Uniform Gaussian Research Articles

Using kernel functions to estimate the probability density function for segmentation images

This paper used nonparametric kernel functions to segment images using the thresholding method. This was done by transforming the image to grey and then estimating the probability density function from the grey image data and taking the highest value of the core function vector as the threshold limit. The study also found that the bandwidth parameter affects the segmentation process because it affects the estimate of the probability density function. The bandwidth parameter smooths the curve and brings it closer to the true curve because of its significant effect on bias and variance. The beam width parameter is known to depend on the size of the sample. Thus, it was found that when the parameter is used to determine the image size into equal rows and columns, it gives good, satisfactory results for segmented images that contain the most important areas of interest with removing unhelpful or important areas. Finally, the uniform Gaussian, cosine, triangular, and logistic Silverman kernel functions proved their efficiency in extracting all image features.

Vanet performance evaluatıon ın terms of nodes dıstrıbutıon, mobılıty models, and routıng protocols

Nowadays, Vehicle Ad Hoc Networks (VANETs) have become a new trend and one of the most attractive areas of research. It has a wide range of applications such as smart cities and the Internet of Things (IoT). The main issue of the VANET networks is the limitation in network resources such as power, and memory. Moreover, since VANET nodes are dynamic and move over time, the connectivity of the networks is also considered an important issue. This paper designs experiments that reflect a variety of scenarios in VANET networks. Many issues and factors in VANET networks have also been investigated in this paper. There are many factors that affect the whole performance of VANET networks (i.e., mobility models, routing protocols, and things distribution) in terms of network resources. Therefore, this paper aims at testing different mobility models such as the Human Mobility model, Cauchy Flight Mobility model, and Correlated Directions Mobility model, and investigate their impact on the consumption of network resources under a particular routing protocol such as Spray and Wait routing protocol, Probabilistic Flooding routing protocol, and Epidemic routing protocol. In addition, testing different distributions such as Uniform distribution, Gaussian (Normal) distribution, and Power-Law distribution). The resources we plan to investigate are energy sources and the amount of data exchanged. In the designed experiments, each simulation includes a combination of a mobility model, nodes distribution, and a routing protocol. The findings showed that each mobility model, routing protocol, or distribution is effective in a particular application. As a result, it was found that determining the application of the VANET network is a crucial step before performing a simulation or designing a network.

Experimental investigation of the upstream turbulent flow modifications in front of a scaled tidal turbine

A 1:20 scaled three-bladed horizontal-axis tidal turbine is positioned in the wake flows of two wall-mounted obstacles: a square cylinder and a combination of a cube in front of a cylinder. The turbine's induction effects are examined with upstream flow measurements without and with the turbine operating at its optimal regime. In front of the turbine (at 0.07D upstream of the hub extremity, with D the turbine diameter), the mean axial and vertical velocities are modified by induction effects whatever the complexity of the flow is. In the other hand, the normal Reynolds tensor components are less impacted by the turbine's blockage. In the presence of an incoming uniform homogeneous Gaussian flow field, a mean axial velocity deficit of 30% is observed in front of the hub while this velocity deficit is around 10% at the rotor edge. Moreover, the turbine's blockage modifies the intermittency leading to non-Gaussian fluctuations. When low-frequency large-scale flow structures are embedded in the incoming turbulent flow, these large-scale flow structures are affected by the hub whereas the rotating blade's blockage effect is of minor contribution. In this case, the turbine does not affect significantly the intermittency.

