\begin{thebibliography}{} \bibitem[Abbott, 1992]{Abbott92} Abbott, L.~F. (1992). \newblock Simple diagrammatic rules for solving dendritic cable problems. \newblock {\em Physica A}, 185:343--356. \bibitem[Abbott et~al., 1991]{Abbott91} Abbott, L.~F., Farhi, E., and Gutmann, S. (1991). \newblock The path integral for dendritic trees. \newblock {\em Biol. Cybern.}, 66(1):49--60. \bibitem[Abramowitz and Stegun, 1970]{Abramowitz70} Abramowitz, M. and Stegun, I.~A. (1970). \newblock {\em Handbook of mathematical functions}. \newblock Dover Publication Inc., New York. \bibitem[Agmon-Snir and Segev, 1993]{Agmon93} Agmon-Snir, H. and Segev, I. (1993). \newblock Signal delay and input synchronization in passive dendritic structures. \newblock {\em J. Neurophysiol.}, 70(5):2066--2085. \bibitem[Barrett and Crill, 1974]{Barrett74} Barrett, J.~N. and Crill, W.~E. (1974). \newblock Specific membrane properties of cat motoneurones. \newblock {\em J. Physiol. (London)}, 239:301--324. \bibitem[Bernander et~al., 1991]{Bernander1991} Bernander, O., Douglas, R., Martin, K., and Koch, C. (1991). \newblock Synaptic background activity determines spatio-temporal integration in single pyramidal cells. \newblock {\em PNAS}, 88:11569--11573. \bibitem[Bernander et~al., 1994]{Bernander1994b} Bernander, O., Koch, C., and Douglas, R.~J. (1994). \newblock Amplification and linearization of distal synaptic input to cortical pyramidal cells. \newblock {\em J. Neurophysiol.}, 72:2743--2753. \bibitem[Bischofberger and Jonas, 1997]{Bischofberger97} Bischofberger, J. and Jonas, P. (1997). \newblock Action potential propagation into the presynaptic dendrites of rat mitral cells. \newblock {\em J. Physiol.}, 504(2):359--365. \bibitem[Bressloff and Taylor, 1993]{Bressloff93} Bressloff, P.~C. and Taylor, j.~G. (1993). \newblock Compartmental-model response function for dendritic trees. \newblock {\em Biol. Cybern.}, 70:199--207. \bibitem[Butz and Cowan, 1974]{Butz74} Butz, E.~G. and Cowan, J.~D. (1974). \newblock Transient potentials in dendritic systems of arbitrary geometry. \newblock {\em Biophys. J.}, 14:661--689. \bibitem[Chen et~al., 1997]{Chen97} Chen, W.~R., Midtgaard, J., and Shepherd, G.~M. (1997). \newblock Forward and backward propagation of dendritic impulses and their synaptic control in mitral cells. \newblock {\em Science}, 278:463--467. \bibitem[Clements and Redman, 1989]{Clements89} Clements, J.~D. and Redman, S.~J. (1989). \newblock Cable properties of cat spinal motoneurones measured by combining voltage clamp, current clamp and intracellular staining. \newblock {\em J. Physiol. (London)}, 409:63--87. \bibitem[De~No, 1947]{DeNo47} De~No, R.~L. (1947). \newblock Action potential of the motoneurons of the hypoglossus nucleus. \newblock {\em J. Cell Comp. Physiol.}, 29:207--287. \bibitem[De~Schutter and Bower, 1994]{DeSchutter1994b} De~Schutter, E. and Bower, J.~M. (1994). \newblock Simulated responses of cerebellar \uppercase{P}urkinje cells are independent of the dendritic location of granule cell synaptic inputs. \newblock {\em Proc. Natl. Acad. Sci. (USA)}, 91:4736--4740. \bibitem[Dodt and Zieglgansberger, 1994]{Dodt1994} Dodt, H.