Journal articles on the topic 'Complex random process'
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Small, Michael, Lvlin Hou, and Linjun Zhang. "Random complex networks." National Science Review 1, no. 3 (July 18, 2014): 357–67. http://dx.doi.org/10.1093/nsr/nwu021.
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Abstract Exactly what is meant by a ‘complex’ network is not clear; however, what is clear is that it is something other than a random graph. Complex networks arise in a wide range of real social, technological and physical systems. In all cases, the most basic categorization of these graphs is their node degree distribution. Particular groups of complex networks may exhibit additional interesting features, including the so-called small-world effect or being scale-free. There are many algorithms with which one may generate networks with particular degree distributions (perhaps the most famous of which is preferential attachment). In this paper, we address what it means to randomly choose a network from the class of networks with a particular degree distribution, and in doing so we show that the networks one gets from the preferential attachment process are actually highly pathological. Certain properties (including robustness and fragility) which have been attributed to the (scale-free) degree distribution are actually more intimately related to the preferential attachment growth mechanism. We focus here on scale-free networks with power-law degree sequences—but our methods and results are perfectly generic.
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Zhang, Hai Jun, Hong Fu Zuo, and Si Hong Zhu. "Study on Modelling Random Deterioration Process for Complex Repairable System." Advanced Materials Research 156-157 (October 2010): 1356–59. http://dx.doi.org/10.4028/www.scientific.net/amr.156-157.1356.
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Traditional probability statistics theory is impossible to obtain failure lifetime data by accelerated test for expensive and complex systems or equipments for real-time work. Due to the variety of system failure modes and the randomness of system deterioration process and the fuzziness of system maintenance threshold, it is difficult to estimate the random deterioration process of a complex repairable system by single parameter. In order to describe system performance deterioration more subjectly, it proposes generalized proportional intensity model(GPIM). considering the effects of various covariates such as performance parameters, environment stress, failure types and maintenance history simultaneously. This method provides a new method to solve the maintenance decision-making problem of complex repairable system. CF6-80C2A5 aero-engine is illustrated as an example for case study to indicate the obvious practical value by the method proposed herein.
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van Rijn, Monique A., Johan Marinus, Hein Putter, Sarah R. J. Bosselaar, G. Lorimer Moseley, and Jacobus J. van Hilten. "Spreading of complex regional pain syndrome: not a random process." Journal of Neural Transmission 118, no. 9 (February 18, 2011): 1301–9. http://dx.doi.org/10.1007/s00702-011-0601-1.
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Attias, H., and Y. Alhassid. "Gaussian random-matrix process and universal parametric correlations in complex systems." Physical Review E 52, no. 5 (November 1, 1995): 4776–92. http://dx.doi.org/10.1103/physreve.52.4776.
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Decreusefond, L., E. Ferraz, H. Randriambololona, and A. Vergne. "Simplicial Homology of Random Configurations." Advances in Applied Probability 46, no. 02 (June 2014): 325–47. http://dx.doi.org/10.1017/s0001867800007114.
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Given a Poisson process on a d-dimensional torus, its random geometric simplicial complex is the complex whose vertices are the points of the Poisson process and simplices are given by the C̆ech complex associated to the coverage of each point. By means of Malliavin calculus, we compute explicitly the three first-order moments of the number of k-simplices, and provide a way to compute higher-order moments. Then we derive the mean and the variance of the Euler characteristic. Using the Stein method, we estimate the speed of convergence of the number of occurrences of any connected subcomplex as it converges towards the Gaussian law when the intensity of the Poisson point process tends to infinity. We use a concentration inequality for Poisson processes to find bounds for the tail distribution of the Betti number of first order and the Euler characteristic in such simplicial complexes.
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Decreusefond, L., E. Ferraz, H. Randriambololona, and A. Vergne. "Simplicial Homology of Random Configurations." Advances in Applied Probability 46, no. 2 (June 2014): 325–47. http://dx.doi.org/10.1239/aap/1401369697.
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Given a Poisson process on a d-dimensional torus, its random geometric simplicial complex is the complex whose vertices are the points of the Poisson process and simplices are given by the C̆ech complex associated to the coverage of each point. By means of Malliavin calculus, we compute explicitly the three first-order moments of the number of k-simplices, and provide a way to compute higher-order moments. Then we derive the mean and the variance of the Euler characteristic. Using the Stein method, we estimate the speed of convergence of the number of occurrences of any connected subcomplex as it converges towards the Gaussian law when the intensity of the Poisson point process tends to infinity. We use a concentration inequality for Poisson processes to find bounds for the tail distribution of the Betti number of first order and the Euler characteristic in such simplicial complexes.
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Farahmand, K., A. Grigorash, and P. Flood. "Real almost zeros of random polynomials with complex coefficients." Journal of Applied Mathematics and Stochastic Analysis 2005, no. 2 (January 1, 2005): 195–209. http://dx.doi.org/10.1155/jamsa.2005.195.
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We present a simple formula for the expected number of times that a complex-valued Gaussian stochastic process has a zero imaginary part and the absolute value of its real part is bounded by a constant value M. We show that only some mild conditions on the stochastic process are needed for our formula to remain valid. We further apply this formula to a random algebraic polynomial with complex coefficients. We show how the above expected value in the case of random algebraic polynomials varies for different behaviour of M.
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Assimakopoulos, Nikitas A. "Random environmental processes for complex computer systems: a theoretical approach." Advances in Complex Systems 02, no. 02 (June 1999): 117–35. http://dx.doi.org/10.1142/s0219525999000072.
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In this paper, we consider various computer inventory, computer queueing and reliability computer models where complexity due to interacting components of subsystems is apparent. In particular, our analysis focuses on a multi-item inventory computer model with stochastically dependent demands, a queueing computer network where there are dependent arrival and service processes, or a reliability computer model with stochastically dependent component lifetimes. We discuss cases where this dependence is induced only by a random environmental process which the system operates in. This process represents the sources of variation that affect all deterministic and stochastic parameters of the model. Thus, not only are the parameters of the model now stochastic processes, but they are all dependent due to the common environment they are all subject to. Our objective is to provide a convincing argument that, under fairly reasonable conditions, the analytical techniques used in these models as well as their solutions are not much more complicated than those where there is no environmental variation.
