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An investigation into adolescents perceptions of concepts of randomness, with a questionnaire trialled on 75 adolescent boys between Year 7 and Year 11 in Catholic schools in Melbourne, Australia.

An investigation into adolescents perceptions of concepts of randomness, with a questionnaire trialled on 75 adolescent boys between Year 7 and Year 11 in Catholic schools in Melbourne, Australia.

Whether Kolmogorov-Loveland randomness is equal to the Martin-Löf randomness is a well known open question in the field of algorithmic information theory. Randomness of infinite binary sequences can be defined in terms of betting strategies, a string is non-random if a computable betting strategy wins unbounded capital by successive betting on the sequence. For Martin-Löf randomness, a betting strategy makes a bet by splitting a set of sequences into any two clopen sets, and placing a portion of capital on one of them as a wager. Kolmogorov-Loveland betting strategies are more restricted, they bet on a value of the bit at some position they choose, which splits a set of sequences into two clopen sets, the sequences that have 0 at the chosen position and the sequences that have 1. In this thesis we consider betting strategies that when making a bet are restricted to split a set of sequences into two sets of equal uniform Lebesgue measure. We call this generalization of Kolmogorov-Loveland betting strategies the half-betting strategies. We show that there is a pair of such betting strategies such that for every non-Martin-Löf random sequence one of them wins unbounded capital (the pair is universal). Next, we define a finite betting game where the betting strategies bet on finite binary strings, and show that in this game Kolmogorov-Loveland betting strategies cannot increase capital by more than an arbitrary small amount on all strings on which the unrestricted betting strategy achieves arbitrary large capital. We also look at another relaxation of Kolmogorov-Loveland betting, where a betting strategy is allowed to access bits of the sequence within a set of positions a bounded number of times. We show that if this bound is less than ℓ - log ℓ for the first ℓ positions then a pair of such betting strategies cannot be universal. Furthermore, we show that, at least for some universal betting strategies, this bound is exponential.

In this article, I introduce a novel airborne network mobility model, called the Smooth Turn Mobility Model, that captures the correlation of acceleration for airborne vehicles across time and spatial coordinates. E?ective routing in airborne networks (ANs) relies on suitable mobility models that capture the random movement pattern of airborne vehicles. As airborne vehicles cannot make sharp turns as easily as ground vehicles do, the widely used mobility models for Mobile Ad Hoc Networks such as Random Waypoint and Random Direction models fail. Our model is realistic in capturing the tendency of airborne vehicles toward making straight trajectory and smooth turns with large radius, and whereas is simple enough for tractable connectivity analysis and routing design.

Pseudo-random sequences are a crucial component of cryptography, particularly in stream cipher design. In this thesis we will investigate several measures of randomness for certain classes of finitely generated sequences. We will present a heuristic algorithm for calculating the k-error linear complexity of a general sequence, of either finite or infinite length, and results on the closeness of the approximation generated. We will present an linear time algorithm for determining the linear complexity of a sequence whose characteristic polynomial is a power of an irreducible element, again presenting variations for both finite and infinite sequences. This algorithm allows the linear complexity of such sequences to be determined faster than was previously possible. Finally we investigate the stability of m-sequences, in terms of both k-error linear complexity and k-error period. We show that such sequences are inherently stable, but show that some are more stable than others.

This study takes as its focus young children's intuitive knowledge of randomness. Previous work in this field has studied the misconceptions that people, especially adults, hold in making judgements of chance (see, for example, the work of Kahneman & Tversky and Konold). In contrast, I study how primitive meaningsf or randomnessfo rm a basis for new meanings,a processw hich the misconceptionsa pproachf ails to illuminate. The guiding principle for this study is that the observation of students' evolving thought in a carefully designedc omputer-basedd omain will provide a betteru nderstanding of how the specific features of the domain shape and are shaped by activities within it. There are, then, two deeply connected strands to this thesis: the study of children's evolving meanings for randomness as expressed in a computer-based microworld, and the articulation of design principles which encapsulate pedagogic meaningsfor that microworld. More specifically, the thesis aims to shed light upon the answers to four crucial questions: Meanings for the domain: What do formalisms of stochastic behaviour look like in a domain of abstraction? What structures in the domain for stochastic abstraction optimise the articulation of intuitions and the construction of new meanings? Meanings in the domain: What articulations of informal intuitions of stochastic behaviour do we observe? How do the structures of the domain support the forging of situated meanings? The study uses an iterative design methodology, which cycles between the design of computer-based tools and the observ4tion of children, between the ages of 9 and II years, as they use these tools. The thesis identifies initial meanings for the behaviour of various stochastic phenomena and traces how new pieces of knowledge, especially relating to long term random behaviour, emerge through the forging of connections between the internal and external resources.

Approved for public release; distribution is unlimited / Includes supplementary material / Reissued 30 May 2017 with correction to degree on title page. / Randomness is at the heart of today's computing. There are two categorical methods to generate random numbers: pseudorandom number generation (PRNG) methods and true random number generation (TRNG) methods. While PRNGs operate orders of magnitude faster than TRNGs, the strength of PRNGs lies in their initial seed. TRNGs can function to generate such a seed. This thesis will focus on studying the feasibility of using the next generation Naval Postgraduate School Femto Satellite (NPSFS) as a TRNG. The hardware for the next generation will come from the Intel Quark D2000 along with its onboard BMC150 6-axis eCompass. We simulated 3-dimensional motion to see if any raw data from the BMC150 could be used as an entropy source for random number generation.We studied various "schemes" on how to select and output specific data bits to determine if more entropy and increased bitrate could be reached. Data collected in this thesis suggests that the BMC150 contains certain bits that could be considered good sources of entropy. Various schemes further utilized these bits to yield a strong entropy source with higher bitrate. We propose the NPSFS be studied further to find other sources of entropy. We also propose a prototype be sent into space for experimental verification of these results. / Lieutenant, United States Navy

Title: Generating random data from biometric samples Author: Bc. Romana Sachová Department: Department of Algebra Supervisor: Ing. Mgr. Zdeněk Říha, Ph.D. Supervisor's e-mail address: zriha@fi.muni.cz Abstract: This thesis aims to achieve the generation of random data from the bio- metric samples. Studying the biometric characteristics, randomness and generation of random data suitable for cryptography as well the variability of fingerprint, iris, face and human voice. In the practical part has been tested the variability of 200 prints from the same finger, using three factors: 1) The coordinates of fingerprints cores. Due to the repeatability of coordinates the obtained entropy was low. 2) Fingerprint area approximation. It was able to verify the diversity of all areas. The maximum available entropy remains around 15 bits. 3) Ridge lines distortion. From the core to the top of the fingerprint has been taken boxes containing part of the ridge line. For all boxes was calculated the average phase angle of the gradient which represents the change of intensity in the box. Vector of phase angles describes the ridge line distortion. Maximum estimated entropy of this vectors was estimated at 71,586 bits. Keywords: biometry, randomness, entropy 1

In this paper we analyze how many shuffles are necessary to get close to ran- domness for a deck of n cards. Aldous (1983) shows that approximately 8.55 (n=52) shuffles are necessary when n is large. Bayer and Diaconis (1992) use the variation distance as a measure of randomness to analyze the most commonly used method of shuffling cards, and claim that 7 shuffles are enough when n=52. We provide another idea to measure the distance from randomness for repeated shuffles. The proposed method consists of a goodness of fit test and a simple simulation. Simulation results show that we have a similar conclusion to that of Bayer and Diaconis.