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1

Watson, Ray, and Paul Yip. "A bivariate counting process." Journal of Applied Probability 30, no. 2 (1993): 353–64. http://dx.doi.org/10.2307/3214844.

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We consider a bivariate Markov counting process with transition probabilities having a particular structure, which includes a number of useful population processes. Using a suitable random time-scale transformation, we derive some probability statements about the process and some asymptotic results. These asymptotic results are also derived using martingale methods. Further, it is shown that these methods and results can be used for inference on the rate parameters for the process. The general epidemic model and the square law conflict model are used as illustrative examples.
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2

Camos, Valérie. "Coordination process in counting." International Journal of Psychology 38, no. 1 (2003): 24–36. http://dx.doi.org/10.1080/00207590244000269.

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3

Watson, Ray, and Paul Yip. "A bivariate counting process." Journal of Applied Probability 30, no. 02 (1993): 353–64. http://dx.doi.org/10.1017/s002190020011736x.

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We consider a bivariate Markov counting process with transition probabilities having a particular structure, which includes a number of useful population processes. Using a suitable random time-scale transformation, we derive some probability statements about the process and some asymptotic results. These asymptotic results are also derived using martingale methods. Further, it is shown that these methods and results can be used for inference on the rate parameters for the process. The general epidemic model and the square law conflict model are used as illustrative examples.
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4

Lee, Lena. "Automating the Cell Counting Process." Genetic Engineering & Biotechnology News 34, no. 15 (2014): 34–35. http://dx.doi.org/10.1089/gen.34.15.15.

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5

Freud, Thomas, and Pablo M. Rodriguez. "The Bell–Touchard counting process." Applied Mathematics and Computation 444 (May 2023): 127741. http://dx.doi.org/10.1016/j.amc.2022.127741.

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6

Tsaniya, Ulya, Triastuti Wuryandari, and Dwi Ispriyanti. "ANALISIS SURVIVAL PADA DATA KEJADIAN BERULANG MENGGUNAKAN PENDEKATAN COUNTING PROCESS." Jurnal Gaussian 11, no. 3 (2022): 377–85. http://dx.doi.org/10.14710/j.gauss.11.3.377-385.

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Asthma is a disorder that attacks the respiratory tract and causes bronchial hyperactivity to various stimuli characterized by recurrent episodic symptoms such as wheezing, coughing, shortness of breath, and heaviness in the chest. Asthma sufferers will experience exacerbations, namely episodes of asthma recurrence which gradually worsens progressively accompanied by the same symptoms. The length of time a person experiences an exacerbation can be influenced by various factors. To analyze this, the Cox regression model can be used which is within the scope of survival analysis where time is the dependent variable. In the survival analysis, asthma exacerbations were identical/recurrent events where the individual experienced the event more than once during the study. If the survival data contains identical/recurrent events, the analysis uses a counting process approach. Counting Process is an approach used to deal with survival data with identical recurrent events, meaning that recurrences are caused by the same thing, which in this case is the narrowing of the bronchioles in asthmatics. The purpose of this study was to determine the factors that cause asthma exacerbations by using a counting process approach as a data treatment for recurrent events at Diponegoro National Hospital. Based on the results of the analysis, the factors that influence the length of time a patient experiences an exacerbation are the age, gender, and type of cases
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7

Pellerey, Franco. "Shock models by underlying counting process." Journal of Applied Probability 31, no. 1 (1994): 156–66. http://dx.doi.org/10.2307/3215243.

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Suppose that a device is subjected to shocks governed by a counting process N = {N(t), t ≧0}. The probability that the device survives beyond time t is then H̄(t)=Σk=0∞Q̄ℙ[N(t)=k], where Q̄k is the probability of surviving k shocks. It is known that H is NBU if the interarrivals Uk, ∊ ℕ+, are independent and NBU, and Q̄k+j ≦ Q̄k· Q̄j holds whenever k, j ∊ ℕ. Similar results hold for the classes of the NBUE and HNBUE distributions. We show that some other ageing classes have similar properties.
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8

Suydam, Marilyn N. "Research Report: The Process of Counting." Arithmetic Teacher 33, no. 5 (1986): 29. http://dx.doi.org/10.5951/at.33.5.0029.