Residual Strength Analysis of C/SiC Ceramic Matrix Composite Panels Subjected to Combined Thermal-Acoustic Loadings

A study was undertaken to develop a methodology for assessing the residual strength of C/SiC ceramic matrix composite panels subjected to combined thermal-acoustic loadings. A 2D plain-woven C/SiC ceramic matrix composite panel subjected to spatially uniform thermal loading and band-limited Gaussian white noise is chosen as the computational test article, with its geometric nonlinear response determined via numerical simulation. As the input, the material properties (static strength, residual strength, and fatigue life) of this material are fully characterized under tensile and compression loads, for fiber direction at elevated temperature in static and fatigue loading conditions. Based on the methodology, a computer code is developed that simulates the cycle-by-cycle behavior of composite panels under fatigue loadings. The methodology is validated with the residual strength test of 2D plain-woven C/SiC composite panel subjected to combined thermal-acoustic loadings. It has been shown that the results of residual strength predicted by the methodology are well correlated with the experimental results.

Design exploration of 3D-printed triply periodic minimal surface scaffolds for bone implants

Triply Periodic Minimal Surface (TPMS) scaffolds have recently received considerable attention because of their potentials to be used as internal structures of additively manufactured bone implants. Advantages of TPMS-based implant were from their implicit natures, allowing for precise geometric modification. As a result, many physical characteristics such as surface-to-volume ratio, pore size, elastic properties, and fluid behaviors became controllable parameters. Therefore, TPMS structures offered an opportunity to design bone implants, which were both mechanically and biologically optimized. Nonetheless, the interconnection among structures, mechanical properties, biological performances, and manufacturing limitations was not clearly understood. As a result, the present study utilized an analytical approach, FE modeling, and CFD analysis to examine the synergistic effects of six different TPMS structures including Primitive, Gyroid, Diamond, Neovius, FRD, and IWP on their applicability as bone substitute structures. According to our analysis, we found that pore size, elastic properties, and flow behaviors were highly dependent on the choices of TPMS models. Also, TPMS structures could exhibit both isotropic and anisotropic elastic properties, in which Primitive and Neovius were among the most anisotropic structures. In addition, Gaussian curvature and fluid-induced wall shear stress were suggested to be considered for both mean values and local distributions when evaluating different TPMS models. Ultimately, the design map was constructed to display designable regions, where geometries, preferable pore sizes, mechanical properties, and manufacturing constraints were fulfilled. We found that there was no single optimal structure since optimal geometries varied with different given constraints. Nonetheless, Gyroid, Diamond, and IWP were shown as promising candidates thanks to their flexible design space, isotropic elastic property, adequately uniform Gaussian curvature and fluid-induced wall shear stress, as well as high permeability.

Numerical and experimental study of a multimode optical fiber sensor based on Fresnel reflection at the fiber tip for refractive index measurement

This paper presents the numerical and experimental study of a multimode optical fiber (MMF) sensor based on Fresnel reflection at the fiber tip. Considering different modal power distributions (uniform mode distribution, gaussian and equilibrium mode distribution), the effective fraction of the incident light reflected at the interface between the end of the fiber and the surrounding medium is first calculated numerically with a ray model. Even when considering modal power distribution and non-normal incidence influence, simplifying assumptions such as normal incidence hypothesis can be made to facilitate experimental data exploitation, with a maximum error on the deduced medium refractive index of the 10-4 order. A statistical analysis of noise is then made, to study the influence of a random noise between 0.1% and 5% noise level: results show that the approximation error made by using normal incidence formula for a Fresnel sensor based on a MMF is significantly smaller than the repeatability error. These assumptions are then verified experimentally with two experimental setups by measuring the refractive index at 1550 nm of reference solutions (distilled water-isopropanol and distilled water-sodium chloride mixtures) with a Fresnel based on a multimode fiber, and a Fresnel based on single-mode fiber for comparison. Good agreement is found with refractive index values from the literature with a maximum relative difference of only 0.1%, and the maximum experimental uncertainties in this work is 1.1×10-4. Differences between refractive index measured with a Fresnel based on single-mode and multimode fiber are found to be in accordance with values from the statistical study.

Effects of external noise on threshold-induced correlations in ferromagnetic systems.

