Showing papers by "University of Minnesota published in 1976"
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17 Aug 1976TL;DR: The Hopf bifurcation refers to the development of periodic orbits ("self-oscillations") from a stable fixed point, as a parameter crosses a critical value as mentioned in this paper.
Abstract: The goal of these notes is to give a reasonably complete, although not exhaustive, discussion of what is commonly referred to as the Hopf bifurcation with applications to specific problems, including stability calculations Historically, the subject had its origins in the works of Poincare [1] around 1892 and was extensively discussed by Andronov and Witt [1] and their co-workers starting around 1930 Hopf's basic paper [1] appeared in 1942 Although the term "Poincare-Andronov-Hopf bifurcation" is more accurate (sometimes Friedrichs is also included), the name "Hopf Bifurcation" seems more common, so we have used it Hopf's crucial contribution was the extension from two dimensions to higher dimensions
The principal technique employed in the body of the text is that of invariant manifolds The method of Ruelle-Takens [1] is followed, with details, examples and proofs added Several parts of the exposition in the main text come from papers of P Chernoff, J Dorroh, O Lanford and F Weissler to whom we are grateful
The general method of invariant manifolds is common in dynamical systems and in ordinary differential equations; see for example, Hale [1,2] and Hartman [1] Of course, other methods are also available In an attempt to keep the picture balanced, we have included samples of alternative approaches Specifically, we have included a translation (by L Howard and N Kopell) of Hopf's original (and generally unavailable) paper These original methods, using power series and scaling are used in fluid mechanics by, amongst many others, Joseph and Sattinger [1]; two sections on these ideas from papers of Iooss [1-6] and Kirchgassner and Kielhoffer [1] (contributed by G Childs and O Ruiz) are given
The contributions of S Smale, J Guckenheimer and G Oster indicate applications to the biological sciences and that of D Schmidt to Hamiltonian systems For other applications and related topics, we refer to the monographs of Andronov and Chaiken [1], Minorsky [1] and Thom [1]
The Hopf bifurcation refers to the development of periodic orbits ("self-oscillations") from a stable fixed point, as a parameter crosses a critical value In Hopf's original approach, the determination of the stability of the resulting periodic orbits is, in concrete problems, an unpleasant calculation We have given explicit algorithms for this calculation which are easy to apply in examples (See Section 4, and Section 5A for comparison with Hopf's formulae) The method of averaging, exposed here by S Chow and J Mallet-Paret in Section 4C gives another method of determining this stability, and seems to be especially useful for the next bifurcation to invariant tori where the only recourse may be to numerical methods, since the periodic orbit is not normally known explicitly
In applications to partial differential equations, the key assumption is that the semi-flow defined by the equations be smooth in all variables for t > O This enables the invariant manifold machinery, and hence the bifurcation theorems to go through (Marsden [2]) To aid in determining smoothness in examples we have presented parts of the results of Dorroh-Marsden [1] Similar ideas for utilizing smoothness have been introduced independently by other authors, such as D Henry [1]
Some further directions of research and generalization are given in papers of Jost and Zehnder [1], Takens [1, 2], Crandall-Rabinowitz [1, 2], Arnold [2], and Kopell-Howard [1-6] to mention just a few that are noted but are not discussed in any detail here We have selected results of Chafee [1] and Ruelle [3] (the latter is exposed here by S Schecter) to indicate some generalizations that are possible
The subject is by no means closed Applications to instabilities in biology (see, eg Zeeman [2], Gurel [1-12] and Section 10, 11); engineering (for example, spontaneous "flutter" or oscillations in structural, electrical, nuclear or other engineering systems; cf Aronson [1], Ziegler [1] and Knops and Wilkes [1]), and oscillations in the atmosphere and the earth's magnetic field (cf Durand [1]) are appearing at a rapid rate Also, the qualitative theory proposed by Ruelle-Takens [1] to describe turbulence is not yet well understood (see Section 9) In this direction, the papers of Newhouse and Peixoto [1] and Alexander and Yorke [1] seem to be important Stable oscillations in nonlinear waves may be another fruitful area for application; cf Whitham [1] We hope these notes provide some guidance to the field and will be useful to those who wish to study or apply these fascinating methods
