scholarly journals Sample Space Dimensionality Refinement for Symmetrical Object Detection

2014 ◽  
Vol 9 (11) ◽  
pp. 1953-1961 ◽  
Author(s):  
Yun-Fu Liu ◽  
Jing-Ming Guo ◽  
Chih-Hsien Hsia ◽  
Sheng-Yao Su ◽  
Hua Lee
Keyword(s):  
Object Detection ◽  
Sample Space ◽  
Symmetrical Object

Structural role of copper in the minerals of the pearceite-polybasite group: the case of the new minerals cupropearceite and cupropolybasite

2007 ◽  
Vol 71 (06) ◽  
pp. 641-650 ◽  
Author(s):  
L. Bindi ◽  
M. Evain ◽  
P. G. Spry ◽  
K. T. Tait ◽  
S. Menchetti
Keyword(s):  
Chemical Characterization ◽  
Sample Space ◽  
The Other ◽  
Crystal Chemical ◽  
Structural Position ◽  
Space Group ◽  
Cu Content ◽  
Own Name

Abstract The pearceite-polybasite group of minerals, general formula [M6T2S7][Ag9CuS4] with M = Ag, Cu; and T = As, Sb, show a crystal structure which can be described as the succession, along the c axis, of two pseudo-layer modules: a [M6T2S7]2– A module layer and a [Ag9CuS4]2+ B module layer. Copper is present in one structural position of the B module layer and replaces Ag in the only fully occupied M position of the A module layer. When the Cu content is >4.00 a.p.f.u., the structural position of the A module layer becomes Cu-dominant and, consequently, the mineral deserves its own name. In this paper we report the crystal-chemical characterization of two Cu-rich members exhibiting the 111 unitcell type (corresponding to the Tac polytype). One sample (space group (P )m1, a 7.3218(8), c 11.8877(13) Å, V 551.90(10) Å3, Z = 1) having As >Sb and with the structural position of the A module layer dominated by Cu, has been named cupropearceite and the other sample (space group (P3̄)m1, a 7.3277(3), c 11.7752(6) Å, V 547.56(8) Å3, Z = 1) having Sb >As has been named cupropolybasite. Both the new minerals and mineral names have been approved by the IMA-CNMNC.

Optimization of a vacuum cleaner fan suction and shaft power using Kriging surrogate model and MIGA

2021 ◽  
pp. 095765092110496
Author(s):  
Soheil Almasi ◽  
Mohammad Mahdi Ghorani ◽  
Mohammad Hadi Sotoude Haghighi ◽  
Seyed Mohammad Mirghavami ◽  
Alireza Riasi
Keyword(s):  
Optimization Design ◽  
Optimization Technique ◽  
Internal Flow ◽  
Latin Hypercube Sampling ◽  
Sample Space ◽  
Geometrical Parameters ◽  
Vacuum Cleaner ◽  
Time Saving ◽  
Design Variables ◽  
Shaft Power

Optimization of vacuum cleaner fan components is a low-cost and time-saving solution to satisfy the increasing requirement for compact energy-efficient cleaners. In this study, surrogate-based optimization technique is used and for the first time it is focused on maximization of Airwatt parameter, which describes the fan suction power, as an objective function (Case II). Besides, the shaft power is minimized (Case I) as another optimization target in order to reduce the power consumption of the vacuum cleaner. 11 geometrical variables of 3 fan components including impeller, diffuser and return channel are selected as the optimization design variables. 80 training points are distributed in the sample space using Advanced Latin Hypercube Sampling (ALHS) technique and the outputs of sample points are calculated by means of CFD simulations. Kriging and RSA surrogate models have been fitted to the outputs of the sample space. Through coupling of constructed Kriging models and Multi-Island Genetic Algorithm (MIGA), the optimal design for each of the optimization cases is presented and evaluated using numerical simulations. A 20.22% reduction in shaft power in Case I and an improvement of 27.73% in Airwatt in Case II have been achieved as the overall results of this study. Despite achieving goals in both optimization cases, a slight decrease in Airwatt in Case I (−6.20%) and a slight increase in shaft power in Case II (+4.82%) are observed relative to primary fan. Furthermore, the Analysis of Variance (ANOVA) determines the importance level of design variables and their 2-way interactions on the objective functions. It was concluded that geometrical parameters related to all of the fan components must be considered simultaneously to conduct a comprehensive optimization. The reasons of enhancement in optimal cases compared with the reference design have been further investigated by analysis of the fan internal flow field. Post-processing of the CFD results demonstrates that the applied geometrical modifications cause a more uniform flow through the flow passages of the optimal fan components.

