Continuous Uniform Distribution Research Articles

Comparative Study of Different Statistical Distributions in Generating Noise Components for Privacy Preserving Data Clustering

Privacy Preserving Data mining is one of the recent areas of research. Privacy preserving clustering is one of the functionalities of privacy preserving data mining. The present work makes a comparative study of different statistical distributions such as Poisson distribution, Normal distribution, Discrete Uniform distribution, Continuous Uniform distribution, and Exponential distribution in generating noise components for additive data perturbation in the context of privacy preserving data clustering. The results obtained show that the mean squared error obtained from the perturbed data generated by adding noise generated from both discrete uniform distribution and continuous uniform distribution is same as the mean squared error obtained from the original data but the order of values differ due to random selection of cluster centers.

Non-Laplacian beliefs in a global game with noisy signaling

In standard global games, individual behavior is optimal if it constitutes a best response to agnostic—Laplacian—beliefs about the aggregate behavior of other agents. This paper considers a standard binary action global game augmented with noisy signaling by an informed policy-maker and shows that in this game, equilibrium beliefs depart in quite stark ways from the Laplacian benchmark. In the limit as signals become arbitrarily precise, so that all fundamental uncertainty is removed (leaving only strategic uncertainty), the equilibrium beliefs of the marginal individual concerning the aggregate action collapse to a discrete Bernoulli distribution, giving probability mass only to the polar extreme outcomes. By contrast in the underlying standard global game the marginal individual believes the aggregate action has a continuous uniform distribution, giving equal likelihood to all possible outcomes.

On the longest path of a randomly weighted tournament

Finding a maximum weight path in a directed or undirected graph is a basic combinatorial and algorithmic problem. We consider this problem for tournaments in the well-studied random weighted model. Denote by P(G,D) the probability space obtained by independently assigning weights to the edges of a tournament G according to a nonnegative probability distribution D. Denote by ℓ(G,D) the expected weight of a path with maximum weight.If D has finite mean μ, then ℓ(G,D)≥μ(n−1) is a trivial lower bound, with equality if D is constant, as by Redei’s Theorem, every tournament has a Hamilton path. However, already for very simple nontrivial distributions, it is challenging to determine ℓ(G,D) even asymptotically, and even if the tournament is small and fixed. We consider the two natural distributions of the random weighted model, the continuous uniform distribution U[0,1] and the symmetric Bernoulli distribution U{0,1}. Our first result is that for any tournament, both ℓ(G,U{0,1}) and ℓ(G,U[0,1]) are larger than the above trivial 0.5(n−1) lower bound in the sense that 0.5 can be replaced by a larger constant. To this end we prove the existence of dense partial squares of Hamilton paths in any tournament, a combinatorial result which seems of independent interest. Regarding upper bounds, while for some tournaments one can prove that both ℓ(G,U{0,1}) and ℓ(G,U[0,1]) are n−o(n), we prove that there are other tournaments for which both ℓ(G,U{0,1}) and ℓ(G,U[0,1]) are significantly smaller. In particular, for every n, there are n-vertex tournaments for which ℓ(G,U{0,1})≤0.614(n−1). Finally, we state several natural open problems arising in this setting.

Constitutive behavior of Al2O3np/Al7075 composites with a high solid fraction for thixoforming

Abstract The thixotropic compression tests of nano-Al2O3 (Al2O3np)/Al7075 composites with different particle sizes and contents and containing a high fraction of solid, were conducted under conditions of 560–590 °C and 0.01–5 s−1, and the microstructures were observed. A visco-plastic constitutive model of nanoparticle reinforced composites for thixoforming was proposed, considering the coupling effects of strain, strain rate, deformation temperature and liquid fraction and presence of nanoparticles, to describe constitutive behavior of the composites under various deformation conditions. Furthermore, the influence of deformation parameters on thixoforming was investigated. It could be shown that the predictions by the developed model were consistent with experimental results. Fracture analysis of the thixotropic compression samples revealed that high deformation temperature or/and high strain rate could prompt continuous uniform distribution of the liquid phase along the grain boundary, causing the formation of a thin liquid film around an approximately spherical grain, accordingly improving thixoformability of the composites with a high solid fraction. Moreover, deformation mechanisms of the composites during thixotropic compression process were discussed.

