A comparative evaluation of measures to assess randomness in human-generated sequences.

Whether and how well people can behave randomly is of interest in many areas of psychological research. The ability to generate randomness is often investigated using random number generation (RNG) tasks, in which participants are asked to generate a sequence of numbers that is as random as possible. However, there is no consensus on how best to quantify the randomness of responses in human-generated sequences. Traditionally, psychologists have used measures of randomness that directly assess specific features of human behavior in RNG tasks, such as the tendency to avoid repetition or to systematically generate numbers that have not been generated in the recent choice history, a behavior known as cycling. Other disciplines have proposed measures of randomness that are based on a more rigorous mathematical foundation and are less restricted to specific features of randomness, such as algorithmic complexity. More recently, variants of these measures have been proposed to assess systematic patterns in short sequences. We report the first large-scale integrative study to compare measures of specific aspects of randomness with entropy-derived measures based on information theory and measures based on algorithmic complexity. We compare the ability of the different measures to discriminate between human-generated sequences and truly random sequences based on atmospheric noise, and provide a systematic analysis of how the usefulness of randomness measures is affected by sequence length. We conclude with recommendations that can guide the selection of appropriate measures of randomness in psychological research.

Counting on random number generation: Uncovering mild executive dysfunction in congenital heart disease.

Congenital heart disease (CHD) is associated with various neurocognitive deficits, particularly targeting executive functions (EFs), of which random number generation (RNG) is one indicator. RNG has, however, never been investigated in CHD. We administered the Mental Dice Task (MDT) to 67 young adults with CHD and 55 healthy controls. This 1-minute-task requires the generation of numbers 1 to 6 in a random sequence. RNG performance was correlated with a global EF score. Participants underwent MRI to examine structural-volumetric correlates of RNG. Compared to controls, CHD patients showed increased backward counting, reflecting deficient inhibition of automatized behavior. They also lacked a small-number bias (higher frequency of small relative to large numbers). RNG performance was associated with global EF scores in both groups. In CHD patients, MRI revealed an inverse association of counting bias with most of the volumetric measurements and the amount of small numbers was positively associated with corpus callosum volume, suggesting callosal involvement in the "pseudoneglect in number space". In conclusion, we found an impaired RNG performance in CHD patients, which is associated with brain volumetric measures. RNG, reportedly resistant to learning effects, may be an ideal task for the longitudinal assessment of EFs in patients with CHD.

Generation of Tunable Stochastic Sequences Using the Insulator-Metal Transition.

Probabilistic computing is a paradigm in which data are not represented by stable bits, but rather by the probability of a metastable bit to be in a particular state. The development of this technology has been hindered by the availability of hardware capable of generating stochastic and tunable sequences of "1s" and "0s". The options are currently limited to complex CMOS circuitry and, recently, magnetic tunnel junctions. Here, we demonstrate that metal-insulator transitions can also be used for this purpose. We use an electrical pump/probe protocol and take advantage of the stochastic relaxation dynamics in VO2 to induce random metallization events. A simple latch circuit converts the metallization sequence into a random stream of 1s and 0s. The resetting pulse in between probes decorrelates successive events, providing a true stochastic digital sequence.

Variable-Length Resolvability for General Sources and Channels.

We introduce the problem of variable-length (VL) source resolvability, in which a given target probability distribution is approximated by encoding a VL uniform random number, and the asymptotically minimum average length rate of the uniform random number, called the VL resolvability, is investigated. We first analyze the VL resolvability with the variational distance as an approximation measure. Next, we investigate the case under the divergence as an approximation measure. When the asymptotically exact approximation is required, it is shown that the resolvability under two kinds of approximation measures coincides. We then extend the analysis to the case of channel resolvability, where the target distribution is the output distribution via a general channel due to a fixed general source as an input. The obtained characterization of channel resolvability is fully general in the sense that, when the channel is just an identity mapping, it reduces to general formulas for source resolvability. We also analyze the second-order VL resolvability.

Asymptotically Optimal Adversarial Strategies for the Probability Estimation Framework.

