scholarly journals Random walks in a queueing network environment

2016 ◽  
Vol 53 (2) ◽  
pp. 448-462 ◽  
Author(s):  
M. Gannon ◽  
E. Pechersky ◽  
Y. Suhov ◽  
A. Yambartsev
Keyword(s):  
Random Walks ◽  
Stationary Distribution ◽  
Detailed Balance ◽  
Queueing Network ◽  
Main Tool ◽  
Product Formula ◽  
Network Environment ◽  
Strong Correlations ◽  
Balance Equations ◽  
The Difference

Abstract We propose a class of models of random walks in a random environment where an exact solution can be given for a stationary distribution. The environment is cast in terms of a Jackson/Gordon–Newell network although alternative interpretations are possible. The main tool is the detailed balance equations. The difference compared to earlier works is that the position of the random walk influences the transition intensities of the network environment and vice versa, creating strong correlations. The form of the stationary distribution is closely related to the well-known product formula.

Dielectronic Recombination in the Average-Atom Model

1988 ◽  
Vol 102 ◽  
pp. 215
Author(s):  
R.M. More ◽  
G.B. Zimmerman ◽  
Z. Zinamon
Keyword(s):  
Detailed Balance ◽  
Systematic Errors ◽  
Dielectronic Recombination ◽  
Rate Equations ◽  
Strong Correlations ◽  
Dense Plasmas ◽  
Atom Model ◽  
New Feature ◽  
Average Atom Model ◽  
Attachment Process

Autoionization and dielectronic attachment are usually omitted from rate equations for the non–LTE average–atom model, causing systematic errors in predicted ionization states and electronic populations for atoms in hot dense plasmas produced by laser irradiation of solid targets. We formulate a method by which dielectronic recombination can be included in average–atom calculations without conflict with the principle of detailed balance. The essential new feature in this extended average atom model is a treatment of strong correlations of electron populations induced by the dielectronic attachment process.

Approximating the stationary distribution of an infinite stochastic matrix

1991 ◽  
Vol 28 (1) ◽  
pp. 96-103 ◽  
Author(s):  
Daniel P. Heyman
Keyword(s):  
Markov Chain ◽  
Steady State ◽  
Stationary Distribution ◽  
Numerical Approximation ◽  
Stochastic Matrix ◽  
Sufficient Conditions ◽  
Finite System ◽  
Balance Equations ◽  
The Given ◽  
Steady State Balance

We are given a Markov chain with states 0, 1, 2, ···. We want to get a numerical approximation of the steady-state balance equations. To do this, we truncate the chain, keeping the first n states, make the resulting matrix stochastic in some convenient way, and solve the finite system. The purpose of this paper is to provide some sufficient conditions that imply that as n tends to infinity, the stationary distributions of the truncated chains converge to the stationary distribution of the given chain. Our approach is completely probabilistic, and our conditions are given in probabilistic terms. We illustrate how to verify these conditions with five examples.

Limit theorems and absorption problems for quantum radom walks in one dimension

2002 ◽  
Vol 2 (Special) ◽  
pp. 578-595
Author(s):  
N. Konno
Keyword(s):  
Random Walks ◽  
Limit Theorems ◽  
The Other ◽  
One Dimension ◽  
Unitary Matrices ◽  
Quantum Random Walks ◽  
One Dimensional ◽  
The Difference ◽  
The One

In this paper we consider limit theorems, symmetry of distribution, and absorption problems for two types of one-dimensional quantum random walks determined by $2 \times 2$ unitary matrices using our PQRS method. The one type was introduced by Gudder in 1988, and the other type was studied intensively by Ambainis et al. in 2001. The difference between both types of quantum random walks is also clarified.

Exploring activity-driven network with biased walks

2017 ◽  
Vol 28 (09) ◽  
pp. 1750111
Author(s):  
Yan Wang ◽  
Ding Juan Wu ◽  
Fang Lv ◽  
Meng Long Su
Keyword(s):  
Random Walk ◽  
Diffusion Process ◽  
Random Walks ◽  
Stationary Distribution ◽  
Significant Role ◽  
Search Strategy ◽  
Transition Probability ◽  
Edge Weighting ◽  
Coverage Function ◽  
Analytical Expressions

We investigate the concurrent dynamics of biased random walks and the activity-driven network, where the preferential transition probability is in terms of the edge-weighting parameter. We also obtain the analytical expressions for stationary distribution and the coverage function in directed and undirected networks, all of which depend on the weight parameter. Appropriately adjusting this parameter, more effective search strategy can be obtained when compared with the unbiased random walk, whether in directed or undirected networks. Since network weights play a significant role in the diffusion process.

