Random Space Research Articles

Two Practical Random-Subcarrier-Selection Methods for Secure Precise Wireless Transmissions

In directional modulation networks, two practical random-subcarrier-selection methods are proposed to transmit confidential message, and by constructing random subcarrier set and performing a randomization procedure, only a single receive power peak is formed in the desired user position per orthogonal frequency division multiplexing (OFDM) symbol. This scheme completely addresses the crucial problem facing secure precise wireless transmission (SPWT); how to achieve the SPWT per OFDM symbol while the traditional SPWT holds only in the statistically average sense. Several necessary conditions for SPWT per OFDM are derived and proposed: random, distributed, and distinct subcarrier spacing pattern mapped onto transmit antenna array. Two random subcarrier index sets, quadratic subcarrier set (QSS), and prime subcarrier set (PSS) are constructed. Subsequently, a random metric is defined, and a randomization procedure (RP) is proposed. Its detailed process include the following steps: integer mod, ordering, blocking, and block interleaving (BI) where BI is repeated until the random metric is greater than the predefined value. This yields a single high energy main peak at the desired position while at other positions, i.e., outside the main peak, only weak received energy peak seriously contaminated by the artificial noise are harvested. Simulation results confirm that our proposed two methods, QSS plus RP and PSS plus RP, perform significantly better than conventional methods such as linear subcarrier set plus RP. They actually form a single high energy main peak at desired position, and generate only extremely small leakage outside the main peak.

Efficient topology control for time-varying spacecraft networks with unreliable links

In spacecraft networks, the time-varying topology, intermittent connectivity, and unreliable links make management of the network challenging. Previous works mainly focus on information propagation or routing. However, with a large number of nodes in the future spacecraft networks, it is very crucial regarding how to make efficient network topology controls. In this article, we investigate the topology control problem in spacecraft networks where the time-varying topology can be predicted. We first develop a model that formalizes the time-varying spacecraft network topologies as a directed space–time graph. Compared with most existing static graph models, this model includes both temporal and spatial topology information. To capture the characteristics of practical network, links in our space–time graph model are weighted by cost, efficiency, and unreliability. The purpose of our topology control is to construct a sparse (low total cost) structure from the original topology such that (1) the topology is still connected over space–time graph; (2) the cost efficiency ratio of the topology is minimized; and (3) the unreliability parameter is lower than the required bound. We prove that such an optimization problem is NP-hard. Then, we provide five heuristic algorithms, which can significantly maintain low topology cost efficiency ratio while achieving high reliable connectivity. Finally, simulations have been conducted on random space networks and hybrid low earth orbit/geostationary earth orbit satellite-based sensor network. Simulation results demonstrate the efficiency of our model and topology control algorithms.

A PUF-Based Data-Device Hash for Tampered Image Detection and Source Camera Identification

With the increasing prevalent of digital devices and their abuse for digital content creation, forgeries of digital images and video footage are more rampant than ever. Digital forensics is challenged into seeking advanced technologies for forgery content detection and acquisition device identification. Unfortunately, existing solutions that address image tampering problems fail to identify the device that produces the images or footage while techniques that can identify the camera is incapable of locating the tampered content of its captured images. In this paper, a new perceptual data-device hash is proposed to locate maliciously tampered image regions and identify the source camera of the received image data as a non-repudiable attestation in digital forensics. The presented image may have been either tampered or gone through benign content preserving geometric transforms or image processing operations. The proposed image hash is generated by projecting the invariant image features into a physical unclonable function (PUF)-defined Bernoulli random space. The tamper-resistant random PUF response is unique for each camera and can only be generated upon triggered by a challenge, which is provided by the image acquisition timestamp. The proposed hash is evaluated on the modified CASIA database and CMOS image sensor-based PUF simulated using 180 nm TSMC technology. It achieves a high tamper detection rate of 95.42% with the regions of tampered content successfully located, a good authentication performance of above 98.5% against standard content-preserving manipulations, and 96.25% and 90.42%, respectively, for the more challenging geometric transformations of rotation (0 ~ 360°) and scaling (scale factor in each dimension: 0.5). It is demonstrated to be able to identify the source camera with 100% accuracy and is secure against attacks on PUF.