~U. and Zieglgansberger, W. (1994). \newblock Infrared videomicroscopy: A new look at neuronal structure and function. \newblock {\em TINS}, 17:453--458. \bibitem[Durand, 1984]{Durand84} Durand, D. (1984). \newblock The somatic shunt cable model for neurons. \newblock {\em Biophys. J.}, 46:645--653. \bibitem[Fleshman et~al., 1988]{Fleshman88} Fleshman, J.~W., Segev, I., and Burke, R.~E. (1988). \newblock Electrotonic architecture of type-identified $\alpha$-motoneurons in the cat spinal cord. \newblock {\em J. Neurophysiol.}, 60:60--85. \bibitem[Haag and Borst, 1996]{Haag96} Haag, J. and Borst, A. (1996). \newblock Amplification of high-frequency synaptic inputs by active dendritic membrane processes. \newblock {\em Nature}, 379:639--641. \bibitem[Hille, 1992]{Hille1992} Hille, B. (1992). \newblock {\em Ionic Channels of Excitable Membranes.} \newblock Sinauer Associates Inc., Sunderland, MA (USA), 2nd edition. \bibitem[Hines and Carnevale, 1997]{Hines1997} Hines, M.~L. and Carnevale, N.~T. (1997). \newblock The \uppercase{neuron} simulation environment. \newblock {\em Neural Comput.}, 9:1179--1209. \bibitem[Hoffman et~al., 1997]{Hoffman97} Hoffman, D.~A., Magee, J.~C., Colbert, C.~M., and Johnston, D. (1997). \newblock ${K}^+$ channels regulation of signal propagation in dendrites of hippocampal pyramidal neurons. \newblock {\em Nature}, 387:869--875. \bibitem[Holmes and Woody, 1989]{Holmes1989a} Holmes, W. and Woody, C.~D. (1989). \newblock Effects of uniform and non-uniform synaptic `activation- distributions' on cable properties of modeled cortical pyramidal neurons. \newblock {\em Brain Res.}, 505:12--22. \bibitem[Holmes, 1989]{Holmes89b} Holmes, W.~R. (1989). \newblock The role of dendritic diameters in maximizing the effectiveness of synaptic inputs. \newblock {\em Brain Res.}, 478:127--137. \bibitem[Holmes and Rall, 1992a]{Holmes92b} Holmes, W.~R. and Rall, W. (1992a). \newblock Electrotonic length estimates in neurons with dendritic tapering or somatic shunt. \newblock {\em J. Neurophysiol.}, 68(4):1421--1437. \bibitem[Holmes and Rall, 1992b]{Holmes92c} Holmes, W.~R. and Rall, W. (1992b). \newblock Estimating the electrotonic structure of neurons with compartmental models. \newblock {\em J. Neurophysiol.}, 68(4):1438--1451. \bibitem[Holmes et~al., 1992]{Holmes92a} Holmes, W.~R., Segev, I., and Rall, W. (1992). \newblock Interpretation of time constant and electrotonic length estimates in multicylinder or branched neuronal structures. \newblock {\em J. Neurophysiol.}, 68(4):1401--1420. \bibitem[Horwitz, 1981]{Horwitz81} Horwitz, B. (1981). \newblock An analytical method for investigating transient potentials in neurons with branching dendritic trees. \newblock {\em Biophys. J.}, 36:155--192. \bibitem[Horwitz, 1983]{Horwitz83} Horwitz, B. (1983). \newblock Unequal diameters and their effects on time-varying voltages in branched neurons. \newblock {\em Biophys. J.}, 41:51--66. \bibitem[Iansek and Redman, 1973]{Iansek1973b} Iansek, R. and Redman, S.~J. (1973). \newblock An analysis of the cable properties of spinal motoneurones using a brief intracellular current pulse. \newblock {\em J. Physiol.}, 234:613--636. \bibitem[Johnston et~al., 1996]{Johnston96} Johnston, D., Magee, J.~C., Colbert, C.