@article{11677, abstract = {We present an algorithm for maintaining the biconnected components of a graph during a sequence of edge insertions and deletions. It requires linear storage and preprocessing time. The amortized running time for insertions and for deletions isO(m 2/3 ), wherem is the number of edges in the graph. Any query of the form ‘Are the verticesu andv biconnected?’ can be answered in timeO(1). This is the first sublinear algorithm for this problem. We can also output all articulation points separating any two vertices efficiently. If the input is a plane graph, the amortized running time for insertions and deletions drops toO(√n logn) and the query time isO(log2 n), wheren is the number of vertices in the graph. The best previously known solution takes timeO(n 2/3 ) per update or query.}, author = {Henzinger, Monika H}, issn = {1432-0541}, journal = {Algorithmica}, number = {6}, pages = {503--538}, publisher = {Springer Nature}, title = {{Fully dynamic biconnectivity in graphs}}, doi = {10.1007/bf01189067}, volume = {13}, year = {1995}, } @inproceedings{11684, abstract = {This paper presents an algorithm for the fully dynamic biconnectivity problem whose running time is exponentially faster than all previously known solutions. It is the first dynamic algorithm that answers biconnectivity queries in time O(log/sup 2/n) in a n-node graph and can be updated after an edge insertion or deletion in polylogarithmic time. Our algorithm is a Las-Vegas style randomized algorithm with the update time amortized update time O(log/sup 4/n). Only recently the best deterministic result for this problem was improved to O(/spl radic/nlog/sup 2/n). We also give the first fully dynamic and a novel deletions-only transitive closure (i.e. directed connectivity) algorithms. These are randomized Monte Carlo algorithms. Let n be the number of nodes in the graph and let m/spl circ/ be the average number of edges in the graph during the whole update sequence: The fully dynamic algorithms achieve (1) query time O(n/logn) and update time O(m/spl circ//spl radic/nlog/sup 2/n+n); or (2) query time O(n/logn) and update time O(nm/spl circ//sup /spl mu/-1/)log/sup 2/n=O(nm/spl circ//sup 0.58/log/sup 2/n), where /spl mu/ is the exponent for boolean matrix multiplication (currently /spl mu/=2.38). The deletions-only algorithm answers queries in time O(n/logn). Its amortized update time is O(nlog/sup 2/n).}, author = {Henzinger, Monika H and King, V.}, booktitle = {Proceedings of IEEE 36th Annual Foundations of Computer Science}, isbn = {0-8186-7183-1}, issn = {0272-5428}, location = {Milwaukee, WI, United States}, pages = {664--672}, publisher = {Institute of Electrical and Electronics Engineers}, title = {{Fully dynamic biconnectivity and transitive closure}}, doi = {10.1109/SFCS.1995.492668}, year = {1995}, } @inproceedings{11805, abstract = {In this paper, we present sparse certificates for biconnectivity together with algorithms for updating these certificates. We thus obtain fully-dynamic algorithms for biconnectivity in graphs that run in O(√n log n log⌈m/n⌉) amortized time per operation, where m is the number of edges and n is the number of nodes in the graph. This improves upon the results in [11], in which algorithms were presented running in O(√m) amortized time, and solves the open problem to find certificates to speed up biconnectivity, as stated in [2].}, author = {Henzinger, Monika H and Poutré, Han}, booktitle = {3rd Annual European Symposium on Algorithms}, isbn = {9783540603139}, issn = {1611-3349}, location = {Corfu, Greece}, pages = {171–184}, publisher = {Springer Nature}, title = {{Certificates and fast algorithms for biconnectivity in fully-dynamic graphs}}, doi = {10.1007/3-540-60313-1_142}, volume = {979}, year = {1995}, } @inproceedings{11806, abstract = {This paper presents insertions-only algorithms for maintaining the exact and approximate size of the minimum edge cut and the minimum vertex cut of a graph. The algorithms output the approximate or exact size k in time O(1) or O(log n) and a cut of size k in time linear in its size. The amortized time per insertion is O(1/ε 2) for a (2+ε)-approximation, O((log λ)((log n)/ε)2) for a (1+ε)-approximation, and O(λ log n) for the exact size of the minimum edge cut, where n is the number of nodes in the graph, λ is the size of the minimum cut and ε>0. The (2+ε)-approximation algorithm and the exact algorithm are deterministic, the (1+ε)-approximation algorithm is randomized. The algorithms are optimal in the sense that the time needed for m insertions matches the time needed by the best static algorithm on a m-edge graph. We also present a static 2-approximation algorithm for the size κ of the minimum vertex cut in a graph, which takes time O(n 2 min(√n,κ)). This is a factor of κ faster than the best algorithm for computing the exact size, which takes time O(κ 2 n 2 +κ 3 n 1.5). We give an insertionsonly algorithm for maintaining a (2+ε)-approximation of the minimum vertex cut with amortized insertion time O(n(logκk)/ε).