Non-fluorinated superhydrophobic Al7075 aerospace alloy by ps laser processing

The metallic surfaces with low affinity or high repellence towards water molecules are extremely desirable. The present investigation reports the development of non-fluorinated super or ultrahydrophobic aerospace aluminum alloy (Al7075) surface by laser patterning and high vacuum process for 4 h. Lamellar and lotus leaf papillae like structures covered with nanoscale protrusions are found to be formed depends on the laser fluence and spatial shifts of laser scans. The fresh laser processed hydrophilic surface was vacuum processed to create layer of hydrocarbon to reduce the surface free energy for the wetting property transformation. The analysis of the results shows the synergistic effect of hierarchical structures and dominant presence of non-polar elements is critical for superhydrophobic property. The surface geometry is primarily responsible for the wetting property transformation by entrapping μ-volume of air to generate a composite interface of solid-gas-liquid. Micro and nanoscale (dual scale) surface structures are essential for the durable and consistent superhydrophobic property with high degree of water repellence for bigger volume of water droplets. Further, sole presence of nanoscale structures on inherent hydrophilic aluminum alloy surface with predominant presence of non-polar elements can yield only near superhydrophobic surface due to random spacing of nanoscale protrusions.

Spectral estimators for finite non-commutative geometries

A finite non-commutative geometry consists of a fuzzy space together with a Dirac operator satisfying the axioms of a real spectral triple. This paper addresses the question of how to extract information about these geometries from the spectrum of the Dirac operator. Since the Dirac operator is a finite-dimensional matrix, the usual asymptotics of the eigenvalues makes no sense and is replaced by measurements of the spectrum at a finite energy scale. The spectral dimension of the square of the Dirac operator is improved to provide a new spectral measure of the dimension of a space called the spectral variance. Similarly, the volume of a space can be computed from the spectrum once the dimension is known. Two methods of doing this are investigated: the well-known Dixmier trace and a recent improvement due to Abel Stern. Finally, the distance between two geometries is investigated by comparing the spectral zeta functions using the method of Cornelissen and Kontogeorgis. All of these techniques are tested on the explicit examples of the fuzzy spheres and fuzzy tori, which can be regarded as approximations of the usual Riemannian sphere and flat tori. Then they are applied to characterise some random fuzzy spaces using data generated by a Monte Carlo simulation.

Blind gain invariant image watermarking using random projection approach

Digital Watermarking helps us to protect the intellectual property of distributed media by hiding a piece of information within it. In this paper, a robust image watermarking method based on the projection of samples of the host signal into a random space is proposed. First, the vector constructed by the host signal samples is projected on two random vectors. Then, to embed a watermark digit, the ratio of the two projections is quantized. In order to preserve the imperceptibility of the watermark, analytical calculations are made to minimize the resultant distortion. To extract the watermark, a maximum likelihood detector is designed and accordingly the error probability of the proposed method is derived. The performance of the proposed method is investigated in terms of watermark to noise ratio. It is shown that there exists a trade-off between distortion and capacity without any concerns about the error probability. Experimental results verify the theoretical achievements of this study and show the superior performance of the proposed method in comparison to the state-of-the-art methods. Simulation results also demonstrate the robustness of the proposed method against common attacks such as filtering and geometrical attacks.

Uncertainty quantification of unsteady source flows in heterogeneous porous media

Unsteady flow generated by a point-like source takes place into a$d$-dimensional porous formation where the spatial variability of the hydraulic conductivity$K$is modelled within a stochastic framework that regards$K$as a stationary, normally distributed random space function (rsf). As a consequence, the hydraulic head$H$becomes also stochastic, and we aim at quantifying its uncertainty. Towards this aim, we have derived the head covariance by means of a perturbation expansion which regards the variance$\unicode[STIX]{x1D70E}^{2}$of the zero meanrsf$\unicode[STIX]{x1D700}=1-K/\langle K\rangle$(hereafter$\langle \rangle$being the ensemble average operator) as a small parameter. The analytical results are expressed in terms of multiple quadratures which are markedly reduced after adopting specific autocorrelation$\unicode[STIX]{x1D70C}$for$\unicode[STIX]{x1D700}$. This enables one to obtain simple results providing straightforward physical insight into the spatial distribution of$H$as a consequence of the heterogeneity of$K$. In view of those applications (pumping tests) aiming at the identification of the hydraulic properties of geological formations, we have focused on a flow generated by a source of instantaneous and constant strength. The attainment of the large time (steady-state) regime is studied in detail.