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Strahov, Eugene. "Dynamical correlation functions for products of random matrices." Random Matrices: Theory and Applications 04, no. 04 (October 2015): 1550020. http://dx.doi.org/10.1142/s2010326315500203.
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We introduce and study a family of random processes with a discrete time related to products of random matrices. Such processes are formed by singular values of random matrix products, and the number of factors in a random matrix product plays a role of a discrete time. We consider in detail the case when the (squared) singular values of the initial random matrix form a polynomial ensemble, and the initial random matrix is multiplied by standard complex Gaussian matrices. In this case, we show that the random process is a discrete-time determinantal point process. For three special cases (the case when the initial random matrix is a standard complex Gaussian matrix, the case when it is a truncated unitary matrix, or the case when it is a standard complex Gaussian matrix with a source) we compute the dynamical correlation functions explicitly, and find the hard edge scaling limits of the correlation kernels. The proofs rely on the Eynard–Mehta theorem, and on contour integral representations for the correlation kernels suitable for an asymptotic analysis.
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Qi, Xing Guang, Dan Dan Dou, and Hai Lun Zhang. "Complex Paper Disease Detection Based on Probabilistic Hough Transform." Advanced Materials Research 712-715 (June 2013): 2327–30. http://dx.doi.org/10.4028/www.scientific.net/amr.712-715.2327.
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Although advantages of traditional Hough transform of such Good robustness and anti-interference have been found in the process of detection of complex paper diseases such as Streak, fold, however, quantity calculation has imposed limitation on the application of this method in dealing process demanding high instantaneity. Probabilistic Hough Transform fits in a straight line by approach of Hough transform. The approach of selecting fitting points by random drawing and combination with meter counter and output a boundary line where random drawing points locates on condition that such points satisfy limitation of threshold value which has been pre-setted is able to reduce the calculation and period of algorithm operation therefore fitts detection of complex paper diseases demanding high instantaneity.
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Gao, Qi, Xintong Ding, Feng Pan, and Weixing Li. "An improved sampling method of complex network." International Journal of Modern Physics C 25, no. 05 (March 11, 2014): 1440007. http://dx.doi.org/10.1142/s0129183114400075.
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Sampling subnet is an important topic of complex network research. Sampling methods influence the structure and characteristics of subnet. Random multiple snowball with Cohen (RMSC) process sampling which combines the advantages of random sampling and snowball sampling is proposed in this paper. It has the ability to explore global information and discover the local structure at the same time. The experiments indicate that this novel sampling method could keep the similarity between sampling subnet and original network on degree distribution, connectivity rate and average shortest path. This method is applicable to the situation where the prior knowledge about degree distribution of original network is not sufficient.
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Prishchenko, Olga, and Nadezhda Cheremskaya. "RECONSTRUCTION OF GAUSSIAN RANDOM FUNCTIONS FROM SPECTRUM DATA." Bulletin of the National Technical University "KhPI". Series: Mathematical modeling in engineering and technologies, no. 2 (November 30, 2021): 97–103. http://dx.doi.org/10.20998/2222-0631.2021.02.11.
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It is known that a stationary random process is represented as a superposition of harmonic oscillations with real frequencies and uncorrelated amplitudes. In the study of nonstationary processes, it is natural to have increasing or declining oscillationсs. This raises the problem of constructing algorithms that would allow constructing broad classes of nonstationary processes from elementary nonstationary random processes. A natural generalization of the concept of the spectrum of a nonstationary random process is the transition from the real spectrum in the case of stationary to a complex or infinite multiple spectrum in the nonstationary case. There is also the problem of describing within the correlation theory of random processes in which the spectrum has no analogues in the case of stationary random processes, namely, the spectrum point is real, but it has infinite multiplicity for the operator image of the corresponding operator, and when the spectrum itself is complex. Reconstruction of the complex spectrum of a nonstationary random function is a very important problem in both theoretical and applied aspects. In the paper the procedure of reconstruction of random process, sequence, field from a spectrum for Gaussian random functions is developed. Compared to the stationary case, there are wider possibilities, for example, the construction of a nonstationary random process with a real spectrum, which has infinite multiplicity and which can be distributed over the entire finite segment of the real axis. The presence of such a spectrum leads, in contrast to the case of a stationary random process, to the appearance of new components in the spectral decomposition of random functions that correspond to the internal states of «strings», i.e. generated by solutions of systems of equations in partial derivatives of hyperbolic type. The paper deals with various cases of the spectrum of a non-self-adjoint operator , namely, the case of a discrete spectrum and the case of a continuous spectrum, which is located on a finite segment of the real axis, which is the range of values of the real non-decreasing function a(x). The cases a(x)=0, a(x)=a0, a(x)=x and a(x) is a piecewise constant function are studied. The authors consider the recovery of nonstationary sequences for different cases of the spectrum of a non-self-adjoint operator promising since spectral decompositions are a superposition of discrete or continuous internal states of oscillators with complex frequencies and uncorrelated amplitudes and therefore have deep physical meaning.
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Sinclair, Christopher D., and Maxim L. Yattselev. "The reciprocal Mahler ensembles of random polynomials." Random Matrices: Theory and Applications 08, no. 04 (October 2019): 1950012. http://dx.doi.org/10.1142/s2010326319500126.
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We consider the roots of uniformly chosen complex and real reciprocal polynomials of degree [Formula: see text] whose Mahler measure is bounded by a constant. After a change of variables, this reduces to a generalization of Ginibre’s complex and real ensembles of random matrices where the weight function (on the eigenvalues of the matrices) is replaced by the exponentiated equilibrium potential of the interval [Formula: see text] on the real axis in the complex plane. In the complex (real) case, the random roots form a determinantal (Pfaffian) point process, and in both cases, the empirical measure on roots converges weakly to the arcsine distribution supported on [Formula: see text]. Outside this region, the kernels converge without scaling, implying among other things that there is a positive expected number of outliers away from [Formula: see text]. These kernels as well as the scaling limits for the kernels in the bulk [Formula: see text] and at the endpoints [Formula: see text] are presented. These kernels appear to be new, and we compare their behavior with related kernels which arise from the (non-reciprocal) Mahler measure ensemble of random polynomials as well as the classical Sine and Bessel kernels.
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Lapatin, Ivan L., and Anatoly A. Nazarov. "Output process of the M|GI|1 is an asymptotical renewal process." Izvestiya of Saratov University. New Series. Series: Mathematics. Mechanics. Informatics 21, no. 1 (February 24, 2021): 100–110. http://dx.doi.org/10.18500/1816-9791-2021-21-1-100-110.
