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Showing papers by "Cornell University published in 1986"


Book
31 Jan 1986
TL;DR: Numerical Recipes: The Art of Scientific Computing as discussed by the authors is a complete text and reference book on scientific computing with over 100 new routines (now well over 300 in all), plus upgraded versions of many of the original routines, with many new topics presented at the same accessible level.
Abstract: From the Publisher: This is the revised and greatly expanded Second Edition of the hugely popular Numerical Recipes: The Art of Scientific Computing. The product of a unique collaboration among four leading scientists in academic research and industry, Numerical Recipes is a complete text and reference book on scientific computing. In a self-contained manner it proceeds from mathematical and theoretical considerations to actual practical computer routines. With over 100 new routines (now well over 300 in all), plus upgraded versions of many of the original routines, this book is more than ever the most practical, comprehensive handbook of scientific computing available today. The book retains the informal, easy-to-read style that made the first edition so popular, with many new topics presented at the same accessible level. In addition, some sections of more advanced material have been introduced, set off in small type from the main body of the text. Numerical Recipes is an ideal textbook for scientists and engineers and an indispensable reference for anyone who works in scientific computing. Highlights of the new material include a new chapter on integral equations and inverse methods; multigrid methods for solving partial differential equations; improved random number routines; wavelet transforms; the statistical bootstrap method; a new chapter on "less-numerical" algorithms including compression coding and arbitrary precision arithmetic; band diagonal linear systems; linear algebra on sparse matrices; Cholesky and QR decomposition; calculation of numerical derivatives; Pade approximants, and rational Chebyshev approximation; new special functions; Monte Carlo integration in high-dimensional spaces; globally convergent methods for sets of nonlinear equations; an expanded chapter on fast Fourier methods; spectral analysis on unevenly sampled data; Savitzky-Golay smoothing filters; and two-dimensional Kolmogorov-Smirnoff tests. All this is in addition to material on such basic top

12,662 citations


Journal ArticleDOI
TL;DR: A review of research on the influence of external environments on the functioning of families as contexts of human development can be found in this article, with a focus on the patterning of environmental events and transitions over the life course as these affect and are affected by intrafamilial processes.
Abstract: This review collates and examines critically a theoretically convergent but widely dispersed body of research on the influence of external environments on the functioning of families as contexts of human development. Investigations falling within this expanding domain include studies of the interaction of genetics and environment in family processes; transitions and linkages between the family and other major settings influencing development, such as hospitals, day care, peer groups, school, social networks, the world of work (both for parents and children), and neighborhoods and communities; and public policies affecting families and children. A second major focus is on the patterning of environmental events and transitions over the life course as these affect and are affected by intrafamilial processes. Special emphasis is given to critical research gaps in knowledge and priorities for future investigation. The purpose of this article is to document and delineate promising lines of research on external influences that affect the capacity of families to foster the healthy development of their children. The focus differs from that of most studies of the family as a context of human development, because the majority have concentrated on intrafamilial processes of parent-child interaction, a fact that is reflected in Maccoby and Martin's (1983) recent authoritative review of research on family influences on development. By contrast, the focus of the present analysis can be described as "once removed." The research question becomes: How are intrafamilial processes affected by extrafamilial conditions? Paradigm Parameters In tracing the evolution of research models in developmental science, Bronfenbrenner and Crouter (1983) distinguished a series of progressively more sophisticated scientific paradigms for investigating the impact of environment on development. These paradigms provide a useful framework for ordering and analyzing studies bearing on the topic of this review. At the most general level, the research models vary simultaneously along two dimensions. As applied to the subject at hand, the first pertains

6,114 citations


Journal ArticleDOI
24 Oct 1986-Science
TL;DR: It appears that a single protein mediator (cachectin) is capable of inducing many of the deleterious effects of endotoxin.
Abstract: Cachectin (tumor necrosis factor), a protein produced in large quantities by endotoxin-activated macrophages, has been implicated as an important mediator of the lethal effect of endotoxin. Recombinant human cachectin was infused into rats in an effort to determine whether cachectin, by itself, can elicit the derangements of host physiology caused by administration of endotoxin. When administered in quantities similar to those produced endogenously in response to endotoxin, cachectin causes hypotension, metabolic acidosis, hemoconcentration, and death within minutes to hours, as a result of respiratory arrest. Hyperglycemia and hyperkalemia were also observed after infusion. At necropsy, diffuse pulmonary inflammation and hemorrhage were apparent on gross and histopathologic examination, along with ischemic and hemorrhagic lesions of the gastrointestinal tract, and acute renal tubular necrosis. Thus, it appears that a single protein mediator (cachectin) is capable of inducing many of the deleterious effects of endotoxin.

