@article{4589,
  abstract     = {The theory of the natural numbers with linear order and monadic predicates underlies propositional linear temporal logic. To study temporal logics that are suitable for reasoning about real-time systems, we combine this classical theory of infinite state sequences with a theory of discrete time, via a monotonic function that maps every state to its time. The resulting theory of timed state sequences is shown to be decidable, albeit nonelementary, and its expressive power is characterized by ω-regular sets. Several more expressive variants are proved to be highly undecidable. This framework allows us to classify a wide variety of real-time logics according to their complexity and expressiveness. Indeed, it follows that most formalisms proposed in the literature cannot be decided. We are, however, able to identify two elementary real-time temporal logics as expressively complete fragments of the theory of timed state sequences, and we present tableau-based decision procedures for checking validity. Consequently, these two formalisms are well-suited for the specification and verification of real-time systems.

Copyright © 1993 Academic Press. All rights reserved.},
  author       = {Alur, Rajeev and Henzinger, Thomas A},
  issn         = {0890-5401},
  journal      = {Information and Computation},
  number       = {1},
  pages        = {35 -- 77},
  publisher    = {Elsevier},
  title        = {{Real-time logics: Complexity and expressiveness}},
  doi          = {10.1006/inco.1993.1025},
  volume       = {104},
  year         = {1993},
}

@article{3474,
  abstract     = {1. Excitatory postsynaptic currents (EPSCs) were recorded in CA3 pyramidal cells of hippocampal slices of 15- to 24-day-old rats (22 degrees C) using the whole-cell configuration of the patch clamp technique. 2. Composite EPSCs were evoked by extracellular stimulation of the mossy fibre tract. Using the selective blockers 6-cyano-7-nitroquinoxaline-2,3-dione (CNQX) and D-2-amino-5-phosphonopentanoic acid (APV), a major alpha-amino-3-hydroxy-5-methylisoxazole-4-propionate (AMPA)/kainate receptor-mediated component and a minor NMDA receptor-mediated component with slower time course were distinguished. For the AMPA/kainate receptor-mediated component, the peak current-voltage (I-V) relation was linear, with a reversal potential close to 0 mV. The half-maximal blocking concentration of CNQX was 353 nM. 3. Unitary EPSCs of the mossy fibre terminal (MF)-CA3 pyramidal cell synapse were evoked at membrane potentials of -70 to -90 mV by low-intensity extracellular stimulation of granule cell somata using fine-tipped pipettes. The EPSC peak amplitude as a function of stimulus intensity showed all-or-none behaviour. The region of low threshold was restricted to a few micrometres. This suggests that extracellular stimulation was focal, and that the stimulus-evoked EPSCs were unitary. 4. Latency and rise time histograms of EPSCs evoked by granule cell stimulation showed narrow unimodal distributions within each experiment. The mean latency was 4.2 +/- 1.0 ms, and the mean 20-80% rise time was 0.6 +/- 0.1 ms (23 cells). When fitted within the range 0.7 ms to 20 ms after the peak, the decay of the EPSCs with the fastest rise (rise time 0.5 ms or less) could be described by a single exponential function; the mean time constant was in the range 3.0-6.6 ms with a mean of 4.8 ms (8 cells). 5. Peak amplitudes of the EPSCs evoked by suprathreshold granule cell stimulation fluctuated between trials. The apparent EPSC peak conductance in normal extracellular solution (2 mM Ca2+, 1 mM Mg2+), excluding failures, was 1 nS. Reducing the Ca2+ concentration and increasing the Mg2+ concentration reduced the mean peak amplitude in a concentration-dependent manner. 6. Peaks in EPSC peak amplitude distributions were apparent in low Ca2+ and high Mg2+. Using the criteria of equidistance and the presence of peaks and dips in the autocorrelation function, five of nine EPSC peak amplitude distributions were judged to be quantal.},
  author       = {Jonas, Peter M and Major, Guy and Sakmann, Bert},
  issn         = {0022-3751},
  journal      = {Journal of Physiology},
  pages        = {615 -- 663},
  publisher    = {Wiley-Blackwell},
  title        = {{Quantal components of unitary EPSCs at the mossy fibre synapse on CA3 pyramidal cells of rat hippocampus}},
  doi          = {10.1113/jphysiol.1993.sp019965},
  volume       = {472},
  year         = {1993},
}

