Different universal (also called automatic or black-box) methods have been suggested to sample from univariate log-concave distributions. The description of a universal generator for bivariate distributions has not been published up to now. The new algorithm for bivariate log-concave distributions is based on the method of transformed density rejection. In order to construct a hat function for a rejection algorithm the bivariate density is transformed by the logarithm into a concave function. Then it is possible to construct a dominating function by taking the minimum of several tangent planes which are by exponentiation transformed back into the original scale. The choice of the points of contact is automated using adaptive rejection sampling. This means that a point that is rejected by the rejection algorithm is used as additional point of contact until the maximal number of points of contact is reached. The paper describes the details how this main idea can be used to construct Algorithm ULC2D that can generate random pairs from bivariate log-concave distribution with a computable density. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

We give an algorithm that can be used to sample from any discrete log-concave distribution (e.g. the binomial and hypergeometric distributions). It is based on rejection from a discrete dominating distribution that consists of parts of the geometric distribution. The algorithm is uniformly fast for all discrete log-concave distributions and not much slower than algorithms designed for a single distribution. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

abstract: In the middle of the 20th century in the United States, transportation and infrastructure development became a priority on the national agenda, instigating the development of mathematical models that would predict transportation network performance. Approximately 40 years later, transportation planning models again became a national priority, this time instigating the development of highly disaggregate activity-based traffic models called microsimulations. These models predict the travel on a network at the level of the individual decision-maker, but do so with a large computational complexity and processing time requirement. The vast resources and steep learning curve required to integrate microsimulation models into the general transportation plan have deterred planning agencies from incorporating these tools. By researching the stochastic variability in the results of a microsimulation model with varying random number seeds, this paper evaluates the number of simulation trials necessary, and therefore the computational effort, for a planning agency to reach stable model outcomes. The microsimulation tool used to complete this research is the Transportation Analysis and Simulation System (TRANSIMS). The requirements for initiating a TRANSIMS simulation are described in the paper. Two analysis corridors are chosen in the Metropolitan Phoenix Area, and the roadway performance characteristics volume, vehicle-miles of travel, and vehicle-hours of travel are examined in each corridor under both congested and uncongested conditions. Both congested and uncongested simulations are completed in twenty trials, each with a unique random number seed. Performance measures are averaged for each trial, providing a distribution of average performance measures with which to test the stability of the system. The results of this research show that the variability in outcomes increases with increasing congestion. Although twenty trials are sufficient to achieve stable solutions for the uncongested state, convergence in the congested state is not achieved. These results indicate that a highly congested urban environment requires more than twenty simulation runs for each tested scenario before reaching a solution that can be assumed to be stable. The computational effort needed for this type of analysis is something that transportation planning agencies should take into consideration before beginning a traffic microsimulation program. / Dissertation/Thesis / M.S. Civil Engineering 2010

Mon travail porte sur la construction de générateurs aléatoires de conditions de vent en Bretagne. Ces modèles permettent de simuler artificiellement des conditions météorologiques réalistes et sont couramment utilisés pour la gestion des risques liés aux aléas climatiques. Ils sont construits sur la base de données historiques dans le but de produire des simulations cohérentes avec le climat actuel mais peuvent intégrer des scénarios de changement climatique. Les séquences simulées permettent de pallier le manque de données réelles et sont utilisées en entrée de modèles économiques ou écologiques. / This work is aimed at constructing stochastic weather generators. These models enable to simulate artificially weather data that have statistical properties consistent with observed meteorology and climate. Outputs of these models are generally used in impact studies in agriculture or in ecology.

This thesis presents a generalized approach for the fully digital design and implementation of chaos generators through the numerical solution of chaotic ordinary differential equations. In particular, implementations use the Euler approximation with a fixed-point twos complement number representation system for optimal hardware and performance. In general, digital design enables significant benefits in terms of power, area, throughput, reliability, repeatability and portability over analog implementations of chaos due to lower process, voltage and temperature sensitivities and easy compatibility with other digital systems such as microprocessors, digital signal processing units, communication systems and encryption systems. Furthermore, this thesis introduces the idea of implementing multidimensional chaotic systems rather than 1-D chaotic maps to enable wider throughputs and multiplier-free architectures that provide significant performance and area benefits. This work focuses efforts on the well-understood family of autonomous 3rd order "jerk" chaotic systems. The effect of implementation precision, internal delay cycles and external delay cycles on the chaotic response are assessed. Multiplexing of parameters is implemented to enable switching between chaotic and periodic modes of operation. Enhanced chaos generators that exploit long-term divergence in two identical systems of different precision are also explored. Digital design is shown to enable real-time controllability of 1D multiscroll systems and 4th order hyperchaotic systems, essentially creating non-autonomous chaos that has thus far been difficult to implement in the analog domain. Seven different systems are mathematically assessed for chaotic properties, implemented at the register transfer level in Verilog HDL and experimentally verified on a Xilinx Virtex 4 FPGA. The statistical properties of the output are rigorously studied using the NIST SP. 800-22 statistical testing suite. The output is adapted for pseudo random number generation by truncating statistically defective bits. Finally, a novel post-processing technique using the Fibonacci series is proposed and implemented with a non-autonomous driven hyperchaotic system to provide pseudo random number generators with high nonlinear complexity and controllable period length that enables full utilization of all branches of the chaotic output as statistically secure pseudo random output.

