Statistical properties of weighted random and pseudo-random sequences Final report
Statistical properties of weighted binary random and pseudorandom sequences
Cramer, R. L.↗
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Results for “randomizer”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Randomly fluctuating flow in a channel due to randomly fluctuating pressure gradients
Superimposition of fluctuating velocity on steady incompressible channel flow by randomly fluctuating pressure gradients
Perlmutter, M.↗
Is random access memory random?
Most software is contructed on the assumption that the programs and data are stored in random access memory (RAM). Physical limitations on the relative speeds of processor and memory elements lead to a variety of memory organizations that match processor addressing rate with memory service rate. These include interleaved and cached memory. A very high fraction of a processor's address requests can be satified from the cache without reference to the main memory. The cache requests information from main memory in blocks that can be transferred at the full memory speed. Programmers who organize algorithms for locality can realize the highest performance from these computers.
Denning, P. J.↗
Predictors of intraspecific morphological variability in a tropical hotspot: comparing the influence of random and non‐random factors
Explore the source record for details and available documents.
Renan Maestri↗
Analytical procedure for determining random load acting on a spacecraft due to a primary random load acting on an exterior structure Quarterly report no. 2, 1 Sep. - 30 Nov. 1965
Sound and vibration transmission in OGO SPACECRAFT shroud system
STRUCTURAL VIBRATION↗
Traceable random numbers from a non-local quantum advantage
The unpredictability of random numbers is fundamental to both digital security and applications that fairly distribute resources. However, existing random number generators have limitations—the generation processes cannot be fully traced, audited and certified to be unpredictable. The algorithmic steps used in pseudorandom number generators are auditable, but they cannot guarantee that their outputs were a priori unpredictable given knowledge of the initial seed. Device-independent quantum random number generators can ensure that the source of randomness was unknown beforehand, but the steps used to extract the randomness are vulnerable to tampering. Here we demonstrate a fully traceable random number generation protocol based on device-independent techniques. Our protocol extracts randomness from unpredictable non-local quantum correlations, and uses distributed intertwined hash chains to cryptographically trace and verify the extraction process. This protocol forms the basis for a public traceable and certifiable quantum randomness beacon that we have launched. Over the first 40 days of operation, we completed the protocol 7,434 out of 7,454 attempts—a success rate of 99.7%. Each time the protocol succeeded, the beacon emitted a pulse of 512 bits of traceable randomness. The bits are certified to be uniform with error multiplied by actual success probability bounded by 2−64. Further, the generation of certifiable and traceable randomness represents a public service that operates with an entanglement-derived advantage over comparable classical approaches.
97 MATHEMATICS AND COMPUTING↗
Variance of phase fluctuations of waves propagating through a random medium
As an electromagnetic wave propagates through a random scattering medium, such as a forest, its energy is attenuated and random phase fluctuations are induced. The magnitude of the random phase fluctuations induced is important in estimating how well a Synthetic Aperture Radar (SAR) can image objects within the scattering medium. The two-layer random medium model, consisting of a scattering layer between free space and ground, is used to calculate the variance of the phase fluctuations induced between a transmitter located above the random medium and a receiver located below the random medium. The scattering properties of the random medium are characterized by a correlation function of the random permittivity fluctuations. The effective permittivity of the random medium is first calculated using the strong fluctuation theory, which accounts for large permittivity fluctuations of the scatterers. The distorted Born approximation is used to calculate the first-order scattered field. A perturbation series for the phase of the received field in the Rytov approximation is then introduced and the variance of the phase fluctuations is also calculated assuming that the transmitter and receiver are in the paraxial limit of the random medium, which allows an analytic solution to be obtained. Results are compared using the paraxial approximation, scalar Green's function formulation, and dyadic Green's function formulation. The effects studied are the dependence of the variance of the phase fluctuations on receiver location in lossy and lossless regions, medium thickness, correlation length and fractional volume of scatterers, depolarization of the incident wave, ground layer permittivity, angle of incidence, and polarization.