2,571 citations


Journal ArticleDOI
TL;DR: In this article, the authors derive a formula which expresses any closed string tree amplitude in terms of a sum of the products of appropriate open string tree amplitudes, which is applicable to the heterotic string as well as to the closed bosonic string and type II superstrings.

1,330 citations


Book
01 Apr 1986
TL;DR: This ebook presents full variant of this ebook in DjVu, PDF, ePub, doc, txt forms, and on the website you may read guides and different art eBooks online, either downloading or downloading.
Abstract: If looking for the ebook Implementing Mathematics with The Nuprl Proof Development System by R L Constable in pdf form, in that case you come on to the right site. We present full variant of this ebook in DjVu, PDF, ePub, doc, txt forms. You can reading Implementing Mathematics with The Nuprl Proof Development System online by R L Constable either downloading. Additionally to this ebook, on our website you may read guides and different art eBooks online, either download their. We wish to invite your note what our site does not store the book itself, but we grant url to website wherever you may load either reading online. So that if want to load pdf Implementing Mathematics with The Nuprl Proof Development System by R L Constable, then you have come on to correct website. We have Implementing Mathematics with The Nuprl Proof Development System txt, ePub, PDF, doc, DjVu forms. We will be pleased if you go back afresh.

1,186 citations


Journal ArticleDOI
TL;DR: In men with mild uncomplicated hypertension, left ventricular hypertrophy detected by echocardiography identifies patients at high risk for cardiovascular morbid events and is a significant risk factor for future morbid events independent of age, blood pressure, or resting ventricular function.
Abstract: To assess whether echocardiographic and electrocardiographic detection of left ventricular hypertrophy could predict cardiovascular morbid events in patients with uncomplicated essential hypertension, we followed 140 men for a mean of 4.8 years. Initial echocardiographic measurements of left ventricular mass were normal (less than 125 g/m2 body surface area) in 111 patients and revealed hypertrophy in 29 patients. Morbid events occurred in more patients with hypertrophy on echocardiography (7 of 29, 4.6/100 patient-years) than with normal ventricular mass (7 of 111, 1.4/100 patient-years; p less than 0.01). Electrocardiography showed hypertrophy in too few patients to be of predictive value. Multiple logistic regression analysis showed that left ventricular mass index had the highest independent relative risk for future events and that systolic and diastolic pressures and age had slightly lower relative risks. In men with mild uncomplicated hypertension, left ventricular hypertrophy detected by echocardiography identifies patients at high risk for cardiovascular morbid events and is a significant risk factor for future morbid events independent of age, blood pressure, or resting ventricular function.

1,101 citations


Journal ArticleDOI
21 Nov 1986-Cell
TL;DR: Transfection of a full-length cDNA in mouse fibroblasts results in stable expression of NGF receptors that are recognized by monoclonal antibodies to the human NGF receptor and that bind [125I]NGF.

1,028 citations


Journal ArticleDOI
TL;DR: In this paper, nonlinear least squares techniques have been applied to Rutherford backscattering spectrometry (RBS), allowing routine multivariable fits of simulated spectra to experimental data.
Abstract: Nonlinear least squares techniques have been applied to Rutherford backscattering spectrometry (RBS), allowing routine multivariable fits of simulated spectra to experimental data. Once a qualitatively correct simulation is made, this algorithm varies parameters of the simulation to obtain quantitative results. Optimization is done according to a maximum likelihood chi-squared definition, so that the best fit values of parameters and their uncertainties can be determined. Convergence of the algorithm is rapid for practical problems, allowing a typical four-variable fit to be accomplished in 30 seconds on a VAX 11/750. This algorithm allows confident treatment of spectra which might otherwise be considered too complex. An implementation of the algorithm is incorporated as part of an RBS analysis and simulation package, making it readily available for routine RBS analysis.

937 citations


Journal ArticleDOI
TL;DR: A renormalization group strategy for the study of bound states in field theory is developed in this paper, which is completely different from conventional analyses, based upon the Bethe-Salpeter equation, and it is far simpler

905 citations


Journal ArticleDOI
TL;DR: The class of combinatorial problems involving the random generation from a uniform distribution is considered in this article, where it is shown that almost uniform generation and randomized approximate counting are inter-reducible, and hence, of similar complexity.

