scholarly journals Computation of transition matrices of positive linear electrical circuits

2019 ◽  
Vol 24 (6) ◽  
pp. 179-184
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Transition Matrix ◽  
Nonnegative Function ◽  
Transition Matrices ◽  
Electrical Circuits ◽  
Finite Series ◽  
Metzler Matrix

A method is proposed for calculation of transition matrices of positive electrical circuits. It is shown that if the transition matrix is presented as finite series of the Metzler matrix with real distinct eigenvalues then the coefficients of the series are nonnegative function of time. The method is applied to positive linear electrical circuits.

Determining Equivalent Resistance and Nodal Potentials of a Resistive Circuit Using a Reduced Transition Matrix

2020 ◽  
Vol 02 (01) ◽  
pp. 2050004
Author(s):  
Je-Young Choi
Keyword(s):  
Markov Chain ◽  
Random Walk ◽  
Random Walks ◽  
Transition Matrix ◽  
Present Approach ◽  
Voltage Source ◽  
Equivalent Resistance ◽  
Electrical Circuits ◽  
Electric Potentials ◽  
Dominant Eigenvector

Several methods have been developed in order to solve electrical circuits consisting of resistors and an ideal voltage source. A correspondence with random walks avoids difficulties caused by choosing directions of currents and signs in potential differences. Starting from the random-walk method, we introduce a reduced transition matrix of the associated Markov chain whose dominant eigenvector alone determines the electric potentials at all nodes of the circuit and the equivalent resistance between the nodes connected to the terminals of the voltage source. Various means to find the eigenvector are developed from its definition. A few example circuits are solved in order to show the usefulness of the present approach.

scholarly journals Casselman’s Basis of Iwahori Vectors and Kazhdan–Lusztig Polynomials

2019 ◽  
Vol 71 (6) ◽  
pp. 1351-1366
Author(s):  
Daniel Bump ◽  
Maki Nakasuji
Keyword(s):  
Representation Theory ◽  
Functional Equations ◽  
Transition Matrix ◽  
Principal Series ◽  
Surprising Result ◽  
Transition Matrices ◽  
Natural Basis ◽  
Series Representations ◽  
The Matrix ◽  
Lusztig Polynomials

AbstractA problem in representation theory of $p$-adic groups is the computation of the Casselman basis of Iwahori fixed vectors in the spherical principal series representations, which are dual to the intertwining integrals. We shall express the transition matrix $(m_{u,v})$ of the Casselman basis to another natural basis in terms of certain polynomials that are deformations of the Kazhdan–Lusztig R-polynomials. As an application we will obtain certain new functional equations for these transition matrices under the algebraic involution sending the residue cardinality $q$ to $q^{-1}$. We will also obtain a new proof of a surprising result of Nakasuji and Naruse that relates the matrix $(m_{u,v})$ to its inverse.

Duality results for block-structured transition matrices

1999 ◽  
Vol 36 (4) ◽  
pp. 1045-1057 ◽  
Author(s):  
Yiqiang Q. Zhao ◽  
Wei Li ◽  
Attahiru Sule Alfa
Keyword(s):  
Transition Matrix ◽  
Markov Renewal Process ◽  
Renewal Processes ◽  
Transition Kernel ◽  
Transition Matrices ◽  
Duality Results ◽  
Markov Renewal Processes ◽  
The Matrix ◽  
Probabilistic Measures ◽  
Block Structured

In this paper, we consider a certain class of Markov renewal processes where the matrix of the transition kernel governing the Markov renewal process possesses some block-structured property, including repeating rows. Duality conditions and properties are obtained on two probabilistic measures which often play a key role in the analysis and computations of such a block-structured process. The method used here unifies two different concepts of duality. Applications of duality are also provided, including a characteristic theorem concerning recurrence and transience of a transition matrix with repeating rows and a batch arrival queueing model.

scholarly journals Research on the Combination Method of Temporal Conflict Evidence Based on Transition Matrix