The probability estimation framework involves direct estimation of the probability of occurrences of outcomes conditioned on measurement settings and side information. It is a powerful tool for certifying randomness in quantum nonlocality experiments. In this paper, we present a self-contained proof of the asymptotic optimality of the method. Our approach refines earlier results to allow a better characterisation of optimal adversarial attacks on the protocol. We apply these results to the (2,2,2) Bell scenario, obtaining an analytic characterisation of the optimal adversarial attacks bound by no-signalling principles, while also demonstrating the asymptotic robustness of the PEF method to deviations from expected experimental behaviour. We also study extensions of the analysis to quantum-limited adversaries in the (2,2,2) Bell scenario and no-signalling adversaries in higher (n,m,k) Bell scenarios.

Demonstration of Nanosecond Operation in Stochastic Magnetic Tunnel Junctions.

Magnetic tunnel junctions operating in the superparamagnetic regime are promising devices in the field of probabilistic computing, which is suitable for applications like high-dimensional optimization or sampling problems. Further, random number generation is of interest in the field of cryptography. For such applications, a device's uncorrelated fluctuation time-scale can determine the effective system speed. It has been theoretically proposed that a magnetic tunnel junction designed to have only easy-plane anisotropy provides fluctuation rates determined by its easy-plane anisotropy field and can perform on a nanosecond or faster time-scale as measured by its magnetoresistance's autocorrelation in time. Here, we provide experimental evidence of nanosecond scale fluctuations in a circular-shaped easy-plane magnetic tunnel junction, consistent with finite-temperature coupled macrospin simulation results and prior theoretical expectations. We further assess the degree of stochasticity of such a signal.

From Random Numbers to Random Objects.

Many security-related scenarios including cryptography depend on the random generation of passwords, permutations, Latin squares, CAPTCHAs and other types of non-numerical entities. Random generation of each entity type is a different problem with different solutions. This study is an attempt at a unified solution for all of the mentioned problems. This paper is the first of its kind to pose, formulate, analyze and solve the problem of random object generation as the general problem of generating random non-numerical entities. We examine solving the problem via connecting it to the well-studied random number generation problem. To this end, we highlight the challenges and propose solutions for each of them. We explain our method using a case study; random Latin square generation.

Various Auto-Correlation Functions of m-Bit Random Numbers Generated from Chaotic Binary Sequences.

This paper discusses the auto-correlation functions of m-bit random numbers obtained from m chaotic binary sequences generated by one-dimensional nonlinear maps. First, we provide the theoretical auto-correlation function of an m-bit sequence obtained by m binary sequences that are assumed to be uncorrelated to each other. The auto-correlation function is expressed by a simple form using the auto-correlation functions of the binary sequences. This implies that the auto-correlation properties of the m-bit sequences can be easily controlled by the auto-correlation functions of the original binary sequences. In numerical experiments using a computer, we generated m-bit random sequences using some chaotic binary sequences with prescribed auto-correlations generated by one-dimensional chaotic maps. The numerical experiments show that the numerical auto-correlation values are almost equal to the corresponding theoretical ones, and we can generate m-bit sequences with a variety of auto-correlation properties. Furthermore, we also show that the distributions of the generated m-bit sequences are uniform if all of the original binary sequences are balanced (i.e., the probability of 1 (or 0) is equal to 1/2) and independent of one another.

A method of generating multivariate non-normal random numbers with desired multivariate skewness and kurtosis.

In social and behavioral sciences, data are typically not normally distributed, which can invalidate hypothesis testing and lead to unreliable results when being analyzed by methods developed for normal data. The existing methods of generating multivariate non-normal data typically create data according to specific univariate marginal measures such as the univariate skewness and kurtosis, but not multivariate measures such as Mardia's skewness and kurtosis. In this study, we propose a new method of generating multivariate non-normal data with given multivariate skewness and kurtosis. Our approach allows researchers to better control their simulation designs in evaluating the influence of multivariate non-normality.

True Random Number Generator (TRNG) Utilizing FM Radio Signals for Mobile and Embedded Devices in Multi-Access Edge Computing.

As transmissions of data between mobile and embedded devices in multi-access edge computing (MEC) increase, data must be protected, ensuring confidentiality and integrity. These issues are usually solved with cryptographic algorithms systems, which utilize a random number generator to create seeds and keys randomly. Their role in cryptography is so important that they need to be generated securely. In this paper, a true random number generator (TRNG) utilizing FM radio signals as a source is proposed. The proposed method can generate random numbers with high entropy, increased by at least 118% and up to 431% compared to existing generators.