@article{4177,
  abstract     = {Thyroid hormones play an important role in brain development, but the mechanism(s) by which triiodothyronine (T3) mediates neuronal differentiation is poorly understood. Here we demonstrate that T3 regulates the neurotrophic factor, neurotrophin-3 (NT-3), in developing rat cerebellar granule cells both in cell culture and in vivo. In situ hybridization experiments showed that developing Purkinje cells do not express NT-3 mRNA but do express trkC, the putative neuronal receptor for NT-3. Addition of recombinant NT-3 to cerebellar cultures from embryonic rat brain induces hypertrophy and neurite sprouting of Purkinje cells, and upregulates the mRNA encoding the calcium-binding protein, calbindin-28 kD. The present study demonstrates a novel interaction between cerebellar granule neurons and developing Purkinje cells in which NT-3 induced by T3 in the granule cells promotes Purkinje cell differentiation.},
  author       = {Lindholm, Dan and Castrén, Eero and Tsoulfas, Pantelis and Kolbeck, Roland and Berzaghi, Maria and Leingärtner, Axel and Heisenberg, Carl-Philipp J and Tesarollo, Lino and Parada, Luis and Thoenen, Hans},
  issn         = {0021-9525},
  journal      = {Journal of Cell Biology},
  number       = {2},
  pages        = {443 -- 450},
  publisher    = {Rockefeller University Press},
  title        = {{Neurotrophin-3 induced by tri-iodothyronine in cerebellar granule cells promotes Purkinje cell differentiation}},
  doi          = {10.1083/jcb.122.2.443},
  volume       = {122},
  year         = {1993},
}

@article{4303,
  abstract     = {In a stably subdivided population with symmetric migration, the chance that a favoured allele will be fixed is independent of population structure. However, random extinction introduces an extra component of sampling drift, and reduces the probability of fixation. In this paper, the fixation probability is calculated using the diffusion approximation; comparison with exact solution of the discrete model shows this to be accurate. The key parameters are the rates of selection, migration and extinction, scaled relative to population size (S = 4Ns, M = 4Nm, Λ = 4Nλ); results apply to a haploid model, or to diploids with additive selection. If new colonies derive from many demes, the fixation probability cannot be reduced by more than half. However, if colonies are initially homogeneous, fixation probability can be much reduced. In the limit of low migration and extinction rates (M, Λ 1), it is 2s/{1 + (Λ/MS)(1 −exp(−S))}, whilst in the opposite limit (S  1), it is 4sM/{Λ(Λ + M)}. In the limit of weak selection (M, Λ  1), it is 4sM/{Λ(Λ + M)}. These factors are not the same as the reduction in effective population size (Ne/N), showing that the effects of population structure on selected alleles cannot be understood from the behaviour of neutral markers.},
  author       = {Barton, Nicholas H},
  issn         = {0016-6723},
  journal      = {Genetics Research},
  number       = {2},
  pages        = {149 -- 158},
  publisher    = {Cambridge University Press},
  title        = {{The probability of fixation of a favoured allele in a subdivided population}},
  doi          = {10.1017/S0016672300031748},
  volume       = {62},
  year         = {1993},
}

@article{2533,
  abstract     = {A cDNA clone for a new metabotropic glutamate receptor, mGluR5, was isolated through polymerase chain reaction-mediated DNA amplification by using primer sequences conserved among the metabotropic glutamate receptor (mGluR) family and by the subsequent screening of a rat brain cDNA library. The cloned receptor consists of 1171 amino acid residues and exhibits a structural architecture common to the mGluR family, possessing a large extracellular domain preceding the seven putative membrane-spanning segments. mGluR5 shows the highest sequence similarity to mGluR1 among the mGluR members and is coupled to the stimulation of phosphatidylinositol hydrolysis/ Ca2+ signal transduction in Chinese hamster ovary cells transfected with the cloned cDNA. This receptor also resembles mGluR1 in its agonist selectivity and antagonist responses; the potency rank order of agonists for mGluR5 was determined to be quisqualate &gt; L-glutamate ≥ ibotenate &gt; trans-1-aminocyclopentane-1,3-dicarboxylate. Blot and in situ hybridization analyses indicated that mGluR5 mRNA is widely distributed in neuronal cells of the central nervous system and is expressed differently from mGluR1 mRNA in many brain regions. This investigation thus demonstrates that there is an additional mGluR subtype which closely resembles mGluR1 in its signal transduction and pharmacological properties and is expressed in specialized neuronal cells in the central nervous system.},
  author       = {Abe, Takaaki and Sugihara, Hidemitsu and Nawa, Hiroyuki and Shigemoto, Ryuichi and Mizuno, Noboru and Nakanishi, Shigetada},
  issn         = {0021-9258},
  journal      = {Journal of Biological Chemistry},
  number       = {19},
  pages        = {13361 -- 13368},
  publisher    = {American Society for Biochemistry and Molecular Biology},
  title        = {{Molecular characterization of a novel metabotropic glutamate receptor mGluR5 coupled to inositol phosphate/Ca2+ signal transduction}},
  doi          = {10.1016/S0021-9258(18)42219-3},
  volume       = {267},
  year         = {1992},
}