899 citations


Journal ArticleDOI
TL;DR: An attempt is made to describe the motion of grouping individuals kinematically as distinct from simple diffusion or random walk, to model the grouping on the basis of dynamics of animal motion, and to interpret the grouping from the standpoint of advection-diffusion processes.

Journal ArticleDOI
TL;DR: In this paper, an approximate theory for post-stall transients in multistage axial compression systems is presented, which leads to a set of three simultaneous nonlinear third-order partial differential equations for pressure rise, and average and disturbed values of flow coefficient, as functions of time and angle around the compressor.
Abstract: An approximate theory is presented for post-stall transients in multistage axial compression systems. The theory leads to a set of three simultaneous nonlinear third-order partial differential equations for pressure rise, and average and disturbed values of flow coefficient, as functions of time and angle around the compressor. By a Galerkin procedure, angular dependence is averaged, and the equations become first order in time. These final equations are capable of describing the growth and possible decay of a rotating-stall cell during a compressor mass-flow transient. It is shown how rotating-stall-like and surgelike motions are coupled through these equations, and also how the instantaneous compressor pumping characteristic changes during the transient stall process.

Journal ArticleDOI
Jack Oliver1
01 Feb 1986-Geology
TL;DR: The thrust sheet acts like a great squeegee, driving fluids ahead of it and producing widespread geologic consequences such as faulting, magma generation, migration of hydrocarbons, transport of minerals, metamorphism, and paleomagnetism as discussed by the authors.
Abstract: This paper presents and supports a speculative hypothesis, the essence of which follows. When continental margins in zones of convergence are buried beneath thrust sheets, fluids expelled from the margin sediments travel into the foreland basin and the continental interior. These tectonic fluids have key roles in phenomena such as faulting, magma generation, migration of hydrocarbons, transport of minerals, metamorphism, and paleomagnetism. The thrust sheet, crudely speaking, acts like a great squeegee, driving fluids ahead of it and producing widespread geologic consequences.

Journal ArticleDOI
TL;DR: When the traditional assumption that the incidence rate is proportional to the product of the numbers of infectives and susceptibles is dropped, the SIRS model can exhibit qualitatively different dynamical behaviors, including Hopf bifurcations, saddle-node bifuriations, and homoclinic loop bifURcations.
Abstract: When the traditional assumption that the incidence rate is proportional to the product of the numbers of infectives and susceptibles is dropped, the SIRS model can exhibit qualitatively different dynamical behaviors, including Hopf bifurcations, saddle-node bifurcations, and homoclinic loop bifurcations. These may be important epidemiologically in that they demonstrate the possibility of infection outbreak and collapse, or autonomous periodic coexistence of disease and host. The possible mechanisms leading to nonlinear incidence rates are discussed. Finally, a modified general criterion for supercritical or subcritical Hopf bifurcation of 2-dimensional systems is presented.

Journal ArticleDOI
11 Sep 1986-Nature
TL;DR: In this article, it is suggested that the upper mantle contains elongated strips of subducted oceanic lithosphere, which are stretched and thinned by the normal and shear strains in the convecting mantle, and are destroyed by being reprocessed at ocean ridges or, on the centimetre scale, by dissolution processes; the result is a marble-cake mantle.
Abstract: It is suggested that the upper mantle contains elongated strips of subducted oceanic lithosphere. These strips are stretched and thinned by the normal and shear strains in the convecting mantle, and are destroyed by being reprocessed at ocean ridges or, on the centimetre scale, by dissolution processes; the result is a marble-cake mantle. Simple theoretical calculations, together with isotopic and structural observations made on high-temperature peridotite massifs, lead to a comprehensive marble-cake model which is consistent with most isotopic and mechanical constraints.

Journal ArticleDOI
TL;DR: This paper develops a technique which utilizes earlier methods to derive even more efficient preconditioners for the discrete systems of equations arising from the numerical approximation of elliptic boundary value problems.
Abstract: In earlier parts of this series of papers, we constructed preconditioners for the discrete systems of equations arising from the numerical approximation of elliptic boundary value problems. The resulting algorithms are well suited for implementation on computers with parallel architecture. In this paper, we will develop a technique which utilizes these earlier methods to derive even more efficient preconditioners. The iterative algorithms using these new preconditioners converge to the solution of the discrete equations with a rate that is independent of the number of unknowns. These preconditioners involve an incomplete Chebyshev iteration for boundary interface conditions which results in a negligible increase in the amount of computational work. Theoretical estimates and the results of numerical experiments are given which demonstrate the effectiveness of the methods.