After we completed our stability calculations we were happy to learn that others had found similar difficulty in applying Hopf's result as it had existed in the literature to concrete examples in dimension ≥ 3 They have developed similar formulae to deal with the problem; cf Hsu and Kazarinoff [1, 2] and Poore [1]
The other main new result here is our proof of the validity of the Hopf bifurcation theory for nonlinear partial differential equations of parabolic type The new proof, relying on invariant manifold theory, is considerably simpler than existing proofs and should be useful in a variety of situations involving bifurcation theory for evolution equations
These notes originated in a seminar given at Berkeley in 1973-4 We wish to thank those who contributed to this volume and wish to apologize in advance for the many important contributions to the field which are not discussed here; those we are aware of are listed in the bibliography which is, admittedly, not exhaustive Many other references are contained in the lengthy bibliography in Cesari [1] We also thank those who have taken an interest in the notes and have contributed valuable comments These include R Abraham, D Aronson, A Chorin, M Crandall, R Cushman, C Desoer, A Fischer, L Glass, J M Greenberg, O Gurel, J Hale, B Hassard, S Hastings, M Hirsch, E Hopf, N D Kazarinoff, J P LaSalle, A Mees, C Pugh, D Ruelle, F Takens, Y Wan and A Weinstein Special thanks go to J A Yorke for informing us of the material in Section 3C and to both he and D Ruelle for pointing out the example of the Lorentz equations (See Example 4B8) Finally, we thank Barbara Komatsu and Jody Anderson for the beautiful job they did in typing the manuscript
Jerrold Marsden
Marjorie McCracken
1,878 citations
TL;DR: For P- complete problems such as traveling salesperson, cycle covers, 0-1 integer programming, multicommodity network flows, quadratic assignment, etc., it is shown that the approximation problem is also P-complete.
Abstract: For P-complete problems such as traveling salesperson, cycle covers, 0-1 integer programming, multicommodity network flows, quadratic assignment, etc., it is shown that the approximation problem is also P-complete. In contrast with these results, a linear time approximation algorithm for the clustering problem is presented.
1,718 citations
1,078 citations
754 citations
TL;DR: In this paper, an experimental and theoretical-numerical investigation has been carried out to extend existing knowledge of velocity and temperature distributions and local heat-transfer coefficients for naturel convection within a horizontal annulus.
Abstract: An experimental and theoretical-numerical investigation has been carried out to extend existing knowledge of velocity and temperature distributions and local heat-transfer coefficients for naturel convection within a horizontal annulus. A Mach—Zehnder interferometer was used to determine temperature distributions and local heat-transfer coefficients experimentally. Results were obtained using water and air at atmospheric pressure with a ratio of gap width to inner-cylinder diameter of 0·8. The Rayleigh number based on the gap width varied from 2·11 × 104to 9·76 × 105. A finite-difference method was used to solve the governing constant-property equations numerically. The Rayleigh number was changed from 102 to 105 with the influence of Prandtl number and diameter ratio obtained near a Rayleigh number of 104. Comparisons between the present experimental and numerical results under similar conditions show good agreement.
716 citations
TL;DR: It is shown that the problem of obtaining minimum finish time nonpreemptive schedules when the open shop has more than two processors is NP-complete.
Abstract: A linear time algorithm to obtain a minimum finish time schedule for the two-processor open shop together with a polynomial time algorithm to obtain a minimum finish time preemptive schedule for open shops with more than two processors are obtained. It is also shown that the problem of obtaining minimum finish time nonpreemptive schedules when the open shop has more than two processors is NP-complete.