In the present paper we investigate the impact of the external noise and detection threshold level on the simulation data for the systems that evolve through metastable states. As a representative model of such systems we chose the nonequilibrium athermal random-field Ising model with two types of the external noise, uniform white noise and Gaussian white noise with various different standard deviations, imposed on the original response signal obtained in model simulations. We applied a wide range of detection threshold levels in analysis of the signal and show how these quantities affect the values of exponent γ_{S/T} (describing the scaling of the average avalanche size with duration), the shift of waiting time between the avalanches, and finally the collapses of the waiting time distributions. The results are obtained via extensive numerical simulations on the equilateral three-dimensional cubic lattices of various sizes and disorders.

Asymmetry of the CMB map: local and global anomalies

We investigate the sources of parity asymmetry in the CMB temperature maps using a pixel domain approach. We demonstrate that this anomaly is mainly associated with the presence of two pairs of high asymmetry regions. The first pair of peaks with Galactic coordinates (l, b) = (212°, -21°) and (32°, 21°) is associated with the Northern Galactic Spur and the direction of the dipole modulation of the power spectrum of the CMB anisotropy. The other pair ((l, b)=(332°, -8°) and (152°, 8°)) is located within the Galactic plane (the Galactic Cold Spot and its antipodal partner). Similar asymmetric peaks, but with smaller amplitudes, belong to the WMAP/Planck Cold Spot and its partner in the Northern Galactic Spur. These local anomalies increase the odd-multipole power to a level consistent with Gaussian simulations. In contrast, the deficit of symmetric peaks is accompanied by a deficit in the even-multipole power and is the source of the parity asymmetry of the CMB temperature maps at the level of about 3 sigma. We also evaluate the influence of the quadrupole, which is another source of the even-multipole deficit. If the low quadrupole is an intrinsic feature of the theoretical model, it will reduce the significance of the parity asymmetry to around the 2 sigma level. We also investigate the relationship between the asymmetry of the power spectrum and the level of the parity asymmetry in the framework of a model with dipole modulation of a statistically uniform Gaussian signal. We show that these two anomalies are innately linked to each other.

Consistent inference for predictive regressions in persistent economic systems

This paper studies standard predictive regressions in economic systems governed by persistent vector autoregressive dynamics for the state variables. In particular, all – or a subset – of the variables may be fractionally integrated, which induces a spurious regression problem. We propose a new inference and testing procedure – the Local speCtruM (LCM) approach – for joint significance of the regressors, that is robust against the variables having different integration orders and remains valid regardless of whether predictors are significant and, if they are, whether they induce cointegration. Specifically, the LCM procedure is based on fractional filtering and band spectrum regression using a suitably selected set of frequency ordinates. Contrary to existing procedures, we establish a uniform Gaussian limit theory and a standard χ2-distributed test statistic. Using the LCM inference and testing techniques, we explore predictive regressions for the realized return variation. Standard least squares inference indicates that popular financial and macroeconomic variables convey valuable information about future return volatility. In contrast, we find no significant evidence using our robust LCM procedure. If anything, our tests support a reverse chain of causality, with rising financial volatility predating adverse innovations to key macroeconomic variables. Simulations are employed to illustrate the relevance of the theoretical arguments for finite-sample inference.

On series expansions for scale functions and other ruin-related quantities

ABSTRACTIn this note, we consider a nonstandard analytic approach to the examination of scale functions in some special cases of spectrally negative Lévy processes. In particular, we consider the compound Poisson risk process with or without perturbation from an independent Brownian motion. New explicit expressions for the first and second scale functions are derived which complement existing results in the literature. We specifically consider cases where the claim size distribution is gamma, uniform or inverse Gaussian. Some ruin-related quantities will also be re-examined in light of the aforementioned results.

