In this article, we consider random occupancy models and the related problems based on the methods of generating functions. The waiting time distributions associated with sequential random occupancy models are investi...
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In this article, we consider random occupancy models and the related problems based on the methods of generating functions. The waiting time distributions associated with sequential random occupancy models are investigated through the probability generating functions. We provide the effective computational tools for the evaluation of the probability functions by making use of the Bell polynomials. The results presented here provide a wide framework for developing the theory of occupancy models. Finally, we treat several examples in order to demonstrate how our theoretical results are employed for the investigation of the random occupancy models along with numerical results.
作者：
Han, QAki, SOsaka Univ
Grad Sch Engn Sci Dept Informat & Math Sci Toyonaka Osaka 560 Japan
Let X-1,X-2,...,X-n be a time-homogeneous {0, 1}-valued Markov chain. Let Y=(Y-1,...,Y-r) denote the r-dimensional random vector, where Y-i (i =1,...,r) represents the number of success runs of length k(i) (i=1,...,r)...
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Let X-1,X-2,...,X-n be a time-homogeneous {0, 1}-valued Markov chain. Let Y=(Y-1,...,Y-r) denote the r-dimensional random vector, where Y-i (i =1,...,r) represents the number of success runs of length k(i) (i=1,...,r), k=(k(1),...,k(r)). In this paper we obtain exact and recurrence formulae for the probability functions and the probability generating functions of Y, based on four different ways of counting numbers of success runs (i.e. overlapping success runs, non-overlapping runs, the runs with a specified length k or more and the runs with just specified length k). Using our methods, we can obtain the probability function and probability generating function of Y, where Y-1,...,Y-r be counted numbers by different ways. (C) 1998 Elsevier Science B.V. All rights reserved.
In this article, we consider the distributions of simple patterns in some types of sequences of infinite exchangeable multi-state trials. The distributions on exchangeable multi-state trials are considered in terms of...
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In this article, we consider the distributions of simple patterns in some types of sequences of infinite exchangeable multi-state trials. The distributions on exchangeable multi-state trials are considered in terms of an extension of de Finetti's theorem. As an application of partially exchangeable sequences, distributions on a Markov exchangeable sequence are studied. Furthermore, we propose a new type of partially exchangeable sequence and examine its properties. In addition, we discuss the distribution theory in the case of the finite exchangeable sequences. The results presented here provide a wide framework for developing the exact distribution theory of simple patterns. Finally, some examples are given in order to illustrate our theoretical results. (C) 2011 Elsevier B.V. All rights reserved.
Given a physical system, one knows that there is a logical duality between its properties and its states. In this paper, we choose its states as the undefined notions of our axiomatic construction. In fact, by means o...
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Given a physical system, one knows that there is a logical duality between its properties and its states. In this paper, we choose its states as the undefined notions of our axiomatic construction. In fact, by means of well-motivated assumptions expressed in terms of a transition probability function defined on the set of all pure states of the system, we construct a system of elementary propositions, i.e., a complete orthomodular atomic lattice satisfying the covering law. We also study in this framework the important notion of compatibility of propositions, and we define the superpositions and the mixtures of the states of the physical system.
In this study, the joint distributions of order statistics of innid discrete random variables are expressed. Also, the joint distributions are obtained in the form of an integral. Then, the results related to pf and d...
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In this study, the joint distributions of order statistics of innid discrete random variables are expressed. Also, the joint distributions are obtained in the form of an integral. Then, the results related to pf and df are given.
Distance constraints, in principle, can be employed to determine information about the location of probes within a three-dimensional volume. Traditional methods for locating probes from distance constraints involve op...
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Distance constraints, in principle, can be employed to determine information about the location of probes within a three-dimensional volume. Traditional methods for locating probes from distance constraints involve optimization of scoring functions that measure how well the probe location fits the distance data, exploring only a small subset of the scoring function landscape in the process. These methods are not guaranteed to find the global optimum and provide no means to relate the identified optimum to all other optima in scoring space. Here, we introduce a method for the location of probes from distance information that is based on probability calculus. This method allows exploration of the entire scoring space by directly combining probability functions representing the distance data and information about attachment sites. The approach is guaranteed to identify the global optimum and enables the derivation of confidence intervals for the probe location as well as statistical quantification of ambiguities. We apply the method to determine the location of a fluorescence probe using distances derived by FRET and show that the resulting location matches that independently derived by electron microscopy. (c) 2013 Elsevier Inc. All rights reserved.
