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The majority of synapses in primary visual cortex mediate excitation between nearby neurons, yet the role of local recurrent connections in visual processing remains unclear. We propose that these connections are responsible for the spatial-phase invariance of complex-cell responses. In a network model with selective cortical amplification, neurons exhibit simple-cell responses when recurrent connections are weak and complex-cell responses when they are strong, suggesting that simple and complex cells are the low- and high-gain limits of the same basic cortical circuit. Given the ubiquity of invariant responses in cognitive processing, the recurrent mechanism we propose for complex cells may be widely applicable.

We explore the effects of short-term synaptic depression on the temporal dynamics of V1 responses to visual images by constructing a model simple cell. Synaptic depression is modeled on the basis of previous detailed fits to experimental data. A component of synaptic depression operating in the range of hundreds of milliseconds can account for a number of the unique temporal characteristics of cortical neurons, including the bandpass nature of frequency-response curves, increases in response amplitude and in cutoff frequency for transient stimuli, nonlinear temporal summation, and contrast-dependent shifts in response phase. Synaptic depression also provides a mechanism for generating the temporal phase shifts needed to produce direction selectivity, and a model constructed along these lines matches both extracellular and intracellular data. A slower component of depression can reproduce the effects of contrast adaptation.

Neurons in the primary visual cortex (VI) exhibit response characteristics qualitatively different from their LGN afferents. Some of these characteristics, such as the oriented structure of simple cell receptive fields, can be explained as arising from linear combinations of LGN receptive fields.1 However, many aspects of VI responses, especially in the temporal domain, reflect underlying nonlinear mechanisms. Here we study the idea that synaptic depression may give rise to many of these nonlinearities. Synaptic depression is observed in intracortical3–5 as well as thalamocortical6,7 synapses and has been proposed as a possible mechanism for contrast adaptation and direction selectivity.2,9 We construct a model VI simple cell and explore the effects of synaptic depression on the temporal dynamics of its responses. Our results indicate that synaptic depression may play an important role in the enhancement of responses to transient stimuli, direction selectivity, and contrast adaptation.

A major question facing computational models of human memory concerns the storage and retrieval of sequentially processed information. Many current models assume a chaining of associations. According to this view, each item, or memory pattern, is associated with the preceding item in the sequence. In reproducing the sequence, each recalled item serves as a retrieval cue for the next item. A serious problem facing these chaining models is their susceptibility to associative interference. This paper presents a novel experimental method designed to assess the effects of associative interference in the retrieval of ordered lists of items. Experimental findings presented here suggest that subjects use multiple prior items, as well as context, to overcome the effects of associative interference in list recall.

Corrigendum: Control of timing, rate and bursts of hippocampal place cells by dendritic and somatic inhibition

Some epidemiological data have linked dietary polyphenols with lower risk of coronary heart disease. Polyphenols might impair lipoprotein oxidation which is believed to be an important step in initiating atherogenesis. The purpose of this study was to determine if grape extract known to contain polyphenolic substances can block copper-induced oxidative modification of human low density lipoprotein (LDL).LDL oxidation was monitored spectrophotometrically by measurement of change in absorbance at 234 nm. Incubation of LDL (0.05 mg protein/ml) with 1.66 microM cupric chloride produced a lag phase of 130 min before onset of the propagation phase where polyunsaturated fatty acids undergo conversion to conjugated lipid hydroperoxides. However, in the presence of grape extract at a final concentration equal to an 8000-fold dilution, the lag phase was extended to 185 min. A 4000-fold and 2000-fold dilution of grape extract produced lag phases of 250 and 465 min, respectively. LDL oxidation was essentially blocked for at least 10 h with a 1000-fold dilution of grape extract. In other experiments, incubation of LDL (0.2 mg protein/ml) with 5 microM cupric chloride for 1-4 h increased both thiobarbituric acid-reactive substances and electrophoretic mobility of LDL on agarose gel. In addition, there was loss of immunoreactivity of LDL with a murine monoclonal antibody against human apolipoprotein B-100. However, these oxidative changes to LDL by copper were prevented when diluted grape extract was present during incubation. It is concluded that grape extract contains antioxidants in the form of polyphenols with the capacity to inhibit oxidative modification of LDL.

Non-inductive steady-state scenarios on ITER will need to operate with internal transport barriers (ITBs) in order to reach adequate fusion gain at typical currents of 9 MA. The large pressure gradients at the location of the internal barrier are conducive to the development of ideal MHD instabilities that may limit the plasma performance and may lead to plasma disruptions. Fully non-inductive scenario simulations with five combinations of heating and current drive sources are presented in this work, with plasma currents in the range 7–10 MA. For each configuration the linear, ideal MHD stability is analysed for variations of the Greenwald fraction and of the pressure peaking factor around the operating point, aiming at defining an operational space for stable, steady-state operations at optimized performance. It is shown that plasmas with lower hybrid heating and current drive maintain the minimum safety factor above 1.5, which is desirable in steady-state operations to avoid neoclassical tearing modes. Operating with moderate ITBs at 2/3 of the minor radius, these plasmas have a minimum safety factor above 2, are ideal MHD stable and reach Q ≳ 5 operating above the ideal no-wall limit.

