Random Source Research Articles

Robust Far-Field Optical Image Transmission with Structured Random Light Beams

The ability to overcome the adverse effect induced by the obstacles within the transmission link is a central challenge in long-distance optical image transmission and is significantly crucial in free-space optical communication. In this work, we introduce an efficient protocol to realize the robust far-field optical image-signal transmission by modulating the spatial-coherence structure of a partially coherent random light source. The image information encoded in the spatial-coherence structure can be stably transmitted to the far field and can resist the influence of obstructions within the communication link. This is due to the self-reconstruction property of the spatial-coherence structure embedded with the cross phase in the far field. We demonstrate experimentally that the image information can be recovered well by measuring the second-order spatial-coherence structure of the obstructed random light in the far field. Our findings open a door for robust optical signal transmission through the complex environment and may find application in optical communication through a turbulent atmosphere.

Crosstalk creates a more secure source of randomness based on quantum phenomena

Using a drawback of the quantum channel for randomness generation

From the Bernoulli factory to a dice enterprise via perfect sampling of Markov chains

Given a p-coin that lands heads with unknown probability p, we wish to produce an f(p)-coin for a given function f:(0,1)→(0,1). This problem is commonly known as the Bernoulli factory and results on its solvability and complexity have been obtained in (ACM Trans. Model. Comput. Simul. 4 (1994) 213–219; Ann. Appl. Probab. 15 (2005) 93–115). Nevertheless, generic ways to design a practical Bernoulli factory for a given function f exist only in a few special cases. We present a constructive way to build an efficient Bernoulli factory when f(p) is a rational function with coefficients in R. Moreover, we extend the Bernoulli factory problem to a more general setting where we have access to an m-sided die and we wish to roll a v-sided one; that is, we consider rational functions between open probability simplices. Our construction consists of rephrasing the original problem as simulating from the stationary distribution of a certain class of Markov chains—a task that we show can be achieved using perfect simulation techniques with the original m-sided die as the only source of randomness. In the Bernoulli factory case, the number of tosses needed by the algorithm has exponential tails and its expected value can be bounded uniformly in p. En route to optimizing the algorithm we show a fact of independent interest: every finite, integer valued, random variable will eventually become log-concave after convolving with enough Bernoulli trials.

Single‐ and Multi‐Pass Magnetometric Subsurface Ocean Detection and Characterization in Icy Worlds Using Principal Component Analysis (PCA): Application to Triton

AbstractMany moons in the solar system are thought to potentially harbor hidden oceans based on the features observed at their surfaces. However, the magnetic induction signatures measured in the vicinity of these moons provide the most compelling evidence for the presence of a subsurface ocean, specifically for the Jovian moons Europa and Callisto. Interpretation of these magnetic signatures can be challenging due to the various systematic and random sources of noise that are present in the magnetic field measurement. In this work, a novel magnetometric ocean detection methodology based on Principal Component Analysis is presented and shown to provide enhanced discrimination and geophysical characterization of ocean properties in the presence of noise and error sources. The proposed methodology is robust for a single‐encounter mission or an orbiting mission with multiple flybys. Here, it is applied to the Neptunian moon Triton as a prime example of an active, potential ocean world residing in the requisite time‐varying magnetic field environment that enables magnetic induction investigation of its interior. In addition to the usual noise sources, other confounding factors are addressed, including the presence of an intense conductive ionosphere, the small amplitude of Neptune's driving magnetic field, and the uncertainty of Neptune's magnetic phase at the time‐of‐arrival which can potentially hinder accurate ocean detection and characterization. The proposed methodology is applicable to any moon in the solar system residing in a time‐varying magnetic field environment.

Lagrangian chaos and scalar advection in stochastic fluid mechanics

We study the Lagrangian flow associated to velocity fields arising from various models of stochastic fluid mechanics. We prove that in many circumstances, these flows are chaotic, that is, the top Lyapunov exponent is strictly positive ( almost surely , all particle trajectories are simultaneously exponentially sensitive with respect to initial conditions). Our main results are for the Navier–Stokes equations on \mathbb{T}^2 and the hyper-viscous regularized Navier–Stokes equations on \mathbb{T}^3 (at arbitrary fixed Reynolds number and hyper-viscosity parameters), subject to white-in-time, H^s -in-space stochastic forcing which is nondegenerate at high frequencies. Using these results, we further make a mathematically rigorous study of “passive scalar turbulence”. To this end, we study statistically stationary solutions to the passive scalar advection-diffusion advected by one of these velocity fields and subjected to a white-in-time random source. We show that the chaotic behavior of Lagrangian dynamics implies a type of anomalous dissipation in the limit of vanishing diffusivity, which in turn, implies Yaglom’s law of scalar turbulence – the universal scaling law analogous to the Kolmogorov 4/5 law. Key features of our study are the use of tools from ergodic theory and random dynamical systems in infinite dimensions, namely the Multiplicative Ergodic Theorem and a version of Furstenberg’s Criterion, combined with hypoellipticity via Malliavin calculus and approximate control arguments.