Winding angle and maximum winding angle of the two-dimensional random walk

1991 ◽  
Vol 28 (4) ◽  
pp. 717-726 ◽  
Author(s):  
Claude Bélisle ◽  
Julian Faraway
Keyword(s):  
Asymptotic Behavior ◽  
Brownian Motion ◽  
Random Walk ◽  
Random Walks ◽  
Computer Simulations ◽  
Asymptotic Distributions ◽  
Two Dimensional ◽  
Exact Distributions ◽  
The Difference ◽  
Winding Angle

Recent results on the winding angle of the ordinary two-dimensional random walk on the integer lattice are reviewed. The difference between the Brownian motion winding angle and the random walk winding angle is discussed. Other functionals of the random walk, such as the maximum winding angle, are also considered and new results on their asymptotic behavior, as the number of steps increases, are presented. Results of computer simulations are presented, indicating how well the asymptotic distributions fit the exact distributions for random walks with 10m steps, for m = 2, 3, 4, 5, 6, 7.

Comparisons of Accelerometer and Pedometer Determined Steps in Free Living Samples

2011 ◽  
Vol 8 (3) ◽  
pp. 390-397 ◽  
Author(s):  
Timothy K. Behrens ◽  
Mary K. Dinger
Keyword(s):  
Secondary Analysis ◽  
Mean Difference ◽  
Measurement Bias ◽  
Strong Correlations ◽  
Free Living ◽  
Analytical Strategies ◽  
The Mean ◽  
The Difference

Background:The purpose of this study was to compare steps·d-1 between an accelerometer and pedometer in 2 free-living samples.Methods:Data from 2 separate studies were used for this secondary analysis (Sample 1: N = 99, Male: n = 28, 20.9 ± 1.4 yrs, BMI = 27.2 ± 5.0 kg·m-2, Female: n = 71, 20.9 ± 1.7 yrs, BMI = 22.7 ± 3.0 kg·m-2; Sample 2: N = 74, Male: n = 27, 38.0 ± 9.5 yrs, BMI = 25.7 ± 4.5 kg·m-2, Female: n = 47, 38.7 ± 10.1 yrs, BMI = 24.6 ± 4.0 kg·m-2). Both studies used identical procedures and analytical strategies.Results:The mean difference in steps·d-1 for the week was 1643.4 steps·d-1 in Study 1 and 2199.4 steps·d-1 in Study 2. There were strong correlations between accelerometer- and pedometer-determined steps·d-1 in Study 1 (r = .85, P < .01) and Study 2 (r = 0.87, P < .01). Bland-Altman plots indicated agreement without bias between steps recorded from the devices in Study 1 (r = −0.14, P < .17) and Study 2 (r = −0.09, P < .40). Correlations examining the difference between accelerometer–pedometer steps·d-1 and MVPA resulted in small, inverse correlations (range: r = −0.03 to −0.28).Conclusions:These results indicate agreement between accelerometer- and pedometer-determined steps·d-1; however, measurement bias may still exist because of known sensitivity thresholds between devices.

Insensitivity and product-form decomposability of reallocatable GSMP

1993 ◽  
Vol 25 (2) ◽  
pp. 415-437 ◽  
Author(s):  
Masakiyo Miyazawa
Keyword(s):  
Stochastic Process ◽  
Stationary Distribution ◽  
Jump Process ◽  
Product Form ◽  
Balance Equations ◽  
Independent Components ◽  
Extended Sense ◽  
Wide Range ◽  
Standard Models

A stochastic process, called reallocatable GSMP (RGSMP for short), is introduced in order to study insensitivity of its stationary distribution. RGSMP extends GSMP with interruptions, and is applicable to a wide range of queues, from the standard models such as BCMP and Kelly's network queues to new ones such as their modifications with interruptions and Serfozo's (1989) non-product form network queues, and can be used to study their insensitivity in a unified way. We prove that RGSMP supplemented by the remaining lifetimes is product-form decomposable, i.e. its stationary distribution splits into independent components if and only if a version of the local balance equations hold, which implies insensitivity of the RGSMP scheme in a certain extended sense. Various examples of insensitive queues are given, which include new results. Our proofs are based on the characterization of a stationary distribution for SCJP (self-clocking jump process) of Miyazawa (1991).