Chu, Nelson C.↗
Autonomous Byte Stream Randomizer
Net-centric networking environments are often faced with limited resources and must utilize bandwidth as efficiently as possible. In networking environments that span wide areas, the data transmission has to be efficient without any redundant or exuberant metadata. The Autonomous Byte Stream Randomizer software provides an extra level of security on top of existing data encryption methods. Randomizing the data s byte stream adds an extra layer to existing data protection methods, thus making it harder for an attacker to decrypt protected data. Based on a generated crypto-graphically secure random seed, a random sequence of numbers is used to intelligently and efficiently swap the organization of bytes in data using the unbiased and memory-efficient in-place Fisher-Yates shuffle method. Swapping bytes and reorganizing the crucial structure of the byte data renders the data file unreadable and leaves the data in a deconstructed state. This deconstruction adds an extra level of security requiring the byte stream to be reconstructed with the random seed in order to be readable. Once the data byte stream has been randomized, the software enables the data to be distributed to N nodes in an environment. Each piece of the data in randomized and distributed form is a separate entity unreadable on its own right, but when combined with all N pieces, is able to be reconstructed back to one. Reconstruction requires possession of the key used for randomizing the bytes, leading to the generation of the same cryptographically secure random sequence of numbers used to randomize the data. This software is a cornerstone capability possessing the ability to generate the same cryptographically secure sequence on different machines and time intervals, thus allowing this software to be used more heavily in net-centric environments where data transfer bandwidth is limited.
Paloulian, George K.↗
TRIM: AI Guided Random Number Generation for Resource-Constrained IoT Systems
Random numbers often serve as the backbone for many security solutions in diverse domains such as cryptography, side channel leakage prevention, and moving target defense. However, generating true random numbers requires a physical source of entropy (e.g. hardware, quantum, environmental phenomenon) making it difficult to realize at a large scale and at a low cost. On the flip side, pseudorandom number generators (easy to implement) following a specific distribution (e.g. Gaussian) can be easily compromised given a sufficient amount of traces. In this work, we have developed a machine learning-guided generative approach that can be used to create portable, resource-efficient, and cost-effective random number generators with high throughput and true randomness characteristics. We implement the proposed approach as a highly parameterized framework and perform extensive evaluation for different settings. The framework was able to learn from true random sources such as irrational numbers and environmental audio noise and imitate those sources towards generating new good quality random numbers on demand. We have generated more than 1 billion bits and observed robust performance in terms of true randomness metrics obtained from NIST SP 800-22 and FIPS 140-1 randomness test suites achieving a throughput of up to 142.85 Mbps. Compared to the state-of-the-art (SOTA) technique, the iso-cost setup of our framework can achieve more than 500 Mbps in a distributed setting. We have evaluated the efficacy of running the true randomness imitation AI models on target edge devices such as Raspberry Pi 4 (Model B), Nvidia Jetson Nano, Nvidia Jetson Orin Nano and Nvidia Jetson Xavier. We have also looked at the security of the TRIM framework itself against different adversarial threat models.