@article{2535,
  abstract     = {We report the molecular characterization of two novel rat helix-loop-helix (HLH) proteins, designated HES-1 and HES-3, that show structural homology to the Drosophila hairy and Enhancer of split [E(spl)] proteins, both of which are required for normal neurogenesis. HES-1 mRNA, expressed in various tissues of both embryos and adults, is present at a high level in the epithelial cells, including the embryonal neuroepithelial cells, as well as in the mesoderm-derived tissues such as the embryonal muscle. In contrast, HES-3 mRNA is produced exclusively in cerebellar Purkinje cells. HES-1 represses transcription by binding to the N box, which is a recognition sequence of E(spl) proteins. Interestingly, neither HES-1 nor HES-3 alone interacts efficiently with the E box, but each protein decreases the transcription induced by E-box-binding HLH activators such as E47. Furthermore, HES-1 also inhibits the functions of MyoD and MASH1 and effectively diminishes the myogenic conversion of C3H10T1/2 cells induced by MyoD. These results suggest that HES-1 may play an important role in mammalian development by negatively acting on the two different sequences while HES-3 acts as a repressor in a specific type of neurons.},
  author       = {Sasai, Yoshiki and Kageyama, Ryoichiro and Tagawa, Yoshiaki and Shigemoto, Ryuichi and Nakanishi, Shigetada},
  issn         = {0890-9369},
  journal      = {Genes and Development},
  number       = {12 B},
  pages        = {2620 -- 2634},
  publisher    = {Cold Spring Harbor Laboratory Press},
  title        = {{Two mammalian helix-loop-helix factors structurally related to Drosophila hairy and Enhancer of split}},
  doi          = {10.1101/gad.6.12b.2620},
  volume       = {6},
  year         = {1992},
}

@article{2722,
  abstract     = {A version of the one-dimensional Rayleigh gas is considered: a point particle of mass M (molecule), confined to the unit interval [0,1], is surrounded by an infinite ideal gas of point particles of mass 1 (atoms). The molecule interacts with the atoms and with the walls via elastic collision. Central limit theorems are proved for a wide class of additive functionals of this system (e.g. the number of collisions with the walls and the total length of the molecular path).},
  author       = {Erdös, László and Tuyen, Dao},
  issn         = {0010-3616},
  journal      = {Communications in Mathematical Physics},
  number       = {3},
  pages        = {451 -- 466},
  publisher    = {Springer},
  title        = {{Central limit theorems for the one-dimensional Rayleigh gas with semipermeable barriers}},
  doi          = {10.1007/BF02099260},
  volume       = {143},
  year         = {1992},
}

