted from a LED using MCP-based WSA photon counting imaging detector. A spatial encoding method is proposed to extract multi-bits random number from the position coordinates of each detected photon. The randomness of bits sequence relies on the intrinsic randomness of the quantum physical processes of photonic emission and subsequent photoelectric conversion. A prototype has been built and the random bit generation rate could reach 8 Mbit/s, with random bit generation efficiency of 16 bits per detected photon. FPGA implementation of Huffman coding is proposed to reduce the bias of raw extracted random bits. The random numbers passed all tests for physical random number generator.
A generator for unique quantum random numbers based on vacuum states
NASA Astrophysics Data System (ADS)
Gabriel, Christian; Wittmann, Christoffer; Sych, Denis; Dong, Ruifang; Mauerer, Wolfgang; Andersen, Ulrik L.; Marquardt, Christoph; Leuchs, Gerd
2010-10-01
Random numbers are a valuable component in diverse applications that range from simulations over gambling to cryptography. The quest for true randomness in these applications has engendered a large variety of different proposals for producing random numbers based on the foundational unpredictability of quantum mechanics. However, most approaches do not consider that a potential adversary could have knowledge about the generated numbers, so the numbers are not verifiably random and unique. Here we present a simple experimental setup based on homodyne measurements that uses the purity of a continuous-variable quantum vacuum state to generate unique random numbers. We use the intrinsic randomness in measuring the quadratures of a mode in the lowest energy vacuum state, which cannot be correlated to any other state. The simplicity of our source, combined with its verifiably unique randomness, are important attributes for achieving high-reliability, high-speed and low-cost quantum random number generators.
Novel pseudo-random number generator based on quantum random walks
NASA Astrophysics Data System (ADS)
Yang, Yu-Guang; Zhao, Qian-Qian
2016-02-01
In this paper, we investigate the potential application of quantum computation for constructing pseudo-random number generators (PRNGs) and further construct a novel PRNG based on quantum random walks (QRWs), a famous quantum computation model. The PRNG merely relies on the equations used in the QRWs, and thus the generation algorithm is simple and the computation speed is fast. The proposed PRNG is subjected to statistical tests such as NIST and successfully passed the test. Compared with the representative PRNG based on quantum chaotic maps (QCM), the present QRWs-based PRNG has some advantages such as better statistical complexity and recurrence. For example, the normalized Shannon entropy and the statistical complexity of the QRWs-based PRNG are 0.999699456771172 and 1.799961178212329e-04 respectively given the number of 8 bits-words, say, 16Mbits. By contrast, the corresponding values of the QCM-based PRNG are 0.999448131481064 and 3.701210794388818e-04 respectively. Thus the statistical complexity and the normalized entropy of the QRWs-based PRNG are closer to 0 and 1 respectively than those of the QCM-based PRNG when the number of words of the analyzed sequence increases. It provides a new clue to construct PRNGs and also extends the applications of quantum computation.
Novel pseudo-random number generator based on quantum random walks
Yang, Yu-Guang; Zhao, Qian-Qian
2016-01-01
In this paper, we investigate the potential application of quantum computation for constructing pseudo-random number generators (PRNGs) and further construct a novel PRNG based on quantum random walks (QRWs), a famous quantum computation model. The PRNG merely relies on the equations used in the QRWs, and thus the generation algorithm is simple and the computation speed is fast. The proposed PRNG is subjected to statistical tests such as NIST and successfully passed the test. Compared with the representative PRNG based on quantum chaotic maps (QCM), the present QRWs-based PRNG has some advantages such as better statistical complexity and recurrence. For example, the normalized Shannon entropy and the statistical complexity of the QRWs-based PRNG are 0.999699456771172 and 1.799961178212329e-04 respectively given the number of 8 bits-words, say, 16Mbits. By contrast, the corresponding values of the QCM-based PRNG are 0.999448131481064 and 3.701210794388818e-04 respectively. Thus the statistical complexity and the normalized entropy of the QRWs-based PRNG are closer to 0 and 1 respectively than those of the QCM-based PRNG when the number of words of the analyzed sequence increases. It provides a new clue to construct PRNGs and also extends the applications of quantum computation. PMID:26842402
Novel pseudo-random number generator based on quantum random walks.
Yang, Yu-Guang; Zhao, Qian-Qian
2016-01-01
In this paper, we investigate the potential application of quantum computation for constructing pseudo-random number generators (PRNGs) and further construct a novel PRNG based on quantum random walks (QRWs), a famous quantum computation model. The PRNG merely relies on the equations used in the QRWs, and thus the generation algorithm is simple and the computation speed is fast. The proposed PRNG is subjected to statistical tests such as NIST and successfully passed the test. Compared with the representative PRNG based on quantum chaotic maps (QCM), the present QRWs-based PRNG has some advantages such as better statistical complexity and recurrence. For example, the normalized Shannon entropy and the statistical complexity of the QRWs-based PRNG are 0.999699456771172 and 1.799961178212329e-04 respectively given the number of 8 bits-words, say, 16Mbits. By contrast, the corresponding values of the QCM-based PRNG are 0.999448131481064 and 3.701210794388818e-04 respectively. Thus the statistical complexity and the normalized entropy of the QRWs-based PRNG are closer to 0 and 1 respectively than those of the QCM-based PRNG when the number of words of the analyzed sequence increases. It provides a new clue to construct PRNGs and also extends the applications of quantum computation. PMID:26842402
a Pseudo-Random Number Generator Employing Multiple RÉNYI Maps
NASA Astrophysics Data System (ADS)
Lui, Oi-Yan; Yuen, Ching-Hung; Wong, Kwok-Wo
2013-11-01
The increasing risk along with the drastic development of multimedia data transmission has raised a big concern on data security. A good pseudo-random number generator is an essential tool in cryptography. In this paper, we propose a novel pseudo-random number generator based on the controlled combination of the outputs of several digitized chaotic Rényi maps. The generated pseudo-random sequences have passed both the NIST 800-22 Revision 1a and the DIEHARD tests. Moreover, simulation results show that the proposed pseudo-random number generator requires less operation time than existing generators and is highly sensitive to the seed.
NASA Astrophysics Data System (ADS)
Lim, Daihyun; Ranasinghe, Damith C.; Devadas, Srinivas; Jamali, Behnam; Abbott, Derek; Cole, Peter H.
2005-05-01
While pseudo random number generators based on computational complexity are widely used for most of cryptographic applications and probabilistic simulations, the generation of true random numbers based on physical randomness is required to guarantee the advanced security of cryptographic systems. In this paper we present a method to exploit manufacturing variations, metastablity, and thermal noise in integrated circuits to generate random numbers. This metastability based physical random number generator provides a compact and low-power solution which can be fabricated using standard IC manufacturing processes. Test-chips were fabricated in TSMC 0.18um process and experimental results show that the generated random bits pass standard randomness tests successfully. The operation of the proposed scheme is robust against environmental changes since it can be re-calibrated to new environmental conditions such as temperature and power supply voltage.
Strenge, Hans; Müller-Deile, Joachim
2007-08-01
Oral random number generation is a widely used neuropsychological task engaging a number of overlapping neural systems of attention, number representation, response generation, and working memory. Although phonological processing is known to be essential for random number generation no information exists on the significance of the auditory feedback of hearing one's own voice on task performance. We therefore examined the influence of auditory feedback in 15 profoundly deaf adults with cochlear implants in a device-on/off experiment. No significant effects of occluding auditory feedback on random number generation were noted, thus supporting an internal response-monitoring model independent of auditory condition. PMID:17691037
Nie, You-Qi; Zhang, Jun Pan, Jian-Wei; Zhang, Hong-Fei; Wang, Jian; Zhang, Zhen; Ma, Xiongfeng
2014-02-03
We present a practical high-speed quantum random number generator, where the timing of single-photon detection relative to an external time reference is measured as the raw data. The bias of the raw data can be substantially reduced compared with the previous realizations. The raw random bit rate of our generator can reach 109 Mbps. We develop a model for the generator and evaluate the min-entropy of the raw data. Toeplitz matrix hashing is applied for randomness extraction, after which the final random bits are able to pass the standard randomness tests.
High-speed quantum-random number generation by continuous measurement of arrival time of photons.
Yan, Qiurong; Zhao, Baosheng; Hua, Zhang; Liao, Qinghong; Yang, Hao
2015-07-01
We demonstrate a novel high speed and multi-bit optical quantum random number generator by continuously measuring arrival time of photons with a common starting point. To obtain the unbiased and post-processing free random bits, the measured photon arrival time is converted into the sum of integral multiple of a fixed period and a phase time. Theoretical and experimental results show that the phase time is an independent and uniform random variable. A random bit extraction method by encoding the phase time is proposed. An experimental setup has been built and the unbiased random bit generation rate could reach 128 Mb/s, with random bit generation efficiency of 8 bits per detected photon. The random numbers passed all tests in the statistical test suite. PMID:26233362
High-speed quantum-random number generation by continuous measurement of arrival time of photons
Yan, Qiurong; Zhao, Baosheng; Hua, Zhang; Liao, Qinghong; Yang, Hao
2015-07-15
We demonstrate a novel high speed and multi-bit optical quantum random number generator by continuously measuring arrival time of photons with a common starting point. To obtain the unbiased and post-processing free random bits, the measured photon arrival time is converted into the sum of integral multiple of a fixed period and a phase time. Theoretical and experimental results show that the phase time is an independent and uniform random variable. A random bit extraction method by encoding the phase time is proposed. An experimental setup has been built and the unbiased random bit generation rate could reach 128 Mb/s, with random bit generation efficiency of 8 bits per detected photon. The random numbers passed all tests in the statistical test suite.
Truly random number generation based on measurement of phase noise of a laser.
Guo, Hong; Tang, Wenzhuo; Liu, Yu; Wei, Wei
2010-05-01
We present a simple approach to realize truly random number generator based on measuring the phase noise of a single-mode vertical cavity surface emitting laser. The true randomness of the quantum phase noise originates from the spontaneous emission of photons and the random bit generation rate is ultimately limited only by the laser linewidth. With the final bit generation rate of 20 Mbit/s, the truly random bit sequence guaranteed by the uncertainty principle of quantum mechanics passes the three standard randomness tests (ENT, Diehard, and NIST Statistical Test Suites). Moreover, a continuously generated random bit sequence, with length up to 14 Gbit, is verified by two additional criteria for its true randomness. PMID:20866215
A novel quantum random number generation algorithm used by smartphone camera
NASA Astrophysics Data System (ADS)
Wu, Nan; Wang, Kun; Hu, Haixing; Song, Fangmin; Li, Xiangdong
2015-05-01
We study an efficient algorithm to extract quantum random numbers (QRN) from the raw data obtained by charge-coupled device (CCD) or complementary metal-oxide semiconductor (CMOS) based sensors, like a camera used in a commercial smartphone. Based on NIST statistical test for random number generators, the proposed algorithm has a high QRN generation rate and high statistical randomness. This algorithm provides a kind of simple, low-priced and reliable devices as a QRN generator for quantum key distribution (QKD) or other cryptographic applications.
Strenge, Hans; Niederberger, Uwe
2008-06-01
The interference effect between Grooved Pegboard task with either hand and the executive task of cued verbal random number generation was investigated. 24 normal right-handed subjects performed each task under separate (single-task) and concurrent (dual-task) conditions. Articulatory suppression was required as an additional secondary task during pegboard performance. Analysis indicated an unambiguous distinction between the two hands. Comparisons of single-task and dual-task conditions showed an asymmetrical pattern of unidirectional interference with no practice effects during pegboard performance. Concurrent performance with nondominant hand but not the dominant hand of random number generation performance became continuously slower. There was no effect of divided attention on pegboard performance. Findings support the idea that the nondominant hand on the pegboard and random number tasks draw from the same processing resources but that for the executive aspect random number generation is more sensitive to changes in allocation of attentional resources. PMID:18712198
The generation of 68 Gbps quantum random number by measuring laser phase fluctuations.
Nie, You-Qi; Huang, Leilei; Liu, Yang; Payne, Frank; Zhang, Jun; Pan, Jian-Wei
2015-06-01
The speed of a quantum random number generator is essential for practical applications, such as high-speed quantum key distribution systems. Here, we push the speed of a quantum random number generator to 68 Gbps by operating a laser around its threshold level. To achieve the rate, not only high-speed photodetector and high sampling rate are needed but also a very stable interferometer is required. A practical interferometer with active feedback instead of common temperature control is developed to meet the requirement of stability. Phase fluctuations of the laser are measured by the interferometer with a photodetector and then digitalized to raw random numbers with a rate of 80 Gbps. The min-entropy of the raw data is evaluated by modeling the system and is used to quantify the quantum randomness of the raw data. The bias of the raw data caused by other signals, such as classical and detection noises, can be removed by Toeplitz-matrix hashing randomness extraction. The final random numbers can pass through the standard randomness tests. Our demonstration shows that high-speed quantum random number generators are ready for practical usage. PMID:26133826
The generation of 68 Gbps quantum random number by measuring laser phase fluctuations
Nie, You-Qi; Liu, Yang; Zhang, Jun Pan, Jian-Wei; Huang, Leilei; Payne, Frank
2015-06-15
The speed of a quantum random number generator is essential for practical applications, such as high-speed quantum key distribution systems. Here, we push the speed of a quantum random number generator to 68 Gbps by operating a laser around its threshold level. To achieve the rate, not only high-speed photodetector and high sampling rate are needed but also a very stable interferometer is required. A practical interferometer with active feedback instead of common temperature control is developed to meet the requirement of stability. Phase fluctuations of the laser are measured by the interferometer with a photodetector and then digitalized to raw random numbers with a rate of 80 Gbps. The min-entropy of the raw data is evaluated by modeling the system and is used to quantify the quantum randomness of the raw data. The bias of the raw data caused by other signals, such as classical and detection noises, can be removed by Toeplitz-matrix hashing randomness extraction. The final random numbers can pass through the standard randomness tests. Our demonstration shows that high-speed quantum random number generators are ready for practical usage.
Loss-tolerant measurement-device-independent quantum random number generation
NASA Astrophysics Data System (ADS)
Cao, Zhu; Zhou, Hongyi; Ma, Xiongfeng
2015-12-01
Quantum random number generators (QRNGs) output genuine random numbers based upon the uncertainty principle. A QRNG contains two parts in general—a randomness source and a readout detector. How to remove detector imperfections has been one of the most important questions in practical randomness generation. We propose a simple solution, measurement-device-independent QRNG, which not only removes all detector side channels but is robust against losses. In contrast to previous fully device-independent QRNGs, our scheme does not require high detector efficiency or nonlocality tests. Simulations show that our protocol can be implemented efficiently with a practical coherent state laser and other standard optical components. The security analysis of our QRNG consists mainly of two parts: measurement tomography and randomness quantification, where several new techniques are developed to characterize the randomness associated with a positive-operator valued measure.
Note: Fully integrated 3.2 Gbps quantum random number generator with real-time extraction
NASA Astrophysics Data System (ADS)
Zhang, Xiao-Guang; Nie, You-Qi; Zhou, Hongyi; Liang, Hao; Ma, Xiongfeng; Zhang, Jun; Pan, Jian-Wei
2016-07-01
We present a real-time and fully integrated quantum random number generator (QRNG) by measuring laser phase fluctuations. The QRNG scheme based on laser phase fluctuations is featured for its capability of generating ultra-high-speed random numbers. However, the speed bottleneck of a practical QRNG lies on the limited speed of randomness extraction. To close the gap between the fast randomness generation and the slow post-processing, we propose a pipeline extraction algorithm based on Toeplitz matrix hashing and implement it in a high-speed field-programmable gate array. Further, all the QRNG components are integrated into a module, including a compact and actively stabilized interferometer, high-speed data acquisition, and real-time data post-processing and transmission. The final generation rate of the QRNG module with real-time extraction can reach 3.2 Gbps.
Note: Fully integrated 3.2 Gbps quantum random number generator with real-time extraction.
Zhang, Xiao-Guang; Nie, You-Qi; Zhou, Hongyi; Liang, Hao; Ma, Xiongfeng; Zhang, Jun; Pan, Jian-Wei
2016-07-01
We present a real-time and fully integrated quantum random number generator (QRNG) by measuring laser phase fluctuations. The QRNG scheme based on laser phase fluctuations is featured for its capability of generating ultra-high-speed random numbers. However, the speed bottleneck of a practical QRNG lies on the limited speed of randomness extraction. To close the gap between the fast randomness generation and the slow post-processing, we propose a pipeline extraction algorithm based on Toeplitz matrix hashing and implement it in a high-speed field-programmable gate array. Further, all the QRNG components are integrated into a module, including a compact and actively stabilized interferometer, high-speed data acquisition, and real-time data post-processing and transmission. The final generation rate of the QRNG module with real-time extraction can reach 3.2 Gbps. PMID:27475609
Efficient pseudo-random number generation for monte-carlo simulations using graphic processors
NASA Astrophysics Data System (ADS)
Mohanty, Siddhant; Mohanty, A. K.; Carminati, F.
2012-06-01
A hybrid approach based on the combination of three Tausworthe generators and one linear congruential generator for pseudo random number generation for GPU programing as suggested in NVIDIA-CUDA library has been used for MONTE-CARLO sampling. On each GPU thread, a random seed is generated on fly in a simple way using the quick and dirty algorithm where mod operation is not performed explicitly due to unsigned integer overflow. Using this hybrid generator, multivariate correlated sampling based on alias technique has been carried out using both CUDA and OpenCL languages.
Scope of Various Random Number Generators in Ant System Approach for TSP
NASA Technical Reports Server (NTRS)
Sen, S. K.; Shaykhian, Gholam Ali
2007-01-01
Experimented on heuristic, based on an ant system approach for traveling Salesman problem, are several quasi and pseudo-random number generators. This experiment is to explore if any particular generator is most desirable. Such an experiment on large samples has the potential to rank the performance of the generators for the foregoing heuristic. This is just to seek an answer to the controversial performance ranking of the generators in probabilistic/statically sense.
25 CFR 547.14 - What are the minimum technical standards for electronic random number generation?
Code of Federal Regulations, 2010 CFR
2010-04-01
... CLASS II GAMES § 547.14 What are the minimum technical standards for electronic random number generation... rules of the game. For example, if a bingo game with 75 objects with numbers or other designations has a... serial correlation (outcomes shall be independent from the previous game); and (x) Test on...
25 CFR 547.14 - What are the minimum technical standards for electronic random number generation?
Code of Federal Regulations, 2012 CFR
2012-04-01
... CLASS II GAMES § 547.14 What are the minimum technical standards for electronic random number generation... rules of the game. For example, if a bingo game with 75 objects with numbers or other designations has a... serial correlation (outcomes shall be independent from the previous game); and (x) Test on...
25 CFR 547.14 - What are the minimum technical standards for electronic random number generation?
Code of Federal Regulations, 2011 CFR
2011-04-01
... CLASS II GAMES § 547.14 What are the minimum technical standards for electronic random number generation... rules of the game. For example, if a bingo game with 75 objects with numbers or other designations has a... serial correlation (outcomes shall be independent from the previous game); and (x) Test on...