A method, framework, and tutorial for efficiently simulating models of decision-making.

Evidence accumulation models (EAMs) have become the dominant models of rapid decision-making. Several variants of these models have been proposed, ranging from the simple linear ballistic accumulator (LBA) to the more complex leaky-competing accumulator (LCA), and further extensions that include time-varying rates of evidence accumulation or decision thresholds. Although applications of the simpler variants have been widespread, applications of the more complex models have been fewer, largely due to their intractable likelihood function and the computational cost of mass simulation. Here, I present a framework for efficiently fitting complex EAMs, which uses a new, efficient method of simulating these models. I find that the majority of simulation time is taken up by random number generation (RNG) from the normal distribution, needed for the stochastic noise of the differential equation. To reduce this inefficiency, I propose using the well-known concept within computer science of "look-up tables" (LUTs) as an approximation to the inverse cumulative density function (iCDF) method of RNG, which I call "LUT-iCDF". I show that when using an appropriately sized LUT, simulations using LUT-iCDF closely match those from the standard RNG method in R. My framework, which I provide a detailed tutorial on how to implement, includes C code for 12 different variants of EAMs using the LUT-iCDF method, and should make the implementation of complex EAMs easier and faster.

Numerical and Non-Asymptotic Analysis of Elias's and Peres's Extractors with Finite Input Sequences.

Many cryptographic systems require random numbers, and the use of weak random numbers leads to insecure systems. In the modern world, there are several techniques for generating random numbers, of which the most fundamental and important methods are deterministic extractors proposed by von Neumann, Elias, and Peres. Elias's extractor achieves the optimal rate (i.e., information-theoretic upper bound) h ( p ) if the block size tends to infinity, where h ( · ) is the binary entropy function and p is the probability that each bit of input sequences occurs. Peres's extractor achieves the optimal rate h ( p ) if the length of the input and the number of iterations tend to infinity. Previous research related to both extractors has made no reference to practical aspects including running time and memory size with finite input sequences. In this paper, based on some heuristics, we derive a lower bound on the maximum redundancy of Peres's extractor, and we show that Elias's extractor is better than Peres's extractor in terms of the maximum redundancy (or the rates) if we do not pay attention to the time complexity or space complexity. In addition, we perform numerical and non-asymptotic analysis of both extractors with a finite input sequence with any biased probability under the same environments. To do so, we implemented both extractors on a general PC and simple environments. Our empirical results show that Peres's extractor is much better than Elias's extractor for given finite input sequences under a very similar running time. As a consequence, Peres's extractor would be more suitable to generate uniformly random sequences in practice in applications such as cryptographic systems.

Low Complexity Estimation Method of Rényi Entropy for Ergodic Sources.

Since the entropy is a popular randomness measure, there are many studies for the estimation of entropies for given random samples. In this paper, we propose an estimation method of the Rényi entropy of order α . Since the Rényi entropy of order α is a generalized entropy measure including the Shannon entropy as a special case, the proposed estimation method for Rényi entropy can detect any significant deviation of an ergodic stationary random source's output. It is shown that the expected test value of the proposed scheme is equivalent to the Rényi entropy of order α . After deriving a general representation of parameters of the proposed estimator, we discuss on the particular orders of Rényi entropy such as α → 1 , α = 1 / 2 , and α = 2 . Because the Rényi entropy of order 2 is the most popular one, we present an iterative estimation method for the application with stringent resource restrictions.

Acute peripheral vestibular deficit increases redundancy in random number generation.

Unilateral peripheral vestibular deficit leads to broad cognitive difficulties and biases in spatial orientation. More specifically, vestibular patients typically show a spatial bias toward their affected ear in the subjective visual vertical, head and trunk orientation, fall tendency, and walking trajectory. By means of a random number generation task, we set out to investigate how an acute peripheral vestibular deficit affects the mental representation of numbers in space. Furthermore, the random number generation task allowed us to test if patients with peripheral vestibular deficit show evidence of impaired executive functions while keeping the head straight and while performing active head turns. Previous research using galvanic vestibular stimulation in healthy people has shown no effects on number space, but revealed increased redundancy of the generated numbers. Other studies reported a spatial bias in number representation during active and passive head turns. In this experiment, we tested 43 patients with acute vestibular neuritis (18 patients with left-sided and 25 with right-sided vestibular deficit) and 28 age-matched healthy controls. We found no bias in number space in patients with peripheral vestibular deficit but showed increased redundancy in patients during active head turns. Patients showed worse performance in generating sequences of random numbers, which indicates a deficit in the updating component of executive functions. We argue that RNG is a promising candidate for a time- and cost-effective assessment of executive functions in patients suffering from a peripheral vestibular deficit.