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Recently, a number of researchers have directed their attention to the process of counting, sometimes in connection with studies of problem solving or of addition and subtraction. The emphasis is on identifying how children learn to count or use counting; however, how the ideas children discover on their own might be applied in instruction is the ultimate goal. For instance, children might be led to discover new ideas by examining their own invented strategies.
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9

Pellerey, Franco. "Shock models by underlying counting process." Journal of Applied Probability 31, no. 01 (1994): 156–66. http://dx.doi.org/10.1017/s0021900200107417.

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Suppose that a device is subjected to shocks governed by a counting process N = {N(t), t ≧0}. The probability that the device survives beyond time t is then H̄(t)=Σk=0 ∞Q̄ℙ[N(t)=k], where Q̄k is the probability of surviving k shocks. It is known that H is NBU if the interarrivals Uk , ∊ ℕ+, are independent and NBU, and Q̄ k+j ≦ Q̄k · Q̄j holds whenever k, j ∊ ℕ. Similar results hold for the classes of the NBUE and HNBUE distributions. We show that some other ageing classes have similar properties.
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10

Klein, John. "Statistical Models Based On Counting Process." Technometrics 36, no. 1 (1994): 111–12. http://dx.doi.org/10.1080/00401706.1994.10485407.

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11

Baryshnikov, Yuliy, and Alexander Gnedin. "Counting intervals in the packing process." Annals of Applied Probability 11, no. 3 (2001): 863–77. http://dx.doi.org/10.1214/aoap/1015345351.

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12

Cha, Ji Hwan, and F. G. Badía. "ON A MULTIVARIATE GENERALIZED POLYA PROCESS WITHOUT REGULARITY PROPERTY." Probability in the Engineering and Informational Sciences 34, no. 4 (2019): 484–506. http://dx.doi.org/10.1017/s0269964819000111.

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Most of the multivariate counting processes studied in the literature are regular processes, which implies, ignoring the types of the events, the non-occurrence of multiple events. However, in practice, several different types of events may occur simultaneously. In this paper, a new class of multivariate counting processes which allow simultaneous occurrences of multiple types of events is suggested and its stochastic properties are studied. For the modeling of such kind of process, we rely on the tool of superposition of seed counting processes. It will be shown that the stochastic properties of the proposed class of multivariate counting processes are explicitly expressed. Furthermore, the marginal processes are also explicitly obtained. We analyze the multivariate dependence structure of the proposed class of counting processes.
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13

Sumita, Ushio, and Jia-Ping Huang. "Dynamic Analysis of a Unified Multivariate Counting Process and Its Asymptotic Behavior." International Journal of Mathematics and Mathematical Sciences 2009 (2009): 1–43. http://dx.doi.org/10.1155/2009/219532.

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The class of counting processes constitutes a significant part of applied probability. The classic counting processes include Poisson processes, nonhomogeneous Poisson processes, and renewal processes. More sophisticated counting processes, including Markov renewal processes, Markov modulated Poisson processes, age-dependent counting processes, and the like, have been developed for accommodating a wider range of applications. These counting processes seem to be quite different on the surface, forcing one to understand each of them separately. The purpose of this paper is to develop a unified multivariate counting process, enabling one to express all of the above examples using its components, and to introduce new counting processes. The dynamic behavior of the unified multivariate counting process is analyzed, and its asymptotic behavior ast→∞is established. As an application, a manufacturing system with certain maintenance policies is considered, where the optimal maintenance policy for minimizing the total cost is obtained numerically.
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14

Sumita, Ushio, and J. George Shanthikumar. "An age-dependent counting process generated from a renewal process." Advances in Applied Probability 20, no. 4 (1988): 739–55. http://dx.doi.org/10.2307/1427358.

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Let {N(t)} be a renewal process having the associated age process {X(t)}. Of interest is the counting process {M(t)} characterized by a non-homogeneous Poisson process with age-dependent intensity function λ (X(t)). The trivariate process {Y(t) = [M(t), N(t), X(t)]} is analyzed obtaining its Laplace transform generating function explicitly. Based on this result, asymptotic behavior of {S(t) = cM(t) + dN(t)} as t → ∞ is discussed. Furthermore, a sufficient condition is given under which {M(t), –N(t), X(t)} is stochastically monotone and associated. This condition also assures increasing stochastic convexity of {M(t)}. The usefulness of these results is demonstrated through an application to the age-dependent minimal repair problem.
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15

Sumita, Ushio, and J. George Shanthikumar. "An age-dependent counting process generated from a renewal process." Advances in Applied Probability 20, no. 04 (1988): 739–55. http://dx.doi.org/10.1017/s0001867800018358.