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Most of the studies on models with retrials are devoted to the research of the number of applications in the system or in the source of repeated calls using asymptotic and numerical approaches or simulation. Although one of the main characteristics that determines the quality of the communication system is the number of applications served by the system per unit of time. Information on the characteristics of the output processes is of great practical interest, since the output process of one system may be incoming to another. The results of the study of the outgoing flows of queuing networks are widely used in the modeling of computer systems, in the design of data transmission networks and in the analysis of complex multi-stage production processes. In this paper, we have considered a single server system with redial, the input of which receives a stationary Poisson process. The service time in considered system is a random value with an arbitrary distribution function B(x). If the customer enters the system and finds the server busy, it instantly joins the orbit and carries out a random delay there during an exponentially distributed time. The object of study is the output process of this system. The output is characterized by the probability distribution of the number of customers that have completed service for time t. We have provided the study using asymptotic analysis method under low rate of retrials limit condition. We have shown in the paper that the output of retrial queue M|GI|1 is an asymptotical renewal process. Moreover, the lengths of the intervals in output process are the sum of an exponential random value with the parameter lambda + kappa and a random variable with the distribution function B(x). The results of a numerical experiment show that the probability distributions of the number of served customers in the system are practically the same for significantly different distribution laws B(x) of service time if the service times have the same first two moments.
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Zhang, Huai, and Hongjuan Zhang. "Determining average trapping time of delayed random walks on Apollonian network." Modern Physics Letters B 33, no. 20 (July 18, 2019): 1950231. http://dx.doi.org/10.1142/s0217984919502312.
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Designing appropriate technology to effectively control the trapping process in complex systems and achieve the desired trapping efficiency is central in the study of trapping problem in complex systems. In this paper, we study delayed random walks on Apollonian network with a trap fixed at a given initial hub node. In more detail, a stochastic parameter p was introduced in the approach to alter the transition probability of random walks. We further derive analytically the average trapping time (ATT) as the measure of trapping efficiency with the obtained analytical expression being in good agreement with the corresponding numerical solutions. The result indicates that ATT scales sublinearly with network size when [Formula: see text]. Therefore, we introduced stochastic parameter p only alter the prefactor of ATT and left the leading scaling of ATT unchanged. Our work may pave the way for understanding how to control trapping process in real complex systems.
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Ma, Shichao, Xin Ning, Liang Wang, Wantao Jia, and Wei Xu. "Complex response analysis of a non-smooth oscillator under harmonic and random excitations." Applied Mathematics and Mechanics 42, no. 5 (May 2021): 641–48. http://dx.doi.org/10.1007/s10483-021-2731-5.
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AbstractIt is well-known that practical vibro-impact systems are often influenced by random perturbations and external excitation forces, making it challenging to carry out the research of this category of complex systems with non-smooth characteristics. To address this problem, by adequately utilizing the stochastic response analysis approach and performing the stochastic response for the considered non-smooth system with the external excitation force and white noise excitation, a modified conducting process has proposed. Taking the multiple nonlinear parameters, the non-smooth parameters, and the external excitation frequency into consideration, the steady-state stochastic P-bifurcation phenomena of an elastic impact oscillator are discussed. It can be found that the system parameters can make the system stability topology change. The effectiveness of the proposed method is verified and demonstrated by the Monte Carlo (MC) simulation. Consequently, the conclusions show that the process can be applied to stochastic non-autonomous and non-smooth systems.
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Larose, Eric, Ludovic Margerin, Arnaud Derode, Bart van Tiggelen, Michel Campillo, Nikolai Shapiro, Anne Paul, Laurent Stehly, and Mickael Tanter. "Correlation of random wavefields: An interdisciplinary review." GEOPHYSICS 71, no. 4 (July 2006): SI11—SI21. http://dx.doi.org/10.1190/1.2213356.
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This paper presents an interdisciplinary review of the correlation properties of random wavefields. We expose several important theoretical results of various fields, ranging from time reversal in acoustics to transport theory in condensed matter physics. Using numerical simulations, we introduce the correlation process in an intuitive manner. We establish a fruitful mapping between time reversal and correlation, which enables us to transpose many known results from acoustics to seismology. We show that the multiple-scattering formalism developed in condensed matter physics provides a rigorous basis to analyze the field correlations in disordered media. We discuss extensively the various factors controlling and affecting the retrieval of the Green’s function of a complex medium from the correlation of either noise or coda. Acoustic imaging of complex samples in the laboratory and seismic tomography of geologic structures give a glimpse of the promising wide range of applications of the correlation method.
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Wang, Fan, Gaogao Dong, Lixin Tian, and H. Eugene Stanley. "Percolation behaviors of finite components on complex networks." New Journal of Physics 24, no. 4 (April 1, 2022): 043027. http://dx.doi.org/10.1088/1367-2630/ac5f86.
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Abstract Percolation behavior is of wide applicability and provides insight into functional structure of complex networks. Different from the percolation behaviors of giant component (GC), the finite components make one more clearly explore network percolation behaviors and critical phenomena from a microscopic perspective, especially for large-scale network systems. Here we focus on the percolation behaviors of small component π s with the size s = 1, 2, 3, … under different failure scenarios such as random attack, localized attack, target attack and intentional attack with limited knowledge. We find theoretically and via simulation that finite components all show the peak shape which is different from GC for random networks including random regular network, Erdős–R e ´ nyi networks and scale-free networks. In particular, we find a new general scaling relationship between 1 s and 1 p max , p max represents the value of p (non-failure fraction of initial nodes) corresponding to the peak point of π s in the network. This finding also provides a potential approach for determining the critical threshold and fill the gap between finite components and GC on the percolation process.
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Wang, Fan, Gaogao Dong, and Lixin Tian. "Dynamical Recovery of Complex Networks under a Localised Attack." Algorithms 14, no. 9 (September 21, 2021): 274. http://dx.doi.org/10.3390/a14090274.