Robust random number generation using steady-state emission of gain-switched laser diodes
Yuan, Z. L. Lucamarini, M.; Dynes, J. F.; Fröhlich, B.; Plews, A.; Shields, A. J.
2014-06-30
We demonstrate robust, high-speed random number generation using interference of the steady-state emission of guaranteed random phases, obtained through gain-switching a semiconductor laser diode. Steady-state emission tolerates large temporal pulse misalignments and therefore significantly improves the interference quality. Using an 8-bit digitizer followed by a finite-impulse-response unbiasing algorithm, we achieve random number generation rates of 8 and 20 Gb/s, for laser repetition rates of 1 and 2.5 GHz, respectively, with a ±20% tolerance in the interferometer differential delay. We also report a generation rate of 80 Gb/s using partially phase-correlated short pulses. In relation to the field of quantum key distribution, our results confirm the gain-switched laser diode as a suitable light source, capable of providing phase-randomized coherent pulses at a clock rate of up to 2.5 GHz.
An efficient algorithm for generating random number pairs drawn from a bivariate normal distribution
NASA Technical Reports Server (NTRS)
Campbell, C. W.
1983-01-01
An efficient algorithm for generating random number pairs from a bivariate normal distribution was developed. Any desired value of the two means, two standard deviations, and correlation coefficient can be selected. Theoretically the technique is exact and in practice its accuracy is limited only by the quality of the uniform distribution random number generator, inaccuracies in computer function evaluation, and arithmetic. A FORTRAN routine was written to check the algorithm and good accuracy was obtained. Some small errors in the correlation coefficient were observed to vary in a surprisingly regular manner. A simple model was developed which explained the qualities aspects of the errors.
Cryptographic random number generators for low-power distributed measurement system
NASA Astrophysics Data System (ADS)
Czernik, Pawel; Olszyna, Jakub
2009-06-01
In this paper we present the State of The Art in Cryptographic Random Number Generators (RNG). We provide analysis of every of the most popular types of RNGs such as linear generators (i.e. congruential, multiple recursive), non-linear generators (i.e. Quadratic, Blum-Blum-Shub) and cryptographic algorithms based (i.e. RSA generator, SHA-1 generator). Finally we choose solutions which are suitable to Distributed Measurement Systems (DMS) specific requirements according to cryptographic security, computational efficiency (throughput) and complexity of implementation (VHDL targeted at FPGA and ASIC devices). Strong asymmetry of computing power and memory capacity is taken into account in both software and hardware solutions.
ERIC Educational Resources Information Center
Bosch, Holger; Steinkamp, Fiona; Boller, Emil
2006-01-01
Seance-room and other large-scale psychokinetic phenomena have fascinated humankind for decades. Experimental research has reduced these phenomena to attempts to influence (a) the fall of dice and, later, (b) the output of random number generators (RNGs). The meta-analysis combined 380 studies that assessed whether RNG output correlated with human…
Geisseler, Olivia; Pflugshaupt, Tobias; Buchmann, Andreas; Bezzola, Ladina; Reuter, Katja; Schuknecht, Bernhard; Weller, David; Linnebank, Michael; Brugger, Peter
2016-09-01
Human subjects typically deviate systematically from randomness when attempting to produce a sequence of random numbers. Despite an increasing number of behavioral and functional neuroimaging studies on random number generation (RNG), its structural correlates have never been investigated. We set out to fill this gap in 44 patients with multiple sclerosis (MS), a disease whose impact on RNG has never been studied. The RNG task required the paced (1 Hz) generation of the numbers from 1 to 6 in a sequence as random as possible. The same task was administered in 39 matched healthy controls. To assess neuroanatomical correlates such as cortical thickness, lesion load and third ventricle width, all subjects underwent high-resolution structural MRI. Compared to controls, MS patients exhibited an enhanced tendency to arrange consecutive numbers in an ascending order ("forward counting"). Furthermore, patients showed a higher susceptibility to rule breaks (producing out-of-category digits like 7) and to skip beats of the metronome. Clinico-anatomical correlation analyses revealed two main findings: First, increased counting in MS patients was associated with higher cortical lesion load. Second, increased number of skipped beats was related to widespread cortical thinning. In conclusion, our test results illustrate a loss of behavioral complexity in the course of MS, while the imaging results suggest an association between this loss and cortical pathology. PMID:27403852
A robust random number generator based on differential comparison of chaotic laser signals.
Zhang, Jianzhong; Wang, Yuncai; Liu, Ming; Xue, Lugang; Li, Pu; Wang, Anbang; Zhang, Mingjiang
2012-03-26
We experimentally realize a robust real-time random number generator by differentially comparing the signal from a chaotic semiconductor laser and its delayed signal through a 1-bit analog-to-digital converter. The probability density distribution of the output chaotic signal based on the differential comparison method possesses an extremely small coefficient of Pearson's median skewness (1.5 × 10⁻⁶), which can yield a balanced random sequence much easily than the previously reported method that compares the signal from the chaotic laser with a certain threshold value. Moveover, we experimently demonstrate that our method can stably generate good random numbers at rates of 1.44 Gbit/s with excellent immunity from external perturbations while the previously reported method fails. PMID:22453429
Scope of Various Random Number Generators in ant System Approach for TSP
NASA Technical Reports Server (NTRS)
Sen, S. K.; Shaykhian, Gholam Ali
2007-01-01
Experimented on heuristic, based on an ant system approach for traveling salesman problem, are several quasi- and pseudo-random number generators. This experiment is to explore if any particular generator is most desirable. Such an experiment on large samples has the potential to rank the performance of the generators for the foregoing heuristic. This is mainly to seek an answer to the controversial issue "which generator is the best in terms of quality of the result (accuracy) as well as cost of producing the result (time/computational complexity) in a probabilistic/statistical sense."
Towse, John N.; Loetscher, Tobias; Brugger, Peter
2014-01-01
We investigate the number preferences of children and adults when generating random digit sequences. Previous research has shown convincingly that adults prefer smaller numbers when randomly choosing between responses 1–6. We analyze randomization choices made by both children and adults, considering a range of experimental studies and task configurations. Children – most of whom are between 8 and 11~years – show a preference for relatively large numbers when choosing numbers 1–10. Adults show a preference for small numbers with the same response set. We report a modest association between children’s age and numerical bias. However, children also exhibit a small number bias with a smaller response set available, and they show a preference specifically for the numbers 1–3 across many datasets. We argue that number space demonstrates both continuities (numbers 1–3 have a distinct status) and change (a developmentally emerging bias toward the left side of representational space or lower numbers). PMID:24478747
Attack on a Chaos-Based Random Number Generator Using Anticipating Synchronization
NASA Astrophysics Data System (ADS)
Yeniçeri, Ramazan; Kilinç, Selçuk; Yalçin, Müştak E.
Chaotic systems have been used in random number generation, owing to the property of sensitive dependence on initial conditions and hence the possibility to produce unpredictable signals. Within the types of chaotic systems, those which are defined by only one delay-differential equation are attractive due to their simple model. On the other hand, it is possible to synchronize to the future states of a time-delay chaotic system by anticipating synchronization. Therefore, random number generator (RNG), which employs such a system, might not be immune to the attacks. In this paper, attack on a chaos-based random number generator using anticipating synchronization is investigated. The considered time-delay chaotic system produces binary signals, which can directly be used as a source of RNG. Anticipating synchronization is obtained by incorporating other systems appropriately coupled to the original one. Quantification of synchronization is given by the bit error between the streams produced by the original and coupled systems. It is shown that the bit streams generated by the original system can be anticipated by the coupled systems beforehand.
Random Numbers and Quantum Computers
ERIC Educational Resources Information Center
McCartney, Mark; Glass, David
2002-01-01
The topic of random numbers is investigated in such a way as to illustrate links between mathematics, physics and computer science. First, the generation of random numbers by a classical computer using the linear congruential generator and logistic map is considered. It is noted that these procedures yield only pseudo-random numbers since…
ERIC Educational Resources Information Center
Boonsathorn, Wasita; Charoen, Danuvasin; Dryver, Arthur L.
2014-01-01
E-Learning brings access to a powerful but often overlooked teaching tool: random number generation. Using random number generation, a practically infinite number of quantitative problem-solution sets can be created. In addition, within the e-learning context, in the spirit of the mastery of learning, it is possible to assign online quantitative…
An On-Demand Optical Quantum Random Number Generator with In-Future Action and Ultra-Fast Response.
Stipčević, Mario; Ursin, Rupert
2015-01-01
Random numbers are essential for our modern information based society e.g. in cryptography. Unlike frequently used pseudo-random generators, physical random number generators do not depend on complex algorithms but rather on a physical process to provide true randomness. Quantum random number generators (QRNG) do rely on a process, which can be described by a probabilistic theory only, even in principle. Here we present a conceptually simple implementation, which offers a 100% efficiency of producing a random bit upon a request and simultaneously exhibits an ultra low latency. A careful technical and statistical analysis demonstrates its robustness against imperfections of the actual implemented technology and enables to quickly estimate randomness of very long sequences. Generated random numbers pass standard statistical tests without any post-processing. The setup described, as well as the theory presented here, demonstrate the maturity and overall understanding of the technology. PMID:26057576
An On-Demand Optical Quantum Random Number Generator with In-Future Action and Ultra-Fast Response
Stipčević, Mario; Ursin, Rupert
2015-01-01
Random numbers are essential for our modern information based society e.g. in cryptography. Unlike frequently used pseudo-random generators, physical random number generators do not depend on complex algorithms but rather on a physicsal process to provide true randomness. Quantum random number generators (QRNG) do rely on a process, wich can be described by a probabilistic theory only, even in principle. Here we present a conceptualy simple implementation, which offers a 100% efficiency of producing a random bit upon a request and simultaneously exhibits an ultra low latency. A careful technical and statistical analysis demonstrates its robustness against imperfections of the actual implemented technology and enables to quickly estimate randomness of very long sequences. Generated random numbers pass standard statistical tests without any post-processing. The setup described, as well as the theory presented here, demonstrate the maturity and overall understanding of the technology. PMID:26057576
Zhmurov, A; Rybnikov, K; Kholodov, Y; Barsegov, V
2011-05-12
The use of graphics processing units (GPUs) in simulation applications offers a significant speed gain as compared to computations on central processing units (CPUs). Many simulation methods require a large number of independent random variables generated at each step. We present two approaches for implementation of random number generators (RNGs) on a GPU. In the one-RNG-per-thread approach, one RNG produces a stream of random numbers in each thread of execution, whereas the one-RNG-for-all-threads method builds on the ability of different threads to communicate, thus, sharing random seeds across an entire GPU device. We used these approaches to implement Ran2, Hybrid Taus, and Lagged Fibonacci algorithms on a GPU. We profiled the performance of these generators in terms of the computational time, memory usage, and the speedup factor (CPU time/GPU time). These generators have been incorporated into the program for Langevin simulations of biomolecules fully implemented on the GPU. The ∼250-fold computational speedup on the GPU allowed us to carry out single-molecule dynamic force measurements in silico to explore the mechanical properties of the bacteriophage HK97 in the experimental subsecond time scale. We found that the nanomechanical response of HK97 depends on the conditions of force application, including the rate of change and geometry of the mechanical perturbation. Hence, using the GPU-based implementation of RNGs, presented here, in conjunction with Langevin simulations, makes it possible to directly compare the results of dynamic force measurements in vitro and in silico. PMID:21194190
Fast physical and pseudo random number generation based on a nonlinear optoelectronic oscillator
NASA Astrophysics Data System (ADS)
Mu, Penghua; Pan, Wei; Xiang, Shuiying; Li, Nianqiang; Liu, Xinkai; Zou, Xihua
2015-08-01
High speed random number generation (RNG) utilizing a nonlinear optoelectronic oscillator (OEO) is explored experimentally. It has been found that by simply adjusting either the injected optical power or the gain of the modulator driver, low complexity dynamics such as square wave, and more complex dynamics including fully developed chaos can be experimentally achieved. More importantly, physical RNG based on high-speed-oscilloscope measurements and pseudo RNG based on post-processing are implemented in this paper. The generated bit sequences pass all the standard statistical random tests, indicating that fast physical and pseudo RNG could be achieved based on the same OEO entropy source. Our results could provide further insight into the implementation of RNG based on chaotic optical systems.
Chaotic oscillation and random-number generation based on nanoscale optical-energy transfer
Naruse, Makoto; Kim, Song-Ju; Aono, Masashi; Hori, Hirokazu; Ohtsu, Motoichi
2014-01-01
By using nanoscale energy-transfer dynamics and density matrix formalism, we demonstrate theoretically and numerically that chaotic oscillation and random-number generation occur in a nanoscale system. The physical system consists of a pair of quantum dots (QDs), with one QD smaller than the other, between which energy transfers via optical near-field interactions. When the system is pumped by continuous-wave radiation and incorporates a timing delay between two energy transfers within the system, it emits optical pulses. We refer to such QD pairs as nano-optical pulsers (NOPs). Irradiating an NOP with external periodic optical pulses causes the oscillating frequency of the NOP to synchronize with the external stimulus. We find that chaotic oscillation occurs in the NOP population when they are connected by an external time delay. Moreover, by evaluating the time-domain signals by statistical-test suites, we confirm that the signals are sufficiently random to qualify the system as a random-number generator (RNG). This study reveals that even relatively simple nanodevices that interact locally with each other through optical energy transfer at scales far below the wavelength of irradiating light can exhibit complex oscillatory dynamics. These findings are significant for applications such as ultrasmall RNGs. PMID:25113239
40 CFR 761.308 - Sample selection by random number generation on any two-dimensional square grid.
Code of Federal Regulations, 2010 CFR
2010-07-01
... 40 Protection of Environment 30 2010-07-01 2010-07-01 false Sample selection by random number generation on any two-dimensional square grid. 761.308 Section 761.308 Protection of Environment... Â§ 761.79(b)(3) § 761.308 Sample selection by random number generation on any two-dimensional...
40 CFR 761.308 - Sample selection by random number generation on any two-dimensional square grid.
Code of Federal Regulations, 2011 CFR
2011-07-01
... 40 Protection of Environment 31 2011-07-01 2011-07-01 false Sample selection by random number generation on any two-dimensional square grid. 761.308 Section 761.308 Protection of Environment... Â§ 761.79(b)(3) § 761.308 Sample selection by random number generation on any two-dimensional...
40 CFR 761.308 - Sample selection by random number generation on any two-dimensional square grid.
Code of Federal Regulations, 2012 CFR
2012-07-01
... 40 Protection of Environment 32 2012-07-01 2012-07-01 false Sample selection by random number generation on any two-dimensional square grid. 761.308 Section 761.308 Protection of Environment... Â§ 761.79(b)(3) § 761.308 Sample selection by random number generation on any two-dimensional...
40 CFR 761.308 - Sample selection by random number generation on any two-dimensional square grid.
Code of Federal Regulations, 2013 CFR
2013-07-01
... 40 Protection of Environment 32 2013-07-01 2013-07-01 false Sample selection by random number generation on any two-dimensional square grid. 761.308 Section 761.308 Protection of Environment... Â§ 761.79(b)(3) § 761.308 Sample selection by random number generation on any two-dimensional...
40 CFR 761.308 - Sample selection by random number generation on any two-dimensional square grid.
Code of Federal Regulations, 2014 CFR
2014-07-01
... 40 Protection of Environment 31 2014-07-01 2014-07-01 false Sample selection by random number generation on any two-dimensional square grid. 761.308 Section 761.308 Protection of Environment... Â§ 761.79(b)(3) § 761.308 Sample selection by random number generation on any two-dimensional...
Capone, Fioravante; Capone, Gianluca; Ranieri, Federico; Di Pino, Giovanni; Oricchio, Gianluca; Di Lazzaro, Vincenzo
2014-10-01
Random number generation (RNG) is a procedurally-simple task related to specific executive functions, such as updating and monitoring of information and inhibition of automatic responses. The effect of practice on executive functions has been widely investigated, however little is known on the impact of practice on RNG. Transcranial direct current stimulation (tDCS) allows to modulate, non-invasively, brain activity and to enhance the effects of training on executive functions. Hence, this study aims to investigate the effect of practice on RNG and to explore the possibility to influence it by tDCS applied over dorsolateral prefrontal cortex. Twenty-six healthy volunteers have been evaluated within single session and between different sessions of RNG using several measures of randomness, which are informative of separable cognitive components servicing random behavior. We found that repetition measures significantly change within single session, seriation measures significantly change both within and between sessions, while cycling measures are not affected by practice. tDCS does not produce any additional effect, however a sub-analysis limited to the first session revealed an increasing trend in seriation measure after anodal compared to cathodal stimulation. Our findings support the hypothesis that practice selectively and consistently influences specific cognitive components related to random behavior, while tDCS transiently affects RNG performance. PMID:24811195
High-Order Photonic W-states for Random Number Generation
NASA Astrophysics Data System (ADS)
Graefe, Markus; Heilmann, Rene; Perez-Leija, Armando; Keil, Robert; Dreisow, Felix; Heinrich, Matthias; Nolte, Stefan; Christodoulides, Demetrios N.; Szameit, Alexander
2014-05-01
Multipartite entanglement plays a key role in a number of counter-intuitive phenomena in quantum me- chances. A particular type of multipartite entangled states are the so called W-states which are in generalized form a coherent superposition of N single qubit states exhibiting equal probability amplitudes. The entanglement carried by these quantum entities has the remarkable property of being intrinsically robust to decoherence in one of the qubits. In our work, we experimentally realize high order W-states by forcing single photons to exist in a uniform coherent superposition of N (up to 16) spatial optical modes within a multi-port integrated system. Interestingly, in the generated W-states, a single photon will emerge from any of the N output ports with exactly the same probability. Based on that fact we have additionally developed a scheme for the generation of genuine random bits on chip, without the need of any post-processig. The authenticity of the random numbers is validated by applying the fifteen statistical tests suggested by National Institute of Standard Technology.