Control of nonlinear processes using versatile random photonic sources: Application to the energy deposition in a dielectric material

We report on the properties of a nonconventional stochastic photonic source. We first describe the principle of nonlinear intensity filtering by using a modified Mach-Zehnder interferometer. The latter alters the characteristics of an input stochastic source based on Bose-Einstein emission. Computed output intensity fluctuations are compared to an analytical model. Adjusting the interferometer parameters, we show theoretically and numerically that the statistical properties of light such as its probability density function can be tailored. Depending on the parameters, the probability density may exhibit large overshoots or smoother fluctuations. We further evaluate the impact of these modified statistics on simple nonlinear processes. Compared to Bose-Einstein emitters, the yield of nonlinear phenomena varies by several orders of magnitude. We finally simulate the nonlinear interaction of such a laser source with a dielectric material (fused silica) within the framework of a more realistic model, including a statistical analysis. It confirms that the deposited energy varies over many decades and can be largely enhanced due to the properties of the presented laser source.

Evaluation of Flame Propagation Speed in a System of Random Discrete Sources for Spherical Particles in a Three-Dimensional Space

Realistic estimation of combustion phenomenon can be achieved by considering a random distribution for the particles instead of uniform distribution. Hence, in this study, theoretical investigation of aluminum particles combustion is studied three dimensionally with the consideration of random dispersion for discrete sources. Moreover, flame propagation speed is predicted through a proposed thermal model in a reaction medium. In addition, it is inferred that the propagation speed of the flame is a function of concentration and diameter of aluminum dust; while the minimum ignition energy is a function of particle diameter and equivalence ratio. A suitable prediction of the model is concluded by comparing the obtained results with the experimental and analytical data.

Online feature selection for multi-source streaming features

Multi-source streaming feature selection in an online manner has attracted considerable attention, from researchers because it can reduce the dimensionality of heterogeneous big data. However, traditional online algorithms such as Alpha-investing, Online Streaming Feature Selection (OSFS), Online Group Feature Selection (OGFS) and Scalable and Accurate OnLine Approach (SAOLA) consider only a single data source with fixed instances, and are not directly applicable to multi-source data. Multi-source Causal Feature Selection (MCFS) can search for an invariant set in multiple interventional datasets. However, fixed feature spaces are restrained, and exactly these same features are required among multi-source data. To overcome these limitations, we propose a novel method known as Multi-source Streaming Feature Selection (MSFS) to tackle the feature selection problem for multi-source streaming features. The MSFS algorithm addresses a new feature from a random source in three phases: relevance, intra-source redundancy, and inter-source redundancy analyses. That is, MSFS attempts to mine the potential relationships among different data sources rather than only independently consider each data source. In particular, each new feature is analyzed online using the overlapping instances from all data sources, and the Markov blanket (MB) of the target variable is dynamically adjusted. To evaluate the performance of the MSFS algorithm, we compare it with that of the abovementioned algorithms on 14 datasets and two real-world scenarios. The results demonstrate that MSFS outperforms the existing algorithms in classification accuracy and number of selected features.

Application of A Priori Map in Dynamic Background Removal for Indoor Human Perception Using a Thermopile Array

Human perception is of great research and application value. Thermopile infrared array sensor (TPAS) is an available solution without privacy invasion. In specific indoor environment like apartment and office, there are inevitable interfering thermal sources except human. Extracting human from the dynamically changing background i.e. background removal is a critical process. Based on the hardware platform built by a thermopile infrared array sensor MLX90640 with an output of 24×32 pixels, this paper proposes an adaptive Gaussian background removal algorithm applying a priori map (AGBR-PM) for indoor single human perception. For each static thermal source, an a priori map is established containing its location and thermal radiation feature in the way of support degree matrix. We build a Gaussian background model consisting of mean and standard deviation matrix. Each frame of thermal image is segmented into foreground and background based on 2σ rule. A state and cross detection algorithm is proposed to compensate the error caused by interfering static thermal sources, and an erosion-connected component analysis and foreground complement algorithm is adopted to reduce the random noise as well. A regional update strategy is designed to adapt to the emergence of random thermal sources in background. The experimental results have shown that AGBR-PM has an excellent adaptability to dynamically changing environment, and can remove the background correctly.

Attaining Fairness in Communication for Omniscience.

