@article{4598, abstract = {A hybrid system is a dynamical system with both discrete and continuous state changes. For analysis purposes, it is often useful to abstract a system in a way that preserves the properties being analyzed while hiding the details that are of no interest. We show that interesting classes of hybrid systems can be abstracted to purely discrete systems while preserving all properties that are definable in temporal logic. The classes that permit discrete abstractions fall into two categories. Either the continuous dynamics must be restricted, as is the case for timed and rectangular hybrid systems, or the discrete dynamics must be restricted, as is the case for o-minimal hybrid systems. In this paper, we survey and unify results from both areas.}, author = {Alur, Rajeev and Henzinger, Thomas A and Lafferriere, Gerardo and Pappas, George}, issn = {0018-9219}, journal = {Proceedings of the IEEE}, number = {7}, pages = {971 -- 984}, publisher = {IEEE}, title = {{Discrete abstractions of hybrid systems}}, doi = {10.1109/5.871304 }, volume = {88}, year = {2000}, } @inproceedings{4627, abstract = {We consider two-player games, which are played on a finite state space for an infinite number of rounds. The games are concurrent, that is, in each round, the two players choose their moves independently and simultaneously; the current state and the two moves determine a successor state. We consider omega-regular winning conditions on the resulting infinite state sequence. To model the independent choice of moves, both players are allowed to use randomization for selecting their moves. This gives rise to the following qualitative modes of winning, which can be studied without numerical considerations concerning probabilities: sure-win (player 1 can ensure winning with certainty), almost-sure-win (player 1 can ensure winning with probability 1), limit-win (player 1 can ensure winning with probability arbitrarily close to 1), bounded-win (player 1 can ensure winning with probability bounded away from 0), positive-win (player 1 can ensure winning with positive probability), and exist-win (player 1 can ensure that at least one possible outcome of the game satisfies the winning condition).We provide algorithms for computing the sets of winning states for each of these winning modes. In particular, we solve concurrent Rabin-chain games in n0 (m) time, where n is the size of the game structure and m is the number of pairs in the Rabin-chain condition. While this complexity is in line with traditional turn-based games, where in each state only one of the two players has a choice of moves, our algorithms are considerably more involved than those for turn-based games are. This is because concurrent games violate two of the most fundamental properties of turn-based games. First, concurrent games are not determined, but rather exhibit a more general duality property, which involves multiple modes of winning. Second, winning strategies for concurrent games may require infinite memory.}, author = {De Alfaro, Luca and Henzinger, Thomas A}, booktitle = {Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science}, isbn = {0769507255}, location = {Santa Barbara, CA, USA}, pages = {141 -- 154}, publisher = {IEEE}, title = {{Concurrent omega-regular games}}, doi = {10.1109/LICS.2000.855763}, year = {2000}, } @inproceedings{4637, abstract = {In the synchronous composition of processes, one process may prevent another process from proceeding unless compositions without a well-defined product behavior are ruled out. They can be ruled out semantically, by insisting on the existence of certain fixed points, or syntactically, by equipping processes with types, which make the dependencies between input and output signals transparent. We classify various typing mechanisms and study their effects on the control problem. A static type enforces fixed, acyclic dependencies between input and output ports. For example, synchronous hardware without combinational loops can be typed statically. A dynamic type may vary the dependencies from state to state, while maintaining acyclicity, as in level-sensitive latches. Then, two dynamically typed processes can be syntactically compatible, if all pairs of possible dependencies are compatible, or semantically compatible, if in each state the combined dependencies remain acyclic. For a given plant process and control objective, there may be a controller of a static type, or only a controller of a syntactically compatible dynamic type, or only a controller of a semantically compatible dynamic type. We show this to be a strict hierarchy of possibilities, and we present algorithms and determine the complexity of the corresponding control problems. Furthermore, we consider versions of the control problem in which the type of the controller (static or dynamic) is given. We show that the solution of these fixed-type