@article{3470,
  abstract     = {Currents activated by glutamate receptor (GluR) agonists were recorded from outside-out patches isolated from the soma of visually identified pyramidal neurones of the (CA3 and CA1 region of rat hippocampal slices. α-Amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA). L-glutamate (L-Glu), and kainate (KA) were delivered either by bath application through perfusion of the recording chamber or by rapid application via a piezo-driven two-barrelled fast application system. 2. Bath application of each of the three agonists activated inward currents in all patches (n = 134) at holding potentials of -50 or -60 mV. The current amplitude increased in size between 3 to 30 μM-AMPA and 100 μM to 1 mM-KA. With this slow mode of bath application, the responses showed no apparent desensitization even at saturating concentrations of AMPA (30 μM) and KA (1 mM). 3. The ratio of currents activated by 30 μM-AMPA and 300 μM-KA showed a characteristic difference between CA3 and CA1 neurones. The ratio was 0.242 ± 0.028 (mean ± S.E.M., n = 16) for CA3 cell patches and 0.097 ± 0.012 (n = 8) for CA1 cell patches indicating that GluRs in the two cell populations are different. 4. The steady-state current-voltage relations (I-Vs) for AMPA- and KA-activated currents showed pronounced outward rectification for both cell types (when the main cations are Na+ in the bath and Cs+ in the pipette solution). The current reversed close to 0 mV and the ratio of chord conductances 80 mV on either side of the reversal potential was 2.66 for KA-activated currents in CA3 cell patches and 2.60 in CA1 cell patches. AMPA-activated currents showed a time-dependent increase after steps to positive membrane potentials and a decrease after steps to negative voltages, indicating that a gating process is responsible for outward rectification of the steady-state I-IV. 5. The permeability (P) of GluR channels was high for Na+ as compared to Cs+ for both cell types (P(Na)/P(Cs) = 0.88 and 0.84). The permeability was low for N-methyl-D-glucamine+ (P(NMG)/P(Cs) ≤ 0.03) and Ca2+ (P(Ca)/P(Cs) ≤0.05). 6. The current noise level increased during application of AMPA or KA. Apparent single-channel conductances obtained from fluctuation analysis were higher for AMPA than for KA, but similar for both cell types. In CA3 cell patches, AMPA activated channels with an apparent chord conductance of 7.2 pS, KA of 3.0 pS conductance. 7. Fast agonist application revealed desensitization of GluR channels which was dependent on the type of agonist, currents activated by AMPA and L-Glu rose rapidly to a peak and then desensitized to a steady-state current. In contrast, currents activated by fast application of KA rose to a plateau and did not desensitize. The steady state current expressed as a percentage of the peak current was higher for L-Glu than for AMPA and slightly higher for CA3 than for CA1 cell patches. For CA3 cell patches, this fraction amounted to 6.2 %, with 300 μM-L-Glu and 2.8%, with 300 μM-AMPA. For CA1 cell patches, corresponding values were 3.6 and 1.9 % 8. The dose response relations for the peak current activated by AMPA and L-Glu and the steady-state current activated by KA were similar for CA3 and CA1 cell patches. The order of potency was AMPA &gt; L-Glu ≃ KA for both cell types EC50 values 189, 342 and 344 μM for CA3 cell patches and 183, 424 and 474 μM for CA1 cell patches). In all cases, the Hill coefficients ranged between 12 and 1.7. 8. The rise of AMPA and L-Glu-activated currents became faster with increasing agonist concentration for both cell types. With L-Glu, rise times decreased from about 3 ms at 100 μM to 500 μs at 3 mM. The delay for agonist concentrations ≥ 300 μM was described by the sum of two exponential functions. The time constant of the predominant fast component was slightly concentration dependent and decreased from about 12 ms at 300 μM to 8 ms at 3 mM-L-Glu. 10. The current voltage relations of the peak currents activated by 300 μM-AMPA were linear for both cell types with a reversal potential close to OmV. 11. It is concluded that the GluR channels in pyramidal cells of hippocampal CA3 and CA1 regions are distinet but share many pharmacological and functional properties. Comparison of the properties of native and recombinant GluRs suggests that in both CA3 and CA1 regions GluR channels are hetero-oligomers containing the GluR-B subunit.},
  author       = {Jonas, Peter M and Sakmann, Bert},
  issn         = {0022-3751},
  journal      = {Journal of Physiology},
  pages        = {143 -- 171},
  publisher    = {Wiley-Blackwell},
  title        = {{Glutamate receptor channels in isolated patches from CA1 and CA3 pyramidal cells of rat hippocampal slices}},
  doi          = {10.1113/jphysiol.1992.sp019294 },
  volume       = {455},
  year         = {1992},
}