scholarly journals Posterior Probability on Finite Set

2012 ◽  
Vol 20 (4) ◽  
pp. 257-263
Author(s):  
Hiroyuki Okazaki
Keyword(s):  
Probability Distribution ◽  
Probability Measure ◽  
Posterior Probability ◽  
Probability Distributions ◽  
Sample Space ◽  
Finite Sample ◽  
Finite Set

Summary In [14] we formalized probability and probability distribution on a finite sample space. In this article first we propose a formalization of the class of finite sample spaces whose element’s probability distributions are equivalent with each other. Next, we formalize the probability measure of the class of sample spaces we have formalized above. Finally, we formalize the sampling and posterior probability.

scholarly journals CROSS-MOMENTS COMPUTATION FOR STOCHASTIC CONTEXT-FREE GRAMMARS

2018 ◽  
Vol 33 (1) ◽  
pp. 041
Author(s):  
Velimir M. Ilić ◽  
Miroslav D. Ćirić ◽  
Miomir S. Stanković
Keyword(s):  
Random Variable ◽  
Sample Space ◽  
Efficient Computation ◽  
Context Free Grammar ◽  
Special Cases ◽  
The Cross ◽  
Stochastic Context Free Grammars ◽  
Context Free ◽  
New Algorithms ◽  
Vector Random Variable

In this paper we consider the problem of efficient computation of cross-moments of a vector random variable represented by a stochastic context-free grammar. Two types of cross-moments are discussed. The sample space for the first one is the set of all derivations of the context-free grammar, and the sample space for the second one is the set of all derivations which generate a string belonging to the language of the grammar. In the past, this problem was widely studied, but mainly for the cross-moments of scalar variables and up to the second order. This paper presents new algorithms for computing the cross-moments of an arbitrary order, while the previously developed ones are derived as special cases.

scholarly journals Theory of the Stereological Analysis of Spheroid Size Distribution – Validation of the Equations

2017 ◽  
Vol 17 (4) ◽  
pp. 67-72
Author(s):  
D. Gurgul ◽  
A. Burbelko ◽  
T. Wiktor
Keyword(s):  
Outer Sphere ◽  
Bimodal Distribution ◽  
Mean Value ◽  
Ductile Cast Iron ◽  
Sample Space ◽  
Cumulative Distribution ◽  
Estimation Errors ◽  
Distribution Parameters ◽  
Chord Method ◽  
Validation Tests

AbstractThe paper presents validation tests for method which is used for the evaluation of the statistical distribution parameters for 3D particles’ diameters. The tested method, as source data, uses chord sets which are registered from a random cutting plane placed inside a sample space. In the sample space, there were individually generated three sets containing 3D virtual spheres. Each set had different Cumulative Distribution Function (CDF3) of the sphere diameters, namely: constant radius, normal distribution and bimodal distribution as a superposition of two normal distributions. It has been shown that having only a chord set it is possible, by using the tested method, to calculate the mean value of the outer sphere areas. For the sets of data, a chord method generates quite large errors for around 10% of the smallest nodules in the analysed population. With the increase of the nodule radii, the estimation errors decrease. The tested method may be applied to foundry issues e.g. for the estimation of gas pore sizes in castings or for the estimation of nodule graphite sizes in ductile cast iron.