control problems requires the evaluation of partially ordered (Henkin) quantifiers on boolean formulas, and is therefore harder (nondeterministic exponential time) than more traditional control questions}, author = {De Alfaro, Luca and Henzinger, Thomas A and Mang, Freddy}, booktitle = {Proceedings of the 11th International Conference on Concurrency Theory}, isbn = {9783540678977}, location = {University Park, PA, USA}, pages = {458 -- 473}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{The control of synchronous systems}}, doi = {10.1007/3-540-44618-4_33}, volume = {1877}, year = {2000}, } @inproceedings{4638, abstract = {Any formal method or tool is almost certainly more often applied in situations where the outcome is failure (a counterexample) rather than success (a correctness proof). We present a method for symbolic model checking that can lead to significant time and memory savings for model-checking runs that fail, while occurring only a small overhead for model-checking runs that succeed. Our method discovers an error as soon as it cannot be prevented, which can be long before it actually occurs; for example, the violation of an invariant may become unpreventable many transitions before the invariant is violated. The key observation is that “unpreventability” is a local property of a single module: an error is unpreventable in a module state if no environment can prevent it. Therefore, unpreventability is inexpensive to compute for each module, yet can save much work in the state exploration of the global, compound system. Based on different degrees of information available about the environment, we define and implement several notions of “unpreventability,” including the standard notion of uncontrollability from discrete-event control. We present experimental results for two examples, a distributed database protocol and a wireless communication protocol.}, author = {De Alfaro, Luca and Henzinger, Thomas A and Mang, Freddy}, booktitle = {Proceedings of the 12th International Conference on Computer Aided Verification}, isbn = {9783540677703}, location = {Chicago, IL, USA}, pages = {186 -- 201}, publisher = {Springer}, title = {{Detecting errors before reaching them}}, doi = {10.1007/10722167_17}, volume = {1855}, year = {2000}, } @article{1455, abstract = {First, a special case of Knaster's problem is proved implying that each symmetric convex body in ℝ3 admits an inscribed cube. It is deduced from a theorem in equivariant topology, which says that there is no S4 - equivariant map from SO(3) to S2, where S4 acts on SO(3) on the right as the rotation group of the cube, and on S2 on the right as the symmetry group of the regular tetrahedron. Some generalizations are also given. Second, it is shown how the above non-existence theorem yields Makeev's conjecture in ℝ3 that each set in ℝ3 of diameter 1 can be covered by a rhombic dodecahedron, which has distance 1 between its opposite faces. This reveals an unexpected connection between inscribing cubes into symmetric bodies and covering sets by rhombic dodecahedra. Finally, a possible application of our second theorem to the Borsuk problem in ℝ3 is pointed out.}, author = {Hausel, Tamas and Makai, Endre and Szücs, András}, issn = {0025-5793}, journal = {Mathematika}, number = {1-2}, pages = {371 -- 397}, publisher = {University College London}, title = {{Inscribing cubes and covering by rhombic dodecahedra via equivariant topology}}, doi = {10.1112/S0025579300015965}, volume = {47}, year = {2000}, } @article{13437, abstract = {Liquid/liquid Phase Transfer Catalysis (PTC) reaction of 4-chlorobutyronitrile with nonenolisable aldehydes leads via an addition-cyclisation reaction sequence to derivatives of tetrahydrofuran-3-carbonitrile.}, author = {Macogonkosza, Mieczysław and Przyborowski, Jacek and Klajn, Rafal and Kwast, Andrzej}, issn = {1437-2096}, journal = {Synlett}, keywords = {Organic Chemistry}, number = {12}, pages = {1773--1774}, publisher = {Georg Thieme Verlag}, title = {{Simple synthesis of 2-substituted Tetrahydrofuran-3-carbonitriles}}, doi = {10.1055/s-2000-8670}, volume = {2000}, year = {2000}, } @inproceedings{11802, abstract = {In this paper we survey algorithmic aspects of Web information retrieval. As an example, we discuss ranking of search engine results using connectivity analysis.}, author = {Henzinger, Monika H}, booktitle = {8th Annual European Symposium on Algorithms}, isbn = {9783540410041}, issn = {1611-3349}, location = {Saarbrücken, Germany}, pages = {1–8}, publisher = {Springer Nature}, title = {{Web information retrieval - an algorithmic perspective}}, doi = {10.1007/3-540-45253-2_1}, volume = {1879}, year = {2000}, } @article{11893, abstract = {We present fully dynamic algorithms for maintaining the biconnected components in general and plane graphs. A fully dynamic algorithm maintains a graph during a sequence of insertions and deletions of edges or isolated vertices. Let m be the number of edges and n be the number of vertices in a graph. The time per operation of the best deterministic algorithms is 𝑂(𝑛√) in general graphs and O(log n) in plane graphs for fully dynamic connectivity and O(min m2/3 ,n}) in general graphs and 𝑂(𝑛√) in plane graphs for fully dynamic biconnectivity. We improve the later running times to 𝑂(𝑚log𝑛‾‾‾‾‾‾‾√) in general graphs and O(log 2n ) in plane graphs. Our algorithm for general graphscan also find the biconnected components of all vertices in time O(n).