Optimal Number of Choices in Rating Contexts

In many settings, people must give numerical scores to entities from a small discrete set—for instance, rating physical attractiveness from 1–5 on dating sites, or papers from 1–10 for conference reviewing. We study the problem of understanding when using a different number of options is optimal. We consider the case when scores are uniform random and Gaussian. We study computationally when using 2, 3, 4, 5, and 10 options out of a total of 100 is optimal in these models (though our theoretical analysis is for a more general setting with k choices from n total options as well as a continuous underlying space). One may expect that using more options would always improve performance in this model, but we show that this is not necessarily the case, and that using fewer choices—even just two—can surprisingly be optimal in certain situations. While in theory for this setting it would be optimal to use all 100 options, in practice, this is prohibitive, and it is preferable to utilize a smaller number of options due to humans’ limited computational resources. Our results could have many potential applications, as settings requiring entities to be ranked by humans are ubiquitous. There could also be applications to other fields such as signal or image processing where input values from a large set must be mapped to output values in a smaller set.

Assessment of Optimal Bragg Grating Length for Optical performance using Two Apodization Functions

Fiber Bragg gratings (FBGs) are one of the most effective technologies because of their suitability in many applications of the fiber techniques. Moreover, it can be utilized in sensing elements and estimating the physical parameters of the optical fiber. In the current research, various fiber bragg lengths are considered and a comparative investagtion is made for the performance of the refractive index modulation at two different apodization profiles namely: Gaussian index profiles and uniform index profiles. Also, a comparative study of the optical communication system performance has been carried out of refractive indexes with two apodization functions. A comprehensive comparison in terms of gain, noise figure, OSNR, quality factor, bit error rate and power has been performed where the performance of the optical system is studied under various optical channel lengths (from 25 km to 100 km) with various FBG lengths, which are ranged from 4 mm to 14 mm in both apodization profiles, i.e. uniform profile and Gaussian profile. In order to carry out the simulation of the performance RZ, the optisystem version 9 is used for single channel based on over single mode fiber. The results showed that the maximum Q.F. as the performance parameter is obtained at the FBG length of 8 mm at all optical lengths. Moreover, the varation effect of optical fiber channel length was greater than the varation effect of refractive index for all the studied parameters (gain, noise figure, OSNR, quality factor, BER, and power) for two apodization functions.

Large-Eddy Simulation of Sandia Flame D with Efficient Explicit Filtering

A uniform Gaussian filter has been applied explicitly to the LES conservation equations for mass, momentum and mixture to simulate a piloted non-premixed methane-air flame (Sandia Flame D). Using a basic property of exponential functions, the three dimensional Gaussian filter is decomposed into the product of three one dimensional filters, greatly reducing the cost of filtering. Seven simulations on three different grids have been performed to investigate the influence of grid refinement with a purely implicit filter, the effects of explicit filtering with increasing filter width and the effect of grid refinement at constant filter-size. Overall, consistent results have been achieved at a cost that is moderate with implicit or explicit filtering, so that explicit filtering can be applied in cases where the numerical error should be independent of the modelling error.

Consistent Inference for Predictive Regressions in Persistent Economic Systems

We study standard predictive regressions in economic systems governed by persistent vector autoregressive dynamics for the state variables. In particular, all – or a subset – of the variables may be fractionally integrated, which induces a spurious regression problem. We propose a new inference and testing procedure – the Local speCtruM (LCM) approach – for joint significance of the regressors, that is robust against the variables having different integration orders and remains valid regardless of whether predictors are significant and if they induce cointegration. Specifically, the LCM procedure is based on fractional filtering and band-spectrum regression using a suitably selected set of frequency ordinates. Contrary to existing procedures, we establish a uniform Gaussian limit theory and a standard χ2-distributed test statistic. Using LCM inference and testing techniques, we explore predictive regressions for the realized return variation. Standard least squares inference indicates that popular financial and macroeconomic variables convey valuable information about future return volatility. In contrast, we find no significant evidence using our robust LCM procedure. If anything, our tests support a reverse chain of causality: rising financial volatility predates adverse innovations to macroeconomic variables. Simulations illustrate the relevance of the theoretical arguments for finite-sample inference. Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at www.nber.org.