Li, Dongfang; Lu, Zhaojun; Zou, Xuecheng; Liu, Zhenglin
2015-01-01
Random number generators (RNG) play an important role in many sensor network systems and applications, such as those requiring secure and robust communications. In this paper, we develop a high-security and high-throughput hardware true random number generator, called PUFKEY, which consists of two kinds of physical unclonable function (PUF) elements. Combined with a conditioning algorithm, true random seeds are extracted from the noise on the start-up pattern of SRAM memories. These true random seeds contain full entropy. Then, the true random seeds are used as the input for a non-deterministic hardware RNG to generate a stream of true random bits with a throughput as high as 803 Mbps. The experimental results show that the bitstream generated by the proposed PUFKEY can pass all standard national institute of standards and technology (NIST) randomness tests and is resilient to a wide range of security attacks. PMID:26501283
Li, Dongfang; Lu, Zhaojun; Zou, Xuecheng; Liu, Zhenglin
2015-01-01
Random number generators (RNG) play an important role in many sensor network systems and applications, such as those requiring secure and robust communications. In this paper, we develop a high-security and high-throughput hardware true random number generator, called PUFKEY, which consists of two kinds of physical unclonable function (PUF) elements. Combined with a conditioning algorithm, true random seeds are extracted from the noise on the start-up pattern of SRAM memories. These true random seeds contain full entropy. Then, the true random seeds are used as the input for a non-deterministic hardware RNG to generate a stream of true random bits with a throughput as high as 803 Mbps. The experimental results show that the bitstream generated by the proposed PUFKEY can pass all standard national institute of standards and technology (NIST) randomness tests and is resilient to a wide range of security attacks. PMID:26501283
NASA Astrophysics Data System (ADS)
Czernik, Pawel
2013-10-01
The hardware random number generator based on the 74121 monostable multivibrators for applications in cryptographically secure distributed measurement and control systems with asymmetric resources was presented. This device was implemented on the basis of the physical electronic vibration generator in which the circuit is composed of two "loop" 74121 monostable multivibrators, D flip-flop and external clock signal source. The clock signal, witch control D flip-flop was generated by a computer on one of the parallel port pins. There was presented programmed the author's acquisition process of random data from the measuring system to a computer. The presented system was designed, builded and thoroughly tested in the term of cryptographic security in our laboratory, what there is the most important part of this publication. Real cryptographic security was tested based on the author's software and the software environment called RDieHarder. The obtained results was here presented and analyzed in detail with particular reference to the specificity of distributed measurement and control systems with asymmetric resources.
Random numbers from vacuum fluctuations
NASA Astrophysics Data System (ADS)
Shi, Yicheng; Chng, Brenda; Kurtsiefer, Christian
2016-07-01
We implement a quantum random number generator based on a balanced homodyne measurement of vacuum fluctuations of the electromagnetic field. The digitized signal is directly processed with a fast randomness extraction scheme based on a linear feedback shift register. The random bit stream is continuously read in a computer at a rate of about 480 Mbit/s and passes an extended test suite for random numbers.
Oomens, Wouter; Maes, Joseph H. R.; Hasselman, Fred; Egger, Jos I. M.
2015-01-01
The concept of executive functions plays a prominent role in contemporary experimental and clinical studies on cognition. One paradigm used in this framework is the random number generation (RNG) task, the execution of which demands aspects of executive functioning, specifically inhibition and working memory. Data from the RNG task are best seen as a series of successive events. However, traditional RNG measures that are used to quantify executive functioning are mostly summary statistics referring to deviations from mathematical randomness. In the current study, we explore the utility of recurrence quantification analysis (RQA), a non-linear method that keeps the entire sequence intact, as a better way to describe executive functioning compared to traditional measures. To this aim, 242 first- and second-year students completed a non-paced RNG task. Principal component analysis of their data showed that traditional and RQA measures convey more or less the same information. However, RQA measures do so more parsimoniously and have a better interpretation. PMID:26097449
Oomens, Wouter; Maes, Joseph H R; Hasselman, Fred; Egger, Jos I M
2015-01-01
The concept of executive functions plays a prominent role in contemporary experimental and clinical studies on cognition. One paradigm used in this framework is the random number generation (RNG) task, the execution of which demands aspects of executive functioning, specifically inhibition and working memory. Data from the RNG task are best seen as a series of successive events. However, traditional RNG measures that are used to quantify executive functioning are mostly summary statistics referring to deviations from mathematical randomness. In the current study, we explore the utility of recurrence quantification analysis (RQA), a non-linear method that keeps the entire sequence intact, as a better way to describe executive functioning compared to traditional measures. To this aim, 242 first- and second-year students completed a non-paced RNG task. Principal component analysis of their data showed that traditional and RQA measures convey more or less the same information. However, RQA measures do so more parsimoniously and have a better interpretation. PMID:26097449
Sexton, Nicholas J.; Cooper, Richard P.
2014-01-01
Random number generation (RNG) is a complex cognitive task for human subjects, requiring deliberative control to avoid production of habitual, stereotyped sequences. Under various manipulations (e.g., speeded responding, transcranial magnetic stimulation, or neurological damage) the performance of human subjects deteriorates, as reflected in a number of qualitatively distinct, dissociable biases. For example, the intrusion of stereotyped behavior (e.g., counting) increases at faster rates of generation. Theoretical accounts of the task postulate that it requires the integrated operation of multiple, computationally heterogeneous cognitive control (“executive”) processes. We present a computational model of RNG, within the framework of a novel, neuropsychologically-inspired cognitive architecture, ESPro. Manipulating the rate of sequence generation in the model reproduced a number of key effects observed in empirical studies, including increasing sequence stereotypy at faster rates. Within the model, this was due to time limitations on the interaction of supervisory control processes, namely, task setting, proposal of responses, monitoring, and response inhibition. The model thus supports the fractionation of executive function into multiple, computationally heterogeneous processes. PMID:25071644
Pawlowski, Marcin Piotr; Jara, Antonio; Ogorzalek, Maciej
2015-01-01
Entropy in computer security is associated with the unpredictability of a source of randomness. The random source with high entropy tends to achieve a uniform distribution of random values. Random number generators are one of the most important building blocks of cryptosystems. In constrained devices of the Internet of Things ecosystem, high entropy random number generators are hard to achieve due to hardware limitations. For the purpose of the random number generation in constrained devices, this work proposes a solution based on the least-significant bits concatenation entropy harvesting method. As a potential source of entropy, on-board integrated sensors (i.e., temperature, humidity and two different light sensors) have been analyzed. Additionally, the costs (i.e., time and memory consumption) of the presented approach have been measured. The results obtained from the proposed method with statistical fine tuning achieved a Shannon entropy of around 7.9 bits per byte of data for temperature and humidity sensors. The results showed that sensor-based random number generators are a valuable source of entropy with very small RAM and Flash memory requirements for constrained devices of the Internet of Things. PMID:26506357
Pawlowski, Marcin Piotr; Jara, Antonio; Ogorzalek, Maciej
2015-01-01
Entropy in computer security is associated with the unpredictability of a source of randomness. The random source with high entropy tends to achieve a uniform distribution of random values. Random number generators are one of the most important building blocks of cryptosystems. In constrained devices of the Internet of Things ecosystem, high entropy random number generators are hard to achieve due to hardware limitations. For the purpose of the random number generation in constrained devices, this work proposes a solution based on the least-significant bits concatenation entropy harvesting method. As a potential source of entropy, on-board integrated sensors (i.e., temperature, humidity and two different light sensors) have been analyzed. Additionally, the costs (i.e., time and memory consumption) of the presented approach have been measured. The results obtained from the proposed method with statistical fine tuning achieved a Shannon entropy of around 7.9 bits per byte of data for temperature and humidity sensors. The results showed that sensor-based random number generators are a valuable source of entropy with very small RAM and Flash memory requirements for constrained devices of the Internet of Things. PMID:26506357
Click, Timothy H.; Kaminski, George A.; Liu, Aibing B.
2010-01-01
We have simulated pure liquid butane, methanol and hydrated alanine polypeptide with the Monte Carlo technique using three kinds of random number generators - the standard Linear Congruential Generator (LCG), a modification of the LCG with additional randomization used in the BOSS software, and the “Mersenne Twister” generator by Matsumoto and Nishimura. While using the latter two random number generators leads to reasonably similar physical features, the LCG produces a significant different results. For the pure fluids, a noticeable expansion occurs. Using the original LCG on butane yields a molecular volume of 171.4 Å3 per molecule compared to ca. 163.6–163.9 Å3 for the other two generators, a deviation of about 5%. For methanol, the LCG produces an average volume of 86.3 Å3 per molecule, which is about 24% higher than the 68.8–70.2 Å3 obtained with the random number generator in BOSS and the generator by Matsumoto and Nishimura. In case of the hydrated tridecaalanine peptide, the volume and energy tend to be noticeably greater with the LCG than with the BOSS (modified LCG) random number generator. For the simulated hydrated extended conformation of tridecaalanine, the difference in volume reached ca. 87%. The uniformity and periodicity of the generators do not seem to play the crucial role in these phenomena. We conclude that it is important to test a random number generator by modeling a system such as the pure liquid methanol with a well-established force field before routinely employing it in Monte Carlo simulations. PMID:20734313
Three criteria for quantum random-number generators based on beam splitters
Svozil, Karl
2009-05-15
We propose three criteria for the generation of random digital strings from quantum beam splitters: (i) three or more mutually exclusive outcomes corresponding to the invocation of three- and higher-dimensional Hilbert spaces, (ii) the mandatory use of pure states in conjugated bases for preparation and detection, and (iii) the use of entangled singlet (unique) states for elimination of bias.
Generating Random Samples of a Given Size Using Social Security Numbers.
ERIC Educational Resources Information Center
Erickson, Richard C.; Brauchle, Paul E.
1984-01-01
The purposes of this article are (1) to present a method by which social security numbers may be used to draw cluster samples of a predetermined size and (2) to describe procedures used to validate this method of drawing random samples. (JOW)
A new technique for ultrafast physical random number generation using optical chaos
NASA Astrophysics Data System (ADS)
Elsonbaty, Amr; Hegazy, Salem F.; Obayya, Salah S. A.
2016-04-01
In this paper, we numerically demonstrate a new extraction scheme for generating ultra-fast physically random sequence of bits. For this purpose, we utilize a dual-channel optical chaos source with suppressed time delayed (TD) signature in both the intensity and the phase of its two channels. The proposed technique uses M 1-bit analog-to-digital converters (ADCs) to compare the level of the chaotic intensity signal at time t with its levels after incommensurable delay-interval Tm, where m = {1,2, … , M}. The binary output of each 1-bit ADC is then sampled by a positive-edge-triggered D flip flop. The clock sequence applied to the flip-flops is relatively delayed such that the rising edge of the clock triggering the m flip-flop precedes the rising edge of the clock of a subsequent m+1 flip-flop by a fixed period. The outputs of all flip flops are then combined by means of a parity-check logic. Numerical simulations are carried out using values of parameters at which TD signature is suppressed for chosen values of setup parameters. The 15 statistical tests in Special Publication 800-22 from NIST are applied to the generated random bits in order to examine the randomness quality of these bits for different values of M. The results show that all tests are passed from M = 1 to M = 39 at sampling rate up to 34.5 GHz which indicates that the maximum generation rate of random bits is 2.691 Tb/sec using a chaotic source of single VCSEL and without employing any pre-processing techniques.
Efficient Monte Carlo simulations using a shuffled nested Weyl sequence random number generator.
Tretiakov, K V; Wojciechowski, K W
1999-12-01
The pseudorandom number generator proposed recently by Holian et al. [B. L. Holian, O. E. Percus, T. T. Warnock, and P. A. Whitlock, Phys. Rev. E 50, 1607 (1994)] is tested via Monte Carlo computation of the free energy difference between the defectless hcp and fcc hard sphere crystals by the Frenkel-Ladd method [D. Frenkel and A. J. C. Ladd, J. Chem. Phys. 81, 3188 (1984)]. It is shown that this fast and convenient for parallel computing generator gives results in good agreement with results obtained by other generators. An estimate of high accuracy is obtained for the hcp-fcc free energy difference near melting. PMID:11970727
Koyama, Kento; Hokunan, Hidekazu; Hasegawa, Mayumi; Kawamura, Shuso; Koseki, Shigenobu
2016-12-01
We investigated a bacterial sample preparation procedure for single-cell studies. In the present study, we examined whether single bacterial cells obtained via 10-fold dilution followed a theoretical Poisson distribution. Four serotypes of Salmonella enterica, three serotypes of enterohaemorrhagic Escherichia coli and one serotype of Listeria monocytogenes were used as sample bacteria. An inoculum of each serotype was prepared via a 10-fold dilution series to obtain bacterial cell counts with mean values of one or two. To determine whether the experimentally obtained bacterial cell counts follow a theoretical Poisson distribution, a likelihood ratio test between the experimentally obtained cell counts and Poisson distribution which parameter estimated by maximum likelihood estimation (MLE) was conducted. The bacterial cell counts of each serotype sufficiently followed a Poisson distribution. Furthermore, to examine the validity of the parameters of Poisson distribution from experimentally obtained bacterial cell counts, we compared these with the parameters of a Poisson distribution that were estimated using random number generation via computer simulation. The Poisson distribution parameters experimentally obtained from bacterial cell counts were within the range of the parameters estimated using a computer simulation. These results demonstrate that the bacterial cell counts of each serotype obtained via 10-fold dilution followed a Poisson distribution. The fact that the frequency of bacterial cell counts follows a Poisson distribution at low number would be applied to some single-cell studies with a few bacterial cells. In particular, the procedure presented in this study enables us to develop an inactivation model at the single-cell level that can estimate the variability of survival bacterial numbers during the bacterial death process. PMID:27554145
Strenge, Hans; Lesmana, Cokorda Bagus Jaya; Suryani, Luh Ketut
2009-08-01
Verbal random number generation is a procedurally simple task to assess executive function and appears ideally suited for the use under diverse settings in cross-cultural research. The objective of this study was to examine ethnic group differences between young adults in Bali (Indonesia) and Kiel (Germany): 50 bilingual healthy students, 30 Balinese and 20 Germans, attempted to generate a random sequence of the digits 1 to 9. In Balinese participants, randomization was done in Balinese (native language L1) and Indonesian (first foreign language L2), in German subjects in the German (L1) and English (L2) languages. 10 of 30 Balinese (33%), but no Germans, were unable to inhibit habitual counting in more than half of the responses. The Balinese produced significantly more nonrandom responses than the Germans with higher rates of counting and significantly less occurrence of the digits 2 and 3 in L1 compared with L2. Repetition and cycling behavior did not differ between the four languages. The findings highlight the importance of taking into account culture-bound psychosocial factors for Balinese individuals when administering and interpreting a random number generation test. PMID:19831087
Wang, Yonggang; Hui, Cong; Liu, Chong; Xu, Chao
2016-04-01
The contribution of this paper is proposing a new entropy extraction mechanism based on sampling phase jitter in ring oscillators to make a high throughput true random number generator in a field programmable gate array (FPGA) practical. Starting from experimental observation and analysis of the entropy source in FPGA, a multi-phase sampling method is exploited to harvest the clock jitter with a maximum entropy and fast sampling speed. This parametrized design is implemented in a Xilinx Artix-7 FPGA, where the carry chains in the FPGA are explored to realize the precise phase shifting. The generator circuit is simple and resource-saving, so that multiple generation channels can run in parallel to scale the output throughput for specific applications. The prototype integrates 64 circuit units in the FPGA to provide a total output throughput of 7.68 Gbps, which meets the requirement of current high-speed quantum key distribution systems. The randomness evaluation, as well as its robustness to ambient temperature, confirms that the new method in a purely digital fashion can provide high-speed high-quality random bit sequences for a variety of embedded applications. PMID:27131692
NASA Astrophysics Data System (ADS)
Wang, Yonggang; Hui, Cong; Liu, Chong; Xu, Chao
2016-04-01
The contribution of this paper is proposing a new entropy extraction mechanism based on sampling phase jitter in ring oscillators to make a high throughput true random number generator in a field programmable gate array (FPGA) practical. Starting from experimental observation and analysis of the entropy source in FPGA, a multi-phase sampling method is exploited to harvest the clock jitter with a maximum entropy and fast sampling speed. This parametrized design is implemented in a Xilinx Artix-7 FPGA, where the carry chains in the FPGA are explored to realize the precise phase shifting. The generator circuit is simple and resource-saving, so that multiple generation channels can run in parallel to scale the output throughput for specific applications. The prototype integrates 64 circuit units in the FPGA to provide a total output throughput of 7.68 Gbps, which meets the requirement of current high-speed quantum key distribution systems. The randomness evaluation, as well as its robustness to ambient temperature, confirms that the new method in a purely digital fashion can provide high-speed high-quality random bit sequences for a variety of embedded applications.
NASA Astrophysics Data System (ADS)
Liberty, Joshua W.
This dissertation uses the hierarchical q-state Potts model at the critical point to develop a new random number generator test. We start with an exposition of renormalization group approach by means of which one can numerically exactly compute the free energy, specific heat and susceptibility of large, but finite lattices. We then show that generalization of these standard techniques allows one to also compute probability distributions related to the energy and the order parameter. The various computed quantities can be compared with Monte Carlo estimates of the same quantities. We demonstrate that the structure of the hierarchical lattices used allows one to perform the Monte Carlo calculations by direct sampling. This avoids the usual critical slowing down that plagues Monte Carlo calculations at the critical point. As is well known, critical behavior is highly susceptible to perturbations. We expect that flaws of the pseudo random number generator, such as correlations, will cause statistically significant discrepancies between the results of the simulations and the numerically exactly computed results. Details of the computer code generated for these tests are included.
25 CFR 547.14 - What are the minimum technical standards for electronic random number generation?
Code of Federal Regulations, 2013 CFR
2013-04-01
... must not be feasible to predict future outputs of an RNG, even if the algorithm and the past sequence...) Scaling algorithms and scaled numbers. An RNG that provides output scaled to given ranges must: (1) Be... an unbiased algorithm. A scaling algorithm is considered to be unbiased if the measured bias is...
25 CFR 547.14 - What are the minimum technical standards for electronic random number generation?
Code of Federal Regulations, 2014 CFR
2014-04-01
... must not be feasible to predict future outputs of an RNG, even if the algorithm and the past sequence...) Scaling algorithms and scaled numbers. An RNG that provides output scaled to given ranges must: (1) Be... an unbiased algorithm. A scaling algorithm is considered to be unbiased if the measured bias is...
NASA Astrophysics Data System (ADS)
Czernik, Pawel
The chaotic signal generator based on the theory of nonlinear dynamical systems for applications in cryptographically secure distributed measurement and control systems with asymmetric resources is presented. This system was implemented on the basis of the physical chaotic electronic vibration generator in which the resonant circuit is composed of two capacitors, two resistors, coil and transistor, called the Colpitts oscillator. The presented system was designed, programmed and thoroughly tested in the term of cryptographic security in our laboratory, what there is the most important part of this publication. True cryptographic security was tested based on the author's software and the software environment called RDieHarder. The obtained results will be here presented and analyzed in detail with particular reference to the specificity of distributed measurement and control systems with asymmetric resources.
Investigating the Randomness of Numbers
ERIC Educational Resources Information Center
Pendleton, Kenn L.
2009-01-01
The use of random numbers is pervasive in today's world. Random numbers have practical applications in such far-flung arenas as computer simulations, cryptography, gambling, the legal system, statistical sampling, and even the war on terrorism. Evaluating the randomness of extremely large samples is a complex, intricate process. However, the…
Beem, Lance W.