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In real systems, some damaged nodes can spontaneously become active again when recovered from themselves or their active neighbours. However, the spontaneous dynamical recovery of complex networks that suffer a local failure has not yet been taken into consideration. To model this recovery process, we develop a framework to study the resilience behaviours of the network under a localised attack (LA). Since the nodes’ state within the network affects the subsequent dynamic evolution, we study the dynamic behaviours of local failure propagation and node recoveries based on this memory characteristic. It can be found that the fraction of active nodes switches back and forth between high network activity and low network activity, which leads to the spontaneous emergence of phase-flipping phenomena. These behaviours can be found in a random regular network, Erdős-Rényi network and Scale-free network, which shows that these three types of networks have the same or different resilience behaviours under an LA and random attack. These results will be helpful for studying the spontaneous recovery real systems under an LA. Our work provides insight into understanding the recovery process and a protection strategy of various complex systems from the perspective of damaged memory.
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Li, Ling Hao, and Xiao Jun Tong. "A New Video Encryption Algorithm Based on the Complex Chaotic System." Applied Mechanics and Materials 556-562 (May 2014): 3376–79. http://dx.doi.org/10.4028/www.scientific.net/amm.556-562.3376.
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In this article,a new type of video encryption system based on complex chaotic model was proposed. The algorithm selects the more complex the chaos model,generates pseudo random sequence to used encrypt the key data of encryption process,the experimental results show that this encryption algorithm has high security,fast encryption speed.
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Gorin, Vadim, and Adam W. Marcus. "Crystallization of Random Matrix Orbits." International Mathematics Research Notices 2020, no. 3 (April 3, 2018): 883–913. http://dx.doi.org/10.1093/imrn/rny052.
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Abstract Three operations on eigenvalues of real/complex/quaternion (corresponding to $\beta =1,2,4$) matrices, obtained from cutting out principal corners, adding, and multiplying matrices, can be extrapolated to general values of $\beta>0$ through associated special functions. We show that the $\beta \to \infty $ limit for these operations leads to the finite free projection, additive convolution, and multiplicative convolution, respectively. The limit is the most transparent for cutting out the corners, where the joint distribution of the eigenvalues of principal corners of a uniformly-random general $\beta $ self-adjoint matrix with fixed eigenvalues is known as the $\beta $-corners process. We show that as $\beta \to \infty $ these eigenvalues crystallize on an irregular lattice consisting of the roots of derivatives of a single polynomial. In the second order, we observe a version of the discrete Gaussian Free Field put on top of this lattice, which provides a new explanation as to why the (continuous) Gaussian Free Field governs the global asymptotics of random matrix ensembles.
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BARONE, PIERO. "ON THE UNIVERSALITY OF THE DISTRIBUTION OF THE GENERALIZED EIGENVALUES OF A PENCIL OF HANKEL RANDOM MATRICES." Random Matrices: Theory and Applications 02, no. 01 (January 2013): 1250014. http://dx.doi.org/10.1142/s2010326312500141.
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Universality properties of the distribution of the generalized eigenvalues of a pencil of random Hankel matrices, arising in the solution of the exponential interpolation problem of a complex discrete stationary process, are proved under the assumption that every finite set of random variables of the process have a multivariate spherical distribution. An integral representation of the condensed density of the generalized eigenvalues is also derived. The asymptotic behavior of this function turns out to depend only on stationarity and not on the specific distribution of the process.
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Xing, Ruru, Qingfang Yang, and Lili Zheng. "Research on Cascading Failure Model of Urban Regional Traffic Network under Random Attacks." Discrete Dynamics in Nature and Society 2018 (November 11, 2018): 1–14. http://dx.doi.org/10.1155/2018/1915695.
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For better describing the network cascading failure caused by random attacks such as traffic accidents, this paper introduces the ORNL-PSerc-Alaska (OPA) model to analyze the urban regional traffic network vulnerability. Firstly, the double-layer network model is built for analyzing the complex characteristics of the regional traffic network. Secondly, the cascading failure model is built to better describe the process of the network cascading failure under random attacks. Finally, by simulating the network failure process, the vulnerability of the traffic network will be pointed out, which provides the theoretical basis for avoiding the network cascading failure under random attacks.
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Fan, Wei, Jia-lu Li, Shun-hou Fan, Xu Liu, Run-jun Sun, Jia-guang Meng, and Cheng-kun Liu. "Random process model of mechanical property degradation in carbon fiber-reinforced plastics under thermo-oxidative aging." Journal of Composite Materials 51, no. 9 (October 13, 2016): 1253–64. http://dx.doi.org/10.1177/0021998316672089.
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The mechanical properties of carbon fiber-reinforced plastics used in aerospace are vulnerable to degradation under thermo-oxidative aging conditions. However, it is hard to establish a mechanical property prediction model for carbon fiber-reinforced plastics from thermo-oxidative aging mechanism point of view since the thermo-oxidative aging degradation processes are very complex. A mathematical model was proposed based on the theory of stochastic processes for predicting mechanical property degradation of carbon fiber-reinforced plastics under thermo-oxidative aging conditions in the present work. However, the predicted values calculated by the “random process model” were not in good agreement with experimental data. And then a “modified random process model” (namely a wider random process model) was established through Box–Cox transformation for random process model. The verification of the evaluation model showed that the modified random process model can nicely describe the mechanical performance degradation of carbon fiber-reinforced plastics with the increasing of aging time under certain aging temperatures. As the modified random process model was established without limiting the reinforced structure of carbon fiber-reinforced plastics, the described method provides an opportunity to rapidly predict the mechanical properties and the lifetime of any carbon fiber-reinforced plastics by testing the mechanical properties of carbon fiber-reinforced plastics before and after aging for a short period of time.
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Kuijlaars, Arno B. J., and Dries Stivigny. "Singular values of products of random matrices and polynomial ensembles." Random Matrices: Theory and Applications 03, no. 03 (July 2014): 1450011. http://dx.doi.org/10.1142/s2010326314500117.
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Akemann, Ipsen, and Kieburg showed recently that the squared singular values of a product of M complex Ginibre matrices are distributed according to a determinantal point process. We introduce the notion of a polynomial ensemble and show how their result can be interpreted as a transformation of polynomial ensembles. We also show that the squared singular values of the product of M - 1 complex Ginibre matrices with one truncated unitary matrix is a polynomial ensemble, and we derive a double integral representation for the correlation kernel associated with this ensemble. We use this to calculate the scaling limit at the hard edge, which turns out to be the same scaling limit as the one found by Kuijlaars and Zhang for the squared singular values of a product of M complex Ginibre matrices. Our final result is that these limiting kernels also appear as scaling limits for the biorthogonal ensembles of Borodin with parameter θ > 0, in case θ or 1/θ is an integer. This further supports the conjecture that these kernels have a universal character.
