Showing papers by "California Institute of Technology published in 1993"
TL;DR: In this article, the authors used haplotype analysis of linkage disequilibrium to spotlight a small segment of 4p16.3 as the likely location of the defect, which is expanded and unstable on HD chromosomes.
7,224 citations
TL;DR: A comprehensive review of spatiotemporal pattern formation in systems driven away from equilibrium is presented in this article, with emphasis on comparisons between theory and quantitative experiments, and a classification of patterns in terms of the characteristic wave vector q 0 and frequency ω 0 of the instability.
Abstract: A comprehensive review of spatiotemporal pattern formation in systems driven away from equilibrium is presented, with emphasis on comparisons between theory and quantitative experiments. Examples include patterns in hydrodynamic systems such as thermal convection in pure fluids and binary mixtures, Taylor-Couette flow, parametric-wave instabilities, as well as patterns in solidification fronts, nonlinear optics, oscillatory chemical reactions and excitable biological media. The theoretical starting point is usually a set of deterministic equations of motion, typically in the form of nonlinear partial differential equations. These are sometimes supplemented by stochastic terms representing thermal or instrumental noise, but for macroscopic systems and carefully designed experiments the stochastic forces are often negligible. An aim of theory is to describe solutions of the deterministic equations that are likely to be reached starting from typical initial conditions and to persist at long times. A unified description is developed, based on the linear instabilities of a homogeneous state, which leads naturally to a classification of patterns in terms of the characteristic wave vector q0 and frequency ω0 of the instability. Type Is systems (ω0=0, q0≠0) are stationary in time and periodic in space; type IIIo systems (ω0≠0, q0=0) are periodic in time and uniform in space; and type Io systems (ω0≠0, q0≠0) are periodic in both space and time. Near a continuous (or supercritical) instability, the dynamics may be accurately described via "amplitude equations," whose form is universal for each type of instability. The specifics of each system enter only through the nonuniversal coefficients. Far from the instability threshold a different universal description known as the "phase equation" may be derived, but it is restricted to slow distortions of an ideal pattern. For many systems appropriate starting equations are either not known or too complicated to analyze conveniently. It is thus useful to introduce phenomenological order-parameter models, which lead to the correct amplitude equations near threshold, and which may be solved analytically or numerically in the nonlinear regime away from the instability. The above theoretical methods are useful in analyzing "real pattern effects" such as the influence of external boundaries, or the formation and dynamics of defects in ideal structures. An important element in nonequilibrium systems is the appearance of deterministic chaos. A greal deal is known about systems with a small number of degrees of freedom displaying "temporal chaos," where the structure of the phase space can be analyzed in detail. For spatially extended systems with many degrees of freedom, on the other hand, one is dealing with spatiotemporal chaos and appropriate methods of analysis need to be developed. In addition to the general features of nonequilibrium pattern formation discussed above, detailed reviews of theoretical and experimental work on many specific systems are presented. These include Rayleigh-Benard convection in a pure fluid, convection in binary-fluid mixtures, electrohydrodynamic convection in nematic liquid crystals, Taylor-Couette flow between rotating cylinders, parametric surface waves, patterns in certain open flow systems, oscillatory chemical reactions, static and dynamic patterns in biological media, crystallization fronts, and patterns in nonlinear optics. A concluding section summarizes what has and has not been accomplished, and attempts to assess the prospects for the future.
6,145 citations
TL;DR: The field of electron transfer processes has been studied extensively in chemistry, electrochemistry, and biology as mentioned in this paper, and some history, recent trends, and my own involvement are described.
Abstract: Since the late 1940s, the field of electron transfer processes has grown enormously in chemistry, electrochemistry, and biology. The development of the field, experimentally and theoretically, as well as its relation to the study of the other kinds of chemical reactions, presents an intriguing history in which many threads have been brought together. In this article, some history, recent trends, and my own involvement are described.
3,008 citations
TL;DR: Methods for steering systems with nonholonomic c.onstraints between arbitrary configurations are investigated and suboptimal trajectories are derived for systems that are not in canonical form.