Highly purified peroxisomes were obtained from the liver of untreated rats, and rates of peroxisomal beta-oxidation were measured using fatty acyl-CoAs differing in chain length and degree of unsaturation. A 20–24-fold purification of peroxisomes, indicated by the specific activities of the marker enzymes catalase and urate oxidase, respectively, was obtained from crude liver homogenate using differential centrifugation techniques followed by a 30% Nycodenz gradient separation. The use of a 30% Nycodenz gradient in the final step of purification was extremely effective (e.g. 5.5-fold reduction) in removing lysosomal contamination. The rate of peroxisomal beta-oxidation with lauroyl-CoA (C12:0) as substrate was the highest of all fatty acyl-CoAs tested. Butyryl-CoA (C4:0) was not oxidized by purified peroxisomes. In general, as chain length of the fatty acyl-CoAs increased above 12 carbons, the rates of beta-oxidation decreased.

Neurons in primary visual cortex have long been classified into simple and complex cells, but a new paper notes that different firing patterns need not imply different underlying circuitry.

Motivated by experimental observations of apparently triggerless tearing modes, we have performed linear and nonlinear MHD analysis showing that a non-resonant mode with toroidal mode number n = 1 can develop in the National Spherical Torus eXperiment (NSTX) at moderate normalized βN when the shear is low and the central safety factor q 0 is close to but greater than one. This mode, which is related to previously identified ‘infernal’ modes, will saturate and persist, and can develop poloidal mode number m = 2 magnetic islands in agreement with experiments. We have also extended this analysis by performing a free-boundary transport simulation of an entire discharge and showing that, with reasonable assumptions, we can predict the time of mode onset.

For the tokamak magnetic confinement concept, theory has predicted a distinct relationship between the plasma shape, the internal magnetic structure, and the presence or absence of fast ion losses in the presence of plasma instabilities. We have, for the first time, carried out measurements of the magnetic safety factor profile, [ital q]([ital r]), in plasmas unstable to a specific instability, the so-called fishbone'' mode. The experimental equilibria reconstructed from these data have been used to demonstrate that when the plasma is unstable to fishbones, the fast ion confinement properties depend strongly on the radius of the magnetic surface where [ital q]([ital r])=1.

Plasmas exhibiting the ``fishbone`` instability studied on the PBX-M tokamak show a distinct relationship between the plasma shape, the internal magnetic structure, and the presence or absence of fast ion losses associated with the fishbone mode. We have, for the first time, carried out measurements of the magnetic safety factor profile in fishbone-unstable plasmas, and used the knowledge of the associated experimental equilibria to compare the stability and fast ion loss properties of these plasmas with experimental observations.

The generalized Green's function method proposed by Miller and Dewar ( J. Comput. Phys. 66 , 356 (1986)) and Pletzer and Dewar in Computational Techniques & Applications: CTAC-89, Proceedings, Int. Conf. Brisbane, 1989 , edited by W. L. Hogarth and B. J. Noye, in press, for solving the singular differential equation occurring in the finite β tearing mode problem has been tested numerically on a model differential equation. This method is compatible with a variational formulation of the problem and gives accurate numerical answers with high powers of convergence with respect to the number of grid points used. When the method is extended to the more physically relevant two-sided problem at moderate pressure gradients, a less stringent condition on the Frobenius expansion is required because the principal value of the otherwise divergent integrals associated with the method is shown to exist.

Stability against ideal low n kink and infinite n ballooning modes in high beta T H-mode single null DIII-D divertor plasmas is examined. The equilibrium plasma pressure and current profiles are reconstructed self-consistently from experimentally measured magnetic data and kinetic profile data. The results show that the plasma is marginally stable to the ballooning mode near the central region and is stable to the ballooning mode over most of the plasma volume. Although the total volume averaged toroidal beta beta T in these discharges has not reached the limit imposed by the ideal ballooning mode, the pressure gradient near the edge region approaches the ballooning limit locally, particularly just preceding the occurrence of a giant edge localized mode (ELM). The results also indicate that plasmas with high normalized toroidal beta beta N>or=2.7-3.0 marginally stable to the ideal n=1 pressure driven kink mode without a conducting wall.

The MHD spectrum associated with small perturbations about an analytic equilibrium is determined for a configuration with magnetic flux surfaces which are nested similar elliptic cylinders generated by a uniform axial current. Since the system is periodic, it models the essential features of a toroid. Both analytic and numerical techniques are used to investigate many properties of the modes, including the continuous shear Alfven and slow acoustic spectra as well as the discrete modes associated with fast magnetosonic waves, kinks, and instabilities where the interchange criterion is violated. In particular, the relationship between discrete and continuum modes is described both qualitatively and quantitatively, and it is shown how the unstable interchange modes emerge from the shear-Alfven branch of the spectrum.