Precision Pollution - The effects of enrichment yields and timing on galactic chemical evolution

We present an update to the chemical enrichment component of the smoothed-particle hydrodynamics model for galaxy formation presented in Scannapieco et al. (2005) in order to address the needs of modelling galactic chemical evolution in realistic cosmological environments. Attribution of the galaxy-scale abundance patterns to individual enrichment mechanisms such as the winds from asymptotic giant branch (AGB) stars or the presence of a prompt fraction of Type Ia supernovae is complicated by the interaction between them and gas cooling, subsequent star formation and gas ejection. In this work we address the resulting degeneracies by extending our implementation to a suite of mechanisms that encompasses different IMFs, models for yields from the aforementioned stars, models for the prompt component of the delay-time-distribution (DTDs) for Type Ia SNe and metallicity-dependent gas cooling rates, and then applying these to both isolated initial conditions and cosmological hydrodynamical zoom simulations. We find DTDs with a large prompt fraction (such as the bimodal and power-law models) have, at z=0, similar abundance patterns compared to the low-prompt component time distributions (uniform or wide Gaussian models). However, some differences appear, such as the former having systematically higher [X/Fe] ratios and narrower [O/Fe] distributions compared to the latter, and a distinct evolution of the [Fe/H] abundance.

A uniform initialization Gaussian mixture model–based guided wave–hidden Markov model with stable damage evaluation performance

During practical applications, the time-varying service conditions usually lead to difficulties in properly interpreting structural health monitoring signals. The guided wave–hidden Markov model–based damage evaluation method is a promising approach to address the uncertainties caused by the time-varying service condition. However, researches that have been performed to date are not comprehensive. Most of these research studies did not introduce serious time-varying factors, such as those that exist in reality, and hidden Markov model was applied directly without deep consideration of the performance improvement of hidden Markov model itself. In this article, the training stability problem when constructing the guided wave–hidden Markov model initialized by usually adopted k-means clustering method and its influence to damage evaluation were researched first by applying it to fatigue crack propagation evaluation of an attachment lug. After illustrating the problem of stability induced by k-means clustering, a novel uniform initialization Gaussian mixture model–based guided wave–hidden Markov model was proposed that provides steady and reliable construction of the guided wave–hidden Markov model. The advantage of the proposed method is demonstrated by lug fatigue crack propagation evaluation experiments.

Optimal sup-norm rates and uniform inference on nonlinear functionals of nonparametric IV regression

This paper makes several important contributions to the literature about nonparametric instrumental variables (NPIV) estimation and inference on a structural function $h_0$ and its functionals. First, we derive sup-norm convergence rates for computationally simple sieve NPIV (series 2SLS) estimators of $h_0$ and its derivatives. Second, we derive a lower bound that describes the best possible (minimax) sup-norm rates of estimating $h_0$ and its derivatives, and show that the sieve NPIV estimator can attain the minimax rates when $h_0$ is approximated via a spline or wavelet sieve. Our optimal sup-norm rates surprisingly coincide with the optimal root-mean-squared rates for severely ill-posed problems, and are only a logarithmic factor slower than the optimal root-mean-squared rates for mildly ill-posed problems. Third, we use our sup-norm rates to establish the uniform Gaussian process strong approximations and the score bootstrap uniform confidence bands (UCBs) for collections of nonlinear functionals of $h_0$ under primitive conditions, allowing for mildly and severely ill-posed problems. Fourth, as applications, we obtain the first asymptotic pointwise and uniform inference results for plug-in sieve t-statistics of exact consumer surplus (CS) and deadweight loss (DL) welfare functionals under low-level conditions when demand is estimated via sieve NPIV. Empiricists could read our real data application of UCBs for exact CS and DL functionals of gasoline demand that reveals interesting patterns and is applicable to other markets.