Abstract: Methods for steering systems with nonholonomic c.onstraints between arbitrary configurations are investigated. Suboptimal trajectories are derived for systems that are not in canonical form. Systems in which it takes more than one level of bracketing to achieve controllability are considered. The trajectories use sinusoids at integrally related frequencies to achieve motion at a given bracketing level. A class of systems that can be steered using sinusoids (claimed systems) is defined. Conditions under which a class of two-input systems can be converted into this form are given. >
1,787 citations
TL;DR: It is argued that neurons that act as temporal integrators over many synaptic inputs must fire very regularly and only in the presence of either fast and strong dendritic nonlinearities or strong synchronization among individual synaptic events will the degree of predicted variability approach that of real cortical neurons.
Abstract: How random is the discharge pattern of cortical neurons? We examined recordings from primary visual cortex (V1; Knierim and Van Essen, 1992) and extrastriate cortex (MT; Newsome et al., 1989a) of awake, behaving macaque monkey and compared them to analytical predictions. For nonbursting cells firing at sustained rates up to 300 Hz, we evaluated two indices of firing variability: the ratio of the variance to the mean for the number of action potentials evoked by a constant stimulus, and the rate-normalized coefficient of variation (Cv) of the interspike interval distribution. Firing in virtually all V1 and MT neurons was nearly consistent with a completely random process (e.g., Cv approximately 1). We tried to model this high variability by small, independent, and random EPSPs converging onto a leaky integrate-and- fire neuron (Knight, 1972). Both this and related models predicted very low firing variability (Cv << 1) for realistic EPSP depolarizations and membrane time constants. We also simulated a biophysically very detailed compartmental model of an anatomically reconstructed and physiologically characterized layer V cat pyramidal cell (Douglas et al., 1991) with passive dendrites and active soma. If independent, excitatory synaptic input fired the model cell at the high rates observed in monkey, the Cv and the variability in the number of spikes were both very low, in agreement with the integrate-and-fire models but in strong disagreement with the majority of our monkey data. The simulated cell only produced highly variable firing when Hodgkin-Huxley- like currents (INa and very strong IDR) were placed on distal dendrites. Now the simulated neuron acted more as a millisecond- resolution detector of dendritic spike coincidences than as a temporal integrator. We argue that neurons that act as temporal integrators over many synaptic inputs must fire very regularly. Only in the presence of either fast and strong dendritic nonlinearities or strong synchronization among individual synaptic events will the degree of predicted variability approach that of real cortical neurons.
1,736 citations
TL;DR: A tutorial introduction to the complex structured singular value (μ) is presented, with an emphasis on the mathematical aspects of μ.
1,515 citations
TL;DR: An early step in ethylene signal transduction in plants may involve transfer of phosphate as in prokaryotic two-component systems.
Abstract: Ethylene behaves as a hormone in plants, regulating such aspects of growth and development as fruit ripening, flower senescence, and abscission. Ethylene insensitivity is conferred by dominant mutations in the ETR1 gene early in the ethylene signal transduction pathway of Arabidopsis thaliana. The ETR1 gene was cloned by the method of chromosome walking. Each of the four known etr1 mutant alleles contains a missense mutation near the amino terminus of the predicted protein. Although the sequence of the amino-terminal half of the deduced ETR1 protein appears to be novel, the carboxyl-terminal half is similar in sequence to both components of the prokaryotic family of signal transducers known as the two-component systems. Thus, an early step in ethylene signal transduction in plants may involve transfer of phosphate as in prokaryotic two-component systems. The dominant etr1-1 mutant gene conferred ethylene insensitivity to wild-type Arabidopsis plants when introduced by transformation.
1,482 citations
TL;DR: Since the late 1940s, the field of electron transfer processes has grown enormously, both in chemistry and biology as discussed by the authors, and the development of the field, experimentally and theoretically, as well as its relation to the study of other kinds of chemical reactions, presents an intriguing history, one in which many threads have been brought together.
Abstract: Since the late 1940s, the field of electron transfer processes has grown enormously, both in chemistry and biology. The development of the field, experimentally and theoretically, as well as its relation to the study of other kinds of chemical reactions, presents to us an intriguing history, one in which many threads have been brought together. In this lecture, some history, recent trends, and my own involvement in this research are described.
1,459 citations
TL;DR: Observations suggest that Mash-1, like its Drosophila homologs of the AS-C, controls a basic operation in development of neuronal progenitors in distinct neural lineages.
1,049 citations
01 Jun 1993
TL;DR: In this paper, it is shown that quantum mechanical effects cause black holes to create and emit particles as if they were hot bodies with temperature, which leads to a slow decrease in the mass of the black hole and to its eventual disappearance.