Power Systems Stability through Piecewise Monotonic Data Approximations – Part 1: Comparative Benchmarking of L1PMA, L2WPMA and L2CXCV in Overhead Medium-Voltage Broadband over Power Lines Networks

This first paper assesses the performance of three well-known piecewise monotonic data approximations ( i.e. , L1PMA, L2WPMA, and L2CXCV) during the mitigation of measurement differences in the overhead medium-voltage broadband over power lines (OV MV BPL) transfer functions. The contribution of this paper is triple. First, based on the inherent piecewise monotonicity of OV MV BPL transfer functions, L2WPMA and L2CXCV are outlined and applied during the determination of theoretical and measured OV MVBPL transfer functions. Second, L1PMA, L2WPMA, and L2CXCV are comparatively benchmarked by using the performance metrics of the percent error sum (PES) and fault PES. PES and fault PES assess the efficiency and accuracy of the three piecewise monotonic data approximations during the determination of transmission BPL transfer functions. Third, the performance of L1PMA, L2WPMA, and L2CXCV is assessed with respect to the nature of faults — i.e. faults that follow either continuous uniform distribution (CUD) or normal distribution (ND) of different magnitudes—. The goal of this set of two papers is the establishment of a more effective identification and restoration of the measurement differences during the OV MV BPL coupling transfer function determination that may significantly help towards a more stable and self-healing power system. Citation:  Lazaropoulos, A. G. (2017). Power Systems Stability through Piecewise Monotonic Data Approximations – Part 1: Comparative Benchmarking of L1PMA, L2WPMA and L2CXCV in Overhead Medium-Voltage Broadband over Power Lines Networks. Trends in Renewable Energy , 3(1), 2-32. DOI: 10.17737/tre.2017.3.1.0029

Best L1 Piecewise Monotonic Data Approximation in Overhead and Underground Medium-Voltage and Low-Voltage Broadband over Power Lines Networks: Theoretical and Practical Transfer Function Determination

This paper investigates the efficiency and accuracy of the best L1 piecewise monotonic data approximation (best L1PMA) in order either to approximate the transfer functions of distribution BPL networks or to reveal the aforementioned transfer functions when various faults occur during their determination. The contribution of this paper is quadruple. First, based on the inherent piecewise monotonicity of distribution BPL transfer functions, a piecewise monotonic data approximation is first applied in BPL networks; best L1PMA is outlined and applied during the determination of distribution BPL transfer functions. Second, suitable performance metrics such as the percent error sum (PES) and fault PES are reported and applied so as to assess the efficiency and accuracy of the best L1PMA during the determination of distribution BPL transfer functions. Third, the factors of distribution BPL networks that influence the performance of best L1PMA are identified. Fourth, the accuracy of the best L1PMA is assessed with respect to its inherent properties, namely, the assumed number of monotonic sections and the nature of faults, that is, faults that follow either continuous uniform distribution (CUD) or normal distribution (ND), during the determination of distribution BPL transfer functions. Finally, best L1PMA may operate as the necessary intermediate antifault method for the theoretical and practical transfer function determination of distribution BPL networks.

Microstructure Modification of Powder Compact of Al–Zn–Mg Nanostructured Alloy by a Semisolid Thermomechanical Processing

A thermomechanical process (TMP) consisting of three cycles of cold pressing at 154 MPa and liquid-phase sintering at 600 °C for 30 min in each cycle was applied to modify the microstructure of nanostructured Al–Zn–Mg alloy. The alloy powders were produced by mechanical alloying. Also, solid-state sintering at 550 °C for 90 min was done to compare the results with those obtained from the TMP. The powders and the thermomechanically (TM) processed samples were analyzed by XRD to reveal the present phases in addition to calculating the crystallite size changes by the Williamson–Hall method. Moreover, scanning electron microscope was employed to observe the morphology of the powder and the microstructures of the sintered and the TM processed samples. The results revealed that the TMP affected the microstructure noticeably as well as the microhardness by removing the continuous grain boundary porosities and uniform distribution of the intermetallic phase particles as well as obtaining a near globular microstructure after the second cycle. Also, the average grain sizes in the first and the second cycles of the TMP were lower than those of the sintered sample. Furthermore, nanocrystalline grains were stable up to the second cycle of the TMP.