~M., and Cristie, B.~R. (1996). \newblock Active properties of neuronal dendrites. \newblock {\em Annu Rev Neurosci}, 19:165--186. \bibitem[Kavalali et~al., 1997]{Kavalali97} Kavalali, E., Zhuo, M., Bito, H., and Tsien, R. (1997). \newblock Dendritic \uppercase{C}a${}^{2+}$ channels characterized by recordings from isolated hippocampal dendritic segments. \newblock {\em Neuron}, 18:651--663. \bibitem[Kawato, 1984]{Kawato1984} Kawato, M. (1984). \newblock Cable properties of a neuron model with nonuniform membrane resistivity. \newblock {\em J. Theor. Biol.}, 111:149--169. \bibitem[Koch, 1999]{Koch1999} Koch, C. (1999). \newblock {\em Biophysics of Computation: information processing in single neurons}. \newblock Oxford University Press, Oxford. \bibitem[Landau and Lifschitz, 1997]{Landau97} Landau, L.~D. and Lifschitz, E.~M. (1997). \newblock {\em Quantum mechanics}. \newblock Butterworth-Heinemann, Oxford, UK, 3rd edition. \bibitem[Laurent et~al., 1993]{Laurent93} Laurent, G., Seymour-Laurent, K.~J., and Johnson, K. (1993). \newblock Dendritic excitability and a voltage-gated calcium current in locust nonspiking local interneurons. \newblock {\em J. Neurophysiol.}, 69(5):1484--1498. \bibitem[Llinas and Sugimori, 1980]{Llinas80b} Llinas, R. and Sugimori, M. (1980). \newblock Electrophysiological properties of in vitro \uppercase{P}urkinje cell dendrites in mammalian cerebellar slices. \newblock {\em J. Physiol.}, 305:197--213. \bibitem[Magee, 1998]{Magee98} Magee, J.~C. (1998). \newblock Dendritic hyperpolarization-activated currents modify the integrative properties of hippocampal \uppercase{CA}1 pyramidal neurons. \newblock {\em J. neurosci.}, 18(19):7613--7624. \bibitem[Mainen and Sejnowski, 1996]{Mainen1996} Mainen, Z.~F. and Sejnowski, T. (1996). \newblock Influence of dendritic structure on firing pattern in model neocortical neurons. \newblock {\em Nature}, 382:363--366. \bibitem[Major et~al., 1993a]{Major93a} Major, G., Evans, J.~D., and Jack, J. J.~B. (1993a). \newblock Solutions for transients in arbitrarily branching cables: I. voltage recording with a somatic shunt. \newblock {\em Biophys. J.}, 65:423--449. \bibitem[Major et~al., 1993b]{Major93b} Major, G., Evans, J.~D., and Jack, J. J.~B. (1993b). \newblock Solutions for transients in arbitrarily branching cables: \uppercase{II}. voltage clamp theory. \newblock {\em Biophys. J.}, 65:450--468. \bibitem[Major et~al., 1993c]{Major93c} Major, G., Evans, J.~D., and Jack, J. J.~B. (1993c). \newblock Solutions for transients in arbitrarily branching cables: \uppercase{III}. voltage clamp problems. \newblock {\em Biophys. J.}, 65:469--491. \bibitem[Mel, 1994]{Mel94} Mel, B.~W. (1994). \newblock Information processing in dendritic trees. \newblock {\em Neural Comput.}, 6:1427--1439. \bibitem[Miller et~al., 1985]{Miller85} Miller, J.~P., Rall, W., and Rinzel, J. (1985). \newblock Synaptic amplification by active membrane in dendritic spines. \newblock {\em Brain Res.}, 325:325--330. \bibitem[Nicoll et~al., 1993]{Nicoll1993} Nicoll, A., Larkman, A., and Blakemore, C. (1993). \newblock Modulation of epsp shape and efficacy by intrinsic membrane conductances in rat neocortical pyramidal neurons in vitro. \newblock {\em J. Physiol.