This paper studies how to attain fairness in communication for omniscience that models the multi-terminal compress sensing problem and the coded cooperative data exchange problem where a set of users exchange their observations of a discrete multiple random source to attain omniscience—the state that all users recover the entire source. The optimal rate region containing all source coding rate vectors that achieve omniscience with the minimum sum rate is shown to coincide with the core (the solution set) of a coalitional game. Two game-theoretic fairness solutions are studied: the Shapley value and the egalitarian solution. It is shown that the Shapley value assigns each user the source coding rate measured by their remaining information of the multiple source given the common randomness that is shared by all users, while the egalitarian solution simply distributes the rates as evenly as possible in the core. To avoid the exponentially growing complexity of obtaining the Shapley value, a polynomial-time approximation method is proposed which utilizes the fact that the Shapley value is the mean value over all extreme points in the core. In addition, a steepest descent algorithm is proposed that converges in polynomial time on the fractional egalitarian solution in the core, which can be implemented by network coding schemes. Finally, it is shown that the game can be decomposed into subgames so that both the Shapley value and the egalitarian solution can be obtained within each subgame in a distributed manner with reduced complexity.

Embedding Tamper-Resistant, Publicly Verifiable Random Number Seeds in Permissionless Blockchain Systems

Many blockchain processes require pseudo-random numbers. This is especially true of blockchain consensus mechanisms that aim to fairly distribute the opportunity to propose new blocks between the participants in the system. The starting point for these processes is a source of randomness that participants cannot manipulate. This paper proposes two methods for embedding random number seeds in a blockchain data structure to serve as inputs to pseudo-random number generators. Because the output of a pseudo-random number generator depends deterministically on its seed, the properties of the seed are critical to the quality of the eventual pseudo-random number produced. Our protocol, B-Rand, embeds random number seeds that are <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">confidential</i> , <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">tamper-resistant</i> , <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">unpredictable</i> , <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">collision-resistant</i> , and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">publicly verifiable</i> as part of every transaction. These seeds may then be used by transaction owners to participate in processes in the blockchain system that require pseudo-random numbers. Both the Single Secret and Double Secret B-Rand protocols are highly scalable with low space and computational cost, and the worst case is linear in the number of transactions per block.

An inverse source problem for the stochastic wave equation

&lt;p style='text-indent:20px;'&gt;This paper is concerned with an inverse source problem for the stochastic wave equation driven by a fractional Brownian motion. Given the random source, the direct problem is to study the solution of the stochastic wave equation. The inverse problem is to determine the statistical properties of the source from the expectation and covariance of the final-time data. For the direct problem, it is shown to be well-posed with a unique mild solution. For the inverse problem, the uniqueness is proved for a certain class of functions and the instability is characterized. Numerical experiments are presented to illustrate the reconstructions by using a truncation-based regularization method.&lt;/p&gt;

Protokoli za ustanovljavanje tajnih simetričnih ključeva - savremen pristup

Introduction/purpose: The problem of efficient distribution of cryptographic keys in communication systems has existed since its first days and is especially emphasized by the emergence of mass communication systems. Defining and implementing efficient protocols for symmetric cryptographic keys establishment in such circumstances is of great importance in raising information security in cyberspace. Methods: Using the methods of Information Theory and Secure Multiparty Computation, protocols for direct establishment of cryptographic keys between communication parties have been defined. Results: The paper defines two new approaches to the problem of establishing cryptographic keys. The novelty in the protocol defined in the security model based on information theory is based on the source of common randomness, which in this case is the EEG signal of each subject participating in the communication system. Experimental results show that the amount of information leaking to the attacker is close to zero. A novelty in the second case, which provides security with keys at the level of computer security by applying Secure Multiparty Computation, is in the new application field, namely generation and distribution of symmetric cryptographic keys. It is characteristic of both approaches that within the framework of formal theories, it is possible to draw conclusions about their security characteristics in a formal way. Conclusions: The paper describes two new approaches for establishing cryptographic keys in symmetric cryptographic systems with experimental results. The significance of the proposed solutions lies in the fact that they enable the establishment of secure communication between communication parties from end to end, avoiding the influence of a trusted third party. In that way, the achieved communication level security significantly increases in relation to classical cryptographic systems.

Random Pulse Source with the Temporal Mutil-Complex Degree of Coherence

Random Pulse Source with the Temporal Mutil-Complex Degree of Coherence

Extending the Lifetime of Wireless Sensor Networks Based on an Improved Multi-objective Artificial Bees Colony Algorithm

Reducing the sensors' energy expenditure to prolong the network lifespan as long as possible remains a fundamental problem in the field of wireless networks. Particularly in applications with inaccessible environments, which impose crucial constraints on sensor replacement. It is, therefore, necessary to design adaptive routing protocols, taking into account the environmental constraints and the limited energy of sensors. To have an energy-efficient routing protocol, a new cluster heads’ (CHs) selection strategy using a modified multi-objective artificial bees colony (MOABC) optimization is defined. The modified MOABC is based on the roulette wheel selection over non-dominated solutions of the repository (hyper-cubes) in which a rank is assigned to each hypercube based on its density in dominated solutions of the current iteration and then a random food source is elected by roulette from the densest hypercube. The proposed work aims to find the optimal set of CHs based on their residual energies to ensure an optimal balance between the nodes' energy consumption. The achieved results proved that the proposed MOABC-based protocol considerably outperforms recent studies and well-known energy-efficient protocols, namely: LEACH, C-LEACH, SEP, TSEP, DEEC, DDEEC, and EDEEC in terms of energy efficiency, stability, and network lifespan extension.

