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238
THE ELECTRICAL RESISTANCE OF A GRAPH CAPTURES ITS COMMUTE AND COVER TIMES
"... View an nvertex, medge undirected graph as an electrical network with unit resistors as edges. We extend known relations between random walks and electrical networks by showing that resistance in this network is intimately connected with the lengths of random walks on the graph. For example, the c ..."
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Cited by 141 (5 self)
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View an nvertex, medge undirected graph as an electrical network with unit resistors as edges. We extend known relations between random walks and electrical networks by showing that resistance in this network is intimately connected with the lengths of random walks on the graph. For example, the commute time between two vertices s and t (the expected length of a random walk from s to t and back) is precisely characterized by the e ective resistance Rst between s and t: commute time = 2mRst. As a corollary, the cover time (the expected length of a random walk visiting all vertices) is characterized by the maximum resistance R in the graph to within a factor of log n: mR cover time O(mR log n). For many graphs, the bounds on cover time obtained in this manner are better than those obtained from previous techniques such as the eigenvalues of the adjacency matrix. In particular, we improve known bounds on cover times for highdegree graphs and expanders, and give new proofs of known results for multidimensional meshes. Moreover, resistance seems to provide an intuitively appealing and tractable approach to these problems.
A COMBINATORIAL PROOF OF THE ALL MINORS MATRIX TREE THEOREM
, 1982
"... Let (A tl), i, j E V be the matrix with entriesail if i r = j and diagonal entries such that all the column sums are zero. Let alj be a variable associated with arc ij in the complete digraph G on vertices V. Let A(WI U) be the matrix that results from deleting sets of k rows Wand columns U from A. ..."
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Cited by 56 (3 self)
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Let (A tl), i, j E V be the matrix with entriesail if i r = j and diagonal entries such that all the column sums are zero. Let alj be a variable associated with arc ij in the complete digraph G on vertices V. Let A(WI U) be the matrix that results from deleting sets of k rows Wand columns U from A. The all minors matrix tree theorem states that IA(WI U)I enumerates the forests in G that have (a) k trees, (b) each tree contains exactly one vertex in U and exactly one vertex in W, and (c) each arc is directed away from the vertex in U of the tree containing the arc. We give an elementary combinatorial proof in which we show that each of the terms in IA(WI U)I that corresponds to an enumerated forest occurs just once and the other terms cancel. The sign of each term is determined by the parity of the linking from U to W contained in the forest, and is easy to calculate explicitly in the proof. The results are extended to signed graphs. The theorem provides a coordinatization (linear representation) of gammoids that is in a certain sense natural.
Effective conductivity of a suspension of permeabilized cells: a theoretical analysis, Biophys
 J
, 2003
"... ABSTRACT During the electroporation cell membrane undergoes structural changes, which increase the membrane conductivity and consequently lead to a change in effective conductivity of a cell suspension. To correlate microscopic membrane changes to macroscopic changes in conductivity of a suspension, ..."
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Cited by 19 (6 self)
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ABSTRACT During the electroporation cell membrane undergoes structural changes, which increase the membrane conductivity and consequently lead to a change in effective conductivity of a cell suspension. To correlate microscopic membrane changes to macroscopic changes in conductivity of a suspension, we analyzed the effective conductivity theoretically, using two different approaches: numerically, using the finite elements method; and analytically, by using the equivalence principle. We derived the equation, which connects membrane conductivity with effective conductivity of the cell suspension. The changes in effective conductivity were analyzed for different parameters: cell volume fraction, membrane and medium conductivity, critical transmembrane potential, and cell orientation. In our analysis we used a tensor form of the effective conductivity, thus taking into account the anisotropic nature of the cell electropermeabilization and rotation of the cells. To determine the effect of cell rotation, as questioned by some authors, the difference between conductivity of a cell suspension with normally distributed orientations and parallel orientation was also calculated, and determined to be \10%. The presented theory provides a theoretical basis for the analysis of measurements of the effective conductivity during electroporation.
Electric Field Imaging
, 1999
"... The physical user interface is an increasingly significant factor limiting the effectiveness of our interactions with and through technology. This thesis introduces Electric Field Imaging, a new physical channel and inference framework for machine perception of human action. Though electric field se ..."
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Cited by 18 (5 self)
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The physical user interface is an increasingly significant factor limiting the effectiveness of our interactions with and through technology. This thesis introduces Electric Field Imaging, a new physical channel and inference framework for machine perception of human action. Though electric field sensing is an important sensory modality for several species of fish, it has not been seriously explored as a channel for machine perception. Technological applications of field sensing, from the Theremin to the capacitive elevator button, have been limited to simple proximity detection tasks. This thesis presents a solution to the inverse problem of inferring geometrical information about the configuration and motion of the human body from electric field measurements. It also presents simple, inexpensive hardware and signal processing techniques for making the field measurements, and several new applications of electric field sensing. The signal
Effect of cell electroporation on the conductivity of a cell suspension
 Biophys. J
, 2005
"... ABSTRACT An increased permeability of a cell membrane during the application of highvoltage pulses results in increased transmembrane transport of molecules that otherwise cannot enter the cell. Increased permeability of a cell membrane is accompanied by increased membrane conductivity; thus, by me ..."