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Let {N(t)} be a renewal process having the associated age process {X(t)}. Of interest is the counting process {M(t)} characterized by a non-homogeneous Poisson process with age-dependent intensity function λ (X(t)). The trivariate process {Y(t) = [M(t), N(t), X(t)]} is analyzed obtaining its Laplace transform generating function explicitly. Based on this result, asymptotic behavior of {S(t) = cM(t) + dN(t)} as t → ∞ is discussed. Furthermore, a sufficient condition is given under which {M(t), –N(t), X(t)} is stochastically monotone and associated. This condition also assures increasing stochastic convexity of {M(t)}. The usefulness of these results is demonstrated through an application to the age-dependent minimal repair problem.
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16

Sztrik, J., and P. J. C. Spreij. "Counting Process Systems: Identification and Stochastic Realization." Journal of the Operational Research Society 43, no. 7 (1992): 725. http://dx.doi.org/10.2307/2583582.

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17

Aven, T. "A counting process approach to replacement models." Optimization 18, no. 2 (1987): 285–96. http://dx.doi.org/10.1080/02331938708843240.

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18

Sztrik, J. "Counting Process Systems: Identification and Stochastic Realization." Journal of the Operational Research Society 43, no. 7 (1992): 725. http://dx.doi.org/10.1057/jors.1992.104.

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19

Lutes, Loren D. "Counting level crossings by a stochastic process." Probabilistic Engineering Mechanics 22, no. 3 (2007): 293–300. http://dx.doi.org/10.1016/j.probengmech.2007.02.003.

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20

Czyż, H. "Mirror fermions and the neutrino counting process." Physics Letters B 235, no. 3-4 (1990): 322–24. http://dx.doi.org/10.1016/0370-2693(90)91972-e.

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21

Matsak, I. K. "A counting process in the max-scheme." Theory of Probability and Mathematical Statistics 91 (February 4, 2016): 115–29. http://dx.doi.org/10.1090/tpms/971.

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22

Møller, Christian Max. "A counting process approach to stochastic interest." Insurance: Mathematics and Economics 17, no. 2 (1995): 181–92. http://dx.doi.org/10.1016/0167-6687(95)00020-s.

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23

Sztrik, J. "Counting process systems: Identification and stochastic realization." European Journal of Operational Research 51, no. 1 (1991): 141–42. http://dx.doi.org/10.1016/0377-2217(91)90155-o.

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24

Di Crescenzo, Antonio, Barbara Martinucci, and Alessandra Meoli. "A fractional counting process and its connection with the Poisson process." Latin American Journal of Probability and Mathematical Statistics 13, no. 1 (2016): 291. http://dx.doi.org/10.30757/alea.v13-12.

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25

Li, Yuying, and Kristina P. Sendova. "A surplus process involving a compound Poisson counting process and applications." Communications in Statistics - Theory and Methods 49, no. 13 (2019): 3238–56. http://dx.doi.org/10.1080/03610926.2019.1586942.

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26

Neuts, Marcel F. "A non-renewal process with renewal counting distributions." Advances in Applied Probability 19, no. 1 (1987): 287–88. http://dx.doi.org/10.2307/1427384.

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A simple example is given of a point process with dependent inter-event intervals for which the distributions of the counting random variables Nt are given by the same formulas as for a renewal process. This example shows the care needed in establishing that a given point process has the renewal property, but also raises interesting questions about the class of point processes with given counting distributions.
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27

Neuts, Marcel F. "A non-renewal process with renewal counting distributions." Advances in Applied Probability 19, no. 01 (1987): 287–88. http://dx.doi.org/10.1017/s0001867800016499.