}, author = {Henzinger, Monika H}, booktitle = {22nd International Colloquium on Automata, Languages and Programming}, isbn = {9783540494256}, issn = {1611-3349}, location = {Szeged, Hungary}, pages = {280–291}, publisher = {Springer Nature}, title = {{Approximating minimum cuts under insertions}}, doi = {10.1007/3-540-60084-1_81}, volume = {944}, year = {1995}, } @inproceedings{11928, abstract = {We present a model with restricted randomness for edge updates in dynamic graph algorithms and a general technique for analyzing the expected running time of an update operation. This model is able to capture the average case in many applications, since (1) it allows restrictions on the set of edges which can be used for insertions and (2) the type (insertion or deletion) of each update operation is arbitrary, i.e., not random. We use our technique to analyze existing and new dynamic algorithms for maximum cardinality matching, minimum spanning forest, connectivity, 2-edge connectivity, k-edge connectivity, k-vertex connectivity, and bipartiteness. Given a random graph G with mo edges and n vertices and a sequence of 1 update operations such that the graph contains rni edges after operation i, the expected time for performing the updates for any 1 is O(1 logn + n xi=, l/fii) in the case of minimum spanning forests, connectivity, 2- edge connectivity, and bipartiteness. The expected time per update operation is O(n) in the case of maximum matching. For k-edge and k-vertex connectivity we also give improved bounds. Additionally we give an insertions-only algorithm for maximum cardinality matching with worst-case O(n) amortized time per insertion. }, author = {Alberts, David and Henzinger, Monika H}, booktitle = {6th Annual ACM-SIAM Symposium on Discrete Algorithms}, isbn = {0898713498}, location = {San Francisco, CA, United States}, pages = {312--321}, publisher = {Society for Industrial and Applied Mathematics}, title = {{Average case analysis of dynamic graph algorithms}}, year = {1995}, } @inbook{2465, abstract = {Auxins play a crucial role in the regulation of spatial and temporal aspects of plant growth and development1. As well as being required for the division, enlargement and differentiation of individual plant cells, auxins also function as signals between cells, tissues and organs. In this way they contribute to the coordination and integration of growth and development in the whole plant and to physiological responses of plants to environmental cues (63). At the individual cell level, fast changes or pulses in hormone concentration may function to initiate or to terminate a developmental process. In contrast, the maintenance of a stable concentration of the hormone (homeostasis) may be necessary to maintain the progress of a developmental event that has already been initiated.}, author = {Morris, David and Friml, Jirí and Zažímalová, Eva}, booktitle = {Plant Hormones: Biosynthesis, Signal Transduction, Action!}, editor = {Davies, Peter}, isbn = {978-1-4020-2684-3}, pages = {451 -- 484}, publisher = {Kluwer}, title = {{Auxin transport}}, doi = {10.1007/978-1-4020-2686-7_21}, year = {1995}, } @article{2491, abstract = {The distribution of mRNAs for metabotropic glutamate receptors, mGluR4 and mGluR7, which are highly sensitive for L-2-amino-4-phosphonobutyrate (L- AP4), was examined in the central nervous system of the rat by in situ hybridization. In general, the hybridization signals of mGluR7 mRNA were more widely distributed than those of mGluR4 mRNA, and differential expression of mGluR4 mRNA and mGluR7 mRNA was clearly indicated in some brain regions. Intense or moderate expression of mGluR4 mRNA was detected in the granule cells of the olfactory bulb and cerebellum, whereas no significant expression of mGluR7 mRNA was found in these cells. In other neurons or regions where mGluR7 mRNA was intensely or moderately expressed, no significant expression of mGluR4 mRNA was observed. Such were the mitral and tufted cells of the olfactory bulb; anterior olfactory nucleus; neocortical regions; cingulate cortex; retrosplenial cortex; piriform cortex; perirhinal cortex; CA1; CA3; granule cells of the dentate gyrus; superficial layers of the subicular cortex; deep