@article{3471,
  abstract     = {1. Outside-out patches were isolated from granule cells of dentate gyrus and pyramidal cells of CA3 and CA1 regions of rat hippocampal slices. Patches were exposed briefly to L-glutamate using a piezo-driven double-barrelled application pipette. 2. Applications of glutamate (1 mM) of 1 ms duration activated patch currents which rose and decayed rapidly. The 20-80% rise time of these glutamate receptor (GluR)-mediated currents was usually 0.2-0.6 ms. At -50 mV the peak current varied from 10 to 500 pA in different patches. 3. The peak current-voltage relation for brief pulses of 1 mM glutamate was virtually linear in normal extracellular solution for patches from the three cell types (-100 to 60 mV). 4. The permeability of GluR channels activated at the peak to Ca2+, relative to K+, was less than 0.1 for all three cell types (under bi-ionic conditions with Ca2+ on the extracellular side and K+ on the intracellular side of the membrane). 5. The offset decay time constant of the current following 1 ms pulses of 1 mM glutamate was brief, with mean values of 3.0 +/- 0.8, 2.5 +/- 0.7, and 2.3 +/- 0.7 ms for dentate, CA3 and CA1 cell patches, respectively. Offset time constants were independent of membrane potential and independent of glutamate concentration (200 microM and 1 mM) for the three cell types. 6. Applications of 1 mM glutamate of 100 ms duration showed that glutamate responses desensitized rapidly. The time constants for desensitization were 9.4 +/- 2.7, 11.3 +/- 2.8, and 9.3 +/- 2.8 ms for patches from dentate, CA3 and CA1 cells respectively. Desensitization time constants were only weakly dependent on glutamate concentration (200 microM and 1 mM) for the three cell types. Thus offset time constants are about four times faster than desensitization time constants for both glutamate concentrations. 7. Double pulse application of glutamate indicated that even a 1 ms pulse of 1 mM glutamate causes partial (about 60%) desensitization of GluR channels. The time course of recovery from desensitization was slower in dentate gyrus granule cell patches than in CA3 or CA1 pyramidal cell patches. 8. Desensitization was studied at equilibrium by exposing patches to low glutamate concentrations for at least 15 s before a 1 ms test pulse of 1 mM glutamate.},
  author       = {Colquhoun, D. and Jonas, Peter M and Sakmann, Bert},
  issn         = {0022-3751},
  journal      = {Journal of Physiology},
  pages        = {261 -- 287},
  publisher    = {Wiley-Blackwell},
  title        = {{Action of brief pulses of glutamate on AMPA/kainate receptors in patches from different neurones of rat hippocampal slices}},
  doi          = {10.1113/jphysiol.1992.sp019417},
  volume       = {458},
  year         = {1992},
}

@article{3581,
  abstract     = {A number of rendering algorithms in computer graphics sort three-dimensional objects by depth and assume that there is no cycle that makes the sorting impossible. One way to resolve the problem caused by cycles is to cut the objects into smaller pieces. In this paper we address the problem of estimating how many such cuts arc always sufficient. We also consider a few related algorithmic and combinatorial geometry problems. For example, we demonstrate that n lines in space can be sorted in randomized expected time O(n4’st’), provided that they define no cycle. We also prove an 0(n7’4) upper bound on the number of points in space so that there are n lines with the property that for each point there are at least three noncoplanar lines that contain it. },
  author       = {Chazelle, Bernard and Edelsbrunner, Herbert and Guibas, Leonidas and Pollack, Richard and Seidel, Raimund and Sharir, Micha and Snoeyink, Jack},
  issn         = {0925-7721},
  journal      = {Computational Geometry: Theory and Applications},
  number       = {6},
  pages        = {305 -- 323},
  publisher    = {Elsevier},
  title        = {{Counting and cutting cycles of lines and rods in space}},
  doi          = {10.1016/0925-7721(92)90009-H},
  volume       = {1},
  year         = {1992},
}

@article{4047,
  abstract     = {Arrangements of curves in the plane are fundamental to many problems in computational and combinatorial geometry (e.g. motion planning, algebraic cell decomposition, etc.). In this paper we study various topological and combinatorial properties of such arrangements under some mild assumptions on the shape of the curves, and develop basic tools for the construction, manipulation, and analysis of these arrangements. Our main results include a generalization of the zone theorem of Edelsbrunner (1986) and Chazelle (1985) to arrangements of curves (in which we show that the combinatorial complexity of the zone of a curve is nearly linear in the number of curves) and an application of that theorem to obtain a nearly quadratic incremental algorithm for the construction of such arrangements.},
  author       = {Edelsbrunner, Herbert and Guibas, Leonidas and Pach, János and Pollack, Richard and Seidel, Raimund and Sharir, Micha},
  issn         = {0304-3975},
  journal      = {Theoretical Computer Science},
  number       = {2},
  pages        = {319 -- 336},
  publisher    = {Elsevier},
  title        = {{Arrangements of curves in the plane - topology, combinatorics, and algorithms}},
  doi          = {10.1016/0304-3975(92)90319-B},
  volume       = {92},
  year         = {1992},
}