}, author = {Henzinger, Monika H}, issn = {1095-7111}, journal = {SIAM Journal on Computing}, number = {6}, pages = {1761--1815}, publisher = {Society for Industrial & Applied Mathematics}, title = {{Improved data structures for fully dynamic biconnectivity}}, doi = {10.1137/s0097539794263907}, volume = {29}, year = {2000}, } @article{12925, abstract = {Normal function of organs and cells is tightly linked to the cytoarchitecture. Control of the cell volume is therefore vital for the organism. A widely established strategy of cells to counteract swelling is the activation of chloride and potassium channels, which leads to a net efflux of salt followed by water - a process termed regulatory volume decrease. Since there is evidence for swelling-dependent chloride channels (IClswell) being activated also during pathological processes, the identification of the molecular entity underlying IClswell is of utmost importance. Several proteins are discussed as the channel forming IClswell, i.e. phospholemman, p-glycoprotein, CLC-3 and ICln. In this review we would like to focus on the properties of ICln, a protein cloned from a Madin Darby canine kidney (MDCK) cell library whose expression in Xenopus laevis oocytes resulted in a nucleotide sensitive outwardly rectifying chloride current closely resembling the biophysical properties of IClswell.}, author = {Fürst, Johannes and Jakab, Martin and König, Matthias and Ritter, Markus and Gschwentner, Martin and Rudzki, Jakob and Danzl, Johann G and Mayer, Michael and Burtscher, Carmen M. and Schirmer, Julia and Maier, Brigitte and Nairz, Manfred and Chwatal, Sabine and Paulmichl, Markus}, issn = {1015-8987}, journal = {Cellular Physiology and Biochemistry}, keywords = {Physiology}, number = {5-6}, pages = {329--334}, publisher = {S. Karger AG}, title = {{Structure and Function of the Ion Channel ICln}}, doi = {10.1159/000016374}, volume = {10}, year = {2000}, } @article{3489, abstract = {We have examined factors that determine the strength and dynamics of GABAergic synapses between interneurons [dentate gyrus basket cells (BCs)] and principal neurons [dentate gyrus granule cells (GCs)] using paired recordings in rat hippocampal slices at 34°C. Unitary IPSCs recorded from BC–GC pairs in high intracellular Cl− concentration showed a fast rise and a biexponential decay, with mean time constants of 2 and 9 msec. The mean quantal conductance change, determined directly at reduced extracellular Ca2+/Mg2+concentration ratios, was 1.7 nS. Quantal release at the BC–GC synapse occurred with short delay and was highly synchronized. Analysis of IPSC peak amplitudes and numbers of failures by multiple probability compound binomial analysis indicated that synaptic transmission at the BC–GC synapse involves three to seven release sites, each of which releases transmitter with high probability (∼0.5 in 2 mMCa2+/1 mM Mg2+). Unitary BC–GC IPSCs showed paired-pulse depression (PPD); maximal depression, measured for 10 msec intervals, was 37%, and recovery from depression occurred with a time constant of 2 sec. Paired-pulse depression was mainly presynaptic in origin but appeared to be independent of previous release. Synaptic transmission at the BC–GC synapse showed frequency-dependent depression, with half-maximal decrease at 5 Hz after a series of 1000 presynaptic action potentials. The relative stability of transmission at the BC–GC synapse is consistent with a model in which an activity-dependent gating mechanism reduces release probability and thereby prevents depletion of the releasable pool of synaptic vesicles. Thus several mechanisms converge on the generation of powerful and sustained transmission at interneuron–principal neuron synapses in hippocampal circuits.