No description available.

The class of generalized feedback shift register (GFSR) random number generators was a promising method for random number generation in the 1980's, but was abandoned because of some flaws such as poor performance on certain tests for randomness. The poor performance may be due to the choice of primitive polynomials used in the generators, rather than inherent flaws in the method. The original GFSR generators were all based on primitive trinomials. This project examines several alternative choices of primitive polynomials with more than one "interior" term to address this problem and hopefully provide access to good random number generators.

In this paper we perform a statistical analysis of dark counts in superconducting nanowire single photon detectors (SNSPDs) with the end goal of creating a quantum random number generator (QRNG) using these dark counts. We confirm that dark counts are Poissonian for low bias currents and that no afterpulsing is present. However, we also show that an increase in bias current causes the dark counts to violate the independence assumption. For the non-Poissonian dark counts we identify three seemingly similar effects and confirm that: (i) a single event is at times regarded as two by the flat-threshold discriminator in the time-tagging device; (ii) a reflection in the readout circuit incites a second detection event shortly after the arrival of a first one, creating a conditionality between dark counts; (iii) a damped oscillation in the effective bias current immediately after a detection event shows itself in the inter-arrival time probability distribution. Finally, we present and evaluate a method for generating random numbers using the Poissonian dark counts as an entropy source with promising results.

Random Numbers form the heart and soul of a discrete-event simulation system. There are few situations where the actions of the entities in the process being simulated can be completely predicted in advance. The real world processes are more probabilistic than deterministic. Hence, such chances are represented in the system by using various statistical models, like random number generators. These random number generators can be used to represent a various number of factors, such as length of the queue. However, simulations have grown in size and are sometimes required to run on multiple machines, which share the various methods or events in the simulation among themselves. These Machines can be distributed across a LAN or even the internet. In such cases, to keep the validity of the simulation model, we need rollback-able random number generators. This thesis is an effort to develop such rollback able random number generators for the Synchronous Parallel Environment for Emulation and Discrete-Event Simulation (SPEEDES) environment developed by NASA. These rollback-able random number generators will also add several statistical distribution models to the already rich SPEEDES library.

Generating random numbers can be accomplished through various methods, with the primary distinction lying between pseudo-random number generators (PRNGs), which are commonly used for applications that require a large amount of random data, and true random number generators (TRNGs), which are commonly used for applications that need security and unpredictability. This thesis explores the feasibility of harnessing frequency variations in the electrical grid as a source of entropy for a TRNG. By employing an iterative approach, the study has substantiated the likelihood that frequency fluctuations can serve as a reliable source of ran-domness for a TRNG. This assertion is supported by statistical testing using the comprehensive RNG testing suite known as DieHarder, where the final implementation of the TRNG yielded favourable outcomes. Nevertheless, it is worth noting that the artefact exhibited weaker resultson three specific tests within the suite, which can likely be attributed to a limited amount of generated data. Despite these limitations, the findings are undeniably promising, and futurere search endeavours should focus primarily on enhancing the generation speed of the TRNG. By doing so, it is anticipated that improved performance on the DieHarder suite and similar RNG testing suites can be achieved. / Generering av slumptal kan åstadkommas mev hjälp av flera olika metoder. De två stora grupperna är pseudo-slumptalsgeneratorer (PRNG:er), som vanligtvis används för applikationer som kräver en stor mängd slumpmässiga data, och sanna slumptalsgeneratorer (TRNG:er), som ofta används för applikationer som behöver säkerhet och oförutsägbarhet. Detta examensarbete undersöker möjligheten att utnyttja frekvensvariationer i det elektriska nätetverket som en källa till entropi för en TRNG. Genom att använda ett iterativt tillvägagångssätt har studien underbyggt sannolikheten att frekvensfluktuationer kan fungera som en pålitlig källa till slumpmässighet för en TRNG. Detta påstående stöds av statistiska tester med den omfattande RNG-testsviten känd som DieHarder, där den slutliga implementeringen av TRNG:n gav gynnsamma resultat. Det är värt att notera att artefacten visade svagare resultat på tre specifika tester inom sviten, vilket sannolikt kan tillskrivas en begränsad mängd genererad data. Trots dessa begränsningar är resultaten onekligen lovande, och framtida forskningsansträngningar bör främst fokusera på att öka generationshastigheten för generatorn. Genom att göra det förväntas det att bättre resultat från DieHarder och liknande RNG-testsviter kan uppnås.