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Mazur-Śniady, Krystyna, Katarzyna Misiurek, Olga Szyłko-Bigus, and Paweł Śniady. "Fuzzy Stochastic Vibrations of Double-Beam Complex System as Model Sandwich Beam with Uncertain Parameters." ISRN Applied Mathematics 2013 (October 22, 2013): 1–12. http://dx.doi.org/10.1155/2013/340145.
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The dynamic behavior of a double Euler-Bernoulli beam system with uncertain parameters (fuzzy random variables) under a fuzzy stochastic excitation and axial compression is being considered. The beams are identical and parallel, one is above the other, and they are continuously coupled by a linear two-parameter (Pasternak subsoil) elastic element. This double Euler-Bernoulli beam system can be also treated as a theoretical model of a sandwich beam. The load process is fuzzy random both in space and time. The top beam carries a fuzzy stochastic load. The solution of the problem was found thanks to the fuzzy random dynamic influence function. The aim of the paper is to find the solution for the membership function of the probabilistic characteristics of the response of the structure.
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Li, Gao Chun, Yu Feng Wang, Ai Min Jiang, and Xiang Yi Liu. "A Micromechanical Model for Debonding Process in Composite Solid Propellants." Applied Mechanics and Materials 148-149 (December 2011): 1107–12. http://dx.doi.org/10.4028/www.scientific.net/amm.148-149.1107.
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The random distribution packing models of particles in the binder of solid propellant were generated based on the Molecular Dynamics method. The generated packing models were then analyzed by finite element method combined with the analytical method. A cohesive interface model was incorporated to capture the debonding process taking place along particles binder interface. The results show that the FEM analyses with cohesive interface can predict the complex heterogeneous stress and strain fields and the progress of debonding of particles from binder. Particles interaction significantly influences the interfacial damage evolution of propellant.
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Weiwei, Weng, Mahardhika Pratama, Andri Ashfahani, and Edward Yapp Kien Yee. "Online Semisupervised Learning Approach for Quality Monitoring of Complex Manufacturing Process." Complexity 2021 (September 1, 2021): 1–16. http://dx.doi.org/10.1155/2021/3005276.
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Data-driven quality monitoring is highly demanded in practice since it enables relieving manual quality inspection of the product quality. Conventional data-driven quality monitoring is constrained by its offline characteristic thus being unable to handle streaming nature of sensory data and nonstationary environments of machine operations. Recently, there have been pioneering works of online quality monitoring taking advantage of online learning concepts in the literature, but it is still far from realization of minimum operator intervention in the quality monitoring because it calls for full supervision in labelling data samples. This paper proposes Parsimonious Network++ (ParsNet++) as an online semisupervised learning approach being able to handle extreme label scarcity in the quality monitoring task. That is, it is capable of coping with varieties of semisupervised learning conditions including random access of ground truth and infinitely delayed access of ground truth. ParsNet++ features the one-pass learning approach to deal with streaming data while characterizing elastic structure to overcome rapidly changing data distributions. That is, it is capable of initiating its learning structure from scratch with the absence of a predefined network structure where its hidden nodes can be added and discarded on the fly in respect to drifting data distributions. Furthermore, it is equipped by a feature extraction layer in terms of 1D convolutional layer extracting natural features of multivariate time-series data samples of sensors and coping well with the many-to-one label relationship, a common problem of practical quality monitoring. Rigorous numerical evaluation has been carried out using the injection molding machine and the industrial transfer molding machine from our own projects. ParsNet++ delivers highly competitive performance even compared to fully supervised competitors.
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Lobaty, A. A., and A. Y. Bumai. "Features of construction of evaluation algorithms multidimensional random processes." «System analysis and applied information science», no. 1 (March 27, 2020): 24–32. http://dx.doi.org/10.21122/2309-4923-2020-1-24-32.
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The problem of evaluating the information which is present in random signals from various sources-meters is considered. It is assumed that the random process which is evaluated and the meter output according mathematical description of the problem are vector random processes. In this case, the dimension of the vector of the measurement can be larger than the dimension of the vector of the process being evaluated. The analysis of analytical methods and algorithms of the estimation that based on the determination of the main probabilistic characteristics of a random process by both the a priori and the a posteriori methods with various optimality criteria is carried out. Based on the analysis, the problem of complexing of the meters of the random process is considered according the proposed criterion for the maximum of posterior verisimilitude, combining the criterion of maximum verisimilitude and the criterion of maximum the a posteriori probability, general methodology complexing is developed. Proposed example of the complexing shows the efficiency of the proposed method. This approach to the construction of the algorithms of the evaluation for multidimensional random processes allows to increase the accuracy of estimation, since it takes into account additional information and its complex processing.
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Potgieter, Cornelis J., Rubin Wei, Victor Kipnis, Laurence S. Freedman, and Raymond J. Carroll. "Moment reconstruction and moment‐adjusted imputation when exposure is generated by a complex, nonlinear random effects modeling process." Biometrics 72, no. 4 (April 8, 2016): 1369–77. http://dx.doi.org/10.1111/biom.12524.
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Pant, Sangeeta, Anuj Kumar, Mangey Ram, Yury Klochkov, and Hitesh Kumar Sharma. "Consistency Indices in Analytic Hierarchy Process: A Review." Mathematics 10, no. 8 (April 7, 2022): 1206. http://dx.doi.org/10.3390/math10081206.
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A well-regarded as well as powerful method named the ‘analytic hierarchy process’ (AHP) uses mathematics and psychology for making and analysing complex decisions. This article aims to present a brief review of the consistency measure of the judgments in AHP. Judgments should not be random or illogical. Several researchers have developed different consistency measures to identify the rationality of judgments. This article summarises the consistency measures which have been proposed so far in the literature. Moreover, this paper describes briefly the functional relationships established in the literature among the well-known consistency indices. At last, some thoughtful research directions that can be helpful in further research to develop and improve the performance of AHP are provided as well.
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Lu, Lin, Liguo Yang, and Xiaochun Luo. "Graph Evaluation and Review Technique for Emergency Logistics Distribution in Complex Environment." Discrete Dynamics in Nature and Society 2021 (April 3, 2021): 1–10. http://dx.doi.org/10.1155/2021/6698910.