layers of the entorhinal, parasubicular, and presubicular cortices; ventral part of the lateral septal nucleus; septohippocampal nucleus; triangular septal nucleus; nuclei of the diagonal band; bed nucleus of the stria terminalis; ventral pallidum; claustrum; amygdaloid nuclei other than the intercalated nuclei; preoptic region; hypothalamic nuclei other than the medial mammillary nucleus; ventral lateral geniculate nucleus; locus coeruleus; Purkinje cells; many nuclei of the lower brainstem other than the superior colliculus, periaqueductal gray, interpeduncular nucleus, pontine nuclei, and dorsal cochlear nucleus; and dorsal horn of the spinal cord. Both mGluR4 mRNA and mGluR7 mRNA were moderately or intensely expressed in the olfactory tubercle, superficial layers of the entorhinal cortex, CA4, septofimbrial nucleus, intercalated nuclei of the amygdala, medial mammillary nucleus, many thalamic nuclei, and pontine nuclei. Intense expression of both mGluR4 mRNA and mGluR7 mRNA was further detected in the trigeminal ganglion and dorsal root ganglia, whereas no significant expression of them was found in the pterygopalatine ganglion and superior cervical ganglion. The results indicate differential roles of the L-AP4-sensitive metabotropic glutamate receptors in the glutamatergic nervous system.}, author = {Ohishi, Hitoshi and Akazawa, Chihiro and Shigemoto, Ryuichi and Nakanishi, Shigetada and Mizuno, Noboru}, issn = {0021-9967}, journal = {Journal of Comparative Neurology}, number = {4}, pages = {555 -- 570}, publisher = {Wiley-Blackwell}, title = {{Distributions of the mRNAs for L-2-amino-4-phosphonobutyrate-sensitive metabotropic glutamate receptors, mGluR4 and mGluR7, in the rat brain}}, doi = {10.1002/cne.903600402}, volume = {360}, year = {1995}, } @article{2556, abstract = {By using substance P receptor (SPR) immunofluorescence histochemistry combined with fluorescent retrograde labeling, SPR-like immunoreactive (SPR-LI) neurons sending their axons to the lateral parabrachial region were observed in the lumbar spinal cord of the rat. After injection of Fluoro-Gold into the lateral parabrachial region, retrogradely labeled neurons with SPR-LI were seen frequently in lamina I and the lateral spinal nucleus, and occasionally in laminae IV and V, with a predominantly contralateral distribution. Some of these neurons, especially those in lamina I, may convey nociceptive information to the lateral parabrachial region.}, author = {Ding, Yu and Takada, Masahiko and Shigemoto, Ryuichi and Mizuno, Noboru}, issn = {0006-8993}, journal = {Brain Research}, number = {2}, pages = {336 -- 340}, publisher = {Elsevier}, title = {{Spinoparabrachial tract neurons showing substance P receptor-like immunoreactivity in the lumbar spinal cord of the rat}}, doi = {10.1016/0006-8993(95)00022-I}, volume = {674}, year = {1995}, } @article{2558, abstract = {Brain areas involved in the genesis and control of daily rhythms receive a prominent neural input that contains the neurotransmitter substance P (SP), a peptide putatively involved in the synchronization of circadian rhythms by environmental light. We investigated the localization of receptors to SP in the suprachiasmatic nucleus of the hypothalamus (SCN) and in the intergeniculate leaflet of the thalamus (IGL) of the rat and hamster using in situ hybridization histochemistry and immunohistochemistry. Consistently with that previously described in the rat, a neuronal population distributed along the lateral margin and at the dorso-latero-caudal aspect of the hamster SCN expresses moderately the mRNA encoding the SP receptor. In both rat and hamster, immunohistochemical data confirm the previous finding and reveal an almost complete absence of SP receptors in the ventral part of the SCN, which receives a direct projection from the retina. In the IGL of both species, numerous neurons prominently express the mRNA encoding the SP receptor. The immunostaining shows a high density of SP receptors on perikarya and dendrites throughout the nucleus. A dense staining is also observed on individual cells and processes bordering the lumen of blood vessels in the SCN and IGL.