2011-01-01
Abstract Background Reiki therapy is documented for relief of pain and stress. Energetic healing has been documented to alter biologic markers of illness such as hematocrit. True random number generators are reported to be affected by energy healers and spiritually oriented conscious awareness. Methods The patient was a then 54-year-old severely ill man who had hepatitis C types 1 and 2 and who did not improve with conventional therapy. He also suffered from obesity, the metabolic syndrome, asthma, and hypertension. He was treated with experimental high-dose interferon/riboviron therapy with resultant profound anemia and neutropenia. Energetic healing and Reiki therapy was administered initially to enhance the patient's sense of well-being and to relieve anxiety. Possible effects on the patient's absolute neutrophil count and hematocrit were incidentally noted. Reiki therapy was then initiated at times of profound neutropenia to assess its possible effect on the patient's absolute neutrophil count (ANC). Reiki and other energetic healing sessions were monitored with a true random number generator (RNG). Results Statistically significant relationships were documented between Reiki therapy, a quieting of the electronically created white noise of the RNG during healing sessions, and improvement in the patient's ANC. The immediate clinical result was that the patient could tolerate the high-dose interferon regimen without missing doses because of absolute neutropenia. The patient was initially a late responder to interferon and had been given a 5% chance of clearing the virus. He remains clear of the virus 1 year after treatment. Conclusions The association between changes in the RNG, Reiki therapy, and a patient's ANC is the first to the authors' knowledge in the medical literature. Future studies assessing the effects of energetic healing on specific biologic markers of disease are anticipated. Concurrent use of a true RNG may prove to correlate with the
Random numbers certified by Bell's theorem.
Pironio, S; Acín, A; Massar, S; de la Giroday, A Boyer; Matsukevich, D N; Maunz, P; Olmschenk, S; Hayes, D; Luo, L; Manning, T A; Monroe, C
2010-04-15
Randomness is a fundamental feature of nature and a valuable resource for applications ranging from cryptography and gambling to numerical simulation of physical and biological systems. Random numbers, however, are difficult to characterize mathematically, and their generation must rely on an unpredictable physical process. Inaccuracies in the theoretical modelling of such processes or failures of the devices, possibly due to adversarial attacks, limit the reliability of random number generators in ways that are difficult to control and detect. Here, inspired by earlier work on non-locality-based and device-independent quantum information processing, we show that the non-local correlations of entangled quantum particles can be used to certify the presence of genuine randomness. It is thereby possible to design a cryptographically secure random number generator that does not require any assumption about the internal working of the device. Such a strong form of randomness generation is impossible classically and possible in quantum systems only if certified by a Bell inequality violation. We carry out a proof-of-concept demonstration of this proposal in a system of two entangled atoms separated by approximately one metre. The observed Bell inequality violation, featuring near perfect detection efficiency, guarantees that 42 new random numbers are generated with 99 per cent confidence. Our results lay the groundwork for future device-independent quantum information experiments and for addressing fundamental issues raised by the intrinsic randomness of quantum theory. PMID:20393558
Random Numbers from a Delay Equation
NASA Astrophysics Data System (ADS)
Self, Julian; Mackey, Michael C.
2016-05-01
Delay differential equations can have "chaotic" solutions that can be used to mimic Brownian motion. Since a Brownian motion is random in its velocity, it is reasonable to think that a random number generator might be constructed from such a model. In this preliminary study, we consider one specific example of this and show that it satisfies criteria commonly employed in the testing of random number generators (from TestU01's very stringent "Big Crush" battery of tests). A technique termed digit discarding, commonly used in both this generator and physical RNGs using laser feedback systems, is discussed with regard to the maximal Lyapunov exponent. Also, we benchmark the generator to a contemporary common method: the multiple recursive generator, MRG32k3a. Although our method is about 7 times slower than MRG32k3a, there is in principle no apparent limit on the number of possible values that can be generated from the scheme we present here.
NASA Astrophysics Data System (ADS)
Barash, L. Yu.; Shchur, L. N.
2014-04-01
The library PRAND for pseudorandom number generation for modern CPUs and GPUs is presented. It contains both single-threaded and multi-threaded realizations of a number of modern and most reliable generators recently proposed and studied in Barash (2011), Matsumoto and Tishimura (1998), L'Ecuyer (1999,1999), Barash and Shchur (2006) and the efficient SIMD realizations proposed in Barash and Shchur (2011). One of the useful features for using PRAND in parallel simulations is the ability to initialize up to 1019 independent streams. Using massive parallelism of modern GPUs and SIMD parallelism of modern CPUs substantially improves performance of the generators.
True random numbers from amplified quantum vacuum.
Jofre, M; Curty, M; Steinlechner, F; Anzolin, G; Torres, J P; Mitchell, M W; Pruneri, V
2011-10-10
Random numbers are essential for applications ranging from secure communications to numerical simulation and quantitative finance. Algorithms can rapidly produce pseudo-random outcomes, series of numbers that mimic most properties of true random numbers while quantum random number generators (QRNGs) exploit intrinsic quantum randomness to produce true random numbers. Single-photon QRNGs are conceptually simple but produce few random bits per detection. In contrast, vacuum fluctuations are a vast resource for QRNGs: they are broad-band and thus can encode many random bits per second. Direct recording of vacuum fluctuations is possible, but requires shot-noise-limited detectors, at the cost of bandwidth. We demonstrate efficient conversion of vacuum fluctuations to true random bits using optical amplification of vacuum and interferometry. Using commercially-available optical components we demonstrate a QRNG at a bit rate of 1.11 Gbps. The proposed scheme has the potential to be extended to 10 Gbps and even up to 100 Gbps by taking advantage of high speed modulation sources and detectors for optical fiber telecommunication devices. PMID:21997077
ERIC Educational Resources Information Center
Rinehart, Nicole J.; Bradshaw, John L.; Moss, Simon A.; Brereton, Avril V.; Tonge, Bruce J.
2006-01-01
The repetitive, stereotyped and obsessive behaviours, which are core diagnostic features of autism, are thought to be underpinned by executive dysfunction. This study examined executive impairment in individuals with autism and Asperger's disorder using a verbal equivalent of an established pseudo-random number generating task. Different patterns…
NASA Technical Reports Server (NTRS)
Lindsey, R. S., Jr. (Inventor)
1975-01-01
An exemplary embodiment of the present invention provides a source of random width and random spaced rectangular voltage pulses whose mean or average frequency of operation is controllable within prescribed limits of about 10 hertz to 1 megahertz. A pair of thin-film metal resistors are used to provide a differential white noise voltage pulse source. Pulse shaping and amplification circuitry provide relatively short duration pulses of constant amplitude which are applied to anti-bounce logic circuitry to prevent ringing effects. The pulse outputs from the anti-bounce circuits are then used to control two one-shot multivibrators whose output comprises the random length and random spaced rectangular pulses. Means are provided for monitoring, calibrating and evaluating the relative randomness of the generator.
Yang, Yu-Guang; Xu, Peng; Yang, Rui; Zhou, Yi-Hua; Shi, Wei-Min
2016-01-01
Quantum information and quantum computation have achieved a huge success during the last years. In this paper, we investigate the capability of quantum Hash function, which can be constructed by subtly modifying quantum walks, a famous quantum computation model. It is found that quantum Hash function can act as a hash function for the privacy amplification process of quantum key distribution systems with higher security. As a byproduct, quantum Hash function can also be used for pseudo-random number generation due to its inherent chaotic dynamics. Further we discuss the application of quantum Hash function to image encryption and propose a novel image encryption algorithm. Numerical simulations and performance comparisons show that quantum Hash function is eligible for privacy amplification in quantum key distribution, pseudo-random number generation and image encryption in terms of various hash tests and randomness tests. It extends the scope of application of quantum computation and quantum information. PMID:26823196
Yang, Yu-Guang; Xu, Peng; Yang, Rui; Zhou, Yi-Hua; Shi, Wei-Min
2016-01-01
Quantum information and quantum computation have achieved a huge success during the last years. In this paper, we investigate the capability of quantum Hash function, which can be constructed by subtly modifying quantum walks, a famous quantum computation model. It is found that quantum Hash function can act as a hash function for the privacy amplification process of quantum key distribution systems with higher security. As a byproduct, quantum Hash function can also be used for pseudo-random number generation due to its inherent chaotic dynamics. Further we discuss the application of quantum Hash function to image encryption and propose a novel image encryption algorithm. Numerical simulations and performance comparisons show that quantum Hash function is eligible for privacy amplification in quantum key distribution, pseudo-random number generation and image encryption in terms of various hash tests and randomness tests. It extends the scope of application of quantum computation and quantum information. PMID:26823196
NASA Astrophysics Data System (ADS)
Yang, Yu-Guang; Xu, Peng; Yang, Rui; Zhou, Yi-Hua; Shi, Wei-Min
2016-01-01
Quantum information and quantum computation have achieved a huge success during the last years. In this paper, we investigate the capability of quantum Hash function, which can be constructed by subtly modifying quantum walks, a famous quantum computation model. It is found that quantum Hash function can act as a hash function for the privacy amplification process of quantum key distribution systems with higher security. As a byproduct, quantum Hash function can also be used for pseudo-random number generation due to its inherent chaotic dynamics. Further we discuss the application of quantum Hash function to image encryption and propose a novel image encryption algorithm. Numerical simulations and performance comparisons show that quantum Hash function is eligible for privacy amplification in quantum key distribution, pseudo-random number generation and image encryption in terms of various hash tests and randomness tests. It extends the scope of application of quantum computation and quantum information.
ERIC Educational Resources Information Center
Griffiths, Martin
2011-01-01
One of the author's undergraduate students recently asked him whether it was possible to generate a random positive integer. After some thought, the author realised that there were plenty of interesting mathematical ideas inherent in her question. So much so in fact, that the author decided to organise a workshop, open both to undergraduates and…
Mohr, Christine; Koutrakis, Nikolaos; Kuhn, Gustav
2014-01-01
Magical ideation and belief in the paranormal is considered to represent a trait-like character; people either believe in it or not. Yet, anecdotes indicate that exposure to an anomalous event can turn skeptics into believers. This transformation is likely to be accompanied by altered cognitive functioning such as impaired judgments of event likelihood. Here, we investigated whether the exposure to an anomalous event changes individuals' explicit traditional (religious) and non-traditional (e.g., paranormal) beliefs as well as cognitive biases that have previously been associated with non-traditional beliefs, e.g., repetition avoidance when producing random numbers in a mental dice task. In a classroom, 91 students saw a magic demonstration after their psychology lecture. Before the demonstration, half of the students were told that the performance was done respectively by a conjuror (magician group) or a psychic (psychic group). The instruction influenced participants' explanations of the anomalous event. Participants in the magician, as compared to the psychic group, were more likely to explain the event through conjuring abilities while the reverse was true for psychic abilities. Moreover, these explanations correlated positively with their prior traditional and non-traditional beliefs. Finally, we observed that the psychic group showed more repetition avoidance than the magician group, and this effect remained the same regardless of whether assessed before or after the magic demonstration. We conclude that pre-existing beliefs and contextual suggestions both influence people's interpretations of anomalous events and associated cognitive biases. Beliefs and associated cognitive biases are likely flexible well into adulthood and change with actual life events. PMID:25653626
Mohr, Christine; Koutrakis, Nikolaos; Kuhn, Gustav
2015-01-01
Magical ideation and belief in the paranormal is considered to represent a trait-like character; people either believe in it or not. Yet, anecdotes indicate that exposure to an anomalous event can turn skeptics into believers. This transformation is likely to be accompanied by altered cognitive functioning such as impaired judgments of event likelihood. Here, we investigated whether the exposure to an anomalous event changes individuals’ explicit traditional (religious) and non-traditional (e.g., paranormal) beliefs as well as cognitive biases that have previously been associated with non-traditional beliefs, e.g., repetition avoidance when producing random numbers in a mental dice task. In a classroom, 91 students saw a magic demonstration after their psychology lecture. Before the demonstration, half of the students were told that the performance was done respectively by a conjuror (magician group) or a psychic (psychic group). The instruction influenced participants’ explanations of the anomalous event. Participants in the magician, as compared to the psychic group, were more likely to explain the event through conjuring abilities while the reverse was true for psychic abilities. Moreover, these explanations correlated positively with their prior traditional and non-traditional beliefs. Finally, we observed that the psychic group showed more repetition avoidance than the magician group, and this effect remained the same regardless of whether assessed before or after the magic demonstration. We conclude that pre-existing beliefs and contextual suggestions both influence people’s interpretations of anomalous events and associated cognitive biases. Beliefs and associated cognitive biases are likely flexible well into adulthood and change with actual life events. PMID:25653626
ERIC Educational Resources Information Center
Ben-Ari, Morechai
2004-01-01
The term "random" is frequently used in discussion of the theory of evolution, even though the mathematical concept of randomness is problematic and of little relevance in the theory. Therefore, since the core concept of the theory of evolution is the non-random process of natural selection, the term random should not be used in teaching the…
Random walks on the mental number line.
Shaki, Samuel; Fischer, Martin H
2014-01-01
The direction of influence between conceptual and motor activation, and its relevance for real-life activities, is still unclear. Here, we use the frequently reported association between small/large numbers and left/right space to investigate this issue during walking. We asked healthy adults to generate random numbers as they made lateral turns and found that (1) lateral turn decisions are predicted by the last few numbers generated prior to turning; (2) the intention to turn left/right makes small/large numbers more accessible; and (3) magnitude but not order of auditorily presented numbers influences the listener's turn selection. Our findings document a bidirectional influence between conceptual and motor activation and point to a hierarchically organized conceptual-motor activation. PMID:24091774
Autocorrelation peaks in congruential pseudorandom number generators
NASA Technical Reports Server (NTRS)
Neuman, F.; Merrick, R. B.
1976-01-01
The complete correlation structure of several congruential pseudorandom number generators (PRNG) of the same type and small cycle length was studied to deal with the problem of congruential PRNG almost repeating themselves at intervals smaller than their cycle lengths, during simulation of bandpass filtered normal random noise. Maximum period multiplicative and mixed congruential generators were studied, with inferences drawn from examination of several tractable members of a class of random number generators, and moduli from 2 to the 5th power to 2 to the 9th power. High correlation is shown to exist in mixed and multiplicative congruential random number generators and prime moduli Lehmer generators for shifts a fraction of their cycle length. The random noise sequences in question are required when simulating electrical noise, air turbulence, or time variation of wind parameters.
Can brains generate random numbers?
NASA Astrophysics Data System (ADS)
Chvátal, V.; Goldsmith, M.
2013-01-01
Motivated by EEG recordings of normal brain activity, we construct arbitrarily large McCulloch-Pitts neural networks that, without any external input, make every subset of their neurons fire in some iteration (and therefore in infinitely many iterations).
Security of practical private randomness generation
NASA Astrophysics Data System (ADS)
Pironio, Stefano; Massar, Serge
2013-01-01
Measurements on entangled quantum systems necessarily yield outcomes that are intrinsically unpredictable if they violate a Bell inequality. This property can be used to generate certified randomness in a device-independent way, i.e., without making detailed assumptions about the internal working of the quantum devices used to generate the random numbers. Furthermore these numbers are also private; i.e., they appear random not only to the user but also to any adversary that might possess a perfect description of the devices. Since this process requires a small initial random seed to sample the behavior of the quantum devices and to extract uniform randomness from the raw outputs of the devices, one usually speaks of device-independent randomness expansion. The purpose of this paper is twofold. First, we point out that in most real, practical situations, where the concept of device independence is used as a protection against unintentional flaws or failures of the quantum apparatuses, it is sufficient to show that the generated string is random with respect to an adversary that holds only classical side information; i.e., proving randomness against quantum side information is not necessary. Furthermore, the initial random seed does not need to be private with respect to the adversary, provided that it is generated in a way that is independent from the measured systems. The devices, however, will generate cryptographically secure randomness that cannot be predicted by the adversary, and thus one can, given access to free public randomness, talk about private randomness generation. The theoretical tools to quantify the generated randomness according to these criteria were already introduced in S. Pironio [Nature (London)NATUAS0028-083610.1038/nature09008 464, 1021 (2010)], but the final results were improperly formulated. The second aim of this paper is to correct this inaccurate formulation and therefore lay out a precise theoretical framework for practical device
Experimental certification of random numbers via quantum contextuality.
Um, Mark; Zhang, Xiang; Zhang, Junhua; Wang, Ye; Yangchao, Shen; Deng, D-L; Duan, Lu-Ming; Kim, Kihwan
2013-01-01
The intrinsic unpredictability of measurements in quantum mechanics can be used to produce genuine randomness. Here, we demonstrate a random number generator where the randomness is certified by quantum contextuality in connection with the Kochen-Specker theorem. In particular, we generate random numbers from measurements on a single trapped ion with three internal levels, and certify the generated randomness by showing a bound on the minimum entropy through observation of violation of the Klyachko-Can-Binicioglu-Shumovsky (KCBS) inequality. Concerning the test of the KCBS inequality, we close the detection efficiency loophole for the first time and make it relatively immune to the compatibility loophole. In our experiment, we generate 1 × 10(5) random numbers that are guaranteed to have 5.2 × 10(4) bits of minimum entropy with a 99% confidence level. PMID:23568082
Experimental Certification of Random Numbers via Quantum Contextuality
Um, Mark; Zhang, Xiang; Zhang, Junhua; Wang, Ye; Yangchao, Shen; Deng, D. -L; Duan, Lu-Ming; Kim, Kihwan
2013-01-01
The intrinsic unpredictability of measurements in quantum mechanics can be used to produce genuine randomness. Here, we demonstrate a random number generator where the randomness is certified by quantum contextuality in connection with the Kochen-Specker theorem. In particular, we generate random numbers from measurements on a single trapped ion with three internal levels, and certify the generated randomness by showing a bound on the minimum entropy through observation of violation of the Klyachko-Can-Binicioglu-Shumovsky (KCBS) inequality. Concerning the test of the KCBS inequality, we close the detection efficiency loophole for the first time and make it relatively immune to the compatibility loophole. In our experiment, we generate 1 × 105 random numbers that are guaranteed to have 5.2 × 104 bits of minimum entropy with a 99% confidence level. PMID:23568082
NASA Astrophysics Data System (ADS)
Tang, X.; Wu, Z. M.; Wu, J. G.; Deng, T.; Fan, L.; Zhong, Z. Q.; Chen, J. J.; Xia, G. Q.
2015-01-01
We propose and experimentally demonstrate a novel technique to generate multi-channel high-speed physical random numbers (PRNs) by taking two chaotic signal outputs from mutually coupled semiconductor lasers (MC-SLs) as entropy sources. First, through controlling the operation parameters of the MC-SL system, two time-delay signature (TDS) suppressed chaotic signals can be obtained. Next, each of these two chaotic signals is sampled by an 8 bit analog-to-digital converter (ADC) with a sampling rate of 10 GHz, and then a bitwise exclusive-OR (XOR) operation on the corresponding bits in samples of the chaotic signal and its time delayed signal is implemented to obtain 8 bit XOR data. Furthermore, through selecting the five least significant bits (LSBs) of 8 bit XOR data to form 5 bit Boolean sequences, two sets of PRN streams with a rate up to 50 Gbits s-1 are generated and successfully pass the NIST statistical tests. Finally, merging these two sets of 50 Gbits s-1 PRN streams by an interleaving operation, another set of the 100 Gbits s-1 PRN stream, which meets all the quality criteria of NIST statistical tests, is also acquired.