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Emergency logistics is one of the important measures to solve the unconventional sudden disaster. The research on the distribution design of emergency logistics project has an important supporting role for the whole emergency rescue system. Therefore, it is necessary to analyze and plan the emergency logistics project scientifically in order to better serve the emergency rescue system. In view of the defect that the current emergency logistics model cannot completely describe the whole emergency logistics process, this paper proposes a new emergency logistics distribution model by using GERT random network. From the perspective of system, this model fully considers the possible situation in the process of emergency material transportation and puts forward the corresponding countermeasures, so as to improve the transportation efficiency of rescue materials in the actual disaster relief activities to speed up disaster relief. Based on the properties of moment generating function and the calculation method of Mason formula, this paper fully considers the success probability, risk probability, delivery time, and other factors of the distribution route and puts forward the transshipment scheme of each logistics site to the disaster sites. After that, the effectiveness of GERT stochastic network in the process of emergency distribution is verified by an example of a logistics distribution route, which provides decision-making basis for relevant departments. Compared with the literature, this paper uses GERT network model to intuitively and clearly express the overall process of emergency material distribution, breaks through the thinking mode of simply choosing the distribution path in the distribution process, combines with the dynamic changes of the distribution environment, and comprehensively considers the timeliness and traffic capacity of emergency material distribution in sudden disasters, so as to provide reference for emergency management in complex and random situations for decision-making reference.
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Zhang, Jia, Xiang Wang, Fang Deng, Bin Xin, and Wenjie Chen. "Battlefield Agent Decision-Making Based on Markov Decision Process." Journal of Advanced Computational Intelligence and Intelligent Informatics 21, no. 2 (March 15, 2017): 221–27. http://dx.doi.org/10.20965/jaciii.2017.p0221.
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Battlefield decision-making is an important part of modern information warfare. It can analyze and integrate battlefield information, reduce operators’ work and assist them to make decisions quickly in complex battlefield environment. The paper presents a dynamic battlefield decision-making method based on Markov Decision Processes (MDP). By this method, operators can get decision support quickly in the case of incomplete information. In order to improve the credibility of decisions, dynamic adaptability and intelligence, softmax regression and random forest are introduced to improve the MDP model. Simulations show that the method is intuitive and practical, and has remarkable advantages in solving the dynamic decision problems under incomplete information.
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Ugrin-parac, D. "Problem of uniqueness in the renewal process generated by the uniform distribution." Journal of Applied Mathematics and Stochastic Analysis 5, no. 4 (January 1, 1992): 291–305. http://dx.doi.org/10.1155/s1048953392000248.
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The renewal process generated by the uniform distribution, when interpreted as a transformation of the uniform distribution into a discrete distribution, gives rise to the question of uniqueness of the inverse image. The paper deals with a particular problem from the described domain, that arose in the construction of a complex stochastic test intended to evaluate pseudo-random number generators. The connection of the treated problem with the question of a unique integral representation of Gamma-function is also mentioned.
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Li, Chunquan, and Jianhua Jin. "A Scalar Expected Value of Intuitionistic Fuzzy Random Individuals and Its Application to Risk Evaluation in Insurance Companies." Mathematical Problems in Engineering 2018 (2018): 1–16. http://dx.doi.org/10.1155/2018/8319859.
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Randomness and uncertainty always coexist in complex systems such as decision-making and risk evaluation systems in the real world. Intuitionistic fuzzy random variables, as a natural extension of fuzzy and random variables, may be a useful tool to characterize some high-uncertainty phenomena. This paper presents a scalar expected value operator of intuitionistic fuzzy random variables and then discusses some properties concerning the measurability of intuitionistic fuzzy random variables. In addition, a risk model based on intuitionistic fuzzy random individual claim amount in insurance companies is established, in which the claim number process is regarded as a Poisson process. The mean chance of the ultimate ruin is investigated in detail. In particular, the expressions of the mean chance of the ultimate ruin are presented in the cases of zero initial surplus and arbitrary initial surplus, respectively, if individual claim amount is an exponentially distributed intuitionistic fuzzy random variable. Finally, two illustrated examples are provided.
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Mi, Yan, Hengwei Zhang, Hao Hu, Jinglei Tan, and Jindong Wang. "Optimal Network Defense Strategy Selection Method: A Stochastic Differential Game Model." Security and Communication Networks 2021 (August 21, 2021): 1–16. http://dx.doi.org/10.1155/2021/5594697.
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In a real-world network confrontation process, attack and defense actions change rapidly and continuously. The network environment is complex and dynamically random. Therefore, attack and defense strategies are inevitably subject to random disturbances during their execution, and the transition of the network security state is affected accordingly. In this paper, we construct a network security state transition model by referring to the epidemic evolution process, use Gaussian noise to describe random effects during the strategy execution, and introduce a random disturbance intensity factor to describe the degree of random effects. On this basis, we establish an attack-defense stochastic differential game model, propose a saddle point equilibrium solution method, and provide an algorithm to select the optimal defense strategy. Our method achieves real-time defense decision-making in network attack-defense scenarios with random disturbances and has better real-time performance and practicality than current methods. Results of a simulation experiment show that our model and algorithm are effective and feasible.
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Kotsonis, S. J., and P. D. Spanos. "Chaotic and Random Whirling Motion of Drillstrings." Journal of Energy Resources Technology 119, no. 4 (December 1, 1997): 217–22. http://dx.doi.org/10.1115/1.2794993.
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Lateral vibrations of stabilized bottomhole assemblies of drillstrings often exhibit quite complicated patterns. Previous work has taken into account nonlinearities due to fluid damping, wall contact, eccentric collars, and initial curvature of the collar. This paper addresses the effects of these forces, along with linear and parametric excitation of the lateral motion due to an applied dynamic weight on bit (WOB). Four state-space nonlinear ordinary differential equations in two-dimensional space are used to describe the model. A time variant zero-mean axial WOB is considered and described as a stationary random process. Random and chaotic whirling characteristics of drillstrings are investigated using the minimum phase-volume deconvolution technique. The reported study serves to point out that even in ordinary engineering practice problems, rather complex phenomena can appear, and should thus be taken into consideration in the design and operation stages.
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Cranmer, Skyler J., Bruce A. Desmarais, and Elizabeth J. Menninga. "Complex Dependencies in the Alliance Network." Conflict Management and Peace Science 29, no. 3 (July 2012): 279–313. http://dx.doi.org/10.1177/0738894212443446.