Cybersecurity↗
Gratings and Random Reflectors for Near-Infrared PIN Diodes
Crossed diffraction gratings and random reflectors have been proposed as means to increase the quantum efficiencies of InGaAs/InP positive/intrinsic/ negative (PIN) diodes designed to operate as near-infrared photodetectors. The proposal is meant especially to apply to focal-plane imaging arrays of such photodetectors to be used for near-infrared imaging. A further increase in quantum efficiency near the short-wavelength limit of the near-infrared spectrum of such a photodetector array could be effected by removing the InP substrate of the array. The use of crossed diffraction gratings and random reflectors as optical devices for increasing the quantum efficiencies of quantum-well infrared photodetectors (QWIPs) was discussed in several prior NASA Tech Briefs articles. While the optical effects of crossed gratings and random reflectors as applied to PIN photodiodes would be similar to those of crossed gratings and random reflectors as applied to QWIPs, the physical mechanisms by which these optical effects would enhance efficiency differ between the PIN-photodiode and QWIP cases: In a QWIP, the multiple-quantum-well layers are typically oriented parallel to the focal plane and therefore perpendicular or nearly perpendicular to the direction of incidence of infrared light. By virtue of the applicable quantum selection rules, light polarized parallel to the focal plane (as normally incident light is) cannot excite charge carriers and, hence, cannot be detected. A pair of crossed gratings or a random reflector scatters normally or nearly normally incident light so that a significant portion of it attains a component of polarization normal to the focal plane and, hence, can excite charge carriers. A pair of crossed gratings or a random reflector on a PIN photodiode would also scatter light into directions away from the perpendicular to the focal plane. However, in this case, the reason for redirecting light away from the perpendicular is to increase the length of the optical path through the detector to increase the probability of absorption of photons and thereby increase the resulting excitation of charge carriers. A pair of crossed gratings or a random reflector according to the proposal would be fabricated as an integral part of photodetector structure on the face opposite the focal plane (see figure). In the presence of crossed gratings, light would make four passes through the device before departing. In the presence of a random reflector, a significant portion of the light would make more than four passes: After each bounce, light would be scattered at a different random angle, and would have a chance to escape only when it was reflected, relative to the normal, at an angle less than the critical angle for total internal reflection. Given the indices of refraction of the photodiode materials, this angle would be about 17 . This amounts to a very narrow cone for escape of trapped light.
Gunapala, Sarath↗
Efficient Unitary Designs from Random Sums and Permutations
A unitary k-design is an ensemble of unitaries that matches the first k moments of the Haar measure. In this work, we provide two efficient constructions of k-designs on n-qubits using new random matrix theory techniques. Our first construction is based on exponentiating sums of random i.i.d. Hermitian matrices and uses O(k2n2)-many gates. In the spirit of central limit theorems, we show that this random sum approximates the Gaussian Unitary Ensemble (GUE). We then show that the product of just two exponentiated GUE matrices is already approximately Haar random. Our second construction is based on products of exponentiated sums of random permutations and uses Õ(k poly (n)) many gates. The k dependence is optimal (up to polylogarithmic factors) and is inherited from the efficiency of existing k-wise independent permutations. Furthermore, replacing random permutations with quantum-secure pseudorandom permutations (PRPs), we also obtain a pseudorandom unitary (PRU) ensemble that is secure under nonadaptive queries. A central feature of both proofs is a new connection between the polynomial method in quantum query complexity and the large-dimension (N) expansion in random matrix theory. In particular, the first construction uses the polynomial method to control high moments of certain random matrix ensembles without requiring delicate Weingarten calculations. In doing so, we define and solve a moment problem on the unit circle, asking whether a finite number of equally weighted points can reproduce a given set of moments. In our second construction, the key step is to exhibit an orthonormal basis for irreducible representations of the partition algebra that has a low-degree large-N expansion. This allows us to show that the distinguishing probability is a low-degree rational polynomial of the dimension N.
algebra↗
Analysis of random drop for gateway congestion control
Lately, the growing demand on the Internet has prompted the need for more effective congestion control policies. Currently No Gateway Policy is used to relieve and signal congestion, which leads to unfair service to the individual users and a degradation of overall network performance. Network simulation was used to illustrate the character of Internet congestion and its causes. A newly proposed gateway congestion control policy, called Random Drop, was considered as a promising solution to the pressing problem. Random Drop relieves resource congestion upon buffer overflow by choosing a random packet from the service queue to be dropped. The random choice should result in a drop distribution proportional to the bandwidth distribution among all contending TCP connections, thus applying the necessary fairness. Nonetheless, the simulation experiments demonstrate several shortcomings with this policy. Because Random Drop is a congestion control policy, which is not applied until congestion has already occurred, it usually results in a high drop rate that hurts too many connections including well-behaved ones. Even though the number of packets dropped is different from one connection to another depending on the buffer utilization upon overflow, the TCP recovery overhead is high enough to neutralize these differences, causing unfair congestion penalties. Besides, the drop distribution itself is an inaccurate representation of the average bandwidth distribution, missing much important information about the bandwidth utilization between buffer overflow events. A modification of Random Drop to do congestion avoidance by applying the policy early was also proposed. Early Random Drop has the advantage of avoiding the high drop rate of buffer overflow. The early application of the policy removes the pressure of congestion relief and allows more accurate signaling of congestion. To be used effectively, algorithms for the dynamic adjustment of the parameters of Early Random Drop to suite the current network load must still be developed.