655 citations
TL;DR: In monetary policy, it is widely agreed that monetary policy should obey a rule, that is, a schedule expressing the setting of the monetary authority's instrument (e.g., the money supply) as a function of all the information it has received up through the current moment as mentioned in this paper.
608 citations
TL;DR: A bicontinuous structure is a bicountinuous partitioning in which each subvolume is filled with a distinct, not necessarily uniform composition or state of matter.
Abstract: For certain ranges of phase-volume ratio, there are two-phase structures in which both phases are continuous and interfacial area is less than in dispersions of globular units having the same volume ratio and average repeat distance. Included are bicontinuous structures defined by multiply connected minimal surfaces of very high genus and everywhere saddleshaped.
563 citations
TL;DR: Three general techniques are presented to obtain approximate solutions for optimization problems solvable in this way, and polynomial time algorithms are applied to obtain “good” approximate solutions.
Abstract: The following job sequencing problems are studied: (i) single processor job sequencing with deadlines, (ii) job sequencing on m-identical processors to minimize finish time and related problems, (iii) job sequencing on 2-identical processors to minimize weighted mean flow time. Dynamic programming type algorithms are presented to obtain optimal solutions to these problems, and three general techniques are presented to obtain approximate solutions for optimization problems solvable in this way. The techniques are applied to the problems above to obtain polynomial time algorithms that generate “good” approximate solutions.
561 citations
548 citations
TL;DR: Exact and approximate algorithms are presented for scheduling independent tasks in a multiprocessor environment in which the processors have different speeds and are guaranteed to obtain solutions that are close to the optimal.
Abstract: Exact and approximate algorithms are presented for scheduling independent tasks in a multiprocessor environment in which the processors have different speeds. Dynamic programming type algorithms are presented which minimize finish time and weighted mean flow time on two processors. The generalization to m processors is direct. These algorithms have a worst-case complexity which is exponential in the number of tasks. Therefore approximation algorithms of low polynomial complexity are also obtained for the above problems. These algorithms are guaranteed to obtain solutions that are close to the optimal. For the case of minimizing mean flow time on m-processors an algorithm is given whose complexity is O(n log mn).
TL;DR: Densitometric scans of sodium dodecyl sulfate-polyacrylamide gels show that the 80 000- and 30 000-dalton subunits make up 85 to 90% of the protein in purified CAF preparations and that these subunits are present in equimolar ratios.
Abstract: Ca2+-activated Z-disk-removing activity in the P0-40 crude muscle extracts described by Busch et al. (Busch, W. A., Stromer, M. H., Goll, D. E., and Suzuki, A. (1972), J. Cell Biol. 52, 367) was purified from porcine skeletal muscle extracts by using five column chromatographic procedures in succession: (1) 6% agarose; (2) DEAE-cellulose; (3) Sephadex G-200; (4) DEAE-cellulose with a very shallow gradient; (5) Sephadex G-150. All Z-disk-removing activity eluted in a single peak off each column. Z-disk-removing activity always coeluted with Ca2+-activated proteolytic activity, so Z-disk-removing activity in the P0-40 crude muscle extract is due to a single Ca2+-activated protease (CAF). The five column chromatographic procedures produced a 140-fold increase in specific activity of the Ca2+-activated proteolytic enzymic activity; because preparation of the P0-40 crude CAF fraction before chromatography produced a 127-fold increase in specific activity, the entire procedure described here produces a 17 800-fold increase in specific activity of CAF. This increase in specific activity suggests that muscle contains 3.4 mug of CAF per g of muscle fresh weight; this content is in reasonably good agreement with our yields of 0.25-0.76 mug of purified CAF per g of muscle. Purified CAF migrated as a single band during polyacrylamide gel electrophoresis in pH 7.5 Tris-HC1 buffer but migrated as two bands with molecular weights of 80 000 and 30 000 during polyacrylamide gel electrophoresis in sodium dodecyl sulfate. Densitometric scans of sodium dodecyl sulfate-polyacrylamide gels show that the 80 000- and 30 000-dalton subunits make up 85 to 90% of the protein in purified CAF preparations and that these subunits are present in equimolar ratios.