}, author = {Mick, Gérard and Shigemoto, Ryuichi and Kitahama, Kunio}, issn = {0764-4469}, journal = {Comptes Rendus de l'Academie des Sciences - Series III}, number = {2}, pages = {209 -- 217}, publisher = {Gauthier Villars Editeur}, title = {{Localization of substance P receptors in central neural structures controlling daily rhythms in nocturnal rodents}}, volume = {318}, year = {1995}, } @article{2559, abstract = {Taking advantage of the restricted expression of metabotropic glutamate receptor subtype 6 (mGIuR6) in retinal ON bipolar cells, we generated knockout mice lacking mGIuR6 expression. The homozygous mutant mice showed a loss of ON responses but unchanged OFF responses to light. The mutant mice displayed no obvious changes in retinal cell organization nor in the projection of optic fibers to the brain. Furthermore, the mGIuR6-deficient mice showed visual behavioral responses to light stimulation as examined by shuttle box avoidance behavior experiments using light exposure as a conditioned stimulus. The results demonstrate that mGIuR6 is essential in synaptic transmission to the ON bipolar cell and that the OFF response provides an important means for transmitting visual information.}, author = {Masu, Masayuki and Iwakabe, Hideki and Tagawa, Yoshiaki and Miyoshi, Tomomitsu and Yamashita, Masayuki and Fukuda, Yutaka and Sasaki, Hitoshi and Hiroi, Kano and Nakamura, Yasuhisa and Shigemoto, Ryuichi and Takada, Masahiko and Nakamura, Kenji and Nakao, Kazuki and Katsuki, Motoya and Nakanishi, Shigetada}, issn = {0092-8674}, journal = {Cell}, number = {5}, pages = {757 -- 765}, publisher = {Cell Press}, title = {{Specific deficit of the ON response in visual transmission by targeted disruption of the mGIuR6 gene}}, doi = {10.1016/0092-8674(95)90354-2}, volume = {80}, year = {1995}, } @article{2560, abstract = {Chemical irritation of the urinary bladder with formalin in the rat induced c-fos protein-like immunoreactivity in more than 80% of substance P receptor-like immunoreactive (SPR-LI) neurons of the dorsal commissural nucleus, sacral parasympathetic nucleus and lamina I in the 6th lumbar and 1st sacral cord segments. These neurons with SPR-LI may receive noxious information from the urinary bladder through the primary afferent fibers with substance P.}, author = {Lü, Yan and Jin, Shan and Xu, Tian and Qin, Bing and Li, Ji and Ding, Yu and Shigemoto, Ryuichi and Mizuno, Noboru}, issn = {0304-3940}, journal = {Neuroscience Letters}, number = {2}, pages = {139 -- 142}, publisher = {Elsevier}, title = {{Expression of c-fos protein in substance P receptor-like immunoreactive neurons in response to noxious stimuli on the urinary bladder: an observation in the lumbosacral cord segments of the rat}}, doi = {10.1016/0304-3940(95)11991-5}, volume = {198}, year = {1995}, } @article{2561, abstract = {An antibody which recognizes specifically a metabotropic glutamate receptor, mGluR7, was produced by using a trpE fusion protein containing a C-terminal sequence of rat mGluR7. Neuropil in laminae I and II of the dorsal horn of the rat, as well as many neuronal cell bodies in the dorsal root ganglion, showed mGluR7-like immunoreactivity; the immunoreactivity in neuropil was seen in axon terminals, which were filled with round synaptic vesicles and constituted axodendritic and axosomatic asymmetric synapses. The mGluR7-like immunoreactivity in laminae I and II in the dorsal horn was reduced after dorsal rhizotomy. The results indicate that some axon terminals of the primary afferent fibers to laminae I and II of the dorsal horn are provided with mGluR7.}, author = {Ohishi, Hitoshi and Nomura, Sakashi and Ding, Yu and Shigemoto, Ryuichi and Wada, Eiki and Kinoshita, Ayae and Li, Jin and Neki, Akio and Nakanishi, Shigetada and Mizuno, Noboru}, issn = {0304-3940}, journal = {Neuroscience Letters}, number = {1-2}, pages = {85 -- 88}, publisher = {Elsevier}, title = {{Presynaptic localization of a metabotropic glutamate receptor, mGluR7, in the primary afferent neurons: An immunohistochemical study in the rat}}, doi = {10.1016/0304-3940(95)12207-9}, volume = {202}, year = {1995}, } @article{2563, abstract = {By means of substance P receptor (SPR) immunofluorescence histochemistry combined with Fluoro-Gold fluorescent retrograde labeling, SPR-like immunoreactive neurons in the caudal subnucleus of the spinal trigeminal nucleus of the rat were observed to send their axons to the nucleus of Kolliker-Fuse and ventrolateral part of the lateral parabrachial nucleus bilaterally with a clear ipsilateral dominance. These neurons were distributed mainly in lamina I, and additionally in lamina III.}, author = {Ding, Yu and Takada, Masahiko and Shigemoto, Ryuichi and Mizuno, Noboru}, issn = {0168-0102}, journal = {Neuroscience Research}, number = {4}, pages = {415 -- 418}, publisher = {Elsevier}, title = {{Trigeminoparabrachial projection neurons showing substance P receptor-like immunoreactivity in the rat}}, doi = {10.1016/0168-0102(95)00961-R}, volume = {23}, year = {1995}, } @inproceedings{2712, abstract = {We study the generalizations of the well-known Lieb-Thirring inequality for the magnetic Schrödinger operator with a nonconstant magnetic field. We use stochastic methods to prove estimates on the moments of the negative eigenvalues.