}, author = {Kraushaar, Udo and Jonas, Peter M}, issn = {0270-6474}, journal = {Journal of Neuroscience}, number = {15}, pages = {5594 -- 5607}, publisher = {Society for Neuroscience}, title = {{Efficacy and stability of quantal GABA release at a hippocampal interneuron-principal neuron synapse}}, doi = {10.1523/JNEUROSCI.20-15-05594.2000}, volume = {20}, year = {2000}, } @article{3490, abstract = {Long-term depression (LTD) is a form of synaptic plasticity that can be induced either by low-frequency stimulation of presynaptic fibers or in an associative manner by asynchronous pairing of presynaptic and postsynaptic activity. We investigated the induction mechanisms of associative LTD in CA1 pyramidal neurons of the hippocampus using whole-cell patch-clamp recordings and Ca2+ imaging in acute brain slices. Asynchronous pairing of postsynaptic action potentials with EPSPs evoked with a delay of 20 msec induced a robust, long-lasting depression of the EPSP amplitude to 43%. Unlike LTD induced by low-frequency stimulation, associative LTD was resistant to the application of D-AP-5, indicating that it is independent of NMDA receptors. In contrast, associative LTD was inhibited by (S)-α-methyl-4-carboxyphenyl-glycine, indicating the involvement of metabotropic glutamate receptors. Furthermore, associative LTD is dependent on the activation of voltage-gated Ca2+ channels by postsynaptic action potentials. Both nifedipine, an L-type Ca2+ channel antagonist, and ω-conotoxin GVIA, a selective N-type channel blocker, abolished the induction of associative LTD. 8-hydroxy-2-dipropylaminotetralin (OH-DPAT), a 5-HT(1A) receptor agonist, inhibited postsynaptic Ca2+ influx through N-type Ca2+ channels, without affecting presynaptic transmitter release. OH-DPAT also inhibited the induction of associative LTD, suggesting that the involvement of N-type channels makes synaptic plasticity accessible to modulation by neurotransmitters. Thus, the modulation of N-type Ca2+ channels provides a gain control for synaptic depression in hippocampal pyramidal neurons.}, author = {Normann, Claus and Peckys, Diana and Schulze, Christian and Walden, Jörg and Jonas, Peter M and Bischofberger, Joseph}, issn = {0270-6474}, journal = {Journal of Neuroscience}, number = {22}, pages = {8290 -- 8297}, publisher = {Society for Neuroscience}, title = {{Associative long-term depression in the hippocampus is dependent on postsynaptic N-type Ca(2+) channels}}, doi = {10.1523/JNEUROSCI.20-22-08290.2000}, volume = {20}, year = {2000}, } @article{3491, abstract = {Fast and reliable activation of inhibitory interneurons is critical for the stability of cortical neuronal networks. Active conductances in dendrites may facilitate interneuron activation, but direct experimental evidence was unavailable. Patch-clamp recordings from dendrites of hippocampal oriens- alveus interneurons revealed high densities of voltage-gated sodium and potassium ion channels. Simultaneous recordings from dendrites and somata suggested that action potential initiation occurs preferentially in the axon with long threshold stimuli, but can be shifted to somatodendritic sites when brief stimuli are applied. After initiation, action potentials propagate over the somatodendritic domain with constant amplitude, high velocity, and reliability, even during high-frequency trains.}, author = {Martina, Marco and Vida, Imre and Jonas, Peter M}, issn = {0036-8075}, journal = {Science}, number = {5451}, pages = {295 -- 300}, publisher = {American Association for the Advancement of Science}, title = {{Distal initiation and active propagation of action potentials in interneuron dendrites}}, doi = {10.1126/science.287.5451.295}, volume = {287}, year = {2000}, } @article{3492, abstract = {Analysis of presynaptic determinants of synaptic strength has been difficult at cortical synapses, mainly due to the lack of direct access to presynaptic elements. Here we report patch-clamp recordings from mossy fiber boutons (MFBs) in rat hippocampal slices. The presynaptic action potential is very short during low-frequency stimulation but is prolonged up to 3-fold during high-frequency stimulation. Voltage-gated K+ channels in MFBs inactivate rapidly but recover from inactivation very slowly, suggesting that cumulative K+ channel inactivation mediates activity-dependent spike broadening. Prolongation of the presynaptic voltage waveform leads to an increase in the number of Ca2+ ions entering the terminal per action potential and to a consecutive potentiation of evoked excitatory postsynaptic currents at MFB-CA3 pyramidal cell synapses. Thus, inactivation of presynaptic K+ channels contributes to the control of efficacy of a glutamatergic synapse in the cortex.}, author = {Geiger, Jörg and Jonas, Peter M}, issn = {0896-6273}, journal = {Neuron}, number = {3}, pages = {927 -- 939}, publisher = {Elsevier}, title = {{Dynamic control of presynaptic Ca(2+) inflow by fast-inactivating K+ channels in hippocampal mossy fiber boutons}}, doi = {10.1016/S0896-6273(00)00164-1}, volume = {28}, year = {2000}, } @article{3532, abstract = {Multichannel tetrode array recording in awake behaving animals provides a powerful method to record the activity of large numbers of neurons. The power of this method could be extended if further information concerning the intracellular state of the neurons could be extracted from the extracellularly recorded signals. Toward this end, we have simultaneously recorded intracellular and extracellular signals