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360
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 158 (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.
Finite elements in computational electromagnetism
, 2002
"... This article discusses finite element Galerkin schemes for a number of linear model problems in electromagnetism. The finite element schemes are introduced as discrete differential forms, matching the coordinateindependent statement of Maxwell’s equations in the calculus of differential forms. Th ..."
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Cited by 108 (6 self)
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This article discusses finite element Galerkin schemes for a number of linear model problems in electromagnetism. The finite element schemes are introduced as discrete differential forms, matching the coordinateindependent statement of Maxwell’s equations in the calculus of differential forms. The asymptotic convergence of discrete solutions is investigated theoretically. As discrete differential forms represent a genuine generalization of conventional Lagrangian finite elements, the analysis is based upon a judicious adaptation of established techniques in the theory of finite elements. Risks and difficulties haunting finite element schemes that do not fit the framework of discrete dif
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 58 (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.
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 36 (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
A review of advances in dielectric and electrical conductivity measurements in soils using time domain reflectometry
 Vadose Zone Journal
, 2003
"... ABSTRACT constant) of a material emerged as an elegant method of estimating water content in porous materials. For theSubstantial advances in the measurement of water content and first time the same physical property (permittivity) couldbulk soil electrical conductivity (EC) using time domain reflec ..."
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Cited by 29 (3 self)
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ABSTRACT constant) of a material emerged as an elegant method of estimating water content in porous materials. For theSubstantial advances in the measurement of water content and first time the same physical property (permittivity) couldbulk soil electrical conductivity (EC) using time domain reflectometry be measured for a range of scales and used to estimate(TDR) have been made in the last two decades. The key to TDR’s success is its ability to accurately measure the permittivity of a material water content. Electromagnetic methods, whether TDR and the fact that there is a good relationship between the permittivity (localized measurement), ground penetrating radar of a material and its water content. A further advantage is the ability (twodimensional profile), or active microwave remote to estimate water content and measure bulk soil EC simultaneously sensing (land surface), all estimate water content based using TDR. The aim of this review is to summarize and examine on the permittivity of the target medium. A further advances that have been made in terms of measuring permittivity and advance was the development of analysis methods usingbulk EC. The review examines issues such as the effective frequency TDR. Time domain reflectometry was adapted to estiof the TDR measurement and waveform analysis in dispersive dielecmate both soil water content (Hoekstra and Delaney,trics. The growing importance of both waveform simulation and in1974; Topp et al., 1980) and soil bulk EC simultaneouslyverse analysis of waveforms is highlighted. Such methods hold great (Dalton et al., 1984). In spite of decades of research,potential for obtaining far more information from TDR waveform analysis. Probe design is considered in some detail and practical guid we are only beginning to efficiently utilize electrical
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.
Laser cooling and trapping of neutral atoms
 Prog. Quantum Electron
, 1997
"... Abstract: The ability to cool, manipulate, and trap atoms using laser light has allowed a new, rapidly expanding field to emerge. Current research focuses on improving existing cooling techniques, and the development of cold atoms as a source for applications ranging from atomic clocks to studies of ..."
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Cited by 19 (0 self)
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Abstract: The ability to cool, manipulate, and trap atoms using laser light has allowed a new, rapidly expanding field to emerge. Current research focuses on improving existing cooling techniques, and the development of cold atoms as a source for applications ranging from atomic clocks to studies of quantum degeneracy. This review explains the basic mechanisms used in laser cooling and
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.
Convergence Acceleration During the 20th Century
 J. Comput. Appl. Math
, 2000
"... This paper, which is based on [31], but includes new developments obtained since 1995, presents my personal views on the historical development of this subject during the 20th century. I do not pretend to be exhaustive nor even to quote every important contribution (if a reference does not appear be ..."
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Cited by 14 (2 self)
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This paper, which is based on [31], but includes new developments obtained since 1995, presents my personal views on the historical development of this subject during the 20th century. I do not pretend to be exhaustive nor even to quote every important contribution (if a reference does not appear below, it does not mean that it is less valuable). I refer the interested reader to the literature and, in particular to the recent books [55, 146, 33, 144]. For an extensive bibliography, see [28]
Methods of Calculating Forces on Rigid Magnetic Media
, 2002
"... Despite 180 years of theory on magnetism, it appears that the practice of calculating forces on magnetic media is ambiguous, as illustrated by a recent article by Casperson [1]. Potentially troubling issues include: Which field B or H should be used? Should the total field be used, or only the exter ..."
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Cited by 13 (13 self)
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Despite 180 years of theory on magnetism, it appears that the practice of calculating forces on magnetic media is ambiguous, as illustrated by a recent article by Casperson [1]. Potentially troubling issues include: Which field B or H should be used? Should the total field be used, or only the external field? And if the latter, what is meant by “external”? Can/should effects of magnetization currents and/or fictitious magnetic poles be included? What is the force on only a portion of a circuit? We review several wellknown approaches to magnetic force calculations on elements of rigid circuits, and find it helpful to use an explicit example to compare and contrast the various methods. Our discussion reinforces that of the most authoritative texts [2, 3], but corrects in an important way somes previous attempts at a systematic review[4,5,6,7]. 1