The Black–Scholes Equation with Impulses at Random Times Via Generalized Riemann Integral

2021 ◽  
Vol 15 (01) ◽  
pp. 45-59
Author(s):  
E. M. Bonotto ◽  
M. Federson ◽  
P. Muldowney
Keyword(s):  
Extension Theorem ◽  
Continuous Functions ◽  
Sample Space ◽  
Asset Valuation ◽  
Itô Calculus ◽  
Black Scholes ◽  
Pricing Theory ◽  
Simple Sets ◽  
Random Times ◽  
Riemann Integration

The classical pricing theory requires that the simple sets of outcomes are extended, using the Kolmogorov Extension Theorem, to a sigma-algebra of measurable sets in an infinite-dimensional sample space whose elements are continuous paths; the process involved are represented by appropriate stochastic differential equations (using Itô calculus); a suitable measure for the sample space can be found by means of the Girsanov and Radon–Nikodym Theorems; the derivative asset valuation is determined by means of an expression using Lebesgue integration. It is known that if we replace Lebesgue’s by the generalized Riemann integration to obtain the expectation, the same result can be achieved by elementary methods. In this paper, we consider the Black–Scholes PDE subject to impulse action. We replace the process which follows a geometric Brownian motion by a process which has additional impulsive displacements at random times. Instead of constants, the volatility and the risk-free interest rate are considered as continuous functions which can vary in time. Using the Feynman–Ka[Formula: see text] formulation based on generalized Riemann integration, we obtain a pricing formula for a European call option which copes with many discontinuities. This paper seeks to develop techniques of mathematical analysis in derivative pricing theory which are less constrained by the standard assumption of lognormality of prices. Accordingly, the paper is aimed primarily at analysis rather than finance. An example is given to illustrate the main results.

Cokriging

2004 ◽  
Author(s):  
Vera Pawlowsky-Glahn ◽  
Richardo A. Olea
Keyword(s):  
Normal Distribution ◽  
Multivariate Normal Distribution ◽  
Real Space ◽  
Sample Space ◽  
Multivariate Normal ◽  
Estimation Variance ◽  
Matrix Formulation ◽  
Simple Kriging ◽  
Usual Procedure ◽  
The Face

The problem of estimation of a coregionalization of size q using cokriging will be discussed in this chapter. Cokriging—a multivariate extension of kriging—is the usual procedure applied to multivariate regionalized problems within the framework of geostatistics. Its fundament is a distribution-free, linear, unbiased estimator with minimum estimation variance, although the absence of constraints on the estimator is an implicit assumption that the multidimensional real space is the sample space of the variables under consideration. If a multivariate normal distribution can be assumed for the vector random function, then the simple kriging estimator is identical with the conditional expectation, given a sample of size N. See Journel (1977, pp. 576-577), Journel (1980, pp. 288-290), Cressie (1991, p. 110), and Diggle, Tawn, and Moyeed (1998, p. 300) for further details. This estimator is in general the best possible linear estimator, as it is unbiased and has minimum estimation variance, but it is not very robust in the face of strong departures from normality. Therefore, for the estimation of regionalized compositions other distributions must also be taken into consideration. Recall that compositions cannot follow a multivariate normal distribution by definition, their sample space being the simplex. Consequently, regionalized compositions in general cannot be modeled under explicit or implicit assumptions of multivariate Gaussian processes. Here only the multivariate lognormal and additive logistic normal distributions will be addressed. Besides the logarithmic and additive logratio transformations, others can be applied, such as the multivariate Box-Cox transformation, as stated by Andrews et al. (1971), Rayens and Srinivasan (1991), and Barcelo-Vidal (1996). Furthermore, distributions such as the multiplicative logistic normal distribution introduced by Aitchison (1986, p. 131) or the additive logistic skew-normal distribution defined by Azzalini and Dalla Valle (1996) can be investigated in a similar fashion. References to the literature for the fundamental principles of the theory discussed in this chapter were given in Chapter 2. Among those, special attention is drawn to the work of Myers (1982), where matrix formulation of cokriging was first presented and the properties included in the first section of this chapter were stated.

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