from hippocampal CA1 pyramidal cells and interneurons in the anesthetized rat. We found that several intracellular parameters can be deduced from extracellular spike waveforms. The width of the intracellular action potential is defined precisely by distinct points on the extracellular spike. Amplitude changes of the intracellular action potential are reflected by changes in the amplitude of the initial negative phase of the extracellular spike, and these amplitude changes are dependent on the state of the network. In addition, intracellular recordings from dendrites with simultaneous extracellular recordings from the soma indicate that, on average, action potentials are initiated in the perisomatic region and propagate to the dendrites at 1.68 m/s. Finally we determined that a tetrode in hippocampal area CA1 theoretically should be able to record electrical signals from similar to 1,000 neurons. Of these, 60-100 neurons should generate spikes of sufficient amplitude to be detectable from the noise and to allow for their separation using current spatial clustering methods. This theoretical maximum is in contrast to the approximately six units that are usually detected per tetrode. From this, we conclude that a large percentage of hippocampal CA1 pyramidal cells are silent in any given behavioral condition.}, author = {Henze, Darrell and Borhegyi, Zsolt and Csicsvari, Jozsef L and Mamiya, Akira and Harris, Kenneth and Buzsáki, György}, issn = {0022-3077}, journal = {Journal of Neurophysiology}, number = {1}, pages = {390 -- 400}, publisher = {American Physiological Society}, title = {{Intracellular features predicted by extracellular recordings in the hippocampus in vivo}}, doi = {10.1152/jn.2000.84.1.390}, volume = {84}, year = {2000}, } @article{3542, abstract = {Transfer of neuronal patterns from the CA3 to CA1 region was studied by simultaneous recording of neuronal ensembles in the behaving rat. A nonlinear interaction among pyramidal neurons was observed during sharp wave (SPW)-related population bursts, with stronger synchrony associated with more widespread spatial coherence. SPW bursts emerged in the CA3a-b subregions and spread to CA3c before invading the CA1 area. Synchronous discharge of >10% of the CA3 within a 100 ms window was required to exert a detectable influence on CA1 pyramidal cells. Activity of some CA3 pyramidal neurons differentially predicted the ripple-related discharge of circumscribed groups of CA1 pyramidal cells. We suggest that, in SPW behavioral state, the coherent discharge of a small group of CA3 cells is the primary cause of spiking activity in CA1 pyramidal neurons.}, author = {Csicsvari, Jozsef L and Hirase, Hajima and Mamiya, Akira and Buzsáki, György}, issn = {0896-6273}, journal = {Neuron}, number = {2}, pages = {585 -- 594}, publisher = {Elsevier}, title = {{Ensemble patterns of hippocampal CA3-CA1 neurons during sharp wave-associated population events}}, doi = {10.1016/S0896-6273(00)00135-5}, volume = {28}, year = {2000}, } @article{3548, abstract = {Simultaneous recording from large numbers of neurons is a prerequisite for understanding their cooperative behavior. Various recording techniques and spike separation methods are being used toward this goal. However, the error rates involved in spike separation have not yet been quantified. We studied the separation reliability of “tetrode” (4-wire electrode) recorded spikes by monitoring simultaneously from the same cell intracellularly with a glass pipette and extracellularly with a tetrode. With manual spike sorting, we found a trade-off between Type I and Type II errors, with errors typically ranging from 0 to 30% depending on the amplitude and firing pattern of the cell, the similarity of the waveshapes of neighboring neurons, and the experience of the operator. Performance using only a single wire was markedly lower, indicating the advantages of multiple-site monitoring techniques over single-wire recordings. For tetrode recordings, error rates were increased by burst activity and during periods of cellular synchrony. The lowest possible separation error rates were estimated by a search for the best ellipsoidal cluster shape. Human operator performance was significantly below the estimated optimum. Investigation of error distributions indicated that suboptimal performance was caused by inability of the operators to mark cluster boundaries accurately in a high-dimensional feature space. We therefore hypothesized that automatic spike-sorting algorithms have the potential to significantly lower error rates. Implementation of a semi-automatic classification system confirms this suggestion, reducing errors close to the estimated optimum, in the range 0-8%.