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The multifaceted and strategic interactions inherent in the formation of international military pacts render the alliance decisions of states highly interdependent. Our aim here is to model the network of alliances in such a way as to capture the effects of covariates and account for the complex dependencies inherent in the network. Regression analysis, due to its foundational assumption of conditional independence, cannot be used to analyze alliance decisions specifically and interdependent decisions generally. We demonstrate how alliance decisions are interdependent and define the problems associated with the regression analysis of nonindependent dyads. We then show that alliances can naturally be conceived of as constituting a network, where alliance formation is an inherently interdependent process. We proceed by introducing the exponential random graph model for analyzing interdependence in the alliance network and estimating the effect of covariates on alliances.
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Dolaeva, A. R., and T. A. Medvedeva. "Mathematical modeling of production process using cluster analysis methods." Journal of Physics: Conference Series 2131, no. 3 (December 1, 2021): 032097. http://dx.doi.org/10.1088/1742-6596/2131/3/032097.
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Abstract Manufacturing process management is a complex problem characterized by decision-making throughout the entire production process and is reduced to finding the best set of possible (alternative) in terms of some criterion or criteria for the use of available resources. The goal of the production process optimization is to analyze a set of alternative production options in complex systems and to determine the most rational possible state depending on the selected management strategies. The system contains many connections between elements and is influenced by random factors. It is not possible to create a real model for the system that is described analytically, but it can be investigated by using simulation modeling. In the mathematical modeling of the production process cluster analysis methods are used which allow to process a large amount of data from all possible states of the system and divide them into similar aggregates according to several characteristics. The analysis of the formed groups is carried out and the regularities that have the most significant impact on the occurrence of states into clusters are revealed.
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Matcharashvili, Teimuraz, Takahiro Hatano, Tamaz Chelidze, and Natalia Zhukova. "Simple statistics for complex Earthquake time distributions." Nonlinear Processes in Geophysics 25, no. 3 (July 10, 2018): 497–510. http://dx.doi.org/10.5194/npg-25-497-2018.
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Abstract. Here we investigated a statistical feature of earthquake time distributions in the southern California earthquake catalog. As a main data analysis tool, we used a simple statistical approach based on the calculation of integral deviation times (IDT) from the time distribution of regular markers. The research objective is to define whether and when the process of earthquake time distribution approaches to randomness. Effectiveness of the IDT calculation method was tested on the set of simulated color noise data sets with the different extent of regularity, as well as for Poisson process data sets. Standard methods of complex data analysis have also been used, such as power spectrum regression, Lempel and Ziv complexity, and recurrence quantification analysis, as well as multiscale entropy calculations. After testing the IDT calculation method for simulated model data sets, we have analyzed the variation in the extent of regularity in the southern California earthquake catalog. Analysis was carried out for different periods and at different magnitude thresholds. It was found that the extent of the order in earthquake time distributions is fluctuating over the catalog. Particularly, we show that in most cases, the process of earthquake time distributions is less random in periods of strong earthquake occurrence compared to periods with relatively decreased local seismic activity. Also, we noticed that the strongest earthquakes occur in periods when IDT values increase.
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Du, Feng, Zhi Wei Guan, and Yi Zhou. "Reliability Evaluation for Complex Machinery Products." Key Engineering Materials 480-481 (June 2011): 763–68. http://dx.doi.org/10.4028/www.scientific.net/kem.480-481.763.
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For those large-scale and complex mechanical products, considering economy and applicability, these products are impossible to be discarded as soon as they take place malfunction. Generally, they can be reused again and again after be repaired repeatedly, that is, they usually have multi-lifespan. Accordingly, it is very necessary to establish a kind of proper reliability evaluation mode for these complex repairable products. In this paper, the treatment procedure of the reliability test data for these repairable products is researched based on the repairable reliability theory, and the method of model identification about failure distributions law is proposed. In addition, how to reasonably determine or predict product lives by using random process model is also introduced. Finally, an analysis case for putting this mean into practice is expounded. This method for product reliability analysis is suitable to most large-scale and complex mechanical products.
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Owada, Takashi, and Andrew M. Thomas. "Limit theorems for process-level Betti numbers for sparse and critical regimes." Advances in Applied Probability 52, no. 1 (March 2020): 1–31. http://dx.doi.org/10.1017/apr.2019.50.
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AbstractThe objective of this study is to examine the asymptotic behavior of Betti numbers of Čech complexes treated as stochastic processes and formed from random points in the d-dimensional Euclidean space ${\mathbb{R}}^d$ . We consider the case where the points of the Čech complex are generated by a Poisson process with intensity nf for a probability density f. We look at the cases where the behavior of the connectivity radius of the Čech complex causes simplices of dimension greater than $k+1$ to vanish in probability, the so-called sparse regime, as well when the connectivity radius is of the order of $n^{-1/d}$ , the critical regime. We establish limit theorems in the aforementioned regimes: central limit theorems for the sparse and critical regimes, and a Poisson limit theorem for the sparse regime. When the connectivity radius of the Čech complex is $o(n^{-1/d})$ , i.e. the sparse regime, we can decompose the limiting processes into a time-changed Brownian motion or a time-changed homogeneous Poisson process respectively. In the critical regime, the limiting process is a centered Gaussian process but has a much more complicated representation, because the Čech complex becomes highly connected with many topological holes of any dimension.
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Lobaty, A. A., and A. S. Radkevich. "Stepwise fuzzy correction of the algorithm filters of random signals." «System analysis and applied information science», no. 1 (July 5, 2019): 35–40. http://dx.doi.org/10.21122/2309-4923-2019-1-35-40.
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The task of estimating the information contained in random signals from various sources – meters. It is assumed that the gauges are discrete and are described, like the original process assessed, by a discrete mathematical model in the form of difference equations. As an estimation algorithm, we consider a discrete Kalman filter, which, in the general case, when mathematical models are inadequate to real processes, can give distorted information. To improve the accuracy of estimation, it is proposed to apply the integration of all possible meters with the introduction of additional a priori information using a fuzzy logic system. At the same time, it is proposed to make a transition from the obtained probability characteristics of the estimated process to the membership functions of fuzzy logic based on the output filter parameters using the normalization of the posterior probability density. This approach allows to increase the accuracy of estimation, as it takes into account additional information and its complex processing.
