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### Gap-free compositions and gap-free samples of geometric random variables

Paweł Hitczenko, Arnold Knopfmacher
2005 Discrete Mathematics
We show that this problem is closely related to the study of the probability that a sample of independent, identically distributed random variables with a geometric distribution is likewise gap-free.  ...  We study the asymptotic probability that a random composition of an integer n is gap-free, that is, that the sizes of parts in the composition form an interval.  ...  This led us to consider the same question for samples of geometric random variables.  ...

### Gaps in samples of geometric random variables

William M.Y. Goh, Pawel Hitczenko
2007 Discrete Mathematics
In this note we continue the study of gaps in samples of geometric random variables originated in Hitczenko and Knopfmacher [Gap-free compositions and gap-free samples of geometric random variables.  ...  Discrete Math. 294 (2005) 225-239] and continued in Louchard and Prodinger [The number of gaps in sequences of geometrically distributed random variables,  ...  Louchard and Prodinger carried out the detailed study of the number of values missed in a sample of geometric random variables.  ...

### Compositions and samples of geometric random variables with constrained multiplicities

Margaret Archibald, Arnold Knopfmacher, Toufik Mansour
2010 Discrete Mathematics & Theoretical Computer Science
This probability is also studied in the related case of samples \$\Gamma =(\Gamma_1,\Gamma_2,\ldots, \Gamma_n)\$ of independent, identically distributed random variables with a geometric distribution.  ...  International audience We investigate the probability that a random composition (ordered partition) of the positive integer \$n\$ has no parts occurring exactly \$j\$ times, where \$j\$ belongs to a specified  ...  A gap-free sample has elements whose values form an interval, namely if elements 2 and 6 are in the sample, then so are 3, 4 and 5. A complete sample is gap-free with minimal element 1.  ...

### Samples of geometric random variables with multiplicity constraints

Margaret Archibald, Arnold Knopfmacher
2006 Discrete Mathematics & Theoretical Computer Science
International audience We investigate the probability that a sample \$\Gamma=(\Gamma_1,\Gamma_2,\ldots,\Gamma_n)\$ of independent, identically distributed random variables with a geometric distribution has  ...  Specific choices of the set \$A\$ enable one to determine the asymptotic probabilities that such a sample has no variable occuring with multiplicity \$b\$, or which has all multiplicities greater than \$b\$,  ...  Acknowledgements We would like to thank Helmut Prodinger for the helpful advice he gave at the start of this project, relating to finding asymptotics from the recursion (2.1).  ...

### Tolerance Analysis Approach based on the Classification of Uncertainty (Aleatory/Epistemic)

J.Y. Dantan, N. Gayton, A.J. Qureshi, M. Lemaire, A. Etienne
2013 Procedia CIRP
It presents: a brief view of the uncertainty classification: Aleatory uncertainty comes from the inherent uncertain nature and phenomena, and epistemic uncertainty comes from the lack of knowledge, a formulation  ...  is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible.  ...  Acknowledgements The authors acknowledge the support of ANR "AHTOLA" project (ANR-11-MONU-013).  ...

### A New MEMS Stochastic Model Order Reduction Method: Research and Application

Bian Xiangjuan, Youping Gong, Chen Guojin, Lv Yunpeng
2015 Journal of Sensors
chaos expansions in terms of the random input variables for the matrices of a finite element model of the system and then uses its transformation matrix to reduce the model; the method is independent  ...  for during the robust design of MEMS actuators caused by uncertain material and/or geometric parameters.  ...  Acknowledgments The paper was supported by the National Natural Science Foundation of China "MEMS Multifields Uniform Simulation Model Construction and Optimism Research" (61100101); the paper was also  ...

### Free Gap Estimates from the Exponential Mechanism, Sparse Vector, Noisy Max and Related Algorithms [article]

Zeyu Ding, Yuxin Wang, Yingtai Xiao, Guanhong Wang, Danfeng Zhang, Daniel Kifer
2020 arXiv   pre-print
This free gap information can improve the accuracy of certain follow-up counting queries by up to 66%. We obtain these results from a careful privacy analysis of these algorithms.  ...  In this paper we show that these algorithms can release additional information related to the gaps between the selected items and the other candidates for free (i.e., at no additional privacy cost).  ...  We further show that using other types of random noise, such as exponential and geometric random variables, in place of the Laplace, makes the free gap information more accurate at the same cost to privacy  ...