Advanced Hydraulic Fracture Characterization Using Pulse Testing Analysis

Effective hydraulic fracture characterization is important for successful reservoir stimulation. This represents one of the primary challenges for completion engineers in the oil and gas industry, especially for unconventional tight gas reservoirs which are important sources of gas production in the US. Multi-stage hydraulic fracturing in horizontal wells is the most popular completion method for these types of reservoirs. An advanced methodology has been developed to characterize hydraulic fractures via pulse testing analysis. This technique combines analytical solutions and numerical modeling based on the pressure pulse response recorded at offset wells before, during, and after horizontal well fracture operations to characterize fracture orientation, height, and length. Different conceptual models were tested for random well pair spacing and orientations to generate correlations and families of type curves for a single-stage vertical fracture characterization. The methodology was then expanded to be implemented in more complex cases of multi-stage fractures. For validation and calibration purposes, a case study for a single fracture characterization was presented to match the numerical results with the field data. A good agreement in fracture orientation, height, and length was obtained with this reasonably cost-effective technique.

Performance and Evaluation of Five-Phase Dual Random SVPWM Strategy With Optimized Probability Density Function

This paper presents a five-phase dual random space vector pulsewidth modulation (FPDR-SVPWM) strategy with an optimized probability density function (PDF) for a five-phase voltage-source inverter, and its performance and evaluation are also analyzed. Based on the nearest four vectors modulation method, the FPDR-SVPWM strategy, combined with random switching frequency and random zero vector, is investigated to significantly reduce the amplitude of high-order harmonics near the switching frequency and its integer multiples. For the nonsinusoidal power supply, third harmonic injection is introduced in this modulation strategy as well. Considering the effect of random numbers on the performance, an optimized Beta distribution is studied in detail. In order to analyze harmonic dispersion degree qualitatively and quantitatively, the power spectral density and the harmonic spread factor are both employed to assess the performance of the FPDR-SVPWM strategy. A series of results of simulation in MATLAB and experiments based on field programmable gate array demonstrate that the proposed modulation strategy is correct and valid, and it distributes high-order harmonics into a wide range without affecting the fundamental wave and third harmonic.

Heterotopy ("Error loci") of the spiral loop of the ascending colon in cattle.

The term heterotopy of the spiral colon encompasses a dysmorphological condition in which the spiral loops of the ascending colon (SLACs) do not form an orderly spiraling mass adjacent to the left side of the mesojejunum. As a consequence, the spiral loops are spread over a larger surface, making them more or less movable. It has been hypothesized that the abnormal position of the spiral loops of the ascending colon might constitute a predisposing factor for an intestinal obstruction or an ileus condition. The objective of the present study was to evaluate the anatomy of the spiral loops of the ascending colon in a population of healthy calves and to determine the prevalence of dysmorphism. The investigation was carried out on 1113 slaughtered veal calves. In 472 out of the 1113 calves, the spiral loops showed conformational aspects different from what has so far been described as normal in reference textbooks. In 91 calves the condition was definitely considered a pathological deviation from normality: in fact, the spiral colon had lost its typical spiral shape with random spacing between the loops, and it was nearly or completely detached from the mesojejunum. The lack of a broad attachment of the spiral loops of the ascending colon to the mesentery could provoke an alteration of the intestinal centre of gravity, enhancing the already asymmetrical distribution of weight between the jejunum and the descending colon.

Snore-GANs: Improving Automatic Snore Sound Classification With Synthesized Data.

One of the frontier issues that severely hamper the development of automatic snore sound classification (ASSC) associates to the lack of sufficient supervised training data. To cope with this problem, we propose a novel data augmentation approach based on semi-supervised conditional generative adversarial networks (scGANs), which aims to automatically learn a mapping strategy from a random noise space to original data distribution. The proposed approach has the capability of well synthesizing "realistic" high-dimensional data, while requiring no additional annotation process. To handle the mode collapse problem of GANs, we further introduce an ensemble strategy to enhance the diversity of the generated data. The systematic experiments conducted on a widely used Munich-Passau snore sound corpus demonstrate that the scGANs-based systems can remarkably outperform other classic data augmentation systems, and are also competitive to other recently reported systems for ASSC.