}, author = {Erdös, László}, location = {Holzhau, Germany}, pages = {127 -- 132}, publisher = {Birkhäuser}, title = {{Magnetic Lieb-Thirring inequalities and stochastic oscillatory integrals}}, doi = {10.1007/978-3-0348-9092-2_13}, volume = {78}, year = {1995}, } @article{2724, abstract = {We study the generalizations of the well-known Lieb-Thirring inequality for the magnetic Schrödinger operator with nonconstant magnetic field. Our main result is the naturally expected magnetic Lieb-Thirring estimate on the moments of the negative eigenvalues for a certain class of magnetic fields (including even some unbounded ones). We develop a localization technique in path space of the stochastic Feynman-Kac representation of the heat kernel which effectively estimates the oscillatory effect due to the magnetic phase factor.}, author = {Erdös, László}, issn = {0010-3616}, journal = {Communications in Mathematical Physics}, number = {3}, pages = {629 -- 668}, publisher = {Springer}, title = {{Magnetic Lieb-Thirring inequalities}}, doi = {10.1007/BF02099152}, volume = {170}, year = {1995}, } @article{1943, abstract = {Transhydrogenase from beef-heart mitochondria was solubilised with Triton X-100 and purified by column chromatography. The detergent-dispersed enzyme catalysed the reduction of acetylpyridine adenine dinucleotide (AcPdAD+) by NADH, but only in the presence of NADP+. Experiments showed that this reaction was cyclic; NADP(H), whilst remaining bound to the enzyme, was alternately reduced by NADH and oxidised by AcPdAD+. A period of incubation of the enzyme with NADPH at pH 6.0 led to inhibition of the simple transhydrogenation reaction between AcPdAD+ and NADPH. However, after such treatment, transhydrogenase acquired the ability to catalyse the (NADPH-dependent) reduction of AcPdAD+ by NADH. It is suggested that this is a similar cycle to the one described above. Evidently, the binding affinity for NADP+ increases as a consequence of the inhibition process resulting from prolonged incubation with NADPH. The pH dependences of simple and cyclic transhydrogenation reactions are described. Though more complex than those in Escherichia coli transhydrogenase, they are consistent with the view [Hutton, M., Day, J.M., Bizouarn, T. and Jackson, J.B. (1994) Eur. J. Biochem. 219, 1041–10511] that, also in the mitochondrial enzyme, binding the release of NADP+ and NADP are accompanied by binding and release of a proton. The enzyme was successfully reconstituted into liposomes by a cholate dilution procedure. The proteoliposomes catalysed cyclic NADPH-dependent reduction of AcPdAD+ by NADH only when they were tightly coupled. However, they catalysed cyclic NADP+-dependent reduction of AcPdAD+ by NADH only when they were uncoupled eg. by addition of carbonylcyanide-p-trifluoromethoxyphenyl hydrazone. These observations are evidence that the proton binding and release which accompany NADP+ binding and release, respectively, take place on the inside of the vesicle, and that they are components of the electrogenic processes of the enzyme.}, author = {Sazanov, Leonid A and Jackson, Baz}, issn = {0005-2728}, journal = {Biochimica et Biophysica Acta - Bioenergetics}, number = {3}, pages = {304 -- 312}, publisher = {Elsevier}, title = {{Cyclic reactions catalysed by detergent-dispersed and reconstituted transhydrogenase from beef heart mitochondria; implications for the mechanism of proton translocation}}, doi = {10.1016/0005-2728(95)00096-2}, volume = {1231}, year = {1995}, } @phdthesis{4428, abstract = {Hybrid systems are real-time systems that react to both discrete and continuous activities (such as analog signals, time, temperature, and speed). Typical examples of hybrid systems are embedded systems, timing-based communication protocols, and digital circuits at the transistor level. Due to the rapid development of microprocessor technology, hybrid systems directly control much of what we depend on in our daily lives. Consequently, the formal specification and verification of hybrid systems has become an active area of research. This dissertation presents the first general framework for the formal specification and verification of hybrid systems, as well as the first hybrid-system analysis tool--HyTech. The framework consists of a graphical finite-state-machine-like language for modeling hybrid systems, a temporal logic for modeling the requirements of hybrid systems, and a computer procedure that verifies modeled