Stabilization for sampled-data systems under noisy sampling interval

In engineering practice, the sampling interval for a sampled-data system often fluctuates around a nominal/ideal value based on certain probability distributions that can be specified a priori through statistical tests. In this paper, a fundamental stabilization problem is investigated for a class of sampled-data systems under noisy sampling interval. The stochastic sampled-data control system under consideration is first converted into a discrete-time system whose system matrix is represented as an equivalent yet tractable form via the matrix exponential computation. Then, by introducing a Vandermonde matrix, the mathematical expectation of the quadratic form of the system matrix is computed. By recurring to the Kronecker product operation, the sampled-data stabilization controller is designed such that the closed-loop system is stochastically stable in the presence of noisy sampling interval. Subsequently, a special case is considered where the sampling interval obeys the continuous uniform distribution and the corresponding stabilization controller is designed. Finally, a numerical simulation example is provided to demonstrate the effectiveness of the proposed design approach.

Simulation and experimental study of phase characteristics in high-gain relativistic klystron amplifier

In order to realize the combination of the coherent high power microwave, an S-band high gain relativistic klystron amplifier with high phase stability is presented and studied theoretically and experimentally. The phase characteristics of the output microwave are explored in particle-in-cell code and experiment. The experimental results accord well with the simulation results, which indicates that the parasitic oscillation excited by retrograde electrons is the main cause of phase variation in the development of high-gain relativistic klystron with high phase stability. When the input RF power is 10 kW, a microwave pulse with about ± 10° in relative phase difference fluctuation between output and input is obtained in experiment. And the corresponding locking duration is about 90 ns. Accordingly, the expectation of power combination efficiency of 10 high-gain relativistic klystron amplifiers can be achieved to be 99% with continuous uniform distribution of random relative phase difference.

Investigation of Hot Stamping Process of 22MnB5 Based on Metallo-Thermo-Mechanical Theory

In this study, based on the metallo-thermo-mechanical coupling theory, a FEM model of hot stamping including forming and quenching is built to investigate the cooling behavior and the microstructure evolution, and to predict the final mechanical properties of hot-stamped components. The results show that, after about 16s, the temperature of the entire component is lower than Mf of 22MnB5 boron steel and with a continuous uniform distribution. Most of austenite in component has transformed into martensite. To satisfy the required mechanical properties, the sufficient holding time of quenching in die is essential and it plays an important role in ensuring the required hardness. The predicted Rockwell hardness of component after hot stamping process is almost 512HV, which shows a good agreement with the experimental results. It implies that the metallo-thermo-mechanical numerical model established in this study is reasonable and reliable, which can provide a theoretical guidance for optimizing the hot stamping procedure.

Using the Average of the Extreme Values of a Triangular Distribution for a Transformation, and Its Approximant via the Continuous Uniform Distribution

This paper introduces a new probability distribution referred to as a transformed triangular distribution (TTD) by using the average of the extreme values (minimum and maximum) of the triangular distribution. The TTD is being approximated by the continuous uniform distribution. The basic moments of the TTD and those of the continuous uniform distribution are compared respectively, and a relationship established. This can be used in modeling and simulation.

Money and price posting under private information

We study price posting with undirected search in a search-theoretic monetary model with divisible money and divisible goods. Ex ante homogeneous buyers experience match-specific preference shocks in bilateral trades. The shocks follow a continuous uniform distribution, and the realizations of the shocks are private information. We show that there exists a unique monetary equilibrium for generic values of the inflation rate. In equilibrium, each seller posts a continuous pricing schedule that exhibits quantity discounts. Buyers may spend nothing, a fraction or all of their money holdings, depending on their preference-shock realizations. Inflation reduces the extent of non-linear pricing. The model captures the hot-potato effect of inflation along both the extensive margin, as an increase in the trading probability, and the intensive margin, as higher fractions of money being spent.