Hashem, Emam Salaheddin↗
Golden Ratio Versus Pi as Random Sequence Sources for Monte Carlo Integration
We discuss here the relative merits of these numbers as possible random sequence sources. The quality of these sequences is not judged directly based on the outcome of all known tests for the randomness of a sequence. Instead, it is determined implicitly by the accuracy of the Monte Carlo integration in a statistical sense. Since our main motive of using a random sequence is to solve real world problems, it is more desirable if we compare the quality of the sequences based on their performances for these problems in terms of quality/accuracy of the output. We also compare these sources against those generated by a popular pseudo-random generator, viz., the Matlab rand and the quasi-random generator ha/ton both in terms of error and time complexity. Our study demonstrates that consecutive blocks of digits of each of these numbers produce a good random sequence source. It is observed that randomly chosen blocks of digits do not have any remarkable advantage over consecutive blocks for the accuracy of the Monte Carlo integration. Also, it reveals that pi is a better source of a random sequence than theta when the accuracy of the integration is concerned.
Sen, S. K.↗
First-Principles Modeling Of Electromagnetic Scattering By Discrete and Discretely Heterogeneous Random Media
A discrete random medium is an object in the form of a finite volume of a vacuum or a homogeneous material medium filled with quasi-randomly and quasi-uniformly distributed discrete macroscopic impurities called small particles. Such objects are ubiquitous in natural and artificial environments. They are often characterized by analyzing theoretically the results of laboratory, in situ, or remote-sensing measurements of the scattering of light and other electromagnetic radiation. Electromagnetic scattering and absorption by particles can also affect the energy budget of a discrete random medium and hence various ambient physical and chemical processes. In either case electromagnetic scattering must be modeled in terms of appropriate optical observables, i.e., quadratic or bilinear forms in the field that quantify the reading of a relevant optical instrument or the electromagnetic energy budget. It is generally believed that time-harmonic Maxwell's equations can accurately describe elastic electromagnetic scattering by macroscopic particulate media that change in time much more slowly than the incident electromagnetic field. However, direct solutions of these equations for discrete random media had been impracticable until quite recently. This has led to a widespread use of various phenomenological approaches in situations when their very applicability can be questioned. Recently, however, a new branch of physical optics has emerged wherein electromagnetic scattering by discrete and discretely heterogeneous random media is modeled directly by using analytical or numerically exact computer solutions of the Maxwell equations. Therefore, the main objective of this Report is to formulate the general theoretical framework of electromagnetic scattering by discrete random media rooted in the Maxwell- Lorentz electromagnetics and discuss its immediate analytical and numerical consequences. Starting from the microscopic Maxwell-Lorentz equations, we trace the development of the first principles formalism enabling accurate calculations of monochromatic and quasi-monochromatic scattering by static and randomly varying multiparticle groups. We illustrate how this general framework can be coupled with state-of-the-art computer solvers of the Maxwell equations and applied to direct modeling of electromagnetic scattering by representative random multi-particle groups with arbitrary packing densities. This first-principles modeling yields general physical insights unavailable with phenomenological approaches. We discuss how the first-order-scattering approximation, the radiative transfer theory, and the theory of weak localization of electromagnetic waves can be derived as immediate corollaries of the Maxwell equations for very specific and well-defined kinds of particulate medium. These recent developments confirm the mesoscopic origin of the radiative transfer, weak localization, and effective-medium regimes and help evaluate the numerical accuracy of widely used approximate modeling methodologies.