Compressive Sensing Based Multiple Source Localization in the Presence of Sensor Position Uncertainty and Nonuniform Noise

Source localization is an important field of research and the received signal strength (RSS)-based method is of particular interest. Further, by exploiting the sparsity of localization problem, the compressive sensing (CS) can be applied to considerably decrease the number of RSS measurements, especially in multi-source scenario. However, most existing CS-based localization methods usually neglect some practical issues. In particular, the sensor positions are assumed be known exactly, while in practice they may not be accurate. Additionally, a uniform Gaussian noise assumption is made that the noise variances of sensors are identical, but in practice the noise should be nonuniform. When these assumptions are violated, the localization performance will deteriorate dramatically. To address such issues, in this paper, we formulate the source localization based on superimposed RSS measurements as a sparse signal recovery problem. Moreover, by regarding the sensor positions as adjustable parameters, the inaccurate sensor positions can be refined through the adjustment of parameters. Following this idea, we develop a novel iterative algorithm for joint signal recovery and parameter optimization based on the variational expectation-maximization algorithm. Consequently, the sensor position uncertainty can be alleviated and thus the signal recovery performance will be improved greatly. Meanwhile, it is also capable of learning the variance of nonuniform noise. Extensive simulation results demonstrate the superiority of the proposed method.

A statistical study on the subthermocline submesoscale eddies in the northwestern Pacific Ocean based on Argo data

AbstractIn this study, statistical characteristics and spatiotemporal variability of the cold‐core subthermocline eddies (STEs) discovered by Zhang et al. (2015) in the northwestern Pacific are investigated with 14 years of Argo temperature/salinity (T/S) data between 2002 and 2015. By applying an objective identification procedure to Argo T/S profiles, a total of 337 lens‐like STEs that trap cold and fresh homogeneous water are obtained. The STEs' cores are primarily located between 26.5 and 26.9 (300–800 m) and their shapes share a uniform Gaussian structure in vertical. Vertical and horizontal scale of the STEs is generally between 100 and 200 m and 5 and 15 km, respectively, suggesting that they are in the category of submesoscale processes. According to their different densities and seasonalities, the STEs are classified into upper and lower types with density interface of 26.7 . The number of upper‐type STEs is much larger in spring and summer than in autumn and winter while that of lower‐type ones show relatively uniform seasonal distributions. Spatially, the STEs are primarily distributed within the region between the Kuroshio Extension (KE) and subarctic front (SAF) in meridional and 140°E–155°E in zonal direction. Based on STEs' spatial distributions and vertical locations, we propose to name these STEs as KE intermediate‐layer eddies (Kiddies). Water property analysis suggests that the Kiddies most likely originated from the SAF region. For the upper‐type Kiddies, they are probably generated through subduction associated with mixed‐layer frontogenesis, which at least contribute to 0.25 Sv annual subduction rate for the layers 26.2–26.7 .

Single-image super-resolution using orthogonal rotation invariant moments

In this paper, we propose an interpolation-based single-frame image super-resolution approach using orthogonal rotation invariant moments (ORIMs). The ORIMs have several useful characteristics in addition to having the property of image reconstruction. Therefore, they have been used successfully in many image processing applications. Among the various ORIMs, Zernike moments (ZMs), pseudo-Zernike moments (PZMs) and orthogonal Fourier-Mellin moments (OFMMs) have been considered in our proposed framework. The SR performance of the proposed approach has been compared with the classical interpolation-based approaches like bicubic, cubic B-spline, and Lanczos, as well as with nonlocal-means (NLM), and recently developed NLM+ZMs and NLM+PZMs-based SR approaches on twelve standard test images. The experiments have been conducted on both noise-free and noisy LR images corrupted with uniform blur and Gaussian noise. The results demonstrate the superiority of the proposed ORIMs-based approach in super-resolving both noise-free and noisy images over recently developed NLM+ORIMs-based SR approaches. Also, a comparative performance analysis, among various ORIMs (ZMs, PZMs, and OFMMs), is also presented to determine the ORIM which performs better over others under a given condition. A time complexity analysis shows that the proposed method is very fast as compared to NLM, NLM+ZMs and NLM+PZMs-based methods.