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A simple example is given of a point process with dependent inter-event intervals for which the distributions of the counting random variables Nt are given by the same formulas as for a renewal process. This example shows the care needed in establishing that a given point process has the renewal property, but also raises interesting questions about the class of point processes with given counting distributions.
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28

Chen, Yi-Hau. "Classes of life distributions and renewal counting process." Journal of Applied Probability 31, no. 4 (1994): 1110–15. http://dx.doi.org/10.2307/3215334.

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We prove that if the renewal function M(t) corresponding to a life distribution F is convex (concave) then F is NBU (NWU), and hence answer two questions posed by Shaked and Zhu (1992). Moreover, based-on the renewal function, some characterizations of the exponential distribution within certain classes of life distributions are given.
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29

KÔZUKI, Yasushi, Junko KUCHIKI, Yoshimaro TEZUKA, Tadashi NAKANO, and Teruo TSUNODA. "Preplating Process Characterization by Atmospheric Ultraviolet Photoelectron Counting." Journal of the Surface Finishing Society of Japan 48, no. 1 (1997): 102–3. http://dx.doi.org/10.4139/sfj.48.102.

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30

Patil, Prakash N., and Andrew T. A. Wood. "Counting process intensity estimation by orthogonal wavelet methods." Bernoulli 10, no. 1 (2004): 1–24. http://dx.doi.org/10.3150/bj/1077544601.

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31

K., Ratheesan, and Anilkumar P. "SMOOTHING INTENSITIES OF COUNTING PROCESS BY USING POLYNOMIAL." JP Journal of Biostatistics 18, no. 2 (2021): 209–30. http://dx.doi.org/10.17654/jb018020209.

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32

Guerineau, Lise, and Evans Gouno. "Inference for a Failure Counting Process Partially Observed." IEEE Transactions on Reliability 64, no. 1 (2015): 311–19. http://dx.doi.org/10.1109/tr.2014.2354171.

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33

Chen, Yi-Hau. "Classes of life distributions and renewal counting process." Journal of Applied Probability 31, no. 04 (1994): 1110–15. http://dx.doi.org/10.1017/s0021900200099629.

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We prove that if the renewal function M(t) corresponding to a life distribution F is convex (concave) then F is NBU (NWU), and hence answer two questions posed by Shaked and Zhu (1992). Moreover, based-on the renewal function, some characterizations of the exponential distribution within certain classes of life distributions are given.
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34

McKeague, Ian W., and Klaus J. Utikal. "Inference for a Nonlinear Counting Process Regression Model." Annals of Statistics 18, no. 3 (1990): 1172–87. http://dx.doi.org/10.1214/aos/1176347745.

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35

Aven, Terje. "Condition based replacement policies—a counting process approach." Reliability Engineering & System Safety 51, no. 3 (1996): 275–81. http://dx.doi.org/10.1016/0951-8320(95)00057-7.

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36

Ycart, Bernard. "Letter counting." Historiographia Linguistica 40, no. 3 (2013): 303–30. http://dx.doi.org/10.1075/hl.40.3.01yca.

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Summary Counting letters in written texts is a very ancient practice. It has accompanied the development of cryptology, quantitative linguistics, and statistics. In cryptology, counting frequencies of the different characters in an encrypted message is the basis of the so called frequency analysis method. In quantitative linguistics, the proportion of vowels to consonants in different languages was studied long before authorship attribution. In statistics, the alternation vowel-consonants was the only example that Markov ever gave of his theory of chained events. A short history of letter counting is presented. The three domains, cryptology, quantitative linguistics, and statistics, are then examined, focusing on the interactions with the other two fields through letter counting. As a conclusion, the eclecticism of the scholars of past centuries, their background in humanities, and their familiarity with cryptograms, are identified as contributing factors to the mutual enrichment process which is described here.
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37

Saian, Pratyaksa Ocsa Nugraha. "Parallel Counting Sort: A Modified of Counting Sort Algorithm." International Journal of Information Technology and Business 1, no. 1 (2018): 10–15. http://dx.doi.org/10.24246/ijiteb.112018.10-15.