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Bin Wu ◽  
Xiao Yi
Keyword(s):  
Transition Matrix ◽  
Transition Probability ◽  
Evidence Theory ◽  
Research Topic ◽  
Combination Method ◽  
Evidence Based ◽  
Important Research ◽  
Transition Matrices ◽  
Important Research Topic ◽  
Evidence Combination

Conflict evidence combination is an important research topic in evidence theory. In this paper, two kinds of transition matrices are constructed based on the Markov model; one is the unordered transition matrix, which satisfies the commutative law, and the other is the temporal transition matrix, which does not satisfy the commutative law, but it can handle the combination of temporal evidence well. Then, a temporal conflict evidence combination model is proposed based on these two transition matrices. First, the transition probability at the first n time is calculated through the model of unordered transition probability, and then, the transition matrix from the N + 1 time is used to solve the combination problem of temporal conflict evidence. The effectiveness of the transition matrix in the research of conflict evidence combination method is proved by the example analysis.

scholarly journals Observables in terms of connection and curvature variables for Einstein’s equations with two commuting Killing vectors

2015 ◽  
Vol 471 (2183) ◽  
pp. 20150350
Author(s):  
P. Kordas
Keyword(s):  
Transition Matrix ◽  
Momentum Density ◽  
Transition Matrices ◽  
Einstein’S Equations ◽  
Integrals Of Motion ◽  
Einstein's Equations ◽  
Killing Vectors ◽  
Klein Gordon ◽  
Quantum Operators ◽  
Energy And Momentum

Einstein’s equations with two commuting Killing vectors and the associated Lax pair are considered. The equations for the connection A ( ς , η , γ )= Ψ , γ Ψ −1 , where γ the variable spectral parameter are considered. A transition matrix T = A ( ς , η , γ ) A −1 ( ξ , η , γ ) for A is defined relating A at ingoing and outgoing light cones. It is shown that it satisfies equations familiar from integrable PDE theory. A transition matrix on ς = constant is defined in an analogous manner. These transition matrices allow us to obtain a hierarchy of integrals of motion with respect to time, purely in terms of the trace of a function of the connections g , ς g −1 and g , η g −1 . Furthermore, a hierarchy of integrals of motion in terms of the curvature variable B = A , γ A −1 , involving the commutator [ A (1), A (−1)], is obtained. We interpret the inhomogeneous wave equation that governs σ = lnN , N the lapse, as a Klein–Gordon equation, a dispersion relation relating energy and momentum density, based on the first connection observable and hence this first observable corresponds to mass. The corresponding quantum operators are ∂/∂ t , ∂/∂ z and this means that the full Poincare group is at our disposal.

There is no best method for constructing size-transition matrices for size-structured stock assessments

2019 ◽  
Vol 77 (1) ◽  
pp. 136-147
Author(s):  
Lee Cronin-Fine ◽  
André E Punt
Keyword(s):  
Numerical Integration ◽  
Transition Matrix ◽  
Integration Method ◽  
Growth Parameters ◽  
Stock Assessment ◽  
Traditional Approach ◽  
Estimation Method ◽  
Size Class ◽  
Numerical Integration Method ◽  
Transition Matrices

Abstract Stock assessment methods for many invertebrate stocks, including crab stocks in the Bering Sea of Alaska, rely on size-structured population dynamics models. A key component of these models is the size-transition matrix, which specifies the probability of growing from one size-class to another after a certain period of time. Size-transition matrices can be defined using three parameters, the growth rate (k), asymptotic size (L∞), and variability in the size increment. Most assessments use mark-recapture data to estimate these parameters and assume that all individuals follow the same growth curve, but this can lead to biased estimates of growth parameters. We compared three approaches: the traditional approach, the platoon method, and a numerical integration method that allows k, L∞, or both to vary among individuals, under a variety of scenarios using simulated data based on golden king crabs (Lithodes aequispinus) in the Aleutian Islands region of Alaska. No estimation method performed best for all scenarios. The number of size-classes in the size-transition matrix and how the data are generated heavily dictate performance. However, we recommend the numerical integration method that allows L∞ to vary among individuals and smaller size-class widths.