@article{4052,
  abstract     = {This paper describes an effective procedure for stratifying a real semi-algebraic set into cells of constant description size. The attractive feature of our method is that the number of cells produced is singly exponential in the number of input variables. This compares favorably with the doubly exponential size of Collins' decomposition. Unlike Collins' construction, however, our scheme does not produce a cell complex but only a smooth stratification. Nevertheless, we are able to apply our results in interesting ways to problems of point location and geometric optimization.},
  author       = {Chazelle, Bernard and Edelsbrunner, Herbert and Guibas, Leonidas and Sharir, Micha},
  issn         = {1879-2294},
  journal      = {Theoretical Computer Science},
  number       = {1},
  pages        = {77 -- 105},
  publisher    = {Elsevier},
  title        = {{A singly exponential stratification scheme for real semi-algebraic varieties and its applications}},
  doi          = {10.1016/0304-3975(91)90261-Y},
  volume       = {84},
  year         = {1991},
}

@article{4056,
  abstract     = {This paper proves that for every n ≥ 4 there is a convex n-gon such that the vertices of 2n - 7 vertex pairs are one unit of distance apart. This improves the previously best lower bound of ⌊ (5n - 5) 3⌋ given by Erdo{combining double acute accent}s and Moser if n ≥ 17.},
  author       = {Edelsbrunner, Herbert and Hajnal, Péter},
  issn         = {1096-0899},
  journal      = {Journal of Combinatorial Theory Series A},
  number       = {2},
  pages        = {312 -- 316},
  publisher    = {Elsevier},
  title        = {{A lower bound on the number of unit distances between the vertices of a convex polygon}},
  doi          = {10.1016/0097-3165(91)90042-F},
  volume       = {56},
  year         = {1991},
}

@article{4057,
  author       = {Edelsbrunner, Herbert},
  issn         = {1090-2724},
  journal      = {Journal of Computer and System Sciences},
  number       = {2},
  pages        = {249 -- 251},
  publisher    = {Elsevier},
  title        = {{Corrigendum}},
  doi          = {10.1016/0022-0000(91)90013-U},
  volume       = {42},
  year         = {1991},
}

@article{4061,
  abstract     = {We present an algorithm to compute a Euclidean minimum spanning tree of a given set S of N points in Ed in time O(Fd (N,N) logd N), where Fd (n,m) is the time required to compute a bichromatic closest pair among n red and m green points in Ed . If Fd (N,N)=Ω(N1+ε), for some fixed e{open}&gt;0, then the running time improves to O(Fd (N,N)). Furthermore, we describe a randomized algorithm to compute a bichromatic closest pair in expected time O((nm log n log m)2/3+m log2 n+n log2 m) in E3, which yields an O(N4/3 log4/3 N) expected time, algorithm for computing a Euclidean minimum spanning tree of N points in E3. In d≥4 dimensions we obtain expected time O((nm)1-1/([d/2]+1)+ε+m log n+n log m) for the bichromatic closest pair problem and O(N2-2/([d/2]+1)ε) for the Euclidean minimum spanning tree problem, for any positive e{open}.},
  author       = {Agarwal, Pankaj and Edelsbrunner, Herbert and Schwarzkopf, Otfried and Welzl, Emo},
  issn         = {1432-0444},
  journal      = {Discrete & Computational Geometry},
  number       = {1},
  pages        = {407 -- 422},
  publisher    = {Springer},
  title        = {{Euclidean minimum spanning trees and bichromatic closest pairs}},
  doi          = {10.1007/BF02574698},
  volume       = {6},
  year         = {1991},
}

@article{4062,
  abstract     = {We prove that for any set S of n points in the plane and n3-α triangles spanned by the points in S there exists a point (not necessarily in S) contained in at least n3-3α/(c log5 n) of the triangles. This implies that any set of n points in three-dimensional space defines at most {Mathematical expression} halving planes.},
  author       = {Aronov, Boris and Chazelle, Bernard and Edelsbrunner, Herbert and Guibas, Leonidas and Sharir, Micha and Wenger, Rephael},
  issn         = {1432-0444},
  journal      = {Discrete & Computational Geometry},
  number       = {1},
  pages        = {435 -- 442},
  publisher    = {Springer},
  title        = {{Points and triangles in the plane and halving planes in space}},
  doi          = {10.1007/BF02574700},
  volume       = {6},
  year         = {1991},
}