TL;DR: In this paper, the impact of several organizational climate variables on job satisfaction of a cross-section of industrial salesmen was investigated, and it was shown that climate affects job satisfaction.
Abstract: This report concerns the impact of several organizational climate variables on the job satisfaction of a cross-section of industrial salesmen. To gain greater insight into how climate affects salem...
TL;DR: Modell and Hershberg as discussed by the authors presented a paper at the annual meeting of the American Sociological Association (ASA) in San Francisco, August, 1975, entitled "Rules can be found in every society governing the passage to adulthood".
Abstract: *John Modell is Associate Professor of History, University of Minnesota, and Research Associate, Philadelphia Social History Project. Frank F. Furstenberg, Jr. is Associate Professor of Sociology, University of Pennsylvania. Theodore Hershberg is Associate Professor of History, University of Pennsylvania, and Director, Philadelphia Social History Project. An earlier version of this paper was presented at the annual meetings of the American Sociological Association in San Francisco, August, 1975. Rules can be found in every society governing the passage to adulthood. In some
TL;DR: This paper describes a differential database representation which is shown to be an efficient method for storing large and volatile databases.
Abstract: The representation of a collection of data in terms of its differences from some preestablished point of reference is a basic storage compaction technique which finds wide applicability. This paper describes a differential database representation which is shown to be an efficient method for storing large and volatile databases. The technique confines database modifications to a relatively small area of physical storage and as a result offers two significant operational advantages. First, because the “reference point” for the database is inherently static, it can be simply and efficiently stored. Second, since all modifications to the database are physically localized, the process of backup and the process of recovery are relatively fast and inexpensive.
TL;DR: In this article, sufficient conditions are given for the existence of an exponential dichotomy or equivalently an invariant splitting over invariant subsets of the base space of a translation flow.
TL;DR: In this article, a general approach to the establishment of dosing regimens for drug administration by multiple intravenous infusions is presented, where the elimination kinetics are first order and can be represented by a one-compartment open model.
Abstract: A general approach to the establishment of dosing regimens for drug administration by multiple intravenous infusions is presented. The method is applicable where the elimination kinetics are first order and can be represented by a one-compartment open model. The approach utilizes serum concentration-time data obtained during any dosing interval for the calculation of the apparent distribution volume and the half-life in individual patients. These values are then used to individualize the dosing regimen where it is required to maintain serum concentrations of the drug within a desired range. Estimation of kinetic parameters for gentamicin in burn patients with normal or only slightly reduced renal function demonstrates a relatively constant distribution volume of 0.25 ± 0.086 liter/kg (mean ±sd)but a relatively variable half-life of 2.1 ± 1.3 hr. This finding supports the view that gentamicin regimens should be individualized even in patients with essentially normal renal function.
TL;DR: Evidence is presented in normal lymphocytes that aerobic glycolysis not only is associated with cellular proliferation, but more specifically is temporally related to DNA synthesis.