Efficient generation of large random networks
NASA Astrophysics Data System (ADS)
Batagelj, Vladimir; Brandes, Ulrik
2005-03-01
Random networks are frequently generated, for example, to investigate the effects of model parameters on network properties or to test the performance of algorithms. Recent interest in the statistics of large-scale networks sparked a growing demand for network generators that can generate large numbers of large networks quickly. We here present simple and efficient algorithms to randomly generate networks according to the most commonly used models. Their running time and space requirement is linear in the size of the network generated, and they are easily implemented.
Physical tests for random numbers in simulations
Vattulainen, I.; Ala-Nissila, T.; Kankaala, K. , FIN-00014 University of Helsinki Department of Electrical Engineering, Tampere University of Technology, P.O. Box 692, FIN-3310, Tampere Center for Scientific Computing, P.O. Box 405, FIN-02101 Espoo )
1994-11-07
We propose three physical tests to measure correlations in random numbers used in Monte Carlo simulations. The first test uses autocorrelation times of certain physical quantities when the Ising model is simulated with the Wolff algorithm. The second test is based on random walks, and the third on blocks of [ital n] successive numbers. We apply the tests to show that recent errors in high precision Ising simulations using generalized feedback shift register algorithms are due to short range correlations in random number sequences.
Computer generation of random deviates.
Cormack, J; Shuter, B
1991-06-01
The need for random deviates arises in many scientific applications, such as the simulation of physical processes, numerical evaluation of complex mathematical formulae and the modeling of decision processes. In medical physics, Monte Carlo simulations have been used in radiology, radiation therapy and nuclear medicine. Specific instances include the modelling of x-ray scattering processes and the addition of random noise to images or curves in order to assess the effects of various processing procedures. Reliable sources of random deviates with statistical properties indistinguishable from true random deviates are a fundamental necessity for such tasks. This paper provides a review of computer algorithms which can be used to generate uniform random deviates and other distributions of interest to medical physicists, along with a few caveats relating to various problems and pitfalls which can occur. Source code listings for the generators discussed (in FORTRAN, Turbo-PASCAL and Data General ASSEMBLER) are available on request from the authors. PMID:1747086
NASA Astrophysics Data System (ADS)
Taylor, Adam; Bennie, Peter; Guyon, Fredric; Cameron, Iain; Glanfield, James; Emam, Omar
2013-08-01
This paper describes a proposal for a space flight demonstration of a low power, compact Dynamically Reconfigurable Programmable Board (DRPB) based upon a minor evolution of the Astrium Janus payload for UKube 1. The Janus payload is one of a number of the payloads selected to be part of the first national UK-Cube satellite (UKube) [1] to be sponsored by the UK Space Agency. In the UKube configuration the demonstrator performs two experiments the first uses firmware to realise an Astrium patented cosmic random number generator for generating secure cryptographic keys while the second monitors the large high performance SRAM based FPGA for SEU and SEFI events allowing correlation with predicted upset rates. This experiment is called the Janus experiment after the two-faced roman god of beginnings and transitions, transitioning from clear text to encrypted and marking the beginning of flying advanced FPGA's on suitable missions.
Quasi-Random Sequence Generators.
Energy Science and Technology Software Center (ESTSC)
1994-03-01
Version 00 LPTAU generates quasi-random sequences. The sequences are uniformly distributed sets of L=2**30 points in the N-dimensional unit cube: I**N=[0,1]. The sequences are used as nodes for multidimensional integration, as searching points in global optimization, as trial points in multicriteria decision making, as quasi-random points for quasi Monte Carlo algorithms.
Fast generation of sparse random kernel graphs
Hagberg, Aric; Lemons, Nathan; Du, Wen -Bo
2015-09-10
The development of kernel-based inhomogeneous random graphs has provided models that are flexible enough to capture many observed characteristics of real networks, and that are also mathematically tractable. We specify a class of inhomogeneous random graph models, called random kernel graphs, that produces sparse graphs with tunable graph properties, and we develop an efficient generation algorithm to sample random instances from this model. As real-world networks are usually large, it is essential that the run-time of generation algorithms scales better than quadratically in the number of vertices n. We show that for many practical kernels our algorithm runs in timemore » at most ο(n(logn)²). As an example, we show how to generate samples of power-law degree distribution graphs with tunable assortativity.« less
Fast generation of sparse random kernel graphs
Hagberg, Aric; Lemons, Nathan; Du, Wen -Bo
2015-09-10
The development of kernel-based inhomogeneous random graphs has provided models that are flexible enough to capture many observed characteristics of real networks, and that are also mathematically tractable. We specify a class of inhomogeneous random graph models, called random kernel graphs, that produces sparse graphs with tunable graph properties, and we develop an efficient generation algorithm to sample random instances from this model. As real-world networks are usually large, it is essential that the run-time of generation algorithms scales better than quadratically in the number of vertices n. We show that for many practical kernels our algorithm runs in time at most ο(n(logn)²). As an example, we show how to generate samples of power-law degree distribution graphs with tunable assortativity.
Fast Generation of Sparse Random Kernel Graphs
2015-01-01
The development of kernel-based inhomogeneous random graphs has provided models that are flexible enough to capture many observed characteristics of real networks, and that are also mathematically tractable. We specify a class of inhomogeneous random graph models, called random kernel graphs, that produces sparse graphs with tunable graph properties, and we develop an efficient generation algorithm to sample random instances from this model. As real-world networks are usually large, it is essential that the run-time of generation algorithms scales better than quadratically in the number of vertices n. We show that for many practical kernels our algorithm runs in time at most 𝒪(n(logn)2). As a practical example we show how to generate samples of power-law degree distribution graphs with tunable assortativity. PMID:26356296
Security of Semi-Device-Independent Random Number Expansion Protocols
Li, Dan-Dan; Wen, Qiao-Yan; Wang, Yu-Kun; Zhou, Yu-Qian; Gao, Fei
2015-01-01
Semi-device-independent random number expansion (SDI-RNE) protocols require some truly random numbers to generate fresh ones, with making no assumptions on the internal working of quantum devices except for the dimension of the Hilbert space. The generated randomness is certified by non-classical correlation in the prepare-and-measure test. Until now, the analytical relations between the amount of the generated randomness and the degree of non-classical correlation, which are crucial for evaluating the security of SDI-RNE protocols, are not clear under both the ideal condition and the practical one. In the paper, first, we give the analytical relation between the above two factors under the ideal condition. As well, we derive the analytical relation under the practical conditions, where devices’ behavior is not independent and identical in each round and there exists deviation in estimating the non-classical behavior of devices. Furthermore, we choose a different randomness extractor (i.e., two-universal random function) and give the security proof. PMID:26503335
Security of Semi-Device-Independent Random Number Expansion Protocols.
Li, Dan-Dan; Wen, Qiao-Yan; Wang, Yu-Kun; Zhou, Yu-Qian; Gao, Fei
2015-01-01
Semi-device-independent random number expansion (SDI-RNE) protocols require some truly random numbers to generate fresh ones, with making no assumptions on the internal working of quantum devices except for the dimension of the Hilbert space. The generated randomness is certified by non-classical correlation in the prepare-and-measure test. Until now, the analytical relations between the amount of the generated randomness and the degree of non-classical correlation, which are crucial for evaluating the security of SDI-RNE protocols, are not clear under both the ideal condition and the practical one. In the paper, first, we give the analytical relation between the above two factors under the ideal condition. As well, we derive the analytical relation under the practical conditions, where devices' behavior is not independent and identical in each round and there exists deviation in estimating the non-classical behavior of devices. Furthermore, we choose a different randomness extractor (i.e., two-universal random function) and give the security proof. PMID:26503335
Entanglement generation of nearly random operators.
Weinstein, Yaakov S; Hellberg, C Stephen
2005-07-15
We study the entanglement generation of operators whose statistical properties approach those of random matrices but are restricted in some way. These include interpolating ensemble matrices, where the interval of the independent random parameters are restricted, pseudorandom operators, where there are far fewer random parameters than required for random matrices, and quantum chaotic evolution. Restricting randomness in different ways allows us to probe connections between entanglement and randomness. We comment on which properties affect entanglement generation and discuss ways of efficiently producing random states on a quantum computer. PMID:16090726
Physical Principle for Generation of Randomness
NASA Technical Reports Server (NTRS)
Zak, Michail
2009-01-01
A physical principle (more precisely, a principle that incorporates mathematical models used in physics) has been conceived as the basis of a method of generating randomness in Monte Carlo simulations. The principle eliminates the need for conventional random-number generators. The Monte Carlo simulation method is among the most powerful computational methods for solving high-dimensional problems in physics, chemistry, economics, and information processing. The Monte Carlo simulation method is especially effective for solving problems in which computational complexity increases exponentially with dimensionality. The main advantage of the Monte Carlo simulation method over other methods is that the demand on computational resources becomes independent of dimensionality. As augmented by the present principle, the Monte Carlo simulation method becomes an even more powerful computational method that is especially useful for solving problems associated with dynamics of fluids, planning, scheduling, and combinatorial optimization. The present principle is based on coupling of dynamical equations with the corresponding Liouville equation. The randomness is generated by non-Lipschitz instability of dynamics triggered and controlled by feedback from the Liouville equation. (In non-Lipschitz dynamics, the derivatives of solutions of the dynamical equations are not required to be bounded.)
The correlation structure of several popular pseudorandom number generators
NASA Technical Reports Server (NTRS)
Neuman, F.; Merrick, R.; Martin, C. F.
1973-01-01
One of the desirable properties of a pseudorandom number generator is that the sequence of numbers it generates should have very low autocorrelation for all shifts except for zero shift and those that are multiples of its cycle length. Due to the simple methods of constructing random numbers, the ideal is often not quite fulfilled. A simple method of examining any random generator for previously unsuspected regularities is discussed. Once they are discovered it is often easy to derive the mathematical relationships, which describe the mathematical relationships, which describe the regular behavior. As examples, it is shown that high correlation exists in mixed and multiplicative congruential random number generators and prime moduli Lehmer generators for shifts a fraction of their cycle lengths.
Integrated-Circuit Pseudorandom-Number Generator
NASA Technical Reports Server (NTRS)
Steelman, James E.; Beasley, Jeff; Aragon, Michael; Ramirez, Francisco; Summers, Kenneth L.; Knoebel, Arthur
1992-01-01
Integrated circuit produces 8-bit pseudorandom numbers from specified probability distribution, at rate of 10 MHz. Use of Boolean logic, circuit implements pseudorandom-number-generating algorithm. Circuit includes eight 12-bit pseudorandom-number generators, outputs are uniformly distributed. 8-bit pseudorandom numbers satisfying specified nonuniform probability distribution are generated by processing uniformly distributed outputs of eight 12-bit pseudorandom-number generators through "pipeline" of D flip-flops, comparators, and memories implementing conditional probabilities on zeros and ones.
Computer routines for probability distributions, random numbers, and related functions
Kirby, W.
1983-01-01
Use of previously coded and tested subroutines simplifies and speeds up program development and testing. This report presents routines that can be used to calculate various probability distributions and other functions of importance in statistical hydrology. The routines are designed as general-purpose Fortran subroutines and functions to be called from user-written main progress. The probability distributions provided include the beta, chi-square, gamma, Gaussian (normal), Pearson Type III (tables and approximation), and Weibull. Also provided are the distributions of the Grubbs-Beck outlier test, Kolmogorov 's and Smirnov 's D, Student 's t, noncentral t (approximate), and Snedecor F. Other mathematical functions include the Bessel function, I sub o, gamma and log-gamma functions, error functions, and exponential integral. Auxiliary services include sorting and printer-plotting. Random number generators for uniform and normal numbers are provided and may be used with some of the above routines to generate numbers from other distributions. (USGS)
Computer routines for probability distributions, random numbers, and related functions
Kirby, W.H.
1980-01-01
Use of previously codes and tested subroutines simplifies and speeds up program development and testing. This report presents routines that can be used to calculate various probability distributions and other functions of importance in statistical hydrology. The routines are designed as general-purpose Fortran subroutines and functions to be called from user-written main programs. The probability distributions provided include the beta, chisquare, gamma, Gaussian (normal), Pearson Type III (tables and approximation), and Weibull. Also provided are the distributions of the Grubbs-Beck outlier test, Kolmogorov 's and Smirnov 's D, Student 's t, noncentral t (approximate), and Snedecor F tests. Other mathematical functions include the Bessel function I (subzero), gamma and log-gamma functions, error functions and exponential integral. Auxiliary services include sorting and printer plotting. Random number generators for uniform and normal numbers are provided and may be used with some of the above routines to generate numbers from other distributions. (USGS)
Configurable Cellular Automata for Pseudorandom Number Generation
NASA Astrophysics Data System (ADS)
Quieta, Marie Therese; Guan, Sheng-Uei
This paper proposes a generalized structure of cellular automata (CA) — the configurable cellular automata (CoCA). With selected properties from programmable CA (PCA) and controllable CA (CCA), a new approach to cellular automata is developed. In CoCA, the cells are dynamically reconfigured at run-time via a control CA. Reconfiguration of a cell simply means varying the properties of that cell with time. Some examples of properties to be reconfigured are rule selection, boundary condition, and radius. While the objective of this paper is to propose CoCA as a new CA method, the main focus is to design a CoCA that can function as a good pseudorandom number generator (PRNG). As a PRNG, CoCA can be a suitable candidate as it can pass 17 out of 18 Diehard tests with 31 cells. CoCA PRNG's performance based on Diehard test is considered superior over other CA PRNG works. Moreover, CoCA opens new rooms for research not only in the field of random number generation, but in modeling complex systems as well.
Random, but Uniform Please: Requirements for Synthetic Weather Generation
Technology Transfer Automated Retrieval System (TEKTRAN)
Synthetic weather generation models often rely on standard uniform random numbers (RN) to simulate stochastic aspects of weather. However, short sequences of RNs, needed to generate certain weather variables, are not necessarily uniformly distributed, as assumed by weather generation models, and may...
Which numbers do you have in mind? Number generation is influenced by reading direction.
Göbel, Silke M; Maier, Carolin A; Shaki, Samuel
2015-09-01
In Western participants, small numbers are associated with left and larger numbers with right space. A biological account proposes that brain asymmetries lead to these attentional asymmetries in number space. In contrast, a cultural account proposes that the direction of this association is shaped by reading direction. We explored whether number generation is influenced by reading direction in participants from a left-to-right (UK) and a right-to-left (Arab) reading culture. Participants generated numbers randomly while lying on their left and right side. The mean number generated by participants from a left-to-right reading culture was smaller when they lay on their left than on their right side, and the opposite was found for participants from a right-to-left reading culture. Asymmetries in number space observed in number generation are more compatible with a cultural than biological account. PMID:26224271
Generating functionals for quantum field theories with random potentials
NASA Astrophysics Data System (ADS)
Jain, Mudit; Vanchurin, Vitaly
2016-01-01
We consider generating functionals for computing correlators in quantum field theories with random potentials. Examples of such theories include cosmological systems in context of the string theory landscape (e.g. cosmic inflation) or condensed matter systems with quenched disorder (e.g. spin glass). We use the so-called replica trick to define two different generating functionals for calculating correlators of the quantum fields averaged over a given distribution of random potentials. The first generating functional is appropriate for calculating averaged (in-out) amplitudes and involves a single replica of fields, but the replica limit is taken to an (unphysical) negative one number of fields outside of the path integral. When the number of replicas is doubled the generating functional can also be used for calculating averaged probabilities (squared amplitudes) using the in-in construction. The second generating functional involves an infinite number of replicas, but can be used for calculating both in-out and in-in correlators and the replica limits are taken to only a zero number of fields. We discuss the formalism in details for a single real scalar field, but the generalization to more fields or to different types of fields is straightforward. We work out three examples: one where the mass of scalar field is treated as a random variable and two where the functional form of interactions is random, one described by a Gaussian random field and the other by a Euclidean action in the field configuration space.
On grey levels in random CAPTCHA generation
NASA Astrophysics Data System (ADS)
Newton, Fraser; Kouritzin, Michael A.
2011-06-01
A CAPTCHA is an automatically generated test designed to distinguish between humans and computer programs; specifically, they are designed to be easy for humans but difficult for computer programs to pass in order to prevent the abuse of resources by automated bots. They are commonly seen guarding webmail registration forms, online auction sites, and preventing brute force attacks on passwords. In the following, we address the question: How does adding a grey level to random CAPTCHA generation affect the utility of the CAPTCHA? We treat the problem of generating the random CAPTCHA as one of random field simulation: An initial state of background noise is evolved over time using Gibbs sampling and an efficient algorithm for generating correlated random variables. This approach has already been found to yield highly-readable yet difficult-to-crack CAPTCHAs. We detail how the requisite parameters for introducing grey levels are estimated and how we generate the random CAPTCHA. The resulting CAPTCHA will be evaluated in terms of human readability as well as its resistance to automated attacks in the forms of character segmentation and optical character recognition.
Random generation of structured linear optimization problems
Arthur, J.; Frendewey, J. Jr.
1994-12-31
We describe the on-going development of a random generator for linear optimization problems (LPs) founded on the concept of block structure. The general LP: minimize z = cx subject to Ax = b, x {ge} 0 can take a variety of special forms determined (primarily) by predefined structures on the matrix A of constraint coefficients. The authors have developed several random problem generators which provide instances of LPs having such structure; in particular (i) general (non-structured) problems, (ii) generalized upper bound (GUB) constraints, (iii) minimum cost network flow problems, (iv) transportation and assignment problems, (v) shortest path problems, (vi) generalized network flow problems, and (vii) multicommodity network flow problems. This paper discusses the general philosophy behind the construction of these generators. In addition, the task of combining the generators into a single generator -- in which the matrix A can contain various blocks, each of a prescribed structure from those mentioned above -- is described.
Recycling random numbers in the stochastic simulation algorithm.
Yates, Christian A; Klingbeil, Guido
2013-03-01
The stochastic simulation algorithm (SSA) was introduced by Gillespie and in a different form by Kurtz. Since its original formulation there have been several attempts at improving the efficiency and hence the speed of the algorithm. We briefly discuss some of these methods before outlining our own simple improvement, the recycling direct method (RDM), and demonstrating that it is capable of increasing the speed of most stochastic simulations. The RDM involves the statistically acceptable recycling of random numbers in order to reduce the computational cost associated with their generation and is compatible with several of the pre-existing improvements on the original SSA. Our improvement is also sufficiently simple (one additional line of code) that we hope will be adopted by both trained mathematical modelers and experimentalists wishing to simulate their model systems. PMID:23485273
Code System to Generate Latin Hypercube and Random Samples.
Energy Science and Technology Software Center (ESTSC)
1999-02-25
Version: 00 LHS was written for the generation of multi variate samples either completely at random or by a constrained randomization termed Latin hypercube sampling (LHS). The generation of these samples is based on user-specified parameters which dictate the characteristics of the generated samples, such as type of sample (LHS or random), sample size, number of samples desired, correlation structure on input variables, and type of distribution specified on each variable. The following distributions aremore » built into the program: normal, lognormal, uniform, loguniform, triangular, and beta. In addition, the samples from the uniform and loguniform distributions may be modified by changing the frequency of the sampling within subintervals, and a subroutine which can be modified by the user to generate samples from other distributions (including empirical data) is provided.« less
Code System to Generate Latin Hypercube and Random Samples.