Abstract: In the classical theory black holes can only absorb and not emit particles. However it is shown that quantum mechanical effects cause black holes to create and emit particles as if they were hot bodies with temperature\(\frac{{h\kappa }}{{2\pi k}} \approx 10^{ - 6} \left( {\frac{{M_ \odot }}{M}} \right){}^ \circ K\) where κ is the surface gravity of the black hole. This thermal emission leads to a slow decrease in the mass of the black hole and to its eventual disappearance: any primordial black hole of mass less than about 1015 g would have evaporated by now. Although these quantum effects violate the classical law that the area of the event horizon of a black hole cannot decrease, there remains a Generalized Second Law:S+1/4A never decreases whereS is the entropy of matter outside black holes andA is the sum of the surface areas of the event horizons. This shows that gravitational collapse converts the baryons and leptons in the collapsing body into entropy. It is tempting to speculate that this might be the reason why the Universe contains so much entropy per baryon.
1,009 citations
TL;DR: A biologically plausible model of an attentional mechanism for forming position- and scale-invariant representations of objects in the visual world that respects key neurophysiological, neuroanatomical, and psychophysical data relating to attention, and it makes a variety of experimentally testable predictions.
Abstract: We present a biologically plausible model of an attentional mechanism for forming position- and scale-invariant representations of objects in the visual world. The model relies on a set of control neurons to dynamically modify the synaptic strengths of intracortical connections so that information from a windowed region of primary visual cortex (V1) is selectively routed to higher cortical areas. Local spatial relationships (i.e., topography) within the attentional window are preserved as information is routed through the cortex. This enables attended objects to be represented in higher cortical areas within an object-centered reference frame that is position and scale invariant. We hypothesize that the pulvinar may provide the control signals for routing information through the cortex. The dynamics of the control neurons are governed by simple differential equations that could be realized by neurobiologically plausible circuits. In preattentive mode, the control neurons receive their input from a low-level “saliency map” representing potentially interesting regions of a scene. During the pattern recognition phase, control neurons are driven by the interaction between top-down (memory) and bottom-up (retinal input) sources. The model respects key neurophysiological, neuroanatomical, and psychophysical data relating to attention, and it makes a variety of experimentally testable predictions.
TL;DR: In this paper, the structure of the intense-vorticity regions is studied in numerically simulated homogeneous, isotropic, equilibrium turbulent flow fields at four different Reynolds numbers, in the range Re, = 35-170.
Abstract: The structure of the intense-vorticity regions is studied in numerically simulated homogeneous, isotropic, equilibrium turbulent flow fields at four different Reynolds numbers, in the range Re, = 35-170. In accordance with previous investigators this vorticity is found to be organized in coherent, cylindrical or ribbon-like, vortices (‘worms’). A statistical study suggests that they are simply especially intense features of the background, O(o’), vorticity. Their radii scale with the Kolmogorov microscale and their lengths with the integral scale of the flow. An interesting observation is that the Reynolds number y/v, based on the circulation of the intense vortices, increases monotonically with ReA, raising the question of the stability of the structures in the limit of Re, --z co. Conversely, the average rate of stretching of these vortices increases only slowly with their peak vorticity, suggesting that self-stretching is not important in their evolution. One- and two-dimensional statistics of vorticity and strain are presented; they are non-Gaussian and the behaviour of their tails depends strongly on the Reynolds number. There is no evidence of convergence to a limiting distribution in this range of Re,, even though the energy spectra and the energy dissipation rate show good asymptotic properties in the higher-Reynolds-number cases. Evidence is presented to show that worms are natural features of the flow and that they do not depend on the particular forcing scheme.
TL;DR: In this article, it is argued that most of the magnetic energy becomes concentrated in thin flux ropes when the field pressure exceeds the turbulent pressure at the smallest scale of turbulence, and the possibilities for dynamo action during the various (precollapse) stages of convective motion that occur in the evolution of a massive star are examined.