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Cited by 15 (8 self)
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ABSTRACT An increased permeability of a cell membrane during the application of highvoltage pulses results in increased transmembrane transport of molecules that otherwise cannot enter the cell. Increased permeability of a cell membrane is accompanied by increased membrane conductivity; thus, by measuring electric conductivity the extent of permeabilized tissue could be monitored in real time. In this article the effect of cell electroporation caused by highvoltage pulses on the conductivity of a cell suspension was studied by currentvoltage measurements during and impedance measurement before and after the pulse application. At the same time the percentage of permeabilized and survived cells was determined and the extent of osmotic swelling measured. For a train of eight pulses a transient increase in conductivity of a cell suspension was obtained above permeabilization threshold in low and highconductive medium with complete relaxation in,1 s. Total conductivity changes and impedance measurements showed substantial changes in conductivity due to the ion efflux in lowconductive medium and colloidosmotic swelling in both media. Our results show that by measuring electric conductivity during the pulses we can detect limit permeabilization threshold but not directly permeabilization level, whereas impedance measurements in seconds after the pulse application are not suitable.
A Homogenized energy framework for ferromagnetic hysteresis
 IEEE Transactions on Magnetics
, 2006
"... In this paper we develop a macroscopic framework quantifying the hysteresis and constitutive nonlinearities inherent to ferromagnetic materials. In the first step of the development, we construct Helmholtz and Gibbs energy relations at the mesoscopic or lattice level based on the assumption that mag ..."
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Cited by 11 (11 self)
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In this paper we develop a macroscopic framework quantifying the hysteresis and constitutive nonlinearities inherent to ferromagnetic materials. In the first step of the development, we construct Helmholtz and Gibbs energy relations at the mesoscopic or lattice level based on the assumption that magnetic moments or spins are restricted to two orientations. Direct minimization of the Gibbs energy yields local average magnetization relations appropriate for operating regimes in which relaxation mechanisms are negligible whereas the balance of the Gibbs and relative thermal energies through Boltzmann principles provides local models which incorporate mechanisms such as thermal aftereffects. To construct macroscopic relations that incorporate material nonhomogeneities, polycrystallinity, and variable effective fields, we employ stochastic homogenization techniques based on the assumption that parameters such as local coercive and interaction fields are manifestations of underlying distributions. The resulting framework quantifies in a natural manner the anhysteretic magnetization provided by decaying AC fields and guarantees the closure of biased minor loops once transient accommodation and aftereffects are complete. Furthermore, noncongruency is achieved with certain choices for the energy functionals. Hence the framework provides an energy basis for certain extended Preisach models and the relation of the framework to several macroscopic hysteresis models is detailed. The behavior of both the nonlinear anhysteretic relations and full hysteresis model are validated through comparison with experimental steel and nickel data. i 1
Action at a Distance as a FullValue Solution of Maxwell Equations: the Basis and Application of the SeparatedPotentials Method”, Phys
 Rev. E
, 1996
"... The inadequacy of LiénardWiechert potentials is demonstrated as one of the examples related to the inconsistency of the conventional classical electrodynamics. The insufficiency of the FaradayMaxwell concept to describe the whole electromagnetic phenomena and the incompleteness of a set of solutio ..."
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Cited by 10 (2 self)
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The inadequacy of LiénardWiechert potentials is demonstrated as one of the examples related to the inconsistency of the conventional classical electrodynamics. The insufficiency of the FaradayMaxwell concept to describe the whole electromagnetic phenomena and the incompleteness of a set of solutions of Maxwell equations are discussed and mathematically proved. Reasons of the introduction of the socalled “electrodynamics dualism concept ” (simultaneous coexistence of instantaneous Newton longrange and FaradayMaxwell shortrange interactions) have been displayed. It is strictly shown that the new concept presents itself as the direct consequence of the complete set of Maxwell equations and makes it possible to consider classical electrodynamics as a selfconsistent and complete theory, devoid of inward contradictions. In the framework of the new approach, all main concepts of classical electrodynamics are reconsidered. In particular, a limited class of motion is revealed when accelerated charges do not radiate electromagnetic field.
Extrapolation algorithms and Padé approximations: a historical survey
, 1994
"... This paper will give a short historical overview of these two subjects. Of course, we do not pretend to be exhaustive nor even to quote every important contribution. We refer the interested reader to the literature and, in particular to the recent books [5, 22, 29, 24, 38, 46, 48, 68, 78, 131]. For ..."
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Cited by 10 (2 self)
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This paper will give a short historical overview of these two subjects. Of course, we do not pretend to be exhaustive nor even to quote every important contribution. We refer the interested reader to the literature and, in particular to the recent books [5, 22, 29, 24, 38, 46, 48, 68, 78, 131]. For an extensive bibliography, see [23]. 1 Extrapolation methods Let (S n ) be the sequence to be accelerated. It is assumed to converge to a limit S. An extrapolation method consists in transforming this sequence into a new one, (T n ), by a sequence transformation T : (S n ) \Gamma! (T n ). The transformation T is said to accelerate the convergence of the sequence (S n ) if and only if lim n!1 T n \Gamma S S n \Gamma S =<F13.
On the bass note of a Schottky group
 Acta Math
, 1994
"... Using a classical method from physics called Rayleigh's cutting method, we prove the conjecture of Phillips and Sarnak that there is a universal lower bound L 2 ? 0 for the lowest eigenvalue of the quotient manifold of a classical Schottky group \Gamma acting on hyperbolic 3space H . By ..."
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Cited by 10 (0 self)
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Using a classical method from physics called Rayleigh's cutting method, we prove the conjecture of Phillips and Sarnak that there is a universal lower bound L 2 ? 0 for the lowest eigenvalue of the quotient manifold of a classical Schottky group \Gamma acting on hyperbolic 3space H . By work of Patterson and Sullivan, this implies that there is a universal upper bound U 2 ! 2 for the Hausdorff dimension of the limit set of \Gamma, or equivalently, for the critical exponent of the Poincar'e series associated with \Gamma. The latter implication answers a question that can be traced back to Schottky and Burnside.