IMAN, RONALD L.
1999-02-25
Version: 00 LHS was written for the generation of multi variate samples either completely at random or by a constrained randomization termed Latin hypercube sampling (LHS). The generation of these samples is based on user-specified parameters which dictate the characteristics of the generated samples, such as type of sample (LHS or random), sample size, number of samples desired, correlation structure on input variables, and type of distribution specified on each variable. The following distributions are built into the program: normal, lognormal, uniform, loguniform, triangular, and beta. In addition, the samples from the uniform and loguniform distributions may be modified by changing the frequency of the sampling within subintervals, and a subroutine which can be modified by the user to generate samples from other distributions (including empirical data) is provided.
Saturation of number variance in embedded random-matrix ensembles
NASA Astrophysics Data System (ADS)
Prakash, Ravi; Pandey, Akhilesh
2016-05-01
We study fluctuation properties of embedded random matrix ensembles of noninteracting particles. For ensemble of two noninteracting particle systems, we find that unlike the spectra of classical random matrices, correlation functions are nonstationary. In the locally stationary region of spectra, we study the number variance and the spacing distributions. The spacing distributions follow the Poisson statistics, which is a key behavior of uncorrelated spectra. The number variance varies linearly as in the Poisson case for short correlation lengths but a kind of regularization occurs for large correlation lengths, and the number variance approaches saturation values. These results are known in the study of integrable systems but are being demonstrated for the first time in random matrix theory. We conjecture that the interacting particle cases, which exhibit the characteristics of classical random matrices for short correlation lengths, will also show saturation effects for large correlation lengths.
Building Kindergartners' Number Sense: A Randomized Controlled Study
ERIC Educational Resources Information Center
Jordan, Nancy C.; Glutting, Joseph; Dyson, Nancy; Hassinger-Das, Brenna; Irwin, Casey
2012-01-01
Math achievement in elementary school is mediated by performance and growth in number sense during kindergarten. The aim of the present study was to test the effectiveness of a targeted small-group number sense intervention for high-risk kindergartners from low-income communities. Children were randomly assigned to 1 of 3 groups (n = 44 in each…
Quantum random bit generation using stimulated Raman scattering.
Bustard, Philip J; Moffatt, Doug; Lausten, Rune; Wu, Guorong; Walmsley, Ian A; Sussman, Benjamin J
2011-12-01
Random number sequences are a critical resource in a wide variety of information systems, including applications in cryptography, simulation, and data sampling. We introduce a quantum random number generator based on the phase measurement of Stokes light generated by amplification of zero-point vacuum fluctuations using stimulated Raman scattering. This is an example of quantum noise amplification using the most noise-free process possible: near unitary quantum evolution. The use of phase offers robustness to classical pump noise and the ability to generate multiple bits per measurement. The Stokes light is generated with high intensity and as a result, fast detectors with high signal-to-noise ratios can be used for measurement, eliminating the need for single-photon sensitive devices. The demonstrated implementation uses optical phonons in bulk diamond. PMID:22273908
The Generation of Random Equilateral Polygons
NASA Astrophysics Data System (ADS)
Alvarado, Sotero; Calvo, Jorge Alberto; Millett, Kenneth C.
2011-04-01
Freely jointed random equilateral polygons serve as a common model for polymer rings, reflecting their statistical properties under theta conditions. To generate equilateral polygons, researchers employ many procedures that have been proved, or at least are believed, to be random with respect to the natural measure on the space of polygonal knots. As a result, the random selection of equilateral polygons, as well as the statistical robustness of this selection, is of particular interest. In this research, we study the key features of four popular methods: the Polygonal Folding, the Crankshaft Rotation, the Hedgehog, and the Triangle Methods. In particular, we compare the implementation and efficacy of these procedures, especially in regards to the population distribution of polygons in the space of polygonal knots, the distribution of edge vectors, the local curvature, and the local torsion. In addition, we give a rigorous proof that the Crankshaft Rotation Method is ergodic.
Uniqueness: skews bit occurrence frequencies in randomly generated fingerprint libraries.
Chen, Nelson G
2016-08-01
Requiring that randomly generated chemical fingerprint libraries have unique fingerprints such that no two fingerprints are identical causes a systematic skew in bit occurrence frequencies, the proportion at which specified bits are set. Observed frequencies (O) at which each bit is set within the resulting libraries systematically differ from frequencies at which bits are set at fingerprint generation (E). Observed frequencies systematically skew toward 0.5, with the effect being more pronounced as library size approaches the compound space, which is the total number of unique possible fingerprints given the number of bit positions each fingerprint contains. The effect is quantified for varying library sizes as a fraction of the overall compound space, and for changes in the specified frequency E. The cause and implications for this systematic skew are subsequently discussed. When generating random libraries of chemical fingerprints, the imposition of a uniqueness requirement should either be avoided or taken into account. PMID:27230477
Efficient biased random bit generation for parallel processing
Slone, D.M.
1994-09-28
A lattice gas automaton was implemented on a massively parallel machine (the BBN TC2000) and a vector supercomputer (the CRAY C90). The automaton models Burgers equation {rho}t + {rho}{rho}{sub x} = {nu}{rho}{sub xx} in 1 dimension. The lattice gas evolves by advecting and colliding pseudo-particles on a 1-dimensional, periodic grid. The specific rules for colliding particles are stochastic in nature and require the generation of many billions of random numbers to create the random bits necessary for the lattice gas. The goal of the thesis was to speed up the process of generating the random bits and thereby lessen the computational bottleneck of the automaton.
EPCGen2 Pseudorandom Number Generators: Analysis of J3Gen
Peinado, Alberto; Munilla, Jorge; Fúster-Sabater, Amparo
2014-01-01
This paper analyzes the cryptographic security of J3Gen, a promising pseudo random number generator for low-cost passive Radio Frequency Identification (RFID) tags. Although J3Gen has been shown to fulfill the randomness criteria set by the EPCglobal Gen2 standard and is intended for security applications, we describe here two cryptanalytic attacks that question its security claims: (i) a probabilistic attack based on solving linear equation systems; and (ii) a deterministic attack based on the decimation of the output sequence. Numerical results, supported by simulations, show that for the specific recommended values of the configurable parameters, a low number of intercepted output bits are enough to break J3Gen. We then make some recommendations that address these issues. PMID:24721767
Building Kindergartners’ Number Sense: A Randomized Controlled Study
Jordan, Nancy C.; Glutting, Joseph; Dyson, Nancy; Hassinger-Das, Brenna; Irwin, Casey
2015-01-01
Math achievement in elementary school is mediated by performance and growth in number sense during kindergarten. The aim of the present study was to test the effectiveness of a targeted small group number sense intervention for high-risk kindergartners from low-income communities. Children were randomly assigned to one of three groups (n = 44 in each group): a number sense intervention group, a language intervention group, or a business as usual control group. Accounting for initial skill level in mathematical knowledge, children who received the number sense intervention performed better than controls at immediate post test, with meaningful effects on measures of number competencies and general math achievement. Many of the effects held eight weeks after the intervention was completed, suggesting that children internalized what they had learned. There were no differences between the language and control groups on any math-related measures. PMID:25866417
At least some errors are randomly generated (Freud was wrong)
NASA Technical Reports Server (NTRS)
Sellen, A. J.; Senders, J. W.
1986-01-01
An experiment was carried out to expose something about human error generating mechanisms. In the context of the experiment, an error was made when a subject pressed the wrong key on a computer keyboard or pressed no key at all in the time allotted. These might be considered, respectively, errors of substitution and errors of omission. Each of seven subjects saw a sequence of three digital numbers, made an easily learned binary judgement about each, and was to press the appropriate one of two keys. Each session consisted of 1,000 presentations of randomly permuted, fixed numbers broken into 10 blocks of 100. One of two keys should have been pressed within one second of the onset of each stimulus. These data were subjected to statistical analyses in order to probe the nature of the error generating mechanisms. Goodness of fit tests for a Poisson distribution for the number of errors per 50 trial interval and for an exponential distribution of the length of the intervals between errors were carried out. There is evidence for an endogenous mechanism that may best be described as a random error generator. Furthermore, an item analysis of the number of errors produced per stimulus suggests the existence of a second mechanism operating on task driven factors producing exogenous errors. Some errors, at least, are the result of constant probability generating mechanisms with error rate idiosyncratically determined for each subject.
Number of cliques in random scale-free network ensembles
NASA Astrophysics Data System (ADS)
Bianconi, Ginestra; Marsili, Matteo
2006-12-01
In this paper we calculate the average number of cliques in random scale-free networks in the limit of large network size N≫1. We consider first the hidden variable ensemble and subsequently the Molloy Reed ensemble. In both cases we find that cliques, i.e. fully connected subgraphs, appear also when the average degree is finite. This is in contrast to what happens in Erdös and Renyi graphs in which diverging average degree is required to observe cliques of size c>3. Moreover we show that in random scale-free networks the clique number, i.e. the size of the largest clique present in the network, diverges with the system size.
The random walk of a low-Reynolds-number swimmer
NASA Astrophysics Data System (ADS)
Rafaï, Salima; Garcia, Michaël; Berti, Stefano; Peyla, Philippe
2010-11-01
Swimming at a micrometer scale demands particular strategies. Indeed when inertia is negligible as compared to viscous forces (i.e. Reynolds number Re is lower than unity), hydrodynamics equations are reversible in time. To achieve propulsion a low Reynolds number, swimmers must then deform in a way that is not invariant under time reversal. Here we investigate the dispersal properties of self propelled organisms by means of microscopy and cell tracking. Our system of interest is the microalga Chlamydomonas Reinhardtii, a motile single celled green alga about 10 micrometers in diameter that swims with two flagellae. In the case of dilute suspensions, we show that tracked trajectories are well modelled by a correlated random walk. This process is based on short time correlations in the direction of movement called persistence. At longer times, correlations are lost and a standard random walk caracterizes the trajectories. Moreover, high speed imaging enables us to show how speed fluctuations at very short times affect the statistical description of the dynamics. Finally we show how drag forces modify the characteristics of this particular random walk.
Multistability, chaos, and random signal generation in semiconductor superlattices.
Ying, Lei; Huang, Danhong; Lai, Ying-Cheng
2016-06-01
Historically, semiconductor superlattices, artificial periodic structures of different semiconductor materials, were invented with the purpose of engineering or manipulating the electronic properties of semiconductor devices. A key application lies in generating radiation sources, amplifiers, and detectors in the "unusual" spectral range of subterahertz and terahertz (0.1-10 THz), which cannot be readily realized using conventional radiation sources, the so-called THz gap. Efforts in the past three decades have demonstrated various nonlinear dynamical behaviors including chaos, suggesting the potential to exploit chaos in semiconductor superlattices as random signal sources (e.g., random number generators) in the THz frequency range. We consider a realistic model of hot electrons in semiconductor superlattice, taking into account the induced space charge field. Through a systematic exploration of the phase space we find that, when the system is subject to an external electrical driving of a single frequency, chaos is typically associated with the occurrence of multistability. That is, for a given parameter setting, while there are initial conditions that lead to chaotic trajectories, simultaneously there are other initial conditions that lead to regular motions. Transition to multistability, i.e., the emergence of multistability with chaos as a system parameter passes through a critical point, is found and argued to be abrupt. Multistability thus presents an obstacle to utilizing the superlattice system as a reliable and robust random signal source. However, we demonstrate that, when an additional driving field of incommensurate frequency is applied, multistability can be eliminated, with chaos representing the only possible asymptotic behavior of the system. In such a case, a random initial condition will lead to a trajectory landing in a chaotic attractor with probability 1, making quasiperiodically driven semiconductor superlattices potentially as a reliable
Multistability, chaos, and random signal generation in semiconductor superlattices
NASA Astrophysics Data System (ADS)
Ying, Lei; Huang, Danhong; Lai, Ying-Cheng
2016-06-01
Historically, semiconductor superlattices, artificial periodic structures of different semiconductor materials, were invented with the purpose of engineering or manipulating the electronic properties of semiconductor devices. A key application lies in generating radiation sources, amplifiers, and detectors in the "unusual" spectral range of subterahertz and terahertz (0.1-10 THz), which cannot be readily realized using conventional radiation sources, the so-called THz gap. Efforts in the past three decades have demonstrated various nonlinear dynamical behaviors including chaos, suggesting the potential to exploit chaos in semiconductor superlattices as random signal sources (e.g., random number generators) in the THz frequency range. We consider a realistic model of hot electrons in semiconductor superlattice, taking into account the induced space charge field. Through a systematic exploration of the phase space we find that, when the system is subject to an external electrical driving of a single frequency, chaos is typically associated with the occurrence of multistability. That is, for a given parameter setting, while there are initial conditions that lead to chaotic trajectories, simultaneously there are other initial conditions that lead to regular motions. Transition to multistability, i.e., the emergence of multistability with chaos as a system parameter passes through a critical point, is found and argued to be abrupt. Multistability thus presents an obstacle to utilizing the superlattice system as a reliable and robust random signal source. However, we demonstrate that, when an additional driving field of incommensurate frequency is applied, multistability can be eliminated, with chaos representing the only possible asymptotic behavior of the system. In such a case, a random initial condition will lead to a trajectory landing in a chaotic attractor with probability 1, making quasiperiodically driven semiconductor superlattices potentially as a reliable
A Computer Program for Generating Sequences of Primary Arithmetic Facts in Random Order.
ERIC Educational Resources Information Center
Burns, Edward
A computer program which generates randomly sequenced problems for testing the abilities of students to add, subtract, and multiply one-digit numbers is described. Appendices provide tables of random sequences with directions for using the tables. The 54-statement FORTRAN program which can be used in generating additional sequences is also…
Number of distinct sites visited by N random walkers
NASA Astrophysics Data System (ADS)
Larralde, Hernan; Trunfio, Paul; Havlin, Shlomo; Stanley, H. Eugene; Weiss, George H.
1992-05-01
We study the number of distinct sites visited by N random walkers after t steps SN(t) under the condition that all the walkers are initially at the origin. We derive asymptotic expressions for the mean number of distinct sites
49 CFR 229.105 - Steam generator number.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 49 Transportation 4 2011-10-01 2011-10-01 false Steam generator number. 229.105 Section 229.105..., DEPARTMENT OF TRANSPORTATION RAILROAD LOCOMOTIVE SAFETY STANDARDS Safety Requirements Steam Generators § 229.105 Steam generator number. An identification number shall be marked on the steam...
49 CFR 229.105 - Steam generator number.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 49 Transportation 4 2012-10-01 2012-10-01 false Steam generator number. 229.105 Section 229.105..., DEPARTMENT OF TRANSPORTATION RAILROAD LOCOMOTIVE SAFETY STANDARDS Safety Requirements Steam Generators § 229.105 Steam generator number. An identification number shall be marked on the steam...
49 CFR 229.105 - Steam generator number.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 49 Transportation 4 2010-10-01 2010-10-01 false Steam generator number. 229.105 Section 229.105..., DEPARTMENT OF TRANSPORTATION RAILROAD LOCOMOTIVE SAFETY STANDARDS Safety Requirements Steam Generators § 229.105 Steam generator number. An identification number shall be marked on the steam...
49 CFR 229.105 - Steam generator number.
Code of Federal Regulations, 2013 CFR
2013-10-01
... 49 Transportation 4 2013-10-01 2013-10-01 false Steam generator number. 229.105 Section 229.105..., DEPARTMENT OF TRANSPORTATION RAILROAD LOCOMOTIVE SAFETY STANDARDS Safety Requirements Steam Generators § 229.105 Steam generator number. An identification number shall be marked on the steam...
49 CFR 229.105 - Steam generator number.
Code of Federal Regulations, 2014 CFR
2014-10-01
... 49 Transportation 4 2014-10-01 2014-10-01 false Steam generator number. 229.105 Section 229.105..., DEPARTMENT OF TRANSPORTATION RAILROAD LOCOMOTIVE SAFETY STANDARDS Safety Requirements Steam Generators § 229.105 Steam generator number. An identification number shall be marked on the steam...
Generation of kth-order random toposequences
NASA Astrophysics Data System (ADS)
Odgers, Nathan P.; McBratney, Alex. B.; Minasny, Budiman
2008-05-01
The model presented in this paper derives toposequences from a digital elevation model (DEM). It is written in ArcInfo Macro Language (AML). The toposequences are called kth-order random toposequences, because they take a random path uphill to the top of a hill and downhill to a stream or valley bottom from a randomly selected seed point, and they are located in a streamshed of order k according to a particular stream-ordering system. We define a kth-order streamshed as the area of land that drains directly to a stream segment of stream order k. The model attempts to optimise the spatial configuration of a set of derived toposequences iteratively by using simulated annealing to maximise the total sum of distances between each toposequence hilltop in the set. The user is able to select the order, k, of the derived toposequences. Toposequences are useful for determining soil sampling locations for use in collecting soil data for digital soil mapping applications. Sampling locations can be allocated according to equal elevation or equal-distance intervals along the length of the toposequence, for example. We demonstrate the use of this model for a study area in the Hunter Valley of New South Wales, Australia. Of the 64 toposequences derived, 32 were first-order random toposequences according to Strahler's stream-ordering system, and 32 were second-order random toposequences. The model that we present in this paper is an efficient method for sampling soil along soil toposequences. The soils along a toposequence are related to each other by the topography they are found in, so soil data collected by this method is useful for establishing soil-landscape rules for the preparation of digital soil maps.
Truly random bit generation based on a novel random Brillouin fiber laser.
Xiang, Dao; Lu, Ping; Xu, Yanping; Gao, Song; Chen, Liang; Bao, Xiaoyi
2015-11-15
We propose a novel dual-emission random Brillouin fiber laser (RBFL) with bidirectional pumping operation. Numerical simulations and experimental verification of the chaotic temporal and statistical properties of the RBFL are conducted, revealing intrinsic unpredictable intensity fluctuations and two completely uncorrelated laser outputs. A random bit generator based on quantum noise sources in the random Fabry-Perot resonator of the RBFL is realized at a bit rate of 5 Mbps with verified randomness. PMID:26565888
RANDOM PULSE GENERATOR PRODUCING FIDUCIAL MARKS
Nielsen, W.F.
1960-02-01
The apparatus for automatically applying a fiducial marking, having a nonrepetitive pattern, to a plurality of simultaneously made records comprises, in series, a bypass filter, a trigger circuit, and a pulse generator, with printing means connected to and controlled by the pulse generator for simultaneously making the visible fiducial marks on a plurality of simultaneously produced records.
Image encryption using random sequence generated from generalized information domain
NASA Astrophysics Data System (ADS)
Xia-Yan, Zhang; Guo-Ji, Zhang; Xuan, Li; Ya-Zhou, Ren; Jie-Hua, Wu
2016-05-01
A novel image encryption method based on the random sequence generated from the generalized information domain and permutation–diffusion architecture is proposed. The random sequence is generated by reconstruction from the generalized information file and discrete trajectory extraction from the data stream. The trajectory address sequence is used to generate a P-box to shuffle the plain image while random sequences are treated as keystreams. A new factor called drift factor is employed to accelerate and enhance the performance of the random sequence generator. An initial value is introduced to make the encryption method an approximately one-time pad. Experimental results show that the random sequences pass the NIST statistical test with a high ratio and extensive analysis demonstrates that the new encryption scheme has superior security.