scholarly journals Efficient circuits for quantum walks

2010 ◽  
Vol 10 (5&6) ◽  
pp. 420-434
Author(s):  
C.-F. Chiang ◽  
D. Nagaj ◽  
P. Wocjan
Keyword(s):  
Markov Chain ◽  
Random Walk ◽  
Random Walks ◽  
Probability Distributions ◽  
Quantum Walk ◽  
Quantum Walks ◽  
Problem Size ◽  
Integrable Probability ◽  
The Difference ◽  
General Method

We present an efficient general method for realizing a quantum walk operator corresponding to an arbitrary sparse classical random walk. Our approach is based on Grover and Rudolph's method for preparing coherent versions of efficiently integrable probability distributions \cite{GroverRudolph}. This method is intended for use in quantum walk algorithms with polynomial speedups, whose complexity is usually measured in terms of how many times we have to apply a step of a quantum walk \cite{Szegedy}, compared to the number of necessary classical Markov chain steps. We consider a finer notion of complexity including the number of elementary gates it takes to implement each step of the quantum walk with some desired accuracy. The difference in complexity for various implementation approaches is that our method scales linearly in the sparsity parameter and poly-logarithmically with the inverse of the desired precision. The best previously known general methods either scale quadratically in the sparsity parameter, or polynomially in the inverse precision. Our approach is especially relevant for implementing quantum walks corresponding to classical random walks like those used in the classical algorithms for approximating permanents \cite{Vigoda, Vazirani} and sampling from binary contingency tables \cite{Stefankovi}. In those algorithms, the sparsity parameter grows with the problem size, while maintaining high precision is required.

scholarly journals ANALYSIS OF THE EFFICIENCY OF COMPLEX TREATMENT OF PATIENTS WITH GENERALIZED PERIODONTITIS ACCORDING TO THE CHANGES IN THE ACTIVITY OF BLOOD SERUM ENZYMES

2021 ◽  
pp. 38-43
Author(s):  
H.M. Melnychuk ◽  
R.S. Kashivska ◽  
H.D. Semeniuk ◽  
N.I. Shovkova ◽  
A.S. Melnychuk ◽  
...  
Keyword(s):  
Blood Serum ◽  
Serum Enzymes ◽  
Arginase Activity ◽  
Healthy People ◽  
Comprehensive Treatment ◽  
Complex Treatment ◽  
Strong Correlations ◽  
Initial Degree ◽  
Activity Of Enzymes ◽  
The Difference