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Sorting is one of a classic problem in computer engineer. One well-known sorting algorithm is a Counting Sort algorithm. Counting Sort had one problem, it can’t sort a positive and negative number in the same input list. Then, Modified Counting Sort created to solve that’s problem. The algorithm will split the numbers before the sorting process begin. This paper will tell another modification of this algorithm. The algorithm called Parallel Counting Sort. Parallel Counting Sort able to increase the execution time about 70% from Modified Counting Sort, especially in a big dataset (around 1000 and 10.000 numbers).
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38

Iksanov, Alexander, and Bohdan Rashytov. "A functional limit theorem for general shot noise processes." Journal of Applied Probability 57, no. 1 (2020): 280–94. http://dx.doi.org/10.1017/jpr.2019.95.

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AbstractBy a general shot noise process we mean a shot noise process in which the counting process of shots is arbitrary locally finite. Assuming that the counting process of shots satisfies a functional limit theorem in the Skorokhod space with a locally Hölder continuous Gaussian limit process, and that the response function is regularly varying at infinity, we prove that the corresponding general shot noise process satisfies a similar functional limit theorem with a different limit process and different normalization and centering functions. For instance, if the limit process for the counting process of shots is a Brownian motion, then the limit process for the general shot noise process is a Riemann–Liouville process. We specialize our result for five particular counting processes. Also, we investigate Hölder continuity of the limit processes for general shot noise processes.
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39

Anantharam, Venkat, and Takis Konstantopoulos. "A functional central limit theorem for the jump counts of Markov processes with an application to Jackson networks." Advances in Applied Probability 27, no. 2 (1995): 476–509. http://dx.doi.org/10.2307/1427836.

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Each feasible transition between two distinct states i and j of a continuous-time, uniform, ergodic, countable-state Markov process gives a counting process counting the number of such transitions executed by the process. Traffic processes in Markovian queueing networks can, for instance, be represented as sums of such counting processes. We prove joint functional central limit theorems for the family of counting processes generated by all feasible transitions. We characterize which weighted sums of counts have zero covariance in the limit in terms of balance equations in the transition diagram of the process. Finally, we apply our results to traffic processes in a Jackson network. In particular, we derive simple formulas for the asymptotic covariances between the processes counting the number of customers moving between pairs of nodes in such a network.
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40

Anantharam, Venkat, and Takis Konstantopoulos. "A functional central limit theorem for the jump counts of Markov processes with an application to Jackson networks." Advances in Applied Probability 27, no. 02 (1995): 476–509. http://dx.doi.org/10.1017/s0001867800026963.

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Each feasible transition between two distinct states i and j of a continuous-time, uniform, ergodic, countable-state Markov process gives a counting process counting the number of such transitions executed by the process. Traffic processes in Markovian queueing networks can, for instance, be represented as sums of such counting processes. We prove joint functional central limit theorems for the family of counting processes generated by all feasible transitions. We characterize which weighted sums of counts have zero covariance in the limit in terms of balance equations in the transition diagram of the process. Finally, we apply our results to traffic processes in a Jackson network. In particular, we derive simple formulas for the asymptotic covariances between the processes counting the number of customers moving between pairs of nodes in such a network.
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41

Najnudel, Joseph, and Bálint Virág. "The bead process for beta ensembles." Probability Theory and Related Fields 179, no. 3-4 (2021): 589–647. http://dx.doi.org/10.1007/s00440-021-01034-8.

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AbstractThe bead process introduced by Boutillier is a countable interlacing of the $${\text {Sine}}_2$$ Sine 2 point processes. We construct the bead process for general $${\text {Sine}}_{\beta }$$ Sine β processes as an infinite dimensional Markov chain whose transition mechanism is explicitly described. We show that this process is the microscopic scaling limit in the bulk of the Hermite $$\beta $$ β corner process introduced by Gorin and Shkolnikov, generalizing the process of the minors of the Gaussian Unitary and Orthogonal Ensembles. In order to prove our results, we use bounds on the variance of the point counting of the circular and the Gaussian beta ensembles, proven in a companion paper (Najnudel and Virág in Some estimates on the point counting of the Circular and the Gaussian Beta Ensemble, 2019).
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42

Barbora, Sanjay. "Counting Citizens in Assam." South Atlantic Quarterly 120, no. 1 (2021): 220–31. http://dx.doi.org/10.1215/00382876-8795878.