Generation of large prime numbers from a sequence of previous prime numbers
NASA Astrophysics Data System (ADS)
Samir, Brahim Belhaouari; Rezk, Youssef A. Y.
2012-09-01
A prime number is co-prime with all the primes as well. This paper utilizes this fact by generating larger prime numbers based on a set of smaller prime numbers. The prime numbers are ordered and each two consecutive primes are coupled to generate their co-prime number formula extending this process larger prime sequence is established. Will the process help us produce larger prime numbers faster and more efficiently? This paper investigates the described process.
Pseudorandom number generation using chaotic true orbits of the Bernoulli map
NASA Astrophysics Data System (ADS)
Saito, Asaki; Yamaguchi, Akihiro
2016-06-01
We devise a pseudorandom number generator that exactly computes chaotic true orbits of the Bernoulli map on quadratic algebraic integers. Moreover, we describe a way to select the initial points (seeds) for generating multiple pseudorandom binary sequences. This selection method distributes the initial points almost uniformly (equidistantly) in the unit interval, and latter parts of the generated sequences are guaranteed not to coincide. We also demonstrate through statistical testing that the generated sequences possess good randomness properties.
Pseudorandom number generation using chaotic true orbits of the Bernoulli map.
Saito, Asaki; Yamaguchi, Akihiro
2016-06-01
We devise a pseudorandom number generator that exactly computes chaotic true orbits of the Bernoulli map on quadratic algebraic integers. Moreover, we describe a way to select the initial points (seeds) for generating multiple pseudorandom binary sequences. This selection method distributes the initial points almost uniformly (equidistantly) in the unit interval, and latter parts of the generated sequences are guaranteed not to coincide. We also demonstrate through statistical testing that the generated sequences possess good randomness properties. PMID:27368787
Detail of generator number three, oblique. Control panels on the ...
Detail of generator number three, oblique. Control panels on the main floor and on the mezzanine are visible behind and above the generators. - March Air Force Base, Strategic Air Command, Utility Building, 5220 Riverside Drive, Moreno Valley, Riverside County, CA
Ultra-fast quantum randomness generation by accelerated phase diffusion in a pulsed laser diode.
Abellán, C; Amaya, W; Jofre, M; Curty, M; Acín, A; Capmany, J; Pruneri, V; Mitchell, M W
2014-01-27
We demonstrate a high bit-rate quantum random number generator by interferometric detection of phase diffusion in a gain-switched DFB laser diode. Gain switching at few-GHz frequencies produces a train of bright pulses with nearly equal amplitudes and random phases. An unbalanced Mach-Zehnder interferometer is used to interfere subsequent pulses and thereby generate strong random-amplitude pulses, which are detected and digitized to produce a high-rate random bit string. Using established models of semiconductor laser field dynamics, we predict a regime of high visibility interference and nearly complete vacuum-fluctuation-induced phase diffusion between pulses. These are confirmed by measurement of pulse power statistics at the output of the interferometer. Using a 5.825 GHz excitation rate and 14-bit digitization, we observe 43 Gbps quantum randomness generation. PMID:24515170
The Reliability of Randomly Generated Math Curriculum-Based Measurements
ERIC Educational Resources Information Center
Strait, Gerald G.; Smith, Bradley H.; Pender, Carolyn; Malone, Patrick S.; Roberts, Jarod; Hall, John D.
2015-01-01
"Curriculum-Based Measurement" (CBM) is a direct method of academic assessment used to screen and evaluate students' skills and monitor their responses to academic instruction and intervention. Interventioncentral.org offers a math worksheet generator at no cost that creates randomly generated "math curriculum-based measures"…
Khonina, Svetlana N; Golub, Ilya
2015-09-01
We show that it is possible to generate transversely random, diffraction-free/longitudinally invariant vector optical fields. The randomness in transverse polarization distribution complements a previously studied one in intensity of scalar Bessel-type beams, adding another degree of freedom to control these beams. Moreover, we show that the relative transversely random phase distribution is also conserved along the optical axis. Thus, intensity, phase, and polarization of Bessel-type beams can be transversely random/arbitrary while invariant upon propagation. Such fields may find applications in encryption/secure communications, optical trapping, etc. PMID:26368714
NASA Astrophysics Data System (ADS)
Mironowicz, Piotr; Tavakoli, Armin; Hameedi, Alley; Marques, Breno; Pawłowski, Marcin; Bourennane, Mohamed
2016-06-01
Quantum communication with systems of dimension larger than two provides advantages in information processing tasks. Examples include higher rates of key distribution and random number generation. The main disadvantage of using such multi-dimensional quantum systems is the increased complexity of the experimental setup. Here, we analyze a not-so-obvious problem: the relation between randomness certification and computational requirements of the post-processing of experimental data. In particular, we consider semi-device independent randomness certification from an experiment using a four dimensional quantum system to violate the classical bound of a random access code. Using state-of-the-art techniques, a smaller quantum violation requires more computational power to demonstrate randomness, which at some point becomes impossible with today’s computers although the randomness is (probably) still there. We show that by dedicating more input settings of the experiment to randomness certification, then by more computational postprocessing of the experimental data which corresponds to a quantum violation, one may increase the amount of certified randomness. Furthermore, we introduce a method that significantly lowers the computational complexity of randomness certification. Our results show how more randomness can be generated without altering the hardware and indicate a path for future semi-device independent protocols to follow.
Simulation and study of small numbers of random events
NASA Technical Reports Server (NTRS)
Shelton, R. D.
1986-01-01
Random events were simulated by computer and subjected to various statistical methods to extract important parameters. Various forms of curve fitting were explored, such as least squares, least distance from a line, maximum likelihood. Problems considered were dead time, exponential decay, and spectrum extraction from cosmic ray data using binned data and data from individual events. Computer programs, mostly of an iterative nature, were developed to do these simulations and extractions and are partially listed as appendices. The mathematical basis for the compuer programs is given.
Secure self-calibrating quantum random-bit generator
Fiorentino, M.; Santori, C.; Spillane, S. M.; Beausoleil, R. G.; Munro, W. J.
2007-03-15
Random-bit generators (RBGs) are key components of a variety of information processing applications ranging from simulations to cryptography. In particular, cryptographic systems require 'strong' RBGs that produce high-entropy bit sequences, but traditional software pseudo-RBGs have very low entropy content and therefore are relatively weak for cryptography. Hardware RBGs yield entropy from chaotic or quantum physical systems and therefore are expected to exhibit high entropy, but in current implementations their exact entropy content is unknown. Here we report a quantum random-bit generator (QRBG) that harvests entropy by measuring single-photon and entangled two-photon polarization states. We introduce and implement a quantum tomographic method to measure a lower bound on the 'min-entropy' of the system, and we employ this value to distill a truly random-bit sequence. This approach is secure: even if an attacker takes control of the source of optical states, a secure random sequence can be distilled.
Narrow-band generation in random distributed feedback fiber laser.
Sugavanam, Srikanth; Tarasov, Nikita; Shu, Xuewen; Churkin, Dmitry V
2013-07-15
Narrow-band emission of spectral width down to ~0.05 nm line-width is achieved in the random distributed feedback fiber laser employing narrow-band fiber Bragg grating or fiber Fabry-Perot interferometer filters. The observed line-width is ~10 times less than line-width of other demonstrated up to date random distributed feedback fiber lasers. The random DFB laser with Fabry-Perot interferometer filter provides simultaneously multi-wavelength and narrow-band (within each line) generation with possibility of further wavelength tuning. PMID:23938497
Fully photonics-based physical random bit generator.
Li, Pu; Sun, Yuanyuan; Liu, Xianglian; Yi, Xiaogang; Zhang, Jianguo; Guo, Xiaomin; Guo, Yanqiang; Wang, Yuncai
2016-07-15
We propose a fully photonics-based approach for ultrafast physical random bit generation. This approach exploits a compact nonlinear loop mirror (called a terahertz optical asymmetric demultiplexer, TOAD) to sample the chaotic optical waveform in an all-optical domain and then generate random bit streams through further comparison with a threshold level. This method can efficiently overcome the electronic jitter bottleneck confronted by existing RBGs in practice. A proof-of-concept experiment demonstrates that this method can continuously extract 5 Gb/s random bit streams from the chaotic output of a distributed feedback laser diode (DFB-LD) with optical feedback. This limited generation rate is caused by the bandwidth of the used optical chaos. PMID:27420532
Biased Random Number Generator Based on Bell's Theorem
NASA Astrophysics Data System (ADS)
Yong-Gang, Tan; Yao-Hua, Hu; Hai-Feng, Yang
2016-03-01
Not Available Supported by the National Natural Science Foundation of China under Grant Nos 61378011, U1204616 and 11447143, the Program for Science and Technology Innovation Talents in Universities of Henan Province under Grant No 2012HASTIT028, and the Program for Science and Technology Innovation Research Team in University of Henan Province under Grant No 13IRTSTHN020.
Sum-frequency generation from photon number squeezed light
NASA Technical Reports Server (NTRS)
Wu, Ling-An; Du, Cong-Shi; Wu, Mei-Juan; Li, Shi-Qun
1994-01-01
We investigate the quantum fluctuations of the fields produced in sum-frequency (SF) generation from light initially in the photon number squeezed state. It is found that, to the fourth power term, the output SF light is sub-Poissonian whereas the quantum fluctuations of the input beams increase. Quantum anticorrelation also exists in SF generation.
All-optical quantum random bit generation from intrinsically binary phase of parametric oscillators.
Marandi, Alireza; Leindecker, Nick C; Vodopyanov, Konstantin L; Byer, Robert L
2012-08-13
We demonstrate a novel all-optical quantum random number generator (RNG) based on above-threshold binary phase state selection in a degenerate optical parametric oscillator (OPO). Photodetection is not a part of the random process, and no post processing is required for the generated bit sequence. We show that the outcome is statistically random with 99% confidence, and verify that the randomness is due to the phase of initiating photons generated through spontaneous parametric down conversion of the pump, with negligible contribution of classical noise sources. With the use of micro- and nanoscale OPO resonators, this technique offers a promise for simple, robust, and high-speed on-chip all-optical quantum RNGs. PMID:23038574
The generation of random variates from a relativistic Maxwellian distribution
Swisdak, M.
2013-06-15
A procedure for generating random variates from a relativistic Maxwellian distribution with arbitrary temperature and drift velocity is presented. The algorithm is based on the rejection method and can be used to initialize particle velocities in kinetic simulations of plasmas and gases.
Realistic noise-tolerant randomness amplification using finite number of devices.
Brandão, Fernando G S L; Ramanathan, Ravishankar; Grudka, Andrzej; Horodecki, Karol; Horodecki, Michał; Horodecki, Paweł; Szarek, Tomasz; Wojewódka, Hanna
2016-01-01
Randomness is a fundamental concept, with implications from security of modern data systems, to fundamental laws of nature and even the philosophy of science. Randomness is called certified if it describes events that cannot be pre-determined by an external adversary. It is known that weak certified randomness can be amplified to nearly ideal randomness using quantum-mechanical systems. However, so far, it was unclear whether randomness amplification is a realistic task, as the existing proposals either do not tolerate noise or require an unbounded number of different devices. Here we provide an error-tolerant protocol using a finite number of devices for amplifying arbitrary weak randomness into nearly perfect random bits, which are secure against a no-signalling adversary. The correctness of the protocol is assessed by violating a Bell inequality, with the degree of violation determining the noise tolerance threshold. An experimental realization of the protocol is within reach of current technology. PMID:27098302
Realistic noise-tolerant randomness amplification using finite number of devices
Brandão, Fernando G. S. L.; Ramanathan, Ravishankar; Grudka, Andrzej; Horodecki, Karol; Horodecki, Michał; Horodecki, Paweł; Szarek, Tomasz; Wojewódka, Hanna
2016-01-01
Randomness is a fundamental concept, with implications from security of modern data systems, to fundamental laws of nature and even the philosophy of science. Randomness is called certified if it describes events that cannot be pre-determined by an external adversary. It is known that weak certified randomness can be amplified to nearly ideal randomness using quantum-mechanical systems. However, so far, it was unclear whether randomness amplification is a realistic task, as the existing proposals either do not tolerate noise or require an unbounded number of different devices. Here we provide an error-tolerant protocol using a finite number of devices for amplifying arbitrary weak randomness into nearly perfect random bits, which are secure against a no-signalling adversary. The correctness of the protocol is assessed by violating a Bell inequality, with the degree of violation determining the noise tolerance threshold. An experimental realization of the protocol is within reach of current technology. PMID:27098302
Realistic noise-tolerant randomness amplification using finite number of devices
NASA Astrophysics Data System (ADS)
Brandão, Fernando G. S. L.; Ramanathan, Ravishankar; Grudka, Andrzej; Horodecki, Karol; Horodecki, Michał; Horodecki, Paweł; Szarek, Tomasz; Wojewódka, Hanna
2016-04-01
Randomness is a fundamental concept, with implications from security of modern data systems, to fundamental laws of nature and even the philosophy of science. Randomness is called certified if it describes events that cannot be pre-determined by an external adversary. It is known that weak certified randomness can be amplified to nearly ideal randomness using quantum-mechanical systems. However, so far, it was unclear whether randomness amplification is a realistic task, as the existing proposals either do not tolerate noise or require an unbounded number of different devices. Here we provide an error-tolerant protocol using a finite number of devices for amplifying arbitrary weak randomness into nearly perfect random bits, which are secure against a no-signalling adversary. The correctness of the protocol is assessed by violating a Bell inequality, with the degree of violation determining the noise tolerance threshold. An experimental realization of the protocol is within reach of current technology.
Inkjet aerosol generator as monodisperse particle number standard
NASA Astrophysics Data System (ADS)
Iida, Kenjiro; Sakurai, Hiromu; Ehara, Kensei
2013-05-01
Inkjet technology can be applied to generate highly monodisperse aerosol particles in micrometer range at a precisely controlled rate. AIST has been developing an inkjet aerosol generator (AIST-IAG), and the device will soon become the secondary measurement standard for aerosol particle number concentration in 0.35 μm to 10 μm range. The AIST-IAG can generate both solid and liquid particles consisting of water-soluble ionic compounds. We first report the characteristics of the particle sizes of the generated particles. The full width half maximum of the particle size distribution is about 2 percent, and the particle diameter of the IAG particles was calibrated as a function of the particle mass within 0.6-10 μm range using polystyrene latex sphere as reference material. Then we report the capability of the AIST-IAG as the particle number standard. The particle generation efficiency ηIAG was defined as the number of aerosol particles exiting from the AIST-IAG divided by the rate of the droplet generation, and the values of ηIAG within 0.35-10 μm is essentially 100%, and the 95% confidence interval of the values is less than 1%. The result strongly supports that the AISTIAG can be used to calibrate the counting efficiency of the optical particle counters in submicrometer to micrometer range.
Cascaded Cerenkov third-harmonic generation in random quadratic media
Ayoub, Mousa; Roedig, Philip; Imbrock, Joerg; Denz, Cornelia
2011-12-12
We investigate experimentally and theoretically the conical emission of Cerenkov-type third-harmonic generation in strontium barium niobate of random 2D-{chi}{sup (2)} distribution. The azimuthal intensity distribution is explained by the polarization properties of the fundamental and Cerenkov second-harmonic waves, depending on the cascaded origin of the generation process. Moreover, we show the role of the individual domain shape in an additional modulation on the conical emission, controlled by the electrical switching of the spontaneous polarization of the ferroelectric medium.
On the generation of random variables for radar simulation purposes
NASA Astrophysics Data System (ADS)
Galati, G.; Fanelli, S.
The uniform pseudorandom number generator, available in the subroutine FORTRAN RANDN/FG UNIVAC for 36 bit computers such as the UNIVAC 1100 series, underwent statistical tests. The pure congruence generator performs particularly well. Using these uniform numbers, it is easy to obtain pseudorandom numbers distributed with the laws of practical interest for digital simulations. With the Gaussian law, it is possible to use the central limit theorem and the Box-Muller method. Subroutines for these methods require between 0.6 and 0.15 msec.
Raw and Central Moments of Binomial Random Variables via Stirling Numbers
ERIC Educational Resources Information Center
Griffiths, Martin
2013-01-01
We consider here the problem of calculating the moments of binomial random variables. It is shown how formulae for both the raw and the central moments of such random variables may be obtained in a recursive manner utilizing Stirling numbers of the first kind. Suggestions are also provided as to how students might be encouraged to explore this…
Shteingart, Hanan; Loewenstein, Yonatan
2016-01-01
There is a long history of experiments in which participants are instructed to generate a long sequence of binary random numbers. The scope of this line of research has shifted over the years from identifying the basic psychological principles and/or the heuristics that lead to deviations from randomness, to one of predicting future choices. In this paper, we used generalized linear regression and the framework of Reinforcement Learning in order to address both points. In particular, we used logistic regression analysis in order to characterize the temporal sequence of participants' choices. Surprisingly, a population analysis indicated that the contribution of the most recent trial has only a weak effect on behavior, compared to more preceding trials, a result that seems irreconcilable with standard sequential effects that decay monotonously with the delay. However, when considering each participant separately, we found that the magnitudes of the sequential effect are a monotonous decreasing function of the delay, yet these individual sequential effects are largely averaged out in a population analysis because of heterogeneity. The substantial behavioral heterogeneity in this task is further demonstrated quantitatively by considering the predictive power of the model. We show that a heterogeneous model of sequential dependencies captures the structure available in random sequence generation. Finally, we show that the results of the logistic regression analysis can be interpreted in the framework of reinforcement learning, allowing us to compare the sequential effects in the random sequence generation task to those in an operant learning task. We show that in contrast to the random sequence generation task, sequential effects in operant learning are far more homogenous across the population. These results suggest that in the random sequence generation task, different participants adopt different cognitive strategies to suppress sequential dependencies when
Evolution of dendrimer conformational structure with generation number
NASA Astrophysics Data System (ADS)
Betancourt, Beatriz A. Pazmiño; Douglas, Jack F.
2016-05-01
We simulate the conformational structure of a coarse-grained model of dendrimer molecules in a good solvent as a function of generation number G and find that they evolve through substantially more complex structures than regular star polymers with increasing arms because of their hierarchical topological structure. As G increases, they evolve from 3-arm stars to branched polymers that geometrically resemble lattice animals, and then percolation clusters for G = 4 - 6 range. For larger G, the dendrimers become similar to porous particles, but the molecule segregates segregates into subdomains at G = 9, reflecting the branching complexity of the first dendrimer generation.
Non-random DNA fragmentation in next-generation sequencing
Poptsova, Maria S.; Il'icheva, Irina A.; Nechipurenko, Dmitry Yu.; Panchenko, Larisa A.; Khodikov, Mingian V.; Oparina, Nina Y.; Polozov, Robert V.; Nechipurenko, Yury D.; Grokhovsky, Sergei L.