}, 468:693--710. \bibitem[Ohme and Schierwagen, 1998]{Ohme98} Ohme, M. and Schierwagen, A. (1998). \newblock An equivalent cable model for neuronal trees with active membrane. \newblock {\em Biol. Cybern.}, 78:227--243. \bibitem[Pinsky and Rinzel, 1994]{Pinsky1994} Pinsky, P.~F. and Rinzel, J. (1994). \newblock Intrinsic and network rhythmogenesis in a reduced traub model for ca3 neurons [published erratum appears in {\it \uppercase{j.} \uppercase{c}omput. \uppercase{n}eurosci.} 1995 sep;2(3):275]. \newblock {\em J. Comput. Neurosci.}, 1(1-2):39--60. \bibitem[Poznanski, 1988]{Poznanski88} Poznanski, R.~R. (1988). \newblock Membrane voltage changes in passive dendritic trees: a tapering equivalent cylinder model. \newblock {\em IMA J. Math. Appl. Med. \& Biol.}, 5:113--145. \bibitem[Rall, 1959]{Rall1959} Rall, W. (1959). \newblock Branching dendritic trees and motoneuron membrane resistivity. \newblock {\em Exp. Neurol.}, 1:491--527. \bibitem[Rall, 1962]{Rall1962a} Rall, W. (1962). \newblock Theory of physiological properties of dendrites. \newblock {\em Annl. N.Y. Acad. Sci.}, 96:1071--1092. \bibitem[Rall, 1969]{Rall1969} Rall, W. (1969). \newblock Time constants and electrotonic length of membrane cylinders and neurons. \newblock {\em Biophys. J.}, 9(12):1483--1508. \bibitem[Rall and Agmon-Snir, 1998]{Rall1998} Rall, W. and Agmon-Snir, H. (1998). \newblock Cable theory for dendritic neurons. \newblock In Koch, C. and Segev, I., editors, {\em Methods in neuronal modeling; From Ions to networks}, chapter~2, pages 27--92. MIT Press, Cambridge, MA (USA), 2nd edition. \bibitem[Rall and Rinzel, 1973]{Rall1973} Rall, W. and Rinzel, J. (1973). \newblock Branch input resistance and steady attenuation for input to one branch of a dendritic neuron model. \newblock {\em Biophys. J.}, 13:648--688. \bibitem[Rall and Shepherd, 1968]{Rall1968} Rall, W. and Shepherd, G.~M. (1968). \newblock Theoretical reconstruction of field potentials and dendrodendritic synaptic interactions in olfactory bulb. \newblock {\em J. Neurophysiol.}, 31:884--915. \bibitem[Rapp et~al., 1994]{Rapp1994} Rapp, M., Segev, I., and Yarom, Y. (1994). \newblock Physiology, morphology and detailed passive models of cerebellar \uppercase{P}urkinje cells. \newblock {\em J. Physiol. (London)}, 474:101--118. \bibitem[Rapp et~al., 1992]{Rapp1992} Rapp, M., Yarom, Y., and Segev, I. (1992). \newblock The impact of parallel fiber background activity on the cable properties of cerebellar \uppercase{P}urkinje cells. \newblock {\em Neural Comput.}, 4:518--533. \bibitem[Rinzel and Rall, 1974]{Rinzel1974} Rinzel, J. and Rall, W. (1974). \newblock Transient response in a dendritic neuron model for current injected at one branch. \newblock {\em Biophys. J.}, 14:759--790. \bibitem[Schierwagen, 1989]{Schierwagen89} Schierwagen, A.~K. (1989). \newblock A non-uniform equivalent cable model of membrane voltage changes in a passive dendritic tree. \newblock {\em J. Theor. Biol.}, 141:159--179. \bibitem[Schwindt and Crill, 1995]{Schwindt1995} Schwindt, P.~C. and Crill, W.~E. (1995). \newblock Amplification of synaptic current by persistent sodium conductance in apical dendrite of neocortical neurons. \newblock {\em J. Neurophysiol.