Journal ArticleDOI
TL;DR: A negative answer is given to the question as to whether there exist NP-problems whose instances have solutions that are unique but are hard to find, using the notion of randomized polynomial time reducibility.

Journal ArticleDOI
01 Apr 1986-Nature
TL;DR: A new acute transforming feline retrovirus, the Hardy-Zuckerman 4 feline sarcoma virus (HZ4-FeSV), has been isolated from a feline fibrosarcoma.
Abstract: A new acute transforming feline retrovirus, the Hardy-Zuckerman 4 feline sarcoma virus (HZ4-FeSV), has been isolated from a feline fibrosarcoma The viral genome of HZ4-FeSV contains a new oncogene designated v-kit, has the structure 5' delta gag-kit-delta pol-delta env 3' and specifies a gag-kit polyprotein of relative molecular mass 80,000 The predicted kit amino-acid sequence displays partial homology with tyrosine-specific protein kinase oncogenes HZ4-FeSV appears to have been generated by transduction of feline c-kit sequences with feline leukaemia virus

Journal ArticleDOI
TL;DR: A formal characterization for safety properties and liveness properties is given in terms of the structure of the Buchi automaton that specifies the property.
Abstract: Formal characterizations for safety properties and liveness properties are given in terms of the structure of the Buchi automaton that specifies the property. The characterizations permit a property to be decomposed into a safety property and a liveness property whose conjunction is the original. The characterizations also give insight into techniques required to prove a large class of safety and liveness properties.

Journal ArticleDOI
TL;DR: It is found that the maximum masses of such boson stars may be comparable to the Chandrasekhar mass for fermions of mass m/sub fermion/--lambda/sup -1/4/m/sub boson/.
Abstract: Spherically symmetric gravitational equilibria of self-interacting scalar fields $\ensuremath{\varphi}$ with interaction potential $V(\ensuremath{\varphi})=\frac{1}{4}\ensuremath{\lambda}{|\ensuremath{\varphi}|}^{4}$ are determined. Surprisingly, the resulting configuration may differ markedly from the noninteracting case even when $\ensuremath{\lambda}\ensuremath{\ll}1$. Contrary to generally accepted astrophysical folklore, it is found that the maximum masses of such boson stars may be comparable to the Chandrasekhar mass for fermions of mass ${m}_{\mathrm{fermion}}\ensuremath{\sim}{\ensuremath{\lambda}}^{\ensuremath{-}\frac{1}{4}}{m}_{\mathrm{boson}}$.

Journal ArticleDOI
TL;DR: The hypothesis that suicide completed by violent methods is associated with reduced presynaptic serotonergic activity that has generated compensatory upregulation of the postsynaptic serotonin2 receptor sites is supported and antidepressant pharmacotherapies specifically downregulate cortical beta-adrenergic and/or serotonin2 receptors in depressed subjects are investigated.
Abstract: • A statistically significant 28% increase in the mean (±SD) number of serotonin 2 receptors (127.8±13.4 vs 99.6 ±11.1 fmol/mg of protein) and a 73% increase in β-adrenergic receptor binding (14.5±1.5 vs 8.4 ±1.5 fmol/mg) was found in the frontal cortices of violent suicide victims compared with matched controls. No significant differences were found in the number of serotonin , binding sites (109.5 ± 13.4 vs 99.9 ±8.8 fmol/mg). We have previously reported a reduced density of presynaptic tritiated imipramine binding sites on serotonergic nerve terminals in the frontal cortices of suicide victims. These data support the hypothesis that suicide completed by violent methods is associated with reduced presynaptic serotonergic activity that has generated compensatory upregulation of the postsynaptic serotonin 2 receptor sites. The increase observed in β-adrenergic binding suggests that there may also be a concomitant reduction in presynaptic noradrenergic activity associated with suicide. If antidepressant pharmacotherapies specifically downregulate cortical β-adrenergic and/or serotonin 2 receptors in depressed subjects, as has been demonstrated in animal studies, and since these effects would be in the opposite direction of the receptor changes found in suicide victims, they may account for the therapeutic action of antidepressants on suicidal behavior and depressive disorders.