@article{2480,
  abstract     = {Functional cDNA clones for rat neuromedin K receptor were isolated from a rat brain cDNA library by cross-hybridization with the bovine substance K recepor cDNA. Injection of the mRNA synthesized in vitro from the cloned cDNA into Xenopus oocytes elicited electrophysiological responses to tachykinins, with the most potent sensitivity being to neuromedin K. Ligand-binding displacement in membranes of mammalian COS cells transfected with the cDNA indicated the rank order of affinity of the receptor to tachykinins; neuromedin K &gt; substance K &gt; substance P. The hybridization analysis showed that the neuromedin K receptor mRNA is expressed in both the brain and the peripheral tissues at different levels. The rat neuromedin K receptor consists of 452 amino acid residues and belongs to the family of G protein-coupled receptors, which are thought to have seven transmembrane domains. The sequence comparison of the rat neuromedin K, substance P, and substance K receptors revealed that these receptors are highly conserved in the seven transmembrane domains and the cytoplasmic sides of the receptors. They also show some structural characteristics, including the common presence of histidine residues in transmembrane segments V and VI and the difference in the numbers and distributions of serine and threonine residues as possible phosphorylation sites in the cytoplasmic regions. This paper thus presents the first comprehensive analysis of the molecular nature of the multiple peptide receptors that exhibit similar but pharmacologically distinguishable activities.},
  author       = {Shigemoto, Ryuichi and Yokota, Yoshifumi and Tsuchida, Kunihiro and Nakanishi, Shigetada},
  issn         = {1083-351X},
  journal      = {Journal of Biological Chemistry},
  number       = {2},
  pages        = {623 -- 628},
  publisher    = {American Society for Biochemistry and Molecular Biology},
  title        = {{Cloning and expression of a rat neuromedin K receptor cDNA}},
  doi          = {10.1016/s0021-9258(19)40095-1 },
  volume       = {265},
  year         = {1990},
}

@article{2481,
  abstract     = {The family of mammalian tachykinin receptors consists of substance P receptor (SPR), neuromedin K receptor (NKR) and substance K receptor (SKR). In this investigation, tissue and regional distributions of the mRNAs for the three rat tachykinin receptors were investigated by blot-hybridization and RNase-protection analyses using the previously cloned receptor cDNAs. SPR mRNA is widely distributed in both the nervous system and peripheral tissues and is expressed abundantly in the hypothalamus and olfactory buld, as well as in the urinary bladder, salivary glands and small and large intestines. In contrast, NKR mRNA is predominantly expressed in the nervous system, particularly in the cortex, hypothalamus and cerebellum, whereas SKR mRNA expression is restricted to the peripheral tissues, being abundant in the urinary bladder, large intestine, stomach and adenal glands. Thus, the mRNAs for the three tachykinin receptors show distinct patterns of expression between the nervous system and peripheral tissues. Blot-hybridization analysis in combination with S1 nuclease protection and primer-extension analyses revealed that there are two large forms of SKR mRNA expressed commonly in the peripheral tissues, and two additional small forms of the mRNA expressed specifically in the adrenal gland and eye. These analyses also showed that the multiple forms of SKR mRNA differ in the lengths of the 5' mRNA portions, and that the two small forms of the mRNA, if translated, encode a truncated SKR polypeptide lacking the first two transmembrane domains. This investigation thus provides the comprehensive analysis of the distribution and mode of expression of the mRNAs for the multiple peptide receptors and offers a new basis on which to interpret the diverse functions of multiple tachykinin peptides in the CNS and peripheral tissues.},
  author       = {Tsuchida, Kunihiro and Shigemoto, Ryuichi and Yokota, Yoshifumi and Nakanishi, Shigetada},
  issn         = {1432-1033},
  journal      = {European Journal of Biochemistry},
  number       = {3},
  pages        = {751 -- 757},
  publisher    = {Wiley-Blackwell},
  title        = {{Tissue distribution and quantitation of the mRNAs for three rat tachykinin receptors}},
  doi          = {10.1111/j.1432-1033.1990.tb19396.x},
  volume       = {193},
  year         = {1990},
}