Effect of Model Scale and Particle Size Distribution on PFC3D Simulation Results

This paper investigates the effect of model scale and particle size distribution on the simulated macroscopic mechanical properties, unconfined compressive strength (UCS), Young’s modulus and Poisson’s ratio, using the three-dimensional particle flow code (PFC3D). Four different maximum to minimum particle size (dmax/dmin) ratios, all having a continuous uniform size distribution, were considered and seven model (specimen) diameter to median particle size ratios (L/d) were studied for each dmax/dmin ratio. The results indicate that the coefficients of variation (COVs) of the simulated macroscopic mechanical properties using PFC3D decrease significantly as L/d increases. The results also indicate that the simulated mechanical properties using PFC3D show much lower COVs than those in PFC2D at all model scales. The average simulated UCS and Young’s modulus using the default PFC3D procedure keep increasing with larger L/d, although the rate of increase decreases with larger L/d. This is mainly caused by the decrease of model porosity with larger L/d associated with the default PFC3D method and the better balanced contact force chains at larger L/d. After the effect of model porosity is eliminated, the results on the net model scale effect indicate that the average simulated UCS still increases with larger L/d but the rate is much smaller, the average simulated Young’s modulus decreases with larger L/d instead, and the average simulated Poisson’s ratio versus L/d relationship remains about the same. Particle size distribution also affects the simulated macroscopic mechanical properties, larger dmax/dmin leading to greater average simulated UCS and Young’s modulus and smaller average simulated Poisson’s ratio, and the changing rates become smaller at larger dmax/dmin. This study shows that it is important to properly consider the effect of model scale and particle size distribution in PFC3D simulations.

Features of Drying Water-Atomized Aluminum Alloy Powders

The kinetics of dehydration and heat drying of water-atomized aluminum powders is examined. It is shown that conductive vacuum ovens for reactive substances are inefficient. There is no device for the disintegration of particle aggregates in dryers of this type, which results in the risk of oxidation and thermal self-ignition of powders. Conduction–convection dryers provide disintegration of particle aggregates and continuous mixing and uniform distribution of the powder over the heating surface. The results are used to optimize the drying conditions for aluminum alloy powders and determine the maximum permissible drying temperatures depending on the moisture content of the powder.

Mining and Analyzing Energy Layout on Carbon Emission Intensities of Industrial Sectors

Energy consumption structure optimum is gradually discussed in recent literatures. Based on hierarchical clustering of optimally close to content demand of data group mine and analysis, industrial sectors layout on carbon emission intensity is researched. Computed carbon emission drawn support from IPCC methodological framework, formed carbon emission intensities of emissions divided by sectors GDP respectively, and transformed calculated figures into CDF of the continuous uniform distribution to cultivate the standardized data. Resulting of the case presents that there are two categories with types of v and inversed v after mining and analyzing 37 industrial sectors data in 2006-2011. Findings are that 39% annual max paired difference of emission intensities is appeared, and the divergence of energy consumption structure is significantly obtained, which is conducive to the whole industrial distribution of low carbon policy-making.

Stress state factor evaluation based on a fractographic analysis for use in the crack growth FASTRAN retardation model of the AFGROW computing code

The FASTRAN crack growth retardation model uses stress state descriptors to consider the local stress state ahead of the crack tip. Using the FASTRAN model implemented in the AFGROW computing code, the descriptor is input into the retardation model as a constant tensile (compressive) constraint factor along with the corresponding crack growth rate.The paper presents an evaluation based on a fractographic analysis of fracture surfaces of middle tension M(T) specimens from Al-alloy, which were used for the standard crack growth rate measurement under constant amplitude loading. There are typically three zones on the fracture surface: the flat zone that is perpendicular to the loading force and represents the tension mode of specimen cracking, the slant zone that is approximately 45° deviated from the loading force direction and a transient zone between them. It is shown that a significant correlation between crack length, local crack growth rate and the sizes of the zones exist.Crack lengths relevant to the zones and corresponding crack growth rates were processed by statistical procedures. A continuous uniform distribution is a very good statistical model of the logarithm of the crack growth rates on both sides of the transient zone. In the retardation model, this distribution can be accounted for by using the means of the probability functions.A sub-scale structural model was tested for fatigue crack growth under a random loading process representing real operational conditions. Using the typical values of constraint factors for a “pure” plain stress and plain strain states and the crack growth rates evaluated by the fractographic analysis as input parameters, the crack growth curves calculated by the AFGROW code using the FASTRAN retardation model were compared with the crack growth data measured in the experiment.The AFGROW output crack growth curves fit to the experimental measured ones without any additional tuning of the retardation model parameters.