Book ChapterDOI
TL;DR: In this article, the authors discuss the reflectance properties of soils and the instrumentation used for reflectance measurements, including spectroradiometers and multiband radiometers, which are divided into two broad classes: spectroradometers and multi-band radiometers.
Abstract: Publisher Summary This chapter discusses the reflectance properties of soils. In delineating differences among soils and in describing the characteristics of a soil profile, color is one of the most useful attributes for documenting these differences. Soil visible reflectance, or color, is a differentiating characteristic for many classes in all modern soil classification systems and is an essential part of the definitions for both surface and subsurface diagnostic horizons. The chapter includes instrumentation for reflectance measurements. Instruments that are used to measure the reflectance of soil are divided into two broad classes—namely, spectroradiometers and multiband radiometers. Multiband radiometers contain several optical filters to define the spectral bandpasses. These spectral bandpasses are selected to sample discrete portions of the optical spectrum, e.g., the Landsat multispectral scanner or the thematic mapper bands. The character of reflected light from a soil surface depends on the nature of the surface and the intensity and spectral quality of the radiation incident upon the surface. The soil surface may be irradiated by direct sunlight, scattered skylight, and thermal radiation from the surroundings.

Journal ArticleDOI
TL;DR: If this cytochrome P-450 enzyme is defective, cortisol cannot be synthesized, resulting in congenital adrenal hyperplasia, and the 21-OHase A gene is, therefore, a pseudogene.
Abstract: We have determined the structure of cDNA and two genomic genes encoding steroid 21-hydroxylase [21-OHase; steroid 21-monooxygenase; steroid, hydrogen-donor:oxygen oxidoreductase (21-hydroxylating); EC 1.14.99.10]. If this cytochrome P-450 enzyme is defective, cortisol cannot be synthesized, resulting in congenital adrenal hyperplasia. The cDNA encoding this enzyme is 2.0 kilobases long, and the encoded protein is predicted to contain 494 amino acid residues with a molecular weight of 55,000. This enzyme is at most 28% homologous to other P-450 enzymes that have been studied. The 21-OHase genomic genes, which are located in the HLA major histocompatibility complex on chromosome 6, each contain 10 exons. This structure is distinct from other characterized P-450 genes, which contain 7 or 9 exons. Studies of individuals with homozygous deletions of the 21-OHase A or B genes suggest that only the B gene encodes an active enzyme. This is confirmed by the finding that the A gene has an 8-base deletion within codons 110-112, resulting in a frameshift that brings a stop codon into the reading frame at codon 130. A second frameshift and a nonsense mutation occur downstream. In contrast, the sequence of the exons of the B gene is identical to the cDNA sequence. The 21-OHase A gene is, therefore, a pseudogene.

Journal ArticleDOI
25 Apr 1986-Science
TL;DR: Affinity cross-linking, metabolic labeling and immunoprecipitation, and equilibrium binding with 125I-labeled NGF revealed that this NGF receptor had the same size and binding characteristics as the receptor from human melanoma cells and rat PC12 cells.
Abstract: Nerve growth factor (NGF) and its receptor are important in the development of cells derived from the neural crest. Mouse L cell transformants have been generated that stably express the human NGF receptor gene transfer with total human DNA. Affinity cross-linking, metabolic labeling and immunoprecipitation, and equilibrium binding with 125I-labeled NGF revealed that this NGF receptor had the same size and binding characteristics as the receptor from human melanoma cells and rat PC12 cells. The sequences encoding the NGF receptor were molecularly cloned using the human Alu repetitive sequence as a probe. A cosmid clone that contained the human NGF receptor gene allowed efficient transfection and expression of the receptor.

Journal ArticleDOI
TL;DR: For a large class of d-dimensional disordered systems, it is proved that if an appropriately defined finite-size scaling correlation length diverges at a nontrivial value of the disorder with an exponent, then ..nu.. must satisfy the bound greater than or equal to 2/d.
Abstract: For a large class of $d$-dimensional disordered systems, we prove that if an appropriately defined finite-size scaling correlation length diverges at a nontrivial value of the disorder with an exponent $\ensuremath{ u}$, then $\ensuremath{ u}$ must satisfy the bound $\ensuremath{ u}\ensuremath{\ge}\frac{2}{d}$. Given the assumption that such a correlation length can be defined, the result applies to, e.g., percolation, disordered magnets, and Anderson localization, both with and without interactions. For localization, this puts stringent constraints on scaling theories and interpretation of experiments.