}, author = {Harris, Kenneth and Henze, Darrell and Csicsvari, Jozsef L and Hirase, Hajima and Buzsáki, György}, issn = {0022-3077}, journal = {Journal of Neurophysiology}, number = {1}, pages = {401 -- 414}, publisher = {American Physiological Society}, title = {{Accuracy of tetrode spike separation as determined by simultaneous intracellular and extracellular measurements}}, doi = {10.1152/jn.2000.84.1.401}, volume = {84}, year = {2000}, } @inproceedings{3555, abstract = {A sliver is a tetrahedron whose four vertices lie close to a plane and whose perpendicular projection to that plane is a convex quadrilateral with no short edge. Slivers are both undesirable and ubiquitous in 3-dimensional Delaunay triangulations. Even when the point-set is well-spaced, slivers may result. This paper shows that such a point set permits a small perturbation whose Delaunay triangulation contains no slivers. It also gives deterministic algorithms that compute the perturbation of n points in time O(n log n) with one processor and in time O(log n) with O(n) processors.}, author = {Edelsbrunner, Herbert and Li, Xiang and Miller, Gary and Stathopoulos, Andreas and Talmor, Dafna and Teng, Shang and Üngör, Alper and Walkington, Noel}, booktitle = {Proceedings of the 32nd annual ACM symposium on Theory of computing}, isbn = {9781581131840}, location = {Portland, OR, USA}, pages = {273 -- 277}, publisher = {ACM}, title = {{Smoothing and cleaning up slivers}}, doi = {10.1145/335305.335338}, year = {2000}, } @inbook{3572, abstract = {Allzulange wurde die spielhafte Beschäftigung als Gegensatz zu ernsthafter Arbeit gesehen. Dieser Artikel propagiert die spielerische Untersuchung von Kreis- und Kugelmengen. Gleichzeitig belegt er die nutzbare Anwendung von elementaren Einsichten in der Molekularbiologie und allgemeiner in der Beschreibung von Form und Verformung.}, author = {Edelsbrunner, Herbert}, booktitle = {Zur Kunst des formalen Denkens}, isbn = {3851653580}, pages = {153 -- 171}, publisher = {Passagen Verlag}, title = {{Spielereien mit Kreisen und Kugeln. Zum Thema Form und Verformung}}, year = {2000}, } @article{3583, abstract = {The Delaunay triangulation of a finite point set is a central theme in computational geometry. It finds its major application in the generation of meshes used in the simulation of physical processes. This paper connects the predominantly combinatorial work in classical computational geometry with the numerical interest in mesh generation. It focuses on the two- and three-dimensional case and covers results obtained during the twentieth century.}, author = {Edelsbrunner, Herbert}, journal = {Acta Numerica}, pages = {133 -- 213}, publisher = {Cambridge University Press}, title = {{Triangulations and meshes in computational geometry}}, doi = {10.1017/S0962492900001331}, volume = {9}, year = {2000}, } @article{3623, abstract = {We present the theoretical background to a new method for measuring genetic variation for total fitness in Drosophila. The method allows heterozygous effects on total fitness of whole wild-type chromosomes to be measured under normal demography with overlapping generations. The wild-type chromosomes are competed against two balancer chromosomes (B1, B2, say), providing a standard genotype B1/B2 against which variation in the fitness effects of the wild-type chromosomes can be assessed. Fitness can be assessed in two ways: (i) at equilibrium of all three chromosomes under heterozygote advantage, and (ii) during displacement of one balancer by the other. Equilibrium with all three chromosomes present will be achieved only if the wild-type homozygote is not too fit, and if the fitnesses of the three heterozygotes are not too unequal. These conditions were not satisfied for any of a sample of 12 lethal-bearing chromosomes isolated from a random-bred laboratory population of Drosophila. At equilibrium, genotypic frequencies show low sensitivity to changes in genotypic fitness. Furthermore, where all four genotypes are viable and fertile, supplementary information from cages with only two chromosomes present and from direct measurements of pre-adult viability are required to estimate fitnesses from frequencies. The invasion method has the advantages of a greater sensitivity and of not requiring further data to estimate fitnesses if the wild-type homozygote is fertile. However, it requires that multiple samples be taken as the invasion progresses. In a discrete generation model, generation time influences fitness estimates from this method and is difficult to estimate accurately from the data. A full age-structured model can also be applied to the data from both types of experiment. For the invasion method, this gives fitness estimates close to those from the discrete generation model.}, author = {Barton, Nicholas H and Patridge, Linda}, issn = {0016-6723}, journal = {Genetical Research}, number = {3}, pages = {297 -- 314}, publisher = {Cambridge University Press}, title = {{Measuring fitness by means of balancer chromosomes}}, doi = {10.1017/S0016672399004346}, volume = {75}, year = {2000}, }