Abstract: Neutron star convection is a transient phenomenon and has an extremely high magnetic Reynolds number In this sense, a neutron star dynamo is the quintessential fast dynamo The convective motions are only mildly turbulent on scales larger than the approximately 100 cm neutrino mean free path, but the turbulence is well developed on smaller scales Several fundamental issues in the theory of fast dynamos are raised in the study of a neutron star dynamo, in particular the possibility of dynamo action in mirror-symmetric turbulence It is argued that in any high magnetic Reynolds number dynamo, most of the magnetic energy becomes concentrated in thin flux ropes when the field pressure exceeds the turbulent pressure at the smallest scale of turbulence In addition, the possibilities for dynamo action during the various (pre-collapse) stages of convective motion that occur in the evolution of a massive star are examined, and the properties of white dwarf and neutron star progenitors are contrasted
TL;DR: The stacked aromatic heterocycles of the DNA duplex therefore serve as an efficient medium for coupling electron donors and acceptors over very long distances.
Abstract: Rapid photoinduced electron transfer is demonstrated over a distance of greater than 40 angstroms between metallointercalators that are tethered to the 5' termini of a 15-base pair DNA duplex. An oligomeric assembly was synthesized in which the donor is Ru(phen)2dppz2+ (phen, phenanthroline, and dppz, dipyridophenazine) and the acceptor is Rh(phi)2phen3+ (phi, phenanthrenequinone diimine). These metal complexes are intercalated either one or two base steps in from the helix termini. Although the ruthenium-modified oligonucleotide hybridized to an unmodified complement luminesces intensely, the ruthenium-modified oligomer hybridized to the rhodium-modified oligomer shows no detectable luminescence. Time-resolved studies point to a lower limit of 10(9) per second for the quenching rate. No quenching was observed upon metallation of two complementary octamers by Ru(phen)3(2+) and Rh(phen)3(3+) under conditions where the phen complexes do not intercalate. The stacked aromatic heterocycles of the DNA duplex therefore serve as an efficient medium for coupling electron donors and acceptors over very long distances.
TL;DR: The mesoporous molecular sieves MCM-41 were synthesized and characterized by X-ray powder diffraction, nitrogen adsorption/desorption, cyclohexane and water adaption, transmission electron micrographs (TEM), thermogravimetric analysis (TGA), ammonia temperature-programmed desorption (TPD), FTIR, FT-Raman, 29Si, 27Al and 13C magic angle spinning (MAS) NMR spectroscopy.
TL;DR: In this paper, high-resolution gas chromatography and mass spectrometers were used to identify primary organic aerosol constituents, revealing an annual pattern with high winter and low summer concentrations.
TL;DR: In this article, the effects on plant development of mutations in the Arabidopsis thaliana CLAVATA1 gene were investigated, and it was shown that clavata1 plays a role in establishing and maintaining floral meristem identity.
Abstract: We have investigated the effects on plant development of mutations in the Arabidopsis thaliana CLAVATA1 gene. In clavata1 plants, vegetative, inflorescence and floral meristems are all enlarged relative to wild type. The apical meristem can fasciate in the more severe mutant alleles, and this fasciation can occur prior to the transition to flowering. Flowers of clavata1 plants can have increased numbers of organs in all four whorls, and can also have additional whorls not present in wild-type flowers. Double mutant combinations of clavata1 with agamous, apetala2, apetala3 and pistillata indicate that CLAVATA1 controls the underlying floral meristem structure upon which these homeotic genes act. Double mutant combinations of clavata1 with apetala1 and leafy indicate CLAVATA1 plays a role in establishing and maintaining floral meristem identity, in addition to its role in controlling meristem size. In support of this, RNA expression patterns of AGAMOUS and APETALA1 are altered in clavata1 flowers.
TL;DR: The combined use of SRI and other satellite methods is expected to provide data that will enhance the understanding of ice stream mechanics and help make possible the prediction of ice sheet behavior.
Abstract: Satellite radar interferometry (SRI) provides a sensitive means of monitoring the flow velocities and grounding-line positions of ice streams, which are indicators of response of the ice sheets to climatic change or internal instability. The detection limit is about 1.5 millimeters for vertical motions and about 4 millimeters for horizontal motions in the radar beam direction. The grounding line, detected by tidal motions where the ice goes afloat, can be mapped at a resolution of ∼0.5 kilometer. The SRI velocities and grounding line of the Rutford Ice Stream, Antarctica, agree fairly well with earlier ground-based data. The combined use of SRI and other satellite methods is expected to provide data that will enhance the understanding of ice stream mechanics and help make possible the prediction of ice sheet behavior.