An experimental study on pullout and tensile behavior of ultra-high-performance concrete reinforced with various steel fibers

Abstract This study investigates the effects of steel fiber type on the pullout and tensile performance of ultra-high-performance fiber-reinforced concrete (UHPFRC). For this, four different types of steel fibers, i.e., straight, twisted, hooked, and half-hooked, were used. In order to consider random fiber orientation in UHPFRC, various inclination angles, ranging from 0° to 60°, were considered for the pullout tests. Test results indicated that better pullout resistance was obtained in the deformed (twisted, hooked, and half-hooked) steel fibers embedded in ultra-high-performance concrete (UHPC) than that of the straight steel fiber as fiber breakage was prevented. The highest bond strengths of all steel fiber types were found when they were inclined 30° or 45°, while their slip capacities increased with increasing inclination angle. The hooked steel fiber exhibited the highest bond strengths at all inclination angles, while the twisted and half-hooked steel fibers exhibited the highest pullout energies at aligned and highly inclined (45° and 60°) conditions, respectively. In contrast to the pullout test results, the best tensile performance of UHPFRC was achieved by incorporating straight steel fibers, followed by the twisted, half-hooked, and hooked steel fibers. The poorer tensile performance of UHPCs reinforced with the deformed steel fibers was because of the severe matrix damage from excessive mechanical anchorage and fiber congestion, leading to insufficient matrix volume. Similarly, a relatively weak correlation between the fiber pullout and tensile behaviors of UHPFRC was observed. Therefore, a new pullout test method, which is able to consider the fiber random orientation and spacing, is required in order to improve the correlation.

A scale‐invariant property of the water retention curve in weakly heterogeneous vadose zones

AbstractAbrupt changes of hydraulic properties in a vadose zone are modelled within a stochastic framework, which regards the saturated conductivity and parameters related to the distribution of soil pores as stationary, log‐normally distributed, random space functions. As a consequence, flow variables become random fields, and we aim at deriving an effective Richards equation. To obtain the latter, we adopt a perturbation expansion truncated at the first order (weakly heterogeneous media), which leads to the effective hydraulic conductivity and water retention curves. Overall, the effective properties are scale dependent. However, within the proposed framework, we demonstrate that the inflection point of the laboratory scale retention curve is not affected by the heterogeneity of the vadose zone. Finally, to illustrate the quantitative implications of our results, we consider a monitoring experiment at field scale, and we show how our approach leads to an effective water retention curve, which differs significantly from that which would be obtained without accounting for the above scale‐invariance property.

Convergence of the free Boltzmann quadrangulation with simple boundary to the Brownian disk

Nous démontrons que la quadrangulation de Boltzmann libre avec un bord simple de périmètre fixé, munie de sa métrique de graphe, de sa mesure d’aire naturelle, et du chemin qui décrit sa frontière, converge dans la limite d’échelle vers le disque brownien libre de Boltzmann. La topologie de cette convergence est celle de Gromov–Hausdorff–Prokhorov-uniforme (GHPU), qui est l’analogue naturel de la topologie de Gromov-Hausdroff pour des espaces métriques mesurés décorés par une courbe. Nous déduisons de cela qu’une quadrangulation aléatoire de la sphère, décorée par une marche aléatoire auto-évitante de longueur $2l$, converge en loi pour la topologie GHPU vers l’espace métrique mesuré et décoré par une courbe que l’on obtient en recollant ensemble deux disques browniens indépendants le long de leurs bords.

Uncertainty in cardiac myofiber orientation and stiffnesses dominate the variability of left ventricle deformation response.

Computational cardiac modelling is a mature area of biomedical computing and is currently evolving from a pure research tool to aiding in clinical decision making. Assessing the reliability of computational model predictions is a key factor for clinical use, and uncertainty quantification (UQ) and sensitivity analysis are important parts of such an assessment. In this study, we apply UQ in computational heart mechanics to study uncertainty both in material parameters characterizing global myocardial stiffness and in the local muscle fiber orientation that governs tissue anisotropy. The uncertainty analysis is performed using the polynomial chaos expansion (PCE) method, which is a nonintrusive meta‐modeling technique that surrogates the original computational model with a series of orthonormal polynomials over the random input parameter space. In addition, in order to study variability in the muscle fiber architecture, we model the uncertainty in orientation of the fiber field as an approximated random field using a truncated Karhunen‐Loéve expansion. The results from the UQ and sensitivity analysis identify clear differences in the impact of various material parameters on global output quantities. Furthermore, our analysis of random field variations in the fiber architecture demonstrate a substantial impact of fiber angle variations on the selected outputs, highlighting the need for accurate assignment of fiber orientation in computational heart mechanics models.