The rotationally invariant phase sensitive skew parameter, an indicator of dimensionality of conductivity Structure, is a complicated non-linear function of the impedance tensor elements. In the presence of noise in t...
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The rotationally invariant phase sensitive skew parameter, an indicator of dimensionality of conductivity Structure, is a complicated non-linear function of the impedance tensor elements. In the presence of noise in the impedance data, skew can be significantly biased, leading to a false interpretation of dimensionality. Therefore, the probability function distribution of the skew parameter is derived to obtain its confidence limit, rather than treating a conventional linear propagation error. It is well known that the latter is only appropriate if the parameter is a function of independent random variables with small relative errors. The confidence limit is estimated by deriving its conditional probability function in terms of the tensor elements density function, using the Jacobi-matrix transformation of random variables, assuming the tensor elements to be normally distributed random variables, It is shown with synthetic and experimental data that the statistical confidence limit derived here truly reflects a probability range for the skew value. Bias of skew is seen to be significant with a small 5% of random Gaussian noise added to the tensor elements. Considering the 95% confidence limit instead of the measured skew itself results in a plausible approach to analyse dimensionality. The procedure developed here to estimate the confidence limit can also be extended to other functions of the tensor elements.
Bernoulli trials with success ratep are considered. Peter, who is a gambler of success ratep, gets 1 unit if the first trial results in success and loses the same unit otherwise. For thekth trial (k≧2), he gets or lo...
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Bernoulli trials with success ratep are considered. Peter, who is a gambler of success ratep, gets 1 unit if the first trial results in success and loses the same unit otherwise. For thekth trial (k≧2), he gets or loses 1 according as success or failure unless his previous gainS k−1 is negative. WhenS k−1 is minus, Peter gets or loses −S k−1 . Then Peter's gainS n inn trials is the sum of “dependent” random variables. Therefore, Peter has always the chancep of recovering his minus gain *** probability function ofS n is given and the expected gain is compared with the ordinary (non-symmetric) random walk situation. It will be concluded that Peter should not play the game with one-chance recovery because whenp is less than 1/2, he must be afraid of suffering a bigger risk than the usual case.
A fundamental tenet of statistical mechanics is that the rate of collision of two objects is related to the expectation value of their relative velocities. In pioneering work by Saffman and Turner [J. Fluid Mech. 1, 1...
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A fundamental tenet of statistical mechanics is that the rate of collision of two objects is related to the expectation value of their relative velocities. In pioneering work by Saffman and Turner [J. Fluid Mech. 1, 16 (1956)], two different formulations of this tenet are used to calculate the collision kernel Gamma between two arbitrary particle size groups in a turbulent flow. The first or spherical formulation is based on the radial component w(r) of the relative velocity w between two particles: Gamma(sph) =2 pi R-2[\w(r)\], where w(r)= w.R/R, R is the separation vector, and R=\R\. The second or cylindrical formulation is based on the vector velocity itself: Gamma(cyl)= 2 pi R-2[\w\], which is supported by molecular collision statistical mechanics. Saffman and Turner obtained different results from the two formulations and attributed the difference to the form of the probability function of w used in their work. A more careful examination reveals that there is a fundamental difference between the two formulations. An underlying assumption in the second formulation is that the relative velocity at any instant is locally uniform over a spatial scale on the order of the collision radius R, which is certainly not the case in turbulent flow. Therefore, the second formulation is not expected to be rigorously correct. In fact, both our analysis and numerical simulations show that the second formulation leads to a collision kernel about 25% larger than the first formulation in isotropic turbulence. For a simple uniform shear flow, the second formulation is about 20% too large. The two formulations, however, are equivalent for treating the collision rates among random molecules and the gravitational collision rates. (C) 1998 American Institute of Physics.
It is shown that the concept ''nonlocality'' cannot he deduced, legitimately, from any physical fact. So Gamboa-Eastman's clever speculation rests upon a hypothetical construct.
It is shown that the concept ''nonlocality'' cannot he deduced, legitimately, from any physical fact. So Gamboa-Eastman's clever speculation rests upon a hypothetical construct.
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