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### The Combinatorics of Effective Resistances and Resistive Inverses

Stephen Ponzio
1998 Information and Computation
We call (_ ij ) 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

Changjiang Bu, Haifeng Li, Jiang Zhou
2018 Electronic Journal of Combinatorics
Moreover, relations between 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

Nicholas A Kerna
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.  ...

### 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

Zubeyir Cinkir
2011 Electronic Journal of Combinatorics
We give several formulas for 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

Victoriia Mykytenko, Nataliia Sheludko, A. Generowicz, B. Burkinskyi, V. Koval
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

Richard W. Kenyon, David B. Wilson
2009 Electronic Journal of Combinatorics
These formulas generalize 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 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

Zubeyir Cinkir
2011 European journal of combinatorics (Print)
We express 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

Gian-Carlo Rota
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

Ethan A. Scarl
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 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

Ori Gurel-Gurevich, Asaf Nachmias
2013 Annals of Mathematics
As a corollary, we obtain that 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

David Aldous, Russell Lyons
2007 Electronic Journal of Probability
As a corollary, we obtain that 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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