TL;DR: In this paper, the organic constituents present in fine particulate (d_p ≤ 2.0 µm) road dust, brake lining particles, and tire tread debris (not size segregated) were analyzed using gas chromatography/mass spectrometry.
Abstract: Particulate matter emitted to the atmosphere due to motor
vehicles arises from several sources in addition to tailpipe
exhaust. In this study, the organic constituents present
in fine particulate (d_p ≤ 2.0 µm) road dust, brake lining
wear particles, and tire tread debris (not size segregated)
are analyzed using gas chromatography/mass spectrometry.
The objective is to characterize such traffic-related
sources on an organic compound basis and to search for
molecular markers that will assist the identification of
traffic-associated dusts in the urban atmosphere. More
than 100 organic compounds are quantified in these
samples, including n-alkanes, n-alkanoic acids, n-alkenoic
acids, n-alkanals, n-alkanols, benzoic acids, benzaldehydes,
polyalkylene glycol ethers, PAH, oxy-PAH, steranes,
hopanes, natural resins and other compound classes.
Paved road dust acts as a repository for vehicle-related
particles, which can then be resuspended by the passing
traffic. To evaluate the contributions from major urban
sources to the road dust complex, source profiles representing different types of vehicle exhaust, brake dust, tire debris, and vegetative detritus are compared, and their fractional contributions are estimated using several groups of organic tracer compounds. Likewise, the close relationship between airborne fine particulate organic constituents and road dust organic matter is discussed.
TL;DR: Results demonstrate that mutations in the GTP-binding domain of dynamin block Tfn-endocytosis in mammalian cells and suggest that a functional dynamin GTPase is required for receptor-mediated endocytotic via clathrin-coated pits.
Abstract: The role of human dynamin in receptor-mediated endocytosis was investigated by transient expression of GTP-binding domain mutants in mammalian cells. Using assays which detect intermediates in coated vesicle formation, the dynamin mutants were found to block endocytosis at a stage after the initiation of coat assembly and preceding the sequestration of ligands into deeply invaginated coated pits. Membrane transport from the ER to the Golgi complex was unaffected indicating that dynamin mutants specifically block early events in endocytosis. These results demonstrate that mutations in the GTP-binding domain of dynamin block Tfn-endocytosis in mammalian cells and suggest that a functional dynamin GTPase is required for receptor-mediated endocytosis via clathrin-coated pits.
TL;DR: A transgenic mouse model that mimics the human autoimmune disease multiple sclerosis in its spontaneous induction and pathology is constructed and a unique opportunity to dissect the genetic and environmental variables that may contribute to the development of spontaneous autoimmune disease is afforded.
TL;DR: The first study of absolute metabolite concentrations and T1‐and T2‐relaxation as a function of age is presented, expected to be of particular value in diagnosis and monitoring of pathology in infants, since metabolite ratios are often misleading.
Abstract: Cerebral metabolite concentrations and water content were measured by means of localized proton magnetic resonance spectroscopy in 50 children, while metabolite peak ratios in short echo time spectra were evaluated in 173 examinations. Normative curves for normal development were established for two cerebral locations. The current report presents the first study of absolute metabolite concentrations and T1- and T2- relaxation as a function of age. Myo-inositol was found dominating the spectra at birth (12 mmoles/kg), while choline is responsible for the strongest peak in older infants (2.5 mmoles/kg). Creatine and N-acetyl groups are at significantly lower concentrations in the neonate than in the adult (Cr: 6, NA: 5 mmoles/kg). NA and Cr are determined by gestational age, whereas the concentration of ml correlates best with postnatal age. Quantitative 1H MRS is expected to be of particular value in diagnosis and monitoring of pathology in infants, since metabolite ratios are often misleading.
TL;DR: The AVIRIS system as mentioned in this paper is a full-time system consisting of a flight system, a ground data system, and a calibration facility, which operates year round at NASA's Jet Propulsion Laboratory (JPL).
TL;DR: The cation-pi interaction may be responsible for the ion selectivity in potassium channels, given that several conserved aromatic residues are present in the pore region of such channels.