Optimal observations-based retrieval of topography in 2D shallow water equations using PC-EnKF

Parameter estimation is an important problem because in many instance uncertain parameters cannot be measured accurately, especially in real-time applications. Information about them is commonly inferred via parameter estimation techniques from available measurements of different aspects of the system response. In this work, we consider the reduction of the uncertain topography parameters of 2D shallow water equations to be inconsistency with the physical observations. This is often quite challenging due to its ill-posed nature of the inverse problem, particularly for the present nonlinear case in high-dimensional random space. We have explored an efficient computational strategy for the solution of the problem in the framework of the polynomial chaos (PC)-based ensemble Kalman filter (PC-EnKF for short). The main idea pursued in this methodology is to introduce a determination of the potential optimal observation location followed by the update of the input topography parameters to be retrieved through the PC-EnKF, wherein the identification of the optimal observation locations is accomplished sequentially via the predictive uncertainty controlled by standard deviation, and then places the corresponding measurement for data assimilation purpose. This is not only to provide more informative measurements but also to improve the topography parameters estimation. The numerical experiments indicate that the optimal observations-based PC-EnKF algorithm is effective in dealing with the current retrieval of topography parameters. It is worth mentioning that an iterative PC-basis rotation technique is particularly useful when attempting to enhance the sparsity and the resulting accuracy. The solution strategy is well suited in the current high-dimensional nonlinear inverse modeling and has shown its appealing potential in the real-world application of complex systems.

A new method for reliability analysis and reliability-based design optimization

We present a novel method for reliability-based design optimization, which is based on the approximation of the safe region in the random space by a polytope-like region. This polytope is in its turn transformed into quite a simple region by using generalized spherical coordinates. The failure probability can then be easily estimated by considering simple quadrature rules. One of the advantages of the proposed approach is that by increasing the number of vertices, we can improve arbitrarily the accuracy of the failure probability estimation. The sensitivity analysis of the failure probability is also provided. We show that the proposed approach leads to an optimization problem, where the set of optimization variables includes all the original design variables and all the parameters that control the shape of the polytope. In addition, this problem can be solved by a single iteration scheme of optimization. We illustrate the performance of the new approach by solving several examples of truss topology optimization.

Particle Based gPC Methods for Mean-Field Models of Swarming with Uncertainty

In this work we focus on the construction of numerical schemes for the approximation of stochastic mean--field equations which preserve the nonnegativity of the solution. The method here developed makes use of a mean-field Monte Carlo method in the physical variables combined with a generalized Polynomial Chaos (gPC) expansion in the random space. In contrast to a direct application of stochastic-Galerkin methods, which are highly accurate but lead to the loss of positivity, the proposed schemes are capable to achieve high accuracy in the random space without loosing nonnegativity of the solution. Several applications of the schemes to mean-field models of collective behavior are reported.

A local sensitivity and regularity analysis for the Vlasov-Poisson-Fokker-Planck system with multi-dimensional uncertainty and the spectral convergence of the stochastic Galerkin method

We study the Vlasov-Poisson-Fokker-Planck (VPFP) system with uncertainty and multiple scales. Here the uncertainty, modeled by multi-dimensional random variables, enters the system through the initial data, while the multiple scales lead the system to its high-field or parabolic regimes. We obtain a sharp decay rate of the solution to the global Maxwellian, which reveals that the VPFP system is decreasingly sensitive to the initial perturbation as the Knudsen number goes to zero. The sharp regularity estimates in terms of the Knudsen number lead to the stability of the generalized Polynomial Chaos stochastic Galerkin (gPC-SG) method. Based on the smoothness of the solution in the random space and the stability of the numerical method, we conclude the gPC-SG method has spectral accuracy uniform in the Knudsen number.

Local sensitivity analysis and spectral convergence of the stochastic Galerkin method for discrete-velocity Boltzmann equations with multi-scales and random inputs

In this paper we study the general discrete-velocity models of Boltzmann equation with uncertainties from collision kernel and random inputs. We follow the framework of Kawashima and extend it to the case of diffusive scaling in a random setting. First, we provide a uniform regularity analysis in the random space with the help of a Lyapunov-type functional, and prove a uniformly (in the Knudsen number) exponential decay towards the global equilibrium, under certain smallness assumption on the random perturbation of the collision kernel, for suitably small initial data. Then we consider the generalized polynomial chaos based stochastic Galerkin approximation (gPC-SG) of the model, and prove the spectral convergence and the exponential time decay of the gPC-SG error uniformly in the Knudsen number.