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Çekyay, Bora, and Süleyman Özekici. "OPTIMAL MAINTENANCE OF SEMI-MARKOV MISSIONS." Probability in the Engineering and Informational Sciences 29, no. 1 (September 15, 2014): 77–98. http://dx.doi.org/10.1017/s0269964814000229.
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We analyze optimal replacement and repair problems of semi-Markov missions that are composed of phases with random sequence and durations. The mission process is the minimal semi-Markov process associated with a Markov renewal process. The system is a complex one consisting of non-identical components whose failure properties depend on the mission process. We prove some monotonicity properties for the optimal replacement policy and analyze the optimal repair problem under different cost structures.
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Decreusefond, Laurent, Ian Flint, and Anais Vergne. "A note on the simulation of the Ginibre point process." Journal of Applied Probability 52, no. 04 (December 2015): 1003–12. http://dx.doi.org/10.1017/s002190020011304x.
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The Ginibre point process (GPP) is one of the main examples of determinantal point processes on the complex plane. It is a recurring distribution of random matrix theory as well as a useful model in applied mathematics. In this paper we briefly overview the usual methods for the simulation of the GPP. Then we introduce a modified version of the GPP which constitutes a determinantal point process more suited for certain applications, and we detail its simulation. This modified GPP has the property of having a fixed number of points and having its support on a compact subset of the plane. See Decreusefond et al. (2013) for an extended version of this paper.
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Decreusefond, Laurent, Ian Flint, and Anais Vergne. "A note on the simulation of the Ginibre point process." Journal of Applied Probability 52, no. 4 (December 2015): 1003–12. http://dx.doi.org/10.1239/jap/1450802749.
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The Ginibre point process (GPP) is one of the main examples of determinantal point processes on the complex plane. It is a recurring distribution of random matrix theory as well as a useful model in applied mathematics. In this paper we briefly overview the usual methods for the simulation of the GPP. Then we introduce a modified version of the GPP which constitutes a determinantal point process more suited for certain applications, and we detail its simulation. This modified GPP has the property of having a fixed number of points and having its support on a compact subset of the plane. See Decreusefond et al. (2013) for an extended version of this paper.
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Jarus, Tal, and Tzipi Gutman. "Effects of Cognitive Processes and Task Complexity on Acquisition, Retention, and Transfer of Motor Skills." Canadian Journal of Occupational Therapy 68, no. 4 (October 2001): 255–64. http://dx.doi.org/10.1177/000841740106800409.
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This experiment was designed to investigate the effect of cognitive problem-solving operations (termed contextual interference) and complexity of tasks on the acquisition retention and transfer of motor skills. Ninety-six children, ages 7.5-9.5 practised the task of throwing beanbags under either low contextual interference (blocked practice), high contextual interference (random practice) or medium contextual interference (combined practice). Half of the participants acquired a complex task and the other half a simple task. All participants performed 30 acquisition trials, 9 retention trials and 4 transfer trials. Results indicated that participants who practised in the blocked practice group did not differ in their performance whether they acquired complex or simple tasks. On the other hand, participants from the random and combined practice groups who acquired simple tasks performed better than those who acquired complex tasks. These findings support the hypothesis that there is a limit to the interference during practice that will benefit retention and transfer, thus creating the contextual interference effect. It seems that the complex-task condition combined with random or combined practice schedule increased the difficulty of acquisition, possibly impeding the cognitive processing during acquisition, thus impairing the learning process.
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Wang, Hongxing, and Yu Jiang. "Performance Reliability Prediction of Complex System Based on the Condition Monitoring Information." Mathematical Problems in Engineering 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/836517.
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Complex system performance reliability prediction is one of the means to understand complex systems reliability level, make maintenance decision, and guarantee the safety of operation. By the use of complex system condition monitoring information and condition monitoring information based on support vector machine, the paper aims to provide an evaluation of the degradation of complex system performance. With degradation assessment results as input variables, the prediction model of reliability is established in Winer random process. Taking the aircraft engine as an example, the effectiveness of the proposed method is verified in the paper.
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Gadomski, A. "A Simple Phenomenological Model of the Stress Relaxation in Slowly Evolving 3D Polycrystalline Materials." Modern Physics Letters B 11, no. 15 (June 30, 1997): 645–57. http://dx.doi.org/10.1142/s0217984997000797.
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The phenomenon of propagation of a stress field through complex 3d polycrystalline materials along the grain boundaries performing very slow random motion is studied. After applying the Hall–Petch coupling relation it turns out that the relaxation process proceeds in time anomalously. As a consequence, a fractional evolution equation of order one half for the relaxation function is postulated and its solutions are presented. Interpretations of the process in terms of the diffusion on a comb-like structure (antipersistent Random Walk with d w =4 and/or the generalized Gauss–Kolmogorov (in)homogeneous turbulence scenario with the Hurst exponent of H = 1/4 are proposed.
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López-Rodríguez, Irene, Cesár F. Reyes-Manzano, Ariel Guzmán-Vargas, and Lev Guzmán-Vargas. "The Complex Structure of the Pharmacological Drug–Disease Network." Entropy 23, no. 9 (August 31, 2021): 1139. http://dx.doi.org/10.3390/e23091139.
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The complexity of drug–disease interactions is a process that has been explained in terms of the need for new drugs and the increasing cost of drug development, among other factors. Over the last years, diverse approaches have been explored to understand drug–disease relationships. Here, we construct a bipartite graph in terms of active ingredients and diseases based on thoroughly classified data from a recognized pharmacological website. We find that the connectivities between drugs (outgoing links) and diseases (incoming links) follow approximately a stretched-exponential function with different fitting parameters; for drugs, it is between exponential and power law functions, while for diseases, the behavior is purely exponential. The network projections, onto either drugs or diseases, reveal that the co-ocurrence of drugs (diseases) in common target diseases (drugs) lead to the appearance of connected components, which varies as the threshold number of common target diseases (drugs) is increased. The corresponding projections built from randomized versions of the original bipartite networks are considered to evaluate the differences. The heterogeneity of association at group level between active ingredients and diseases is evaluated in terms of the Shannon entropy and algorithmic complexity, revealing that higher levels of diversity are present for diseases compared to drugs. Finally, the robustness of the original bipartite network is evaluated in terms of most-connected nodes removal (direct attack) and random removal (random failures).