Fabrication of air gap dielectrics by nanoimprint lithography

Graphical abstractDisplay Omitted Highlights? We report a powerful new route to fabricate air gap dielectrics with well-defined pore geometries. ? Method utilizes the combination of nanoimprint lithography and a sacrificial template approach. ? Successful fabrication of defect free mechanically robust air gap films (ultra-low k value of 1.9). ? Attractive candidates as interlayer dielectrics for next-generation integrated circuit applications. We report a simple and high-resolution method to fabricate air gap dielectrics with well-defined geometries. This method utilizes nanoimprint lithography to pattern a thermally labile organic polymer, poly (2-hydroxyethyl methacrylate) (PHEMA), subsequently used as a sacrificial template to form air gap nanochannels in a low-k spin-on-glass, poly(methylsilsesquioxane) (PMSSQ). The morphology and dimensions of obtained structures were characterized by cross-sectional SEM, revealing well-defined, continuous and uniform nanochannels. Dielectric constant measurements showed that introduction of these air gap nanochannels into the PMSSQ layer decreased the dielectric constant value from 2.8 to 1.9, while nanoindentation experiments confirmed that the nanochannels were mechanically robust as the air gap films retained the hardness of 1GPa. Infusion with a fluorescent dye solution and subsequent quenching with gold nanoparticles demonstrated continuous nature and uniform distribution of the nanochannels throughout the sample.

Moment-Based Parameter Estimation and Blind Spectrum Sensing for Quadrature Amplitude Modulation

Knowing accurate noise variance and signal power is crucial to most spectrum-sensing algorithms such as energy detection, matched filter detection, and cyclostationary detection. In this paper, we consider a practical scenario when these two parameters are unknown and are needed to be estimated before the spectrum sensing. This task is non-trivial without knowing the status of the primary user, and we categorize the related spectrum sensing as a blind one. We develop the estimation algorithms for unknown parameters by exploiting the signal constellation of the primary user. Three different parameter estimators that do not require any training are then proposed based on the moments of the received signals. Since the secondary user may not know the primary user's signal constellation, we develop a robust approach that approximates a finite quadrature amplitude modulation (QAM) constellation by a continuous uniform distribution. We also derive the modified Cramer-Rao bound (CRB) for noise variance estimation. Then the optimal moment pair is found from minimizing the mean squared error (MSE) of the signal-to-noise ratio (SNR). The method of choosing the spectrum sensing threshold by taking into consideration the estimation error is also discussed.

Novel methods on comparing grey numbers

Uncertain decision-making is an important branch of decision-making theory. It is crucial to describe uncertain information, which determine the decision-making is effective or not. This paper first presents a brief survey of the existing methods on denoting uncertain information, such as fuzzy mathematics, stochastic and interval methods, analyzes the merits and demerits of these methods. Then the paper proposes a novel method grey systems theory to describe uncertain information and gives the novel definition of grey number on the basis of probability distribution. Subsequently a novel probability method on comparing grey numbers, especially discrete grey numbers and interval grey numbers, is studied. When an interval grey number satisfied to continuous uniform distribution, it will be degenerated into an interval number. Finally three numerical examples are investigated to demonstrate the effectiveness of the present method.

Exact conditional inference for two uniform populations

We discuss the nature of ancillary information in the context of the continuous uniform distribution. In the one-sample problem, the existence of sufficient statistics mitigates conditioning on the ancillary configuration. In the two-sample problem, additional ancillary information becomes available when the ratio of scale parameters is known. We give exact results for conditional inferences about the common scale parameter and for the difference in location parameters of two uniform distributions. The ancillary information affects the precision of the latter through a comparison of the sample value of the ratio of scale parameters with the known population value. A limited conditional simulation compares the Type I errors and power of these exact results with approximate results using the robust pooled t-statistic.