Abstract: GLYCOLYSIS, for most mammalian cells, is only a prelude to the complete respiratory oxidation of glucose. Lactate production is usually barely, if at all, detectable in aerobic conditions1. Consequently, when Warburg2,3 observed that various tumours showed active aerobic glycolysis, he postulated that defective tumour cell respiration was the reason and was, moreover, the basic difference between normal and cancer cells. Although aerobic glycolysis by tumour tissue has been confirmed many times, defective respiration in cancer cells has not been established4. The failure to uncover a respiratory defect in cancer cells has led to other explanations. It has been suggested, for example, that aerobic glycolysis is linked to cell growth rather than to malignancy5, and for several hepatomas a correlation could be made between the amount of lactate produced and the cell doubling time6,7. It follows that if aerobic glycolysis is related to cell growth, it might be possible as much in normal as malignant cells. There is some evidence for this. Aerobic glycolysis has been noted in proliferating fibroblasts during the period of maximum increase in cell numbers8,9. Human lymphocytes have shown an increase in respiration and also produced lactate when stimulated by the mitogen phytohaemagglutinin10,11. In chick embryo and skeletal muscle fibroblasts12,13, glycolysis increased during log phase growth, but several factors seemed to influence lactate production. Medium composition, aggregation state of cells, culture pH and cell density were all considered more important in determining glycolytic activity than growth rate. It should be noted, however, that these factors are also important to the proliferative rate of these cells. We believe that the important question is not whether culture conditions can influence lactate production, but rather whether glycolysis is linked to cell division. So far no systematic study of the relationship of the appearance of aerobic glycolysis to cell proliferation or the phases of the cell cycle has been reported. This report presents evidence in normal lymphocytes that aerobic glycolysis not only is associated with cellular proliferation, but more specifically is temporally related to DNA synthesis.
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TL;DR: For almost 50 years, since insulin therapy was initiated, proponents of "rigid," "tight" or "chemical" control have quoted retrospective evidence of decreased or delayed nephropathy and retinopathy.
Abstract: For almost 50 years, since insulin therapy was initiated, proponents of "rigid," "tight" or "chemical" control have quoted retrospective evidence of decreased or delayed nephropathy and retinopathy...
TL;DR: Transplantation of cells capable of continuous enzyme production could be an effective mode of therapy for congenital enzyme deficiency diseases.
Abstract: A sustained decrease of plasma bilirubin concentrations occurred in homozygous recessive Gunn rats lacking the enzyme uridine diphosphate glucuronyltransferase following infusion into the portal vein of hepatocytes from heterozygous nonjaundiced Gunn rats possessing the enzyme. Transplantation of cells capable of continuous enzyme production could be an effective mode of therapy for congenital enzyme deficiency diseases.
TL;DR: This work compared the courses of right and left lateral (sylvian) fissures by superimposing left lateral and reversed right lateral photographic slide projections and tracing the sulci and fissure of each hemisphere in different colors.
Abstract: We compared the courses of right and left lateral (sylvian) fissures by superimposing left lateral and reversed right lateral photographic slide projections and tracing the sulci and fissures of each hemisphere in different colors. A characteristic pattern of divergence of posterior regions of the lateral fissures was noted in 25 of 36 adult brains. After pursuing similar courses, the right lateral fissure angulates sharply upward into the inferior parietal area while the left one continues posteriorly. As a consequence, on the right, there is a smaller parietal operculum, a shorter planum temporale, a higher sylvian point, and compensatory expansion of the inferior parietal region posterior to the lateral fissure.
TL;DR: In this paper, the authors present a survey of environmental knowledge and attitudes in the field of environmental education, focusing on three categories: knowledge, attitude, knowledge, and knowledge. The Journal of Environmental Education: Vol. 8, No. 1, pp. 10-18
Abstract: (1976). Environmental Knowledge and Attitudes. The Journal of Environmental Education: Vol. 8, No. 1, pp. 10-18.
TL;DR: In this paper, the local cohomology modules H,i(R) of a graded ring R can be expressed as direct limits of Koszul cohomologies, where R is a homogeneous ideal of R and rad(1) = rad((fo,..., fi2)R), where f0,...,fn are forms of R.
01 Jan 1976-Journal of Comparative Physiology A-neuroethology Sensory Neural and Behavioral Physiology
TL;DR: Electroreceptive neurons in the posterior branch of the anterior lateral line nerve of three species of electric fish (Gymnotoidei), Sternopygus macrums, Eigenmannia virescens, andApteronotus albifrons, show speciesspecific differences in the filtering of electrical stimuli.
