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The Combinatorics of Effective Resistances and Resistive Inverses

1998
*
Information and Computation
*

We call (_ ij )

doi:10.1006/inco.1998.2716
fatcat:sptnznkc2veq7gznzvh6d3nyb4
*the**resistive**inverse**of*(R ij ). ... This uniquely determines*the*matrix (R ij )*of**effective**resistances*, defined such that if a potential*of*1 V is applied across nodes i*and*j, a current*of*1ÂR ij will flow. ...*EFFECTIVE**RESISTANCES**AND**RESISTIVE**INVERSES*...##
###
Inverse Perron Values and Connectivity of a Uniform Hypergraph

2018
*
Electronic Journal of Combinatorics
*

Moreover, relations between

doi:10.37236/7410
fatcat:7wn4wrbel5fgzjnaurquj7qmoi
*the**inverse*Perron values*and**resistance*distance*of*a connected graph are presented. ... By using*the**inverse*Perron values, we give an estimation*of**the*edge connectivity*of*a $2$-design,*and*determine*the*explicit edge connectivity*of*a symmetric design. ... Since e(G) is a positive integer, we get e(G) = k = r.*the*electronic journal*of**combinatorics*25(4) (2018), #P4.28*Inverse*Perron values*and**resistance*distance*of*graphs For a vertex i*of*a connected ...##
###
Epidemiological Consideration: The Application of Quantitative Biology in the Analysis of Mortality Rates Affected by Antimicrobial Resistance

2018
*
SM Preventive Medicine and Public Health
*

*The*importance

*of*biostatistical

*and*mathematical models regarding antimicrobial

*resistance*(AMR) cannot be overstated. ... Models help define

*the*system being observed in order to study

*the*influences

*of*various components upon that system

*and*to predict outcomes. ... Acknowledgment

*The*author wishes to acknowledge Distinguished Professor George P. ...

##
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Page 8145 of Mathematical Reviews Vol. , Issue 99k
[page]

1999
*
Mathematical Reviews
*

A proof

*of*an algorithm for finding related descriptions (*effective**resistance*matrix*and**resistive**inverse*matrix) is given. ...*resistive**inverses*. ...##
###
The Tau Constant of a Metrized Graph and its Behavior under Graph Operations

2011
*
Electronic Journal of Combinatorics
*

We give several formulas for

doi:10.37236/568
fatcat:ao55vxnq55e4pefluql74sc3ma
*the*tau constant,*and*show how it changes under graph operations including deletion*of*an edge, contraction*of*an edge,*and*union*of*graphs along one or two points. ... We prove Baker*and*Rumely's lower bound conjecture on*the*tau constant for several classes*of*metrized graphs. ... Then*the**effective**resistance*in Γ between p*and*q is equal to*the**effective**resistance*in β between p*and*q. These are illustrated by*the*first two graphs in Figure 1 . ...##
###
Control of sustainable management according to multilevel combinatorics of homeostatic mechanisms

2021
*
E3S Web of Conferences
*

*The*following is herein substantiated: conditions

*of*homeostasis generation

*and*realization

*of*specific

*effect*

*of*mechanisms

*and*, respectively, regulators

*of*adaptation

*of*managing systems to external ...

*The*article states that

*the*

*combinatorics*

*of*homeostasis controls includes stabilizing, inertial, adaptation, organizational

*and*economic, kinematic, cybernetic, alarm, cognitive information, reparative ...

*And*

*effectiveness*

*of*use

*of*multilevel

*combinatorics*

*of*homeostatic mechanisms

*and*, respectively, their complexity mostly depends on

*the*level

*of*evolutionary development

*of*a managing system, its industry ...

##
###
Page 7269 of Mathematical Reviews Vol. , Issue 97K
[page]

1997
*
Mathematical Reviews
*

Summary: “Matrix-theoretic interpretations are obtained for

*the*Campbell-Youla*inverse**and*its associated terminal weight num- bers*and*network diameter; these concepts are useful for*the**effective*modeling ... H. (3-MGL; Montreal, PQ); Subak-Sharpe, Gerald E. (1-CCNY-EE; New York, NY Inequalities*and*equalities associated with*the*Campbell-Youla generalized*inverse**of**the*indefinite admittance matrix*of**resistive*...##
###
Combinatorics of Tripartite Boundary Connections for Trees and Dimers

2009
*
Electronic Journal of Combinatorics
*

These formulas generalize

doi:10.37236/201
fatcat:2mkrxxndnnfu5iehxo37gbr22m
*the*determinant formulas given by Curtis, Ingerman,*and*Morrow,*and*by Fomin, for parallel pairings. ... In particular, for "tripartite" pairings*of**the*nodes,*the*probability can be computed as a Pfaffian in*the*entries*of**the*Dirichlet-to-Neumann matrix (discrete Hilbert transform)*of**the*graph. ...*The**effective**resistance**and*current response can be expressed in terms*of**the*edge conductances via matrix linear algebra,*and*these formulas can be still be used formally when*the*edge conductances are ...##
###
Calculating effective resistances on underlying networks of association schemes