Linking cognitive abilities with the propensity for risk-taking: the balloon analogue risk task.

There is great interest about the individual differences that influence the ability of dealing with risky decisions. In this light, an intriguing question is whether decision-making during risk is related to other cognitive abilities, especially executive functions. To investigate, in healthy subjects, the existence of a possible correlation between risk-taking and cognitive abilities, the balloon analogue risk task (BART) has been exploited to assess risk-taking propensity and the random number generation (RNG), to investigate cognitive functions. The risk-taking propensity is significantly correlated with the Cycling factor, a feature of RNG performance specifically related to the ability of updating and monitoring information. In particular, an excessive activity of monitoring (expressed by lower values of Cycling factor) is related to a more risk-averse behavior. An overlapping between the circuits involved in both RNG and BART, centered on the dorsolateral prefrontal cortex, could be the possible neurophysiological substrate for this correlation. This study suggests a relevant contribution of executive functions in risk-taking behavior. This could have relevant implications in neuroeconomics and neuropsychiatry of addiction and pathological gambling.

Concurrent Generation of Ordinal and Normal Data.

The use of joint models that are capable of handling different data types is becoming increasingly popular in biopharmaceutical practice. Evaluation of various statistical techniques that have been developed for mixed data in simulated environments requires joint generation of multiple variables. In this article, we propose a unified framework for concurrently simulating ordinal and normal data given the marginal characteristics and correlation structure. We illustrate our technique in two simulation settings where we use artificial data as well as real depression score data from psychiatric research, demonstrating negligibly small deviations between the specified and empirically computed quantities.

Harvesting entropy for random number generation for internet of things constrained devices using on-board sensors.

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.

The effect of practice on random number generation task: a transcranial direct current stimulation study.

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.

Blood-inspired random bit generation using microfluidics system.

The development of random number generators (RNGs) using speckle patterns is pivotal for secure encryption key generation, drawing from the recent statistical properties identified in speckle-based imaging. Speckle-based RNG systems generate a sequence of random numbers through the unpredictable and reproducible nature of speckle patterns, ensuring a source of randomness that is independent of algorithms. However, to guarantee their effectiveness and reliability, these systems demand a meticulous and rigorous approach. In this study, we present a blood-inspired RNG system with a microfluidics device, designed to generate random numbers at a rate of 5.5 MHz and a high-speed of 1250 fps. This process is achieved by directing a laser beam through a volumetric scattering medium to procure speckle patterns. Additionally, designed microfluidic device requires only a minimal blood sample of 5 µl to capture these speckle patterns effectively. After implementing the two-pass tuple-output von Neumann debiasing algorithm to counteract statistical biases, we utilized the randomness statistical test suite from the National Institute of Standards and Technology for validation. The generated numbers successfully passed these tests, ensuring their randomness and unpredictability. Our blood-inspired RNG, utilizing whole blood, offers a pathway for affordable, high-output applications in fields like encryption, computer security, and data protection.

Manipulating number generation: loud + long = large?

Humans make numerous choices every day and tend to perceive these choices as free. The present study shows how simple free choices are biased by experiencing unrelated auditory information. In two experiments, participants categorized tones according to their intensity on the dimensions volume and duration on the majority of trials. On some trials, however, they were to randomly generate a number, and we found these choices to be influenced by tone intensity. Particularly, if participants were cued toward volume, loud tones clearly biased participants to generate larger numbers. For tone duration, a similar effect only emerged if spatial information was reinforced by the motor context of the task. The findings extend previous findings relating to the ATOM framework (A Theory of Magnitude) by an explicit focus on auditory magnitude processing. As such, they also constrain ATOM by showing that the connections between different magnitude dimensions vary to a considerable degree.