Abstract: Electroreceptive neurons in the posterior branch of the anterior lateral line nerve of three species of electric fish (Gymnotoidei):Sternopygus macrums, Eigenmannia virescens, andApteronotus albifrons, show speciesspecific differences in the filtering of electrical stimuli. All of the tuberous electroreceptor fibers of an individual are tuned to the same frequency: that of the electric organ discharge (EOD) of the species, more specifically, to that of the individual. The fibers inSternopygus are tuned to 50–150 Hz; those inEigenmannia to 250–500 Hz, and those inApteronotus to 800–1,200 Hz (Figs. 3, 5, 8). Two classes of organs inSternopygus andEigenmannia, P and T units, respond to sinusoidal stimuli at the unit's best frequency (BF) with a phase-locked partially-adapting (P), or tonic (sustained) (T) discharge. T-units are more sharply tuned and are more sensitive than P-units. Only one class of organs,P or partially adapting units, have been found inApteronotus and phase-locking is less evident than it is in other species.
TL;DR: Two surface samples collected from the Chryse Planitia region of Mars were heated to temperatures up to 500�C, and the volatiles that they evolved were analyzed with a gas chromatograph-mass spectrometer, and only water and carbon dioxide were detected.
Abstract: Two surface samples collected from the Chryse Planitia region of Mars were heated to temperatures up to 500 degrees C, and the volatiles that they evolved were analyzed with a gas chromatograph-mass spectrometer. Only water and carbon dioxide were detected. This implies that organic compounds have not accumulated to the extent that individual components could be detected at levels of a few parts in 10(9) by weight in our samples. Proposed mechanisms for the accumulation and destruction of organic compounds are discussed in the light of this limit.
TL;DR: In this paper, a conduction boundary-layer model is used for heat transfer by conduction, laminar flow and turbulent flow. Butler et al. obtained a correlation for convection from a free horizontal cylinder as the outer cylinder diameter becomes infinite and for quasi-steady heat transfer to fluid within a horizontal cylinder.
TL;DR: In this article, a 6m sediment core from Lake St. Croix, Minnesota, spanning the time range from 445 to 1740 years B.P. was used to obtain relative paleointensities.
TL;DR: A stochastic simulation epidemic model based on discrete time intervals and appropriate for any infectious agent spread by person-to-person contacts is presented, applied to the 1957 Asian and 1968 Hong Kong pandemic strains of influenza A.
Abstract: A stochastic simulation epidemic model based on discrete time intervals and appropriate for any infectious agent spread by person-to-person contacts is presented. The population is highly structured, allowing for five age groups and for subgrouping mixing in families, neighborhoods, schools, and preschool playgroups as well as total community mixing. With proper choice of relative susceptibility by age, length of latency and infectivity periods, pathogenicity and withdrawal patterns, and the relative infectiousness of silent infections, the model becomes highly agent-specific. The model includes flexible immunization routines and variable vaccine response patterns. The model is applied to the 1957 Asian and 1968 Hong Kong pandemic strains of influenza A. The results of several schedules of immunization of school children are presented and compared for the two strains.
TL;DR: Observations show that dietary manipulations have profound effects on immunity functions, including inhibition of the development of life-shortening autoimmune disease.
Abstract: The longevity of mice of the (NZB X NZW)F1 (B/W) strain and the DBA/2f strain of mice is dramatically prolonged by dietary restriction. B/W mice are susceptible to, and die at an early age from, immunocomplex nephritis. Mice of the DBA/2f strain are also relatively short-lived. Restriction of caloric intake prolonged life of B/W mice more than did protein restriction. DBA/2f mice showed prolongation of life when the diet was restricted only with respect to protein. Caloric restriction alone prolonged life less in DBA/2f mice than in B/W mice. These observations show that dietary manipulations have profound effects on immunity functions, including inhibition of the development of life-shortening autoimmune disease.