2008
*
Journal of Mathematical Physics
*

Recently, in Refs. jsj

doi:10.1063/1.2953469
fatcat:mboxx3qpqvberkkc2xf5wopauu
*and*res2, calculation*of**effective**resistances*on distance-regular networks was investigated, where in*the*first paper,*the*calculation was based on stratification*and*Stieltjes ... In this paper, evaluation*of**effective**resistances*on more general networks which are underlying networks*of*association schemes is considered, where by using*the*algebraic*combinatoric*structures*of*association ... Section 4 is devoted to calculation*of**the**effective**resistances*on underlying resistor networks*of*association schemes by using*the*algebraic*combinatoric*structures*of*corresponding association schemes ...##
###
The tau constant and the discrete Laplacian matrix of a metrized graph

2011
*
European journal of combinatorics (Print)
*

We express

doi:10.1016/j.ejc.2011.01.008
fatcat:ogamnznhfbgl5gtbrsnhjgs3fe
*the*tau constant*of*a metrized graph in terms*of**the*discrete Laplacian matrix*and*its pseudo-*inverse*. ... Robert Rumely for his continued support*and*discussions about this paper. ... We start Section 4 with a remarkable relation between*the**resistance*on Γ*and**the*pseudo-*inverse**of**the*discrete Laplacian on Γ [3] . ...##
###
Page 637 of Mathematical Reviews Vol. , Issue 94b
[page]

1994
*
Mathematical Reviews
*

This latter inequality immediately yields

*the*Nash-Williams lower bound formula for*the**effective**resistance**of*an electrical network.” 94b:05103 05C35 Chang, Tony Yu (1-SFL; Tampa, FL); Clark, W. ... (English summary) Proceedings*of**the*Twenty-third Southeastern International Conference on*Combinatorics*, Graph Theory,*and*Computing (Boca Raton, FL, 1992). Congr. Numer. 88 (1992), 57-63. ...##
###
Report on the present state of combinatorics. Inaugural address delivered at 5th formal power series and algebraic combinatorics Florence, 21 June 1993

1996
*
Discrete Mathematics
*

*The*

*resistance*that is still put up against adopting

*the*language

*of*species reminds me

*of*two other similar

*resistances*. ... At

*the*end, Michael Atiyah came up to me

*and*said: "Nice stuff, but I frankly cannot see how it will ever be applied outside

*combinatorics*", or something to that

*effect*. ...

##
###
Diagnostic tolerance for missing sensor data

1989
*
Telematics and informatics
*

For practical automated diagnostic systems to continue functioning after failure, they must not only be able to diagnose sensor failures but also be able to tolerate

doi:10.1016/s0736-5853(89)80020-6
fatcat:avh6nj3vircgvbryjyv6f3kywm
*the*absence*of*data from*the*faulty ... Moreover, attempts to extend*the*operation*of*diagnostic capability past sensor failure will necessarily compound those dificulties. ...*The**combinatorics**of*missing sensor data compound*the**combinatorics**of*sensor diagnosis. ...##
###
Recurrence of planar graph limits

2013
*
Annals of Mathematics
*

As a corollary, we obtain that

doi:10.4007/annals.2013.177.2.10
fatcat:zcwmujczfndpze5lavvsexz7om
*the*uniform infinite planar triangulation*and*quadrangulation (UIPT*and*UIPQ) are almost surely recurrent, resolving a conjecture*of*Angel, Benjamini*and*Schramm. ... We prove that any distributional limit*of*finite planar graphs in which*the*degree*of**the*root has an exponential tail is almost surely recurrent. ... We also thank*the*participants*of**the*circle packing reading seminar held in UBC at*the*fall*of*2011. ...##
###
Processes on Unimodular Random Networks

2007
*
Electronic Journal of Probability
*

As a corollary, we obtain that

doi:10.1214/ejp.v12-463
fatcat:4xcqleefl5ehfktn5jqrixg5za
*the*uniform infinite planar triangulation*and*quadrangulation (UIPT*and*UIPQ) are almost surely recurrent, resolving a conjecture*of*Angel, Benjamini*and*Schramm. ... We prove that any distributional limit*of*finite planar graphs in which*the*degree*of**the*root has an exponential tail is almost surely recurrent. ... We also thank*the*participants*of**the*circle packing reading seminar held in UBC at*the*fall*of*2011. ...
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