hybrid systems against modeled requirements. The tool HyTech is the implementation of the framework using C++ and Mathematica. More specifically, our hybrid-system modeling language, Hybrid Automata, is an extension of timed automata with discrete and continuous variables whose dynamics are governed by differential equations. Our requirement modeling language, ICTL, is a branching-time temporal logic, and is an extension of TCTL with stop-watch variables. Our verification procedure is a symbolic model-checking procedure that verifies linear hybrid automata against ICTL formulas. To make HyTech more efficient and effective, we use model-checking strategies and abstract operators that can expedite the verification process. To enable HyTech to verify nonlinear hybrid automata, we introduce two translations from nonlinear hybrid automata to linear hybrid automata. We have applied HyTech to analyze more than 30 hybrid-system benchmarks. In this dissertation, we present the application of HyTech to three nontrivial hybrid systems taken from the literature.}, author = {Ho, Pei}, pages = {1 -- 188}, publisher = {Cornell University}, title = {{Automatic analysis of hybrid systems}}, year = {1995}, } @inproceedings{4447, abstract = {This paper is addressed to potential users of HyTech, the Cornell Hybrid Technology Tool, an automatic tool for analyzing hybrid systems. We review the formal technologies that have been incorporated into HyTech, and we illustrate the use of HyTech with three nontrivial case studies.}, author = {Henzinger, Thomas A and Ho, Pei}, booktitle = {4th International Hybrid Systems Workshop}, editor = {Panos, Antsaklis and Kohn, Wolf and Nerode, Anil and Sastry, Shankar}, isbn = {9783540683346}, location = { New Brunswick, NJ, United States of America}, pages = {265 -- 293}, publisher = {Springer}, title = {{HyTech: The Cornell Hybrid Technology Tool}}, doi = {10.1007/3-540-60472-3_14}, volume = {999}, year = {1995}, } @inproceedings{4448, abstract = {We report on several abstract interpretation strategies that are designed to improve the performance of HyTech, a symbolic model checker for linear hybrid systems. We (1) simultaneously compute the target region from different directions, (2) conservatively approximate the target region by dropping constraints, and (3) iteratively refine the approximation until sufficient precision is obtained. We consider the standard abstract convex-hull operator and a novel abstract extrapolation operator.}, author = {Henzinger, Thomas A and Ho, Pei}, booktitle = {3rd International Hybrid Systems Workshop}, editor = {Panos, Antsaklis and Kohn, Wolf and Nerode, Anil and Sastry, Shankar}, isbn = {9783540604723}, location = {Ithaca, NY, United States of America}, pages = {252 -- 264}, publisher = {Springer}, title = {{A note on abstract-interpretation strategies for hybrid automata}}, doi = {10.1007/3-540-60472-3_13}, volume = {999}, year = {1995}, } @inproceedings{4450, abstract = {Hybrid systems model discrete programs that are embedded in continuous environments. Model-checking tools are available for the analysis of linear hybrid systems, whose continuous variables are bounded by piecewise-linear trajectories. Most embedded programs, however, operate in nonlinear environments. We present, analyze, and apply two algorithms for translating nonlinear hybrid systems into linear hybrid systems. The clock translation replaces nonlinear variables by clock variables; the rate translation approximates nonlinear variables by piecewise-linear envelopes. Both translations are sound for reachability; that is, if we establish a safety property of the translated linear system, we may conclude that the original nonlinear system satisfies the property. The clock translation is also complete for reachability; that is, the original system and the translated system satisfy the same safety properties. The two translations apply to incomparable classes of nonlinear hybrid systems. From the clock translation we obtain a new decidability result for hybrid systems. With the help of Hytech, a symbolic model checker for linear hybrid systems, we automatically verify a nonlinear railroad gate control program using the clock translation, and a nonlinear temperature control program using the rate translation.}, author = {Henzinger, Thomas A and Ho, Pei}, booktitle = {7th International Conference on Computer Aided Verification}, isbn = {9783540494133}, location = {Liege, Belgium}, pages = {225 -- 238}, publisher = {Springer}, title = {{Algorithmic analysis of nonlinear hybrid systems}}, doi = {10.1007/3-540-60045-0_53}, volume = {939}, year = {1995}, }