A note on recovering the Brownian motion component from a Lévy process

González Cázares and Ivanovs (2021) suggested a new method for “recovering” the Brownian motion component from the trajectory of a Lévy process that required sampling from an independent Brownian motion process. We show that such a procedure works equally well without any additional source of randomness if one uses normal quantiles instead of the ordered increments of the auxiliary Brownian motion process.

Iterative Deblending of Simultaneous-Source Seismic Data via a Robust Singular Spectrum Analysis Filter

We solve the simultaneous source separation problem by adopting the projected gradient descent (PGD) method to iteratively estimate the data one would acquire via a conventional seismic acquisition. The projection operator is a windowed robust singular spectrum analysis (SSA) filter that suppresses source interferences in the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$f-x$ </tex-math></inline-formula> (frequency-space) domain. We reformulate the SSA filter as a robust optimization problem solved via a bifactored gradient descent (BFGD) algorithm. Robustness becomes achievable by adopting Tukey’s biweight loss function for the design of the robust SSA filter. The SSA filter requires breaking down common-receiver gathers or common offset gathers into small overlapping windows. The traditional SSA method needs the filter rank as an input parameter, which can vary from window to window. The latter has been a shortcoming for the application of classical SSA filtering to complex seismic data processing. The proposed robust SSA filter is less sensitive to rank-selection, making it appealing for deblending applications that require windowing. Additionally, the robust SSA projection provides an effective attenuation of random source interferences during the initial iterations of the PGD method. Comparing classical and robust SSA filters, we also report an acceleration of the PGD method convergence when we adopt the robust SSA filter. Finally, we provide synthetic and real data examples, and discuss heuristic strategies for parameter selection.

Semi-device-independent randomness certification with partially free random sources using $$4\rightarrow 1$$ quantum random access code

Semi-device-independent randomness certification with partially free random sources using $$4\rightarrow 1$$ quantum random access code

The Inverse Source Problem for a Class of Stochastic Convection-Diffusion Equations

This paper is concerned with an inverse source problem for a stochastic convection-diffusion equation driven by a fractional Brownian motion with Hurst index <inline-formula><tex-math id="M1">\begin{document}$H\in(0,1)$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="amm-42-0399_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="amm-42-0399_M1.png"/></alternatives></inline-formula>. The direct problem is to study the solution of the stochastic convection-diffusion equation. The inverse problem is to determine the statistical properties of the source from the expectation and covariance of the final-time data. For the direct problem, we know that it is well-posed. The uniqueness of the inverse source problem is proved. Unfortunately, the inverse random source problem is unstable. To verify the theoretical results, some numerical experiments are presented.

On the Unbearable Lightness of FIPS 140–2 Randomness Tests

Random number generation is critical to many applications. Gaming, gambling, and particularly cryptography all require random numbers that are uniform and unpredictable. For testing whether supposedly random sources feature particular characteristics commonly found in random sequences, batteries of statistical tests are used. These are fundamental tools in the evaluation of random number generators and form part of the pathway to certification of secure systems implementing them. Although there have been previous studies into this subject (Becker, 2013), RNG manufacturers and vendors continue to use statistical tests known to be of dubious reliability, in their RNG verification processes. Our research shows that FIPS-140-2 cannot identify adversarial biases effectively, even very primitive ones. Concretely, this work illustrates the inability of the FIPS 140 family of tests to detect bias in three obviously flawed PRNGs. Deprecated by official standards, these tests are nevertheless still widely used, for example in hardware-level self-test schemes incorporated into the design of many True RNGs (TRNGs). They are also popular with engineers and cryptographers for quickly assessing the randomness characteristics of security primitives and protocols, and even with manufacturers aiming to market the randomness features of their products to potential customers. In the following, we present three <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">biased-by-design</i> RNGs to show in explicit detail how simple, glaringly obvious biases are not detected by any of the FIPS 140–2 tests. One of these RNGs is backdoored, leaking key material, while others suffer from significantly reduced unpredictability in their output sequences. To make our point even more straightforward, we show how files containing images can also fool the FIPS 140 family of tests. We end with a discussion on the security issues affecting an interesting and active project to create a randomness beacon. Their authors only tested the quality of their randomness with the FIPS 140 family of tests, and we will show how this has led them to produce predictable output that, albeit passing FIPS fails other randomness tests quite catastrophically.