Abstract: A combination of computational methods has been used to evaluate the interaction between the pi face of a benzene molecule and the monovalent cations of lithium, sodium, potassium, and rubidium. In the gas phase, the ions are strongly bound, and the affinity for benzene follows the expected electrostatic trend (lithium, largest; rubidium, smallest). However, in an aqueous environment, a reordering occurs such that the potassium ion is preferred over all the other ions for 2:1 benzene:ion complexes. The selectivity sequence parallels that seen in voltage-gated potassium channels. Given that several conserved aromatic residues are present in the pore region of such channels, these results suggest that the cation-pi interaction may be responsible for the ion selectivity in potassium channels.
TL;DR: In this article, numerical modeling of mantle convection in a spherical shell with an endothermic phase change at 670 km depth reveals an inherently three-dimensional flow pattern, containing cylindrical plumes and linear sheets which behave differently in their ability to penetrate the phase change.
Abstract: Numerical modelling of mantle convection in a spherical shell with an endothermic phase change at 670 km depth reveals an inherently three-dimensional flow pattern, containing cylindrical plumes and linear sheets which behave differently in their ability to penetrate the phase change. The dynamics are dominated by accumulation of downwelling cold material above 670 km depth, resulting in frequent avalanches of upper-mantle material into the lower mantle. This process generates long-wavelength lateral heterogeneity, helping to resolve the contradiction between seismic tomographic observations and expectations from mantle convection simulations.
TL;DR: Several techniques for detecting temporal changes in satellite synthetic-aperture radar (SAR) imagery are compared, using both theoretical predictions and spaceborne SAR data collected by the first European Remote Sensing Satellite, ERS-1 as mentioned in this paper.
Abstract: Several techniques for detecting temporal changes in satellite synthetic-aperture radar (SAR) imagery are compared, using both theoretical predictions and spaceborne SAR data collected by the first European Remote Sensing Satellite, ERS-1. In a first set of techniques, changes are detected based on differences in the magnitude of the signal intensity between two dates. Ratioing of the multidate radar intensities is shown to be better adapted to the statistical characteristics of SAR data than subtracting, and works best when the number of looks is large. In a second set of techniques, changes are detected based on estimates of the temporal decorrelation of speckle. This method works best with one-look complex amplitude data, but can also be used with intensity data provided that the number of looks is small. The two techniques are compared using actual SAR data collected by ERS-1. The results illustrate the viability as well as the complementary character of these techniques for detecting changes in the structural and dielectric properties of remotely sensed surfaces. >
Proceedings Article•
01 Jan 1993TL;DR: Several techniques for detecting temporal changes in satellite synthetic-aperture radar (SAR) imagery are compared, using both theoretical predictions and spaceborne SAR data collected by the first European Remote Sensing Satellite, ERS-1.
Abstract: Several techniques for detecting temporal changes in satellite synthetic-aperture radar (SAR) imagery are compared, using both theoretical predictions and spaceborne SAR data collected by the first European Remote Sensing Satellite, ERS-1. In a first set of techniques, changes are detected based on differences in the magnitude of the signal intensity between two dates. Ratioing of the multidate radar intensities is shown to be better adapted to the statistical characteristics of SAR data than subtracting, and works best when the number of looks is large. In a second set of techniques, changes are detected based on estimates of the temporal decorrelation of speckle. This method works best with one-look complex amplitude data, but can also be used with intensity data provided that the number of looks is small. The two techniques are compared using actual SAR data collected by ERS-1. The results illustrate the viability as well as the complementary character of these techniques for detecting changes in the structural and dielectric properties of remotely sensed surfaces. >
TL;DR: Molecular analysis identifies a nuclear protein expressed in progenitor cells prior to differentiation in eya mutants, suggesting that eya activity influences the distribution of cells between differentiation and death.
TL;DR: Cell selective for non-Cartesian gratings may constitute an important intermediate stage in pattern recognition and the representation of surface shape in macaque monkey pattern recognition.
Abstract: The neural basis of pattern recognition is a central problem in visual neuroscience. Responses of single cells were recorded in area V4 of macaque monkey to three classes of periodic stimuli that are based on spatial derivative operators: polar (concentric and radial), hyperbolic, and conventional sinusoidal (Cartesian) gratings. Of 118 cells tested, 16 percent responded significantly more to polar or hyperbolic (non-Cartesian) gratings than to Cartesian gratings and only 8 percent showed a significant preference for Cartesian gratings. Among cells selective for non-Cartesian gratings, those that preferred concentric gratings were most common. Cells selective for non-Cartesian gratings may constitute an important intermediate stage in pattern recognition and the representation of surface shape.