}, 74(µ):2220--2224. \bibitem[Segev and Rall, 1988]{Segev88} Segev, I. and Rall, W. (1988). \newblock Computational study of an excitable dendritic spine. \newblock {\em J. Neurophysiol.}, 60(2):499--523. \bibitem[Segev and Rall, 1998]{Segev1998b} Segev, I. and Rall, W. (1998). \newblock Excitable dendrites and spines: earler theoretical insights elucidate recent direct observations. \newblock {\em TINS}, 21(11):453--460. \bibitem[Segev et~al., 1995]{Segev1995b} Segev, I., Rinzel, J., and Shepherd, G., editors (1995). \newblock {\em The Theoretical Foundation of Dendritic Function.} \newblock MIT Press, Massachusetts. \bibitem[Shepherd et~al., 1985]{Shepherd1985} Shepherd, G.~M., Brayton, R.~K., Miller, J.~P., Segev, I., Rinzel, J., and Rall, W. (1985). \newblock Signal enhancement in distal cortical dendrites by means of interactions between active denritic spines. \newblock {\em Proc. Natl. Acad. Sci. (USA)}, 82:2192--2195. \bibitem[Siegel et~al., 1994]{Siegel94} Siegel, M., Marder, E., and Abbott, L.~F. (1994). \newblock Activity-dependent current distributions in model neurons. \newblock {\em Proc. Natl. Acad. Sci. (USA)}, 91:11308--11312. \bibitem[Spencer and Kandel, 1961]{Spencer61} Spencer, W.~A. and Kandel, E.~R. (1961). \newblock Electrophysiology of hippocampal neurons. \uppercase{IV}. fast pre-potentials. \newblock {\em J. Neurophysiol.}, 24:272--285. \bibitem[Spiegel, 1968]{Spiegel89} Spiegel, M.~R. (1968). \newblock {\em Mathematical Handbook}. \newblock Schaum's outline series. McGraw-Hill, New York (USA). \bibitem[Stuart and Hausser, 1994]{Stuart1994b} Stuart, G. and Hausser, M. (1994). \newblock Initiation and spread of sodium action potentials in cerebellar \uppercase{P}urkinje cells. \newblock {\em Neuron}, 13:703--712. \bibitem[Stuart and Sakmann, 1995]{Stuart1995} Stuart, G. and Sakmann, B. (1995). \newblock Amplification of \uppercase{EPSP}s by axosomatic sodium channels in neocortical pyramidal neurons. \newblock {\em Neuron}, 15:1065--1076. \bibitem[Stuart et~al., 1993]{Stuart1993} Stuart, G.~M., Dodt, H.~U., and Sakmann, B. (1993). \newblock Patch-clamp recordings from the soma and dendrites of neurons in brain slices using infrared video microscopy. \newblock {\em Pfl{\"u}ger Arch.}, 423:511--518. \bibitem[Stuart and Spruston, 1998]{Stuart98} Stuart, G.~M. and Spruston, N. (1998). \newblock Determinants of voltage attenuation in neocortical pyramidal neuron dendrites. \newblock {\em J. Neurosci.}, 18(10):3501--3510. \bibitem[Turrigiano et~al., 1995]{Turrigiano95} Turrigiano, G., LeMasson, G., and Marder, E. (1995). \newblock Selective regulation of current densities underlies spontaneous changes in the activity of cultured neurons. \newblock {\em J. Neurosci.}, 15:3640--3652. \bibitem[Wilson, 1995]{Wilson95} Wilson, C.~J. (1995). \newblock Dynamic modification of dendritic cable properties and synaptic transmission by voltage-gated potassium channels. \newblock {\em J. Computational Neuroscience}, 2:91--115. \bibitem[Wolfram, 1991]{Wolfram91} Wolfram, S. (1991). \newblock {\em Mathematica: A System for Doing Mathematics by Computer}. \newblock Addison-Wesley, 2nd edition. \end{thebibliography}