### Stochastic Analysis of Electrostatic MEMS Subjected to Parameter Variations

Nitin Agarwal, Narayana R. Aluru
2009 Journal of microelectromechanical systems
random space.  ...  and gap between microstructures, on relevant quantities of interest such as actuation behavior, resonant frequency, and quality factor.  ...  K = λ/h is the Knudsen number, where λ is the mean free path of the fluid.  ...

### SCALE SELECTION FOR GEOMETRIC FITTING IN NOISY POINT CLOUDS

RANJITH UNNIKRISHNAN, JEAN-FRANÇOIS LALONDE, NICOLAS VANDAPEL, MARTIAL HEBERT
2010 International journal of computational geometry and applications
In recent years, there has been a resurgence in the use of raw point cloud data as the geometric primitive of choice for several modeling tasks such as rendering, editing and compression.  ...  To this goal, we present a new class of locally semi-parametric estimators that allows analysis of accuracy with finite samples, as well as explicitly addresses the problem of selecting optimal support  ...  geometric fitting σ 0 Std. deviation of noise in each coordinate X Random variable for the x-coordinate.  ...

### Mutual fund flows and investor returns: An empirical examination of fund investor timing ability

Geoffrey C. Friesen, Travis R.A. Sapp
2007 Journal of Banking & Finance
We examine the timing ability of mutual fund investors using cash flow data at the individual fund level.  ...  We demonstrate that our empirical results are consistent with investor return-chasing behavior. 1 Studies on the timing ability of fund managers include  ...  Performance gap is the difference between fund geometric and dollar-weighted returns. Panel A reports statistics on the full sample of funds.  ...

### Simulation Tests of the Accuracy of Fitting Two Freeform Surfaces

Damian Groch, Małgorzata Poniatowska
2019 International Journal of Precision Engineering and Manufacturing
The outcome of the study is a spatial model of the gap between the studied surfaces.  ...  The obtained model was verified experimentally by measuring the dimensions of the actual gap between the surfaces, applying a measuring microscope.  ...  Acknowledgements The work is supported by the Polish Ministry of Science and Higher Education under the Project S/WM/2/2017.  ...

### Random perturbation models for boundary extraction sequence

Visvanathan Ramesh, Robert M. Haralick
1997 Machine Vision and Applications
In this paper we illustrate how random perturbation models can be set up for a vision algorithm sequence involving edge finding, edge linking, and gap filling.  ...  It is also shown that the characteristics of random segments generated due to gray-level noise are functions of the probability of false alarm of the edge detector.  ...  A random variable X is exponentially distributed with parameter λ if: p X (x) = λexp −λx . (12) We now show that the exponential distribution is the continuous analog of the geometric distribution.  ...

### Wave attenuation and trapping in 3D printed cantilever-in-mass metamaterials with spatially correlated variability

Danilo Beli, Adriano T. Fabro, Massimo Ruzzene, José Roberto F. Arruda
2019 Scientific Reports
band gap boundary.  ...  The variability also induces a spatially variant locally resonant band gap that progressively slow down the group velocity until an almost zero value, giving rise to wave trapping effect near the lower  ...  Acknowledgements The authors would like to thank the NT3D group from CTI Renato Archer Brazilian Institute (Campinas-SP, Brazil) for manufacturing the metamaterial beam samples through the ProEXP program  ...

### On gaps and unoccupied urns in sequences of geometrically distributed random variables

Guy Louchard, Helmut Prodinger
2008 Discrete Mathematics
This paper continues the study of gaps in sequences of n geometrically distributed random variables, as started by Hitczenko and Knopfmacher [Gap-free samples of geometric random variables, Discrete Math  ...  This might be called weak gaps, as opposed to maximal gaps, as in Hitczenko and Knopfmacher [Gap-free samples of geometric random variables, Discrete Math. 294 (2005) 225-239 ].  ...  Acknowledgments The insightful comments of two referees are gratefully acknowledged.  ...

### Yield analysis of a stripline Wilkinson power divider using Monte Carlo samples of interpolated full wave simulation data using Sonnet

Bashir Souid, Serhend Arvas
2011 2011 XXXth URSI General Assembly and Scientific Symposium
The use of Monte Carlo samples of interpolated data from a linearly spaced grid of electromagnetic simulation data for yield analysis is investigated.  ...  The motivation for this approach stems from a desire to have accurate yield metrics without the need to fabricate a large number of circuits or run a large number of full wave simulations.  ...  ( 2 ) 2 Measure physical geometric dimensions of sample circuits. (3) Construct PDF of the geometric variables. (4) Perform full wave electromagnetic (em) simulations on a linearly spaced grid. a.  ...
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