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The current protests over the government of India’s Citizenship (Amendment) Act (CAA) constitute the most resolute civic resistance to efforts at transforming the country’s political landscape. The government’s need to tamper with the existing laws and procedures for granting citizenship had a contested beginning in Assam. Here, the country’s Supreme Court mandated the enumeration of citizens under the National Register of Citizens (NRC)—a process that was partially attempted in 1951—in order to address long-standing political demands for autonomy and self-determination. Following the contested process that left close to two million people outside the register, the ruling Bharatiya Janata Party (BJP) sought to introduce CAA, ostensibly to ensure that non-Muslims were not affected by exclusion in the NRC. This article focuses on the reasons why this has not resolved the issue of citizenship in Assam, adding instead more layers to the already contentious claims over resources and territory in India’s northeast.
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43

Sicilian, S. P. "Development of Counting Strategies in Congenitally Blind Children." Journal of Visual Impairment & Blindness 82, no. 8 (1988): 331–35. http://dx.doi.org/10.1177/0145482x8808200811.

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Various counting tasks were presented to congenitally, totally blind children between the ages of three and thirteen in order to determine the behaviors they employ to ensure accurate counting. Examination of their counting behaviors revealed three dimensions of tactile strategies, each serving a specific function within the counting process. These functions include “scanning” arrays to gather information about the configuration and characteristics of objects, “organizing” the counting process based on the arrangement of objects, and “partitioning” objects already counted from those still to be counted. A developmental progression in the ontogenesis of each of these dimensions of strategic behavior was identified through an analysis of the subjects’ counting behaviors.
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44

Greenwood, P. E., and W. Wefelmeyer. "Efficient estimation in a nonlinear counting-process regression model." Canadian Journal of Statistics 19, no. 2 (1991): 165–78. http://dx.doi.org/10.2307/3315795.

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45

Oh, Changhyuck. "Derivation of the likelihood function for the counting process." Journal of the Korean Data and Information Science Society 25, no. 1 (2014): 169–76. http://dx.doi.org/10.7465/jkdi.2014.25.1.169.

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46

Zarezadeh, Somayeh, Somayeh Ashrafi, and Majid Asadi. "Network Reliability Modeling Based on a Geometric Counting Process." Mathematics 6, no. 10 (2018): 197. http://dx.doi.org/10.3390/math6100197.

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In this paper, we investigate the reliability and stochastic properties of an n-component network under the assumption that the components of the network fail according to a counting process called a geometric counting process (GCP). The paper has two parts. In the first part, we consider a two-state network (with states up and down) and we assume that its components are subjected to failure based on a GCP. Some mixture representations for the network reliability are obtained in terms of signature of the network and the reliability function of the arrival times of the GCP. Several aging and stochastic properties of the network are investigated. The reliabilities of two different networks subjected to the same or different GCPs are compared based on the stochastic order between their signature vectors. The residual lifetime of the network is also assessed where the components fail based on a GCP. The second part of the paper is concerned with three-state networks. We consider a network made up of n components which starts operating at time t = 0 . It is assumed that, at any time t > 0 , the network can be in one of three states up, partial performance or down. The components of the network are subjected to failure on the basis of a GCP, which leads to change of network states. Under these scenarios, we obtain several stochastic and dependency characteristics of the network lifetime. Some illustrative examples and plots are also provided throughout the article.
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47

Adke, S. R., and N. Balakrishna. "RENEWAL COUNTING PROCESS INDUCED BY A DISCRETE MARKOV CHAIN." Australian Journal of Statistics 34, no. 1 (1992): 115–21. http://dx.doi.org/10.1111/j.1467-842x.1992.tb01049.x.

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48

Sliwinski, Martin. "Aging and counting speed: Evidence for process-specific slowing." Psychology and Aging 12, no. 1 (1997): 38–49. http://dx.doi.org/10.1037/0882-7974.12.1.38.

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49

Ramlau-Hansen, Henrik. "Hattendorff's Theorem: A Markov chain and counting process approach." Scandinavian Actuarial Journal 1988, no. 1-3 (1988): 143–56. http://dx.doi.org/10.1080/03461238.1988.10413845.

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50

Anevski, Dragi. "Interarrival times in a counting process and bird watching." Statistica Neerlandica 61, no. 2 (2007): 198–208. http://dx.doi.org/10.1111/j.1467-9574.2007.00338.x.

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