@article{3467,
  abstract     = {The effects of mast cell degranulating peptide (MCDP), a toxin from the honey bee, and of dendrotoxin (DTX), a toxin from the green mamba snake, were studied in voltage-clamped experiments with myelinated nerve fibres of Xenopus. MCDP and DTX blocked part of the K+ current. About 20% of the K+ current, however, was resistant to the toxins even in high concentrations. In Ringer solution half-maximal block was reached with concentrations of 33 nM MCDP and 11 nM DTX. In high-K+ solution the potency of both toxins was lower. β-Bungarotoxin (β-BuTX), another snake toxin, also blocked part of the K+ current, but was less potent than MCDP and DTX. Tail currents in high-K+ solution were analysed and three K+ current components were separated according to Dubois (1981b). Both MCDP and DTX selectively blocked a fast deactivating, slowly inactivating K+ current component which steeply activates between E = -60 mV and E = -40 mV (component f1). In concentrations around 100 nM, MCDP and DTX blocked neither the slow K+ current (component s) nor the fast deactivating, rapidly inactivating K+ current which activates between E = -40 mV and E = 20 mV (component f2). Similar results could be derived from K+ outward currents in Ringer solution. In high-K+, IC50 of MCDP for component f1 was 99 nM, whereas it was 7.6 μM for f2. Corresponding values for DTX are 68 nM and 1.8 μM. Binding studies with nerve fibre membranes of Xenopus reveal high-affinity binding sites for 125I-labelled DTX )K(D) = 22 pM in Ringer solution and 81 pM in high-K+ solution). 125I-labelled DTX can be displaced from its sites completely by unlabelled DTX, toxin I (black mamba toxin), MCDP, and partially by β-BuTX. Immunocytochemical staining demonstrates that binding sites for DTX are present in nodal and paranodal regions of the axonal membrane. The axonal membrane of motor and sensory nerve fibres is equipped with three types of well-characterized K+ channels and constitutes so far the best preparation to study MCDP- and DTX-sensitive K+ channels with electrophysiological and biochemical methods.},
  author       = {Bräu, Michael and Dreyer, Florian and Jonas, Peter M and Repp, Holger and Vogel, Werner},
  issn         = {1469-7793},
  journal      = {Journal of Physiology},
  pages        = {365 -- 385},
  publisher    = {Wiley-Blackwell},
  title        = {{A K+ channel in Xenopus nerve fibres selectively blocked by bee and snake toxins: binding and voltage-clamp experiments}},
  doi          = {10.1113/jphysiol.1990.sp017918},
  volume       = {420},
  year         = {1990},
}

@article{3650,
  abstract     = {Hybrid zones can yield estimates of natural selection and gene flow. The width of a cline in gene frequency is approximately proportional to gene flow (σ) divided by the square root of per-locus selection ( &amp;s). Gene flow also causes gametic correlations (linkage disequilibria) between genes that differ across hybrid zones. Correlations are stronger when the hybrid zone is narrow, and rise to a maximum roughly equal to s. Thus cline width and gametic correlations combine to give estimates of gene flow and selection. These indirect measures of σ and s are especially useful because they can be made from collections, and require no field experiments. The method was applied to hybrid zones between color pattern races in a pair of Peruvian Heliconius butterfly species. The species are Mullerian mimics of one another, and both show the same changes in warning color pattern across their respective hybrid zones. The expectations of cline width and gametic correlation were generated using simulations of clines stabilized by strong frequency-dependent selection. In the hybrid zone in Heliconius erato, clines at three major color pattern loci were between 8.5 and 10.2 km wide, and the pairwise gametic correlations peaked at R &amp; 0.35. These measures suggest that s &amp; 0.23 per locus, and that σ &amp; 2.6 km. In erato, the shapes of the clines agreed with that expected on the basis of dominance. Heliconius melpomene has a nearly coincident hybrid zone. In this species, cline widths at four major color pattern loci varied between 11.7 and 13.4 km. Pairwise gametic correlations peaked near R &amp; 1.00 for tightly linked genes, and at R &amp; 0.40 for unlinked genes, giving s &amp; 0.25 per locus and σ &amp; 3.7 km. In melpomene, cline shapes did not perfectly fit theoretical shapes based on dominance; this deviation might be explained by long-distance migration and/or strong epistasis. Compared with erato, sample sizes in melpomene are lower and the genetics of its color patterns are less well understood. In spite of these problems, selection and gene flow are clearly of the same order of magnitude in the two species. The relatively high per locus selection coefficients agree with ``major gene'' theories for the evolution of Mullerian mimicry, but the genetic architecture of the color patterns does not. These results show that the genetics and evolution of mimicry are still only sketchily understood.},
  author       = {Mallet, James and Barton, Nicholas H and Lamas, Gerado and Santisteban, José and Muedas, Manuel and Eeley, Harriet},
  issn         = {0016-6731},
  journal      = {Genetics},
  number       = {4},
  pages        = {921 -- 936},
  publisher    = {Genetics Society of America},
  title        = {{Estimates of selection and gene flow from measures of cline width and linkage disequilibrium in Heliconius hybrid zones}},
  doi          = {10.1093/genetics/124.4.921},
  volume       = {124},
  year         = {1990},
}