Journal ArticleDOI
02 Jun 1986
TL;DR: It is shown that TRAVELING SALESPERSON and KNAPSACK are complete for OptP, and that CLIQUE and COLORING arecomplete for a subclass of OptP .
Abstract: We consider NP-complete optimization problems at the level of computing their optimal value, and define a class of functions called OptP to capture this level of structure. We show that TRAVELING SALESPERSON and KNAPSACK are complete for OptP, and that CLIQUE and COLORING are complete for a subclass of OptP. These results show a deeper level of structure in these problems than was previously known. We also show that OptP is closely related to FPSAT, the class of functions computable in polynomial time with an oracle for NP. This allows us to quantify exactly “how much” NP-completeness is in these problems. In particular, in this measure, we show that TRAVELING SALESPERSON is strictly harder than CLIQUE and that CLIQUE is strictly harder than BIN PACKING . A further result is that an OptP-completeness result implies NP-, Dp-, and Δ2P-completeness results, thus tying these four classes closely together.

Journal ArticleDOI
TL;DR: In this paper, the authors present a state estimation algorithm for the IEEE 118 bus system, which involves an admittance-like matrix with the sparsity of the admittance matrix and converges in one step with the same amount of computation as one iteration of existing estimators.
Abstract: The recent introduction of microprocessors into substations for protection and control makes it possible to measure positive sequence voltage phasors and positive sequence transmission line current phasors in real time. It is necessary to synchronize sampling clocks in various substations in order to put the phasors on a common reference. Techniques for synchronizing sampling along with a method for obtaining positive sequence phasors from samples are reviewed. Although it is possible to use these direct measurements in conventional state estimation algorithms, considerable advantage accrues if the state estimation is reformulated in terms of direct measurements of phasor voltages and currents. The resulting estimation algorithm involves an admittance like matrix with the sparsity of the admittance matrix. The new matrix is real rather than complex even for small X/R ratios for the lines. The algorithm requires no assumptions as to decoupling, flat voltage profiles, small resistance, etc. The algorithm converges in one step with the same amount of computation as one iteration of existing estimators. Examples are given for the IEEE 118 bus system.

Journal ArticleDOI
TL;DR: Left ventricular hypertrophy occurred in patients with sustained hypertension who also exhibited increased cardiac output, strongly associated with low plasma renin activity, and at similar levels of blood pressure, black patients were more likely than white patients to exhibit concentric left ventricularhypertrophy.

Journal ArticleDOI
04 Jul 1986-Science
TL;DR: Voyager 2 images of the southern hemisphere of Uranus indicate that submicrometersize haze particles and particles of a methane condensation cloud produce faint patterns in the atmosphere, and Voyager images confirm the extremely low albedo of the ring particles.
Abstract: Voyager 2 images of the southern hemisphere of Uranus indicate that submicrometersize haze particles and particles of a methane condensation cloud produce faint patterns in the atmosphere. The alignment of the cloud bands is similar to that of bands on Jupiter and Saturn, but the zonal winds are nearly opposite. At mid-latitudes (-70 degrees to -27 degrees ), where winds were measured, the atmosphere rotates faster than the magnetic field; however, the rotation rate of the atmosphere decreases toward the equator, so that the two probably corotate at about -20 degrees . Voyager images confirm the extremely low albedo of the ring particles. High phase angle images reveal on the order of 10(2) new ringlike features of very low optical depth and relatively high dust abundance interspersed within the main rings, as well as a broad, diffuse, low optical depth ring just inside the main rings system. Nine of the newly discovered small satellites (40 to 165 kilometers in diameter) orbit between the rings and Miranda; the tenth is within the ring system. Two of these small objects may gravitationally confine the e ring. Oberon and Umbriel have heavily cratered surfaces resembling the ancient cratered highlands of Earth's moon, although Umbriel is almost completely covered with uniform dark material, which perhaps indicates some ongoing process. Titania and Ariel show crater populations different from those on Oberon and Umbriel; these were probably generated by collisions with debris confined to their orbits. Titania and Ariel also show many extensional fault systems; Ariel shows strong evidence for the presence of extrusive material. About halfof Miranda's surface is relatively bland, old, cratered terrain. The remainder comprises three large regions of younger terrain, each rectangular to ovoid in plan, that display complex sets of parallel and intersecting scarps and ridges as well as numerous outcrops of bright and dark materials, perhaps suggesting some exotic composition.