Introduction. The mechanisms of generalized periodontitis (GP) development and methods of its treatment remain obscure, so it is important to study changes in the activity of enzymes responsible for maintaining homeostasis, as well as the inclusion of medicines that regulate them into the complex treatment. Aim of research is to study the influence of comprehensive treatment in patients with GP on the dynamics of the activity of indicator blood serum enzymes in different observation periods. Methods. There were examined 29 people with a healthy periodontium and 143 patients with GP aged 19-45 years, somatically healthy, before, immediately after the treatment, after 6 and 12 months. Patients were divided into subgroups with chronic (A) and acute (B) course: IA and IB – the initial degree; IIA and IIB – the I degree; IIIA and IIIB – the II degree. The activity of lactate-dehydrogenase (LDG), arginase and sorbitol dehydrogenase (SDG) in blood serum has been studied. In addition to the basic periodontal therapy, the microalgal medicine Spirulina platensis was prescribed endogenously, and the paste with the same amount of spirulina powder and enterosorbent and 0.05% chlorhexidine bigluconate solution was exogenously prescribed. Results. In patients with IA and IB subgroups, LDG activity has increased in 1.37- and 1.48-times (p1 <0.01; p1 = 0.001). Under the influence of treatment, it has decreased in all patients, especially after 6 months – in 1.33- and 1.50-times (p2<0.001), but after 12 months it has been increased more (p2> 0.05; p2 <0.05). Arginase activity in IA and IB subgroups has reduced in 1.23- and 1.31-times (p1<0.05; p1=0.005). Due to the therapy, it has increased immediately, after 6 and 12 months, respectively in 1.23- and 1.26-times; in 1.21- and 1.25-times, and in 1.20-1.23-times (p2<0.05; p2> 0.05; p1> 0.05). In subgroups IA and IB, SDG activity has increased in 1.15- and 1.17-times (p1> 0.05), and after the treatment it has decreased immediately in 1.14- and 1.16-times (p2 <0.05); later it increased, but differed slightly from the norm (p1> 0.05). LDG activity in subgroups IIA and IIB has increased in 1.38- and 1.54-times (p1 <0.01; p1=0.001). After the treatment in subgroup IIA, it has decreased in 1.21-times immediately and after 6 months (p2<0.005), and a year later it has increased (p2>0.05; p1>0.05); in subgroup IIB it has decreased in 1.33-, 1.39- and 1.24-times (p2<0.05; p2<0.01; p2 <0.05 and p1> 0.05). In subgroups IIA and IIB, arginase activity has reduced in 1.32-times (p1=0.001). Immediately after the treatment in subgroup IIA, it has increased in 1.21-times (p2=0.005), and subsequently decreased (p2> 0.05). In the IIB subgroup, its increasing was 1.31-, 1.27- and 1.25-times (p2 <0.05), and the difference with the norm was insignificant. SDG activity in subgroups IIA and IIB has increased in 1.18- and 1.24-times (p1 <0.05; p1=0.01). After the treatment, it has decreased at all terms in both subgroups similarly: 1.13- and 1.16-times; 1.17- and 1.17-times; 1.12- and 1.10-times (p2 <0.05; p2 <0.05; p2> 0.05) and it differed slightly from normal one. The largest increase in LDG activity was found in subgroups IIIA and IIIB – 1.45- and 1.62-times (p1≤0.001). As a result of therapy immediately, after 6 and 12 months it has decreased in 1.18- and 1.20-times; 1.26- and 1.23-times; 1.13- and 1.15-times (p2 <0.05; p2 <0.05; p2> 0.05; p1> 0.05). In subgroups IIIA and IIIB, arginase activity has reduced in 1.32- and 1.37-times (p1≤0.005). Treatment has increased the indices in group IIIA in 1.22-, 1.22- and 1.18-times (p2<0.05), and in group IIIB it immediately increased in 1.25-times and then decreased (p2 <0.05; p2> 0.05). The activity of SDG in IIIA and IIIB subgroups has increased in 1.31-times (p1=0.001). Under the influence of therapy in subgroup IIIA, it has decreased immediately, after 6 and 12 months in 1.17-, 1.22- and 1.13-times (p2 <0.05; p1> 0.05), and in subgroup IIIB it initially decreased, but after a year it has increased (p2>0.05) and the difference with healthy people became significant. The altered indices of activity of enzymes studied in patients with GP did not exceed the reference values, but showed a violation of the enzyme system, which was regulated by the treatment. Prior to therapy, reliable (p<0.05-0.005) strong correlations were found between these parameters: LDG with SDG (r> 0.71) and arginase with SDG (r> -0.90). After the treatment, they were not found, six months later one correlation has restored, and a year later – both have restored, which indicates the necessity for the maintenance of endogenous therapy after six months. Conclusion. GP is accompanied by significant (p1<0.05-0.001) changes in the enzymes activity in the blood: in LDG and SDG, it is increased, and in arginase – it is reduced. Comprehensive treatment has regulated these disorders, especially immediately and after 6 months (p2<0.05-0.001). The activity of LDG and SDG of the initial and the I degree immediately and after 6 months and arginase at the initial degree after 6 and 12 months became the closest to norm. In the GP of the II degree, the data of healthy people were not achieved, but the difference with them was insignificant (p1> 0.05).

scholarly journals METHODS FOR CALCULATING DYNAMIC SYSTEMS WITH ELASTOMERIC SUPPORTS UNDER SEISMIC IMPACTS OF THE "PROJECT EARTHQUAKE" LEVEL»

2020 ◽  
Vol 8 (3) ◽  
pp. 23-28
Author(s):  
Maksim Zubrickij ◽  
O. Ushakov ◽  
Linar Sabitov ◽  
A Sagabiev
Keyword(s):  
Surface Area ◽  
Dynamic Systems ◽  
Dynamic Method ◽  
Main Tool ◽  
Seismic Stability ◽  
Earthquake Resistant ◽  
The Difference ◽  
Seismic Impact ◽  
Isolated Systems ◽  
Seismic Impacts

The article provides a brief overview of methods for assessing the seismic stability of systems using elastomeric supports under seismic impacts of the "Project earthquake" level. As part of the study, a set of dynamic and static calculations was performed, and two methods for calculating earthquake-resistant systems were considered: the linear-spectral method (LSM) and the direct dynamic method (PDM). The purpose of the research is to assess the possibility of using LST for seismic impacts of the PZ level on systems with elastomeric supports. It was found that the difference in the results of calculations for the two methods does not exceed 12 %. Thus, the SHEET can be used as the main tool for calculating seismically isolated systems under the seismic impact of the earth's surface area.

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