Michael I Mishchenko↗
Reproducible emission from nonlinear random lasers
Multiple scattering of light serves as a mechanism for feedback in random lasers. Consequently, internal spatial mode patterns, lasing wavelengths, and output directionality can all be random. Strong mode interaction can occur in such devices due to spatially overlapping modes resulting in nonlinearity with respect to the pump input power. Nevertheless, temporal coherence and lasing mode amplitude can be fixed at a constant pumping rate. This is a property desirable for applications where unique randomness is exploited but expected to be reliable over time, such as physical unclonable functions. Random lasers can also be cheaply and easily fabricated, exhibit relatively low lasing thresholds and high emission intensity. However, the precise scattering properties of such structures and fluctuations in the pump field can make device emission irreproducible, thereby limiting random laser applications. Here, in this work, we directly compare the random lasing spectra from zinc oxide samples fabricated in four distinct ways: spin-coating, sputtering, solgel deposition, and atomic layer deposition. The particular method of fabrication has a strong impact. Samples made through atomic layer deposition here exhibit both reproducibility and strong nonlinearity desirable for applications. Randomness in emission spectra persists across hundreds of repeated and averaged measurements irrespective of spatial location and is demonstrably nonlinear with respect to input signal intensity.
47 OTHER INSTRUMENTATION↗
Rotorcraft Blade Mode Damping Identification from Random Responses Using a Recursive Maximum Likelihood Algorithm
An on line technique is presented for the identification of rotor blade modal damping and frequency from rotorcraft random response test data. The identification technique is based upon a recursive maximum likelihood (RML) algorithm, which is demonstrated to have excellent convergence characteristics in the presence of random measurement noise and random excitation. The RML technique requires virtually no user interaction, provides accurate confidence bands on the parameter estimates, and can be used for continuous monitoring of modal damping during wind tunnel or flight testing. Results are presented from simulation random response data which quantify the identified parameter convergence behavior for various levels of random excitation. The data length required for acceptable parameter accuracy is shown to depend upon the amplitude of random response and the modal damping level. Random response amplitudes of 1.25 degrees to .05 degrees are investigated. The RML technique is applied to hingeless rotor test data. The inplane lag regressing mode is identified at different rotor speeds. The identification from the test data is compared with the simulation results and with other available estimates of frequency and damping.
Molusis, J. A.↗
Reduction of display artifacts by random sampling
The application of random-sampling techniques to remove visible artifacts (such as flicker, moire patterns, and paradoxical motion) introduced in TV-type displays by discrete sequential scanning is discussed and demonstrated. Sequential-scanning artifacts are described; the window of visibility defined in spatiotemporal frequency space by Watson and Ahumada (1982 and 1983) and Watson et al. (1983) is explained; the basic principles of random sampling are reviewed and illustrated by the case of the human retina; and it is proposed that the sampling artifacts can be replaced by random noise, which can then be shifted to frequency-space regions outside the window of visibility. Vertical sequential, single-random-sequence, and continuously renewed random-sequence plotting displays generating 128 points at update rates up to 130 Hz are applied to images of stationary and moving lines, and best results are obtained with the single random sequence for the stationary lines and with the renewed random sequence for the moving lines.
Ahumada, A. J., Jr.↗
Electromagnetic Scattering by Fully Ordered and Quasi-Random Rigid Particulate Samples
In this paper we have analyzed circumstances under which a rigid particulate sample can behave optically as a true discrete random medium consisting of particles randomly moving relative to each other during measurement. To this end, we applied the numerically exact superposition T-matrix method to model far-field scattering characteristics of fully ordered and quasi-randomly arranged rigid multiparticle groups in fixed and random orientations. We have shown that, in and of itself, averaging optical observables over movements of a rigid sample as a whole is insufficient unless it is combined with a quasi-random arrangement of the constituent particles in the sample. Otherwise, certain scattering effects typical of discrete random media (including some manifestations of coherent backscattering) may not be accurately replicated.
Radiative transfer↗