2014-01-01
Next Generation Sequencing (NGS) technology is based on cutting DNA into small fragments, and their massive parallel sequencing. The multiple overlapping segments termed “reads” are assembled into a contiguous sequence. To reduce sequencing errors, every genome region should be sequenced several dozen times. This sequencing approach is based on the assumption that genomic DNA breaks are random and sequence-independent. However, previously we showed that for the sonicated restriction DNA fragments the rates of double-stranded breaks depend on the nucleotide sequence. In this work we analyzed genomic reads from NGS data and discovered that fragmentation methods based on the action of the hydrodynamic forces on DNA, produce similar bias. Consideration of this non-random DNA fragmentation may allow one to unravel what factors and to what extent influence the non-uniform coverage of various genomic regions. PMID:24681819
Non-random DNA fragmentation in next-generation sequencing
NASA Astrophysics Data System (ADS)
Poptsova, Maria S.; Il'Icheva, Irina A.; Nechipurenko, Dmitry Yu.; Panchenko, Larisa A.; Khodikov, Mingian V.; Oparina, Nina Y.; Polozov, Robert V.; Nechipurenko, Yury D.; Grokhovsky, Sergei L.
2014-03-01
Next Generation Sequencing (NGS) technology is based on cutting DNA into small fragments, and their massive parallel sequencing. The multiple overlapping segments termed ``reads'' are assembled into a contiguous sequence. To reduce sequencing errors, every genome region should be sequenced several dozen times. This sequencing approach is based on the assumption that genomic DNA breaks are random and sequence-independent. However, previously we showed that for the sonicated restriction DNA fragments the rates of double-stranded breaks depend on the nucleotide sequence. In this work we analyzed genomic reads from NGS data and discovered that fragmentation methods based on the action of the hydrodynamic forces on DNA, produce similar bias. Consideration of this non-random DNA fragmentation may allow one to unravel what factors and to what extent influence the non-uniform coverage of various genomic regions.
K-System Generator of Pseudorandom Numbers on Galois Field
NASA Astrophysics Data System (ADS)
Athanasiu, G. G.; Floratos, E. G.; Savvidy, G. K.
We analyze the structure of the periodic trajectories of the K-system generator of pseudorandom numbers on a rational sublattice which coincides with the Galois field GF[p]. The period of the trajectories increases as a function of the lattice size p and the dimension of the K-matrix d. We emphasize the connection of this approach with the one which is based on primitive matrices over Galois fields.
K-system generator of pseudorandom numbers of Galois field
Athanasiu, G.G.; Floratos, E.G.; Savvidy, G.K.
1997-06-01
We analyze the structure of the periodic trajectories of the K-system generator of pseudorandom numbers on a rational sublattice which coincides with the Galois field GF[p]. The period of the trajectories increases as a function of the lattice size p and the dimension of the K-matrix d. We emphasize the connection of this approach with the one which is based on primitive matrices over Galois fields.
Shteingart, Hanan; Loewenstein, Yonatan
2016-01-01
There is a long history of experiments in which participants are instructed to generate a long sequence of binary random numbers. The scope of this line of research has shifted over the years from identifying the basic psychological principles and/or the heuristics that lead to deviations from randomness, to one of predicting future choices. In this paper, we used generalized linear regression and the framework of Reinforcement Learning in order to address both points. In particular, we used logistic regression analysis in order to characterize the temporal sequence of participants’ choices. Surprisingly, a population analysis indicated that the contribution of the most recent trial has only a weak effect on behavior, compared to more preceding trials, a result that seems irreconcilable with standard sequential effects that decay monotonously with the delay. However, when considering each participant separately, we found that the magnitudes of the sequential effect are a monotonous decreasing function of the delay, yet these individual sequential effects are largely averaged out in a population analysis because of heterogeneity. The substantial behavioral heterogeneity in this task is further demonstrated quantitatively by considering the predictive power of the model. We show that a heterogeneous model of sequential dependencies captures the structure available in random sequence generation. Finally, we show that the results of the logistic regression analysis can be interpreted in the framework of reinforcement learning, allowing us to compare the sequential effects in the random sequence generation task to those in an operant learning task. We show that in contrast to the random sequence generation task, sequential effects in operant learning are far more homogenous across the population. These results suggest that in the random sequence generation task, different participants adopt different cognitive strategies to suppress sequential dependencies when
A program generating homogeneous random graphs with given weights
NASA Astrophysics Data System (ADS)
Bogacz, L.; Burda, Z.; Janke, W.; Waclaw, B.
2005-12-01
We present a program package to generate homogeneous random graphs with probabilities prescribed by the user. The statistical weight of a labeled graph α is given in the form W(α)=∏i=1Np(q), where p(q) is an arbitrary user function and q are the degrees of the graph nodes. The program can be used to generate two types of graphs (simple graphs and pseudo-graphs) from three types of ensembles (micro-canonical, canonical and grand-canonical). Program summaryTitle of the program:GraphGen Catalogue identifier:ADWL Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADWL Program obtainable from:CPC Program Library, Queen's University of Belfast, N. Ireland Computer for which the program is designed and others on which it has been tested: PC, Alpha workstation Operating systems or monitors under which the program has been tested:Linux, Unix, MS Windows XP Programing language used:C Memory required to execute with typical data:300 k words for a graph with 1000 nodes and up to 50 000 links No. of bits in a word:32 No. of processor used:1 Has the code been vectorized or parallelized:No No. of lines in distributed program, including test data, etc.:2253 No. of bytes in distributed program, including test data, etc.:14 330 Distribution format:tar.gz Keywords:Random graphs, complex networks, Markov process, Monte Carlo method Nature of the problem:The program generates random graphs. The probabilities of graph occurrence are proportional to their statistical weight, dependent on node degrees defined by arbitrary distributions Method of solution:The starting graph is taken arbitrary and then a sequence of graphs is generated. Each graph is obtained from the previous one by means of a simple modification. The probability of accepting or rejecting the new graph results from a detailed balance condition realized as Metropolis algorithm. When the length of the generated Markov chain increases, the probabilities of graph occurrence approach the stationary distribution given by
Kanter, Ido; Butkovski, Maria; Peleg, Yitzhak; Zigzag, Meital; Aviad, Yaara; Reidler, Igor; Rosenbluh, Michael; Kinzel, Wolfgang
2010-08-16
Random bit generators (RBGs) constitute an important tool in cryptography, stochastic simulations and secure communications. The later in particular has some difficult requirements: high generation rate of unpredictable bit strings and secure key-exchange protocols over public channels. Deterministic algorithms generate pseudo-random number sequences at high rates, however, their unpredictability is limited by the very nature of their deterministic origin. Recently, physical RBGs based on chaotic semiconductor lasers were shown to exceed Gbit/s rates. Whether secure synchronization of two high rate physical RBGs is possible remains an open question. Here we propose a method, whereby two fast RBGs based on mutually coupled chaotic lasers, are synchronized. Using information theoretic analysis we demonstrate security against a powerful computational eavesdropper, capable of noiseless amplification, where all parameters are publicly known. The method is also extended to secure synchronization of a small network of three RBGs. PMID:20721222
Grid-generated isotropic homogeneous turbulence at high Reynolds numbers
NASA Technical Reports Server (NTRS)
Rosen, G.
1981-01-01
Consideration is given to an empirical formula for the longitudinal correlation function for grid-generated incompressible fluid turbulence at Reynolds numbers above 12,800. The formula, which relates the longitudinal correlation function to the inverse cube of a dimensionless geometrical ratio, is shown to minimize the global correlation integrals into which the two-point velocity correlation tensor has been substituted subject to a global constraint on the Sobolev concomitent of the longitudinal correlation function. Furthermore, the energy spectrum function associated with the empirical formula is shown to satisfy a tertiary Helmholtz-type linear condition throughout the initial period of decay.
Phase transition in a stochastic prime-number generator.
Luque, Bartolo; Lacasa, Lucas; Miramontes, Octavio
2007-07-01
We introduce a stochastic algorithm that acts as a prime-number generator. The dynamics of this algorithm gives rise to a continuous phase transition, which separates a phase where the algorithm is able to reduce a whole set of integers into primes and a phase where the system reaches a frozen state with low prime density. We present both numerical simulations and an analytical approach in terms of an annealed approximation, by means of which the data are collapsed. A critical slowing-down phenomenon is also outlined. PMID:17677398
Generation of Random Particle Packings for Discrete Element Models
NASA Astrophysics Data System (ADS)
Abe, S.; Weatherley, D.; Ayton, T.
2012-04-01
An important step in the setup process of Discrete Element Model (DEM) simulations is the generation of a suitable particle packing. There are quite a number of properties such a granular material specimen should ideally have, such as high coordination number, isotropy, the ability to fill arbitrary bounding volumes and the absence of locked-in stresses. An algorithm which is able to produce specimens fulfilling these requirements is the insertion based sphere packing algorithm originally proposed by Place and Mora, 2001 [2] and extended in this work. The algorithm works in two stages. First a number of "seed" spheres are inserted into the bounding volume. In the second stage the gaps between the "seed" spheres are filled by inserting new spheres in a way so they have D+1 (i.e. 3 in 2D, 4 in 3D) touching contacts with either other spheres or the boundaries of the enclosing volume. Here we present an implementation of the algorithm and a systematic statistical analysis of the generated sphere packings. The analysis of the particle radius distribution shows that they follow a power-law with an exponent ≈ D (i.e. ≈3 for a 3D packing and ≈2 for 2D). Although the algorithm intrinsically guarantees coordination numbers of at least 4 in 3D and 3 in 2D, the coordination numbers realized in the generated packings can be significantly higher, reaching beyond 50 if the range of particle radii is sufficiently large. Even for relatively small ranges of particle sizes (e.g. Rmin = 0.5Rmax) the maximum coordination number may exceed 10. The degree of isotropy of the generated sphere packing is also analysed in both 2D and 3D, by measuring the distribution of orientations of vectors joining the centres of adjacent particles. If the range of particle sizes is small, the packing algorithm yields moderate anisotropy approaching that expected for a face-centred cubic packing of equal-sized particles. However, once Rmin < 0.3Rmax a very high degree of isotropy is demonstrated in
NASA Astrophysics Data System (ADS)
Alamino, R. C.; Saad, D.
2008-06-01
Using methods of statistical physics, we study the average number and kernel size of general sparse random matrices over Galois fields GF(q) , with a given connectivity profile, in the thermodynamical limit of large matrices. We introduce a mapping of GF(q) matrices onto spin systems using the representation of the cyclic group of order q as the q th complex roots of unity. This representation facilitates the derivation of the average kernel size of random matrices using the replica approach, under the replica-symmetric ansatz, resulting in saddle point equations for general connectivity distributions. Numerical solutions are then obtained for particular cases by population dynamics. Similar techniques also allow us to obtain an expression for the exact and average numbers of random matrices for any general connectivity profile. We present numerical results for particular distributions.
NASA Astrophysics Data System (ADS)
Urano, Ryo; Okamoto, Yuko
2015-12-01
We propose a replica-exchange method (REM) which does not use pseudo random numbers. For this purpose, we first give a conditional probability for Gibbs sampling replica-exchange method (GSREM) based on the heat bath method. In GSREM, replica exchange is performed by conditional probability based on the weight of states using pseudo random numbers. From the conditional probability, we propose a new method called deterministic replica-exchange method (DETREM) that produces thermal equilibrium distribution based on a differential equation instead of using pseudo random numbers. This method satisfies the detailed balance condition using a conditional probability of Gibbs heat bath method and thus results can reproduce the Boltzmann distribution within the condition of the probability. We confirmed that the equivalent results were obtained by REM and DETREM with two-dimensional Ising model. DETREM can avoid problems of choice of seeds in pseudo random numbers for parallel computing of REM and gives analytic method for REM using a differential equation.
Feedback control of digital chaotic systems with application to pseudorandom number generator
NASA Astrophysics Data System (ADS)
Deng, Yashuang; Hu, Hanping; Liu, Lingfeng
2015-07-01
The dynamical properties will degrade when chaotic systems are implemented in digital computers with finite precisions, and such degradation often has serious negative influence on some digital chaos-based systems. Degradation reduction for a class of digital chaotic systems is investigated in this paper. A varying parameter control method is proposed based on the state feedback control technology at first. Then two chaotic maps are applied to verify its validity. Finally, a novel pseudorandom number generator is constructed, which can pass all the tests of NIST SP800-22 at both level-one and level-two approaches and also most of the tests of TestU01. Moreover, it performs better than some existing pseudorandom number generators. Thus, it has acceptable quality of randomness and can be used for cryptography and other applications.
Internal wave generation by tidal flow over random topography
NASA Astrophysics Data System (ADS)
Zhao, Jiajun; Zhang, Likun; Swinney, Harry
2015-11-01
The irregularity of oceanic topography plays a critical role in determining the power in internal waves generated by tidal flow over the seafloor. We conduct numerical simulations (for a fluid with a constant buoyancy frequency) for different synthetic random topographies. For topography with small rms height Hrms and small slopes the simulations yield a quadratic dependence of the power on Hrms, in accord with linear theory. However, for tall topography with steep slopes the internal wave power is found to vary linearly with Hrms. The transition from quadratic to linear scaling of the radiated internal wave power on Hrms occurs when the ``valley slope'' exceeds the internal wave slope. (The valley slope, to be defined in this talk, characterizes the maximum slope of topography between adjacent peaks.) The simulations also reveal that the radiated power saturates with increasing topographic resolution, as conjectured in previous studies. The present results should be helpful in improving estimates of the total internal wave power generated by the world's oceans.
Theory of second harmonic generation in randomly oriented species
NASA Astrophysics Data System (ADS)
Andrews, David L.; Allcock, Philip; Demidov, Andrey A.
1995-01-01
It is well known that second harmonic generation (SHG) is a process forbidden within atomic and molecular fluids. Nonetheless recent experimental observations of second harmonic evolution in suspensions of randomly oriented Halobacterium halobium purple membranes have raised new questions about the precise criteria which determine prohibition of the second harmonic. To address the problem a theoretical framework for SHG is developed that specifically deals with molecular systems, and is therefore cast in terms of molecular properties with more regard to the influence of the local structure. This contrasts with the classical approach based on bulk susceptibilities, which has not proved adequate to explain the conflicting experimental results. By properly formulating the detailed procedure for dealing with the necessary orientational averages, the present theory discloses a relationship between the coherent process of second harmonic generation and a directed component of its incoherent counterpart, hyper-Rayleigh scattering. Inter alia, the theory explains the SHG detected in purple membrane suspensions. The polarisation features of the harmonic evolution are also considered more generally, and in particular it is shown that the SHG signal will persist under conditions of circularly polarised pumping. This specific polarisation feature will allow experimental validation of the theory.
Quasi-Monte Carlo, quasi-random numbers and quasi-error estimates
NASA Astrophysics Data System (ADS)
Kleiss, Ronald
We discuss quasi-random number sequences as a basis for numerical integration with potentially better convergence properties than standard Monte Carlo. The importance of the discrepancy as both a measure of smoothness of distribution and an ingredient in the error estimate is reviewed. It is argued that the classical Koksma-Hlawka inequality is not relevant for error estimates in realistic cases, and a new class of error estimates is presented, based on a generalization of the Woźniakowski lemma.
Oracle inequalities for SVMs that are based on random entropy numbers
Steinwart, Ingo
2009-01-01
In this paper we present a new technique for bounding local Rademacher averages of function classes induced by a loss function and a reproducing kernel Hilbert space (RKHS). At the heart of this technique lies the observation that certain expectations of random entropy numbers can be bounded by the eigenvalues of the integral operator associated to the RKHS. We then work out the details of the new technique by establishing two new oracle inequalities for SVMs, which complement and generalize orevious results.
Reconstruction of photon number conditioned states using phase randomized homodyne measurements
NASA Astrophysics Data System (ADS)
Chrzanowski, H. M.; Assad, S. M.; Bernu, J.; Hage, B.; Lund, A. P.; Ralph, T. C.; Lam, P. K.; Symul, T.
2013-05-01
We experimentally demonstrate the reconstruction of a photon number conditioned state without using a photon number discriminating detector. By using only phase randomized homodyne measurements, we reconstruct up to the three photon subtracted squeezed vacuum state. The reconstructed Wigner functions of these states show regions of pronounced negativity, signifying the non-classical nature of the reconstructed states. The techniques presented allow for complete characterization of the role of a conditional measurement on an ensemble of states, and might prove useful in systems where photon counting still proves technically challenging.
Central Limit Theorems and Uniform Laws of Large Numbers for Arrays of Random Fields
Jenish, Nazgul; Prucha, Ingmar R.
2009-01-01
Over the last decades, spatial-interaction models have been increasingly used in economics. However, the development of a sufficiently general asymptotic theory for nonlinear spatial models has been hampered by a lack of relevant central limit theorems (CLTs), uniform laws of large numbers (ULLNs) and pointwise laws of large numbers (LLNs). These limit theorems form the essential building blocks towards developing the asymptotic theory of M-estimators, including maximum likelihood and generalized method of moments estimators. The paper establishes a CLT, ULLN, and LLN for spatial processes or random fields that should be applicable to a broad range of data processes. PMID:20161289
Effect of the driving algorithm on the turbulence generated by a random jet array
NASA Astrophysics Data System (ADS)
Pérez-Alvarado, Alejandro; Mydlarski, Laurent; Gaskin, Susan
2016-02-01
Different driving algorithms for a large random jet array (RJA) were tested and their performance characterized by comparing the statistics of the turbulence generated downstream of the RJA. Of particular interest was the spatial configuration of the jets operating at any given instant (an aspect that has not been documented in previous RJAs studies), as well as the statistics of their respective on/off times. All algorithms generated flows with nonzero skewnesses of the velocity fluctuation normal to the plane of the RJA (identified as an inherent limitation of the system resulting from the unidirectional forcing imposed from only one side of the RJA), and slightly super-Gaussian kurtoses of the velocity fluctuations in all directions. It was observed that algorithms imposing spatial configurations generated the most isotropic flows; however, they suffered from high mean flows and low turbulent kinetic energies. The algorithm identified as RANDOM (also referred to as the "sunbathing algorithm") generated the flow that, on an overall basis, most closely approximated zero-mean-flow homogeneous isotropic turbulence, with variations in horizontal and vertical homogeneities of RMS velocities of no more than ±6 %, deviations from isotropy ( w RMS/ u RMS) in the range of 0.62-0.77, and mean flows on the order of 7 % of the RMS velocities (determined by averaging their absolute values over the three velocity components and three downstream distances). A relatively high turbulent Reynolds number ( Re T = u T ℓ/ ν = 2360, where ℓ is the integral length scale of the flow and u T is a characteristic RMS velocity) was achieved using the RANDOM algorithm and the integral length scale ( ℓ = 11.5 cm) is the largest reported to date. The quality of the turbulence in our large facility demonstrates the ability of RJAs to be scaled-up and to be the laboratory system most capable of generating the largest quasi-homogeneous isotropic turbulent regions with zero mean flow.