A Conceptual Discussion and an Empirical Analysis of Commercial Land-Use Succession

1974 ◽  
Vol 6 (6) ◽  
pp. 655-674 ◽  
Author(s):  
Y Lee
Keyword(s):  
Land Use ◽  
Empirical Analysis ◽  
Transition Matrix ◽  
Nonstationary Process ◽  
Transition Matrices ◽  
Order Probability ◽  
Time Period ◽  
Land Economics ◽  
The Stability ◽  
Succession Theory

Land-use succession theory has been the most thinly developed area in the study of urban land economics. In this paper a brief review of the spotty development of the land-use succession concept is first offered, followed by a discussion of the economic arguments of commercial land-use succession and related problems in succession studies. Then, as an empirical analysis, commercial land use in downtown Denver from 1947 to 1971 is studied. Characteristics of succession are revealed first, by the description of succession by both first- and second-order probability transition matrices; and second, by an examination of the stability of succession via two different approaches. Not unexpectedly, one of the major characteristics found in the study area is the nonstationary process of land-use succession, cautioning against the danger of employing a transition matrix estimated from one time period to predict future land use.

A Dynamic Accounting Model of Intrametropolitan Household Relocation

1980 ◽  
Vol 12 (11) ◽  
pp. 1301-1315 ◽  
Author(s):  
N Varaprasad
Keyword(s):  
Transition Matrix ◽  
Equilibrium Distribution ◽  
Housing Stock ◽  
Research Strategy ◽  
Transition Matrices ◽  
Transport Costs ◽  
Exogenous Variables ◽  
Use Of Data ◽  
Accounting Model ◽  
Household Relocation

This paper demonstrates the use of a dynamic accounting framework of the kinetic type for modelling the intrametropolitan relocation of households. Households are classified into five different categories, and each is subject to a transition matrix, the elements of which are functions of the changing availability of housing stock and job supply, and the different preferences for these of the different households categories. A three-zone concentric configuration was used, and the model was calibrated for the South-East standard region with the use of data for 1961, 1966, 1971, and 1976. The model was then run until 1991 with alternative combinations of projections of strategic exogenous variables such as transport costs, job supply, and housing stock availability. Although the model appears oversensitive to the changes in the number of households in each zone and arrives at an equilibrium distribution quickly, it suggests a research strategy to determine the nature of the elements of the transition matrices. The model also illustrates that it is possible to use the dynamic accounting framework of kinetic theory to embody any given hypothesis of movement.

scholarly journals Addressing the Embeddability Problem in Transition Rate Estimation

2019 ◽  
Author(s):  
Curtis Goolsby ◽  
Mahmoud Moradi
Keyword(s):  
Transition Matrix ◽  
Md Simulations ◽  
Transition Matrices ◽  
One Dimensional ◽  
Kinetic Information ◽  
Markov State Models ◽  
Alternative Approach ◽  
Trajectory Length ◽  
State Models ◽  
Diffusive Processes

Markov State Models (MSM) and related techniques have gained significant traction as a tool for analyzing and guiding molecular dynamics (MD) simulations due to their ability to extract structural, thermodynamic, and kinetic information on proteins using computationally feasible MD simulations. The MSM analysis often relies on spectral decomposition of empirically generated transition matrices. Here, we discuss an alternative approach for extracting the thermodynamic and kinetic information from the so-called rate/generator matrix rather than the transition matrix. Although the rate matrix is itself built from the empirical transition matrix, it provides an alternative approach for estimating both thermodynamic and kinetic quantities, particularly in diffusive processes. We particularly discuss a fundamental issue with this approach, known as the embeddability problem and offer ways to address this issue. We describe six different methods to overcome the embeddability problem. We use a one-dimensional toy model to show the workings of these methods and discuss the robustness of each method in terms of its dependence in lag time and trajectory length.

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