Contrary to previous theoretical predictions, it is shown that the dissipative drift-wave instabilities are absolute in tokamak plasmas. The existence of unstable eigenmodes is shown to be associated with a new eigenmode branch induced by the finite toroidal couplings.

A new type of axisymmetric magnetohydrodynamic equilibrium is presented. It is characterized by a region of pressure and safety factor variation with a short scale length imposed as a perturbation. The equilibrium consistent with these profile variations can be calculated by means of an asymptotic expansion. The flexibility obtained by generating such equilibria allows for a close examination of the mechanisms that are relevant to ballooning instabilities – ideal-MHD modes with large toroidal mode number. The so-called first and second regions of stability against these modes are seen well within the limits of validity of the asymptotic expansion. It appears that the modes must be localized in regions with small values of the local shear of the magnetic field. The second region of stability occurs where the local shear is large throughout the range where the magnetic-field-line curvature is destabilizing.

We studied ballooning instabilities in tokamaks of arbitrary cross sections and finite shear. These azimuthally localized, ideal magnetohydrodynamic modes have large toroidal-mode numbers, but finite variation along the field and across the flux surfaces. Stability is determined by solving a second-order ordinary differential equation on each flux surface, subject to the proper boundary conditions. Qualitative agreement is achieved with the Princeton PEST stability code.

Princeton Beta Experiment (PBX) discharges run at the lowest q and highest βt always terminated in a hard disruption. The discharges, with βt values of up to 5.5% and q-values down to 2.2, were obtained by employing large current ramps and large gas feed rates during neutral beam injection. Previous work has indicated that the achieved βt values were consistent with the limit imposed by the n = l ideal external kink with a conducting wall at b/a = 2. The authors of the paper investigate further the validity of ideal MHD theory in explaining the low qψ disruptions. In particular, the characteristics of the pre-disruption MHD activity in these low-q discharges, specifically the time-scale of growth and internal and external mode structures, are compared with those determined from theoretical calculations. The results of these comparisons indicate that non-ideal effects must be considered in order to obtain detailed agreement between theory and experiment.

The results of numerical calculations of ..delta..' for a class of equilibria typical of those encountered during the early formation stage of the S1 Spheromak are presented. The equilibrium plasma is assumed to be cylindrically symmetric and pressureless. It encloses a current carrying perfect conductor (flux core) and is surrounded by a vacuum with zero longitudinal field. Stability boundaries in the space formed by the equilibrium parameters are mapped. The plasma is tearing mode stable provided B/sub z//B/sub theta/ at the flux core is below a certain critical value which depends on the equilibrium parameters. For typical equilibria, this critical value is 0.65.

Indentation of a tokamak plasma on its inner-major-radius side is shown to be strongly beneficial for achieving high-$\ensuremath{\beta}$ stability against ballooning modes. With use of a set of reasonable equilibrium profiles, it is found that moderate indentation provides accessibility to the second region of stability. Ohmic equilibrium configurations which exhibit the second stability region have not yet been found.

Finite-ion-Larmor-radius (FLR) effects provide a band of additional stability for values of β(≡ plasma pressure/magnetic pressure) exceeding the limit predicted for ideal magnetohydrodynamic (MHD) ballooning modes. The effect of particle collisions on the stable modes of the FLR-modified ideal theory that exist in this range of β values is examined.

The MHD equilibrium and stability of a vertically elongated tokamak configuration are analysed in the one-dimensional limit corresponding to infinite elongation. Stability against all ideal-MHD modes can be obtained for beta values arbitrarily close to unity. In the finite-resistivity stability analysis, axisymmetric (m = 0) tearing modes, centred on the null trace of the poloidal field, can be stabilized by a loosely fitting conducting shell. The presence of the toroidal field component, however, introduces the possibility of non-symmetric tearing modes (m ? 0), centred away from the null trace. These modes can be stabilized only by a more tightly fitting shell, plus reliance on finite-pressure effects on the small-major-radius side of the plasma profile. Under these conditions, stable configurations with peak beta values approaching unity are readily found.

A self‐adjoint, gauge invariant stability functional δWTG for determination of a sufficient condition of tearing mode stability is obtained for a plasma with a uniform pressure. The plasma is stable if there is no free energy available to support energy flux into the singular layer. The Δ’ concept, valid in simple geometries, is generalized to reflect variation of equilibrium quantities on the flux surface. The relationship of δWTG to the ideal stability functional and other possible forms of tearing mode stability functionals is clarified through gauge transformations.

The behavior of shear-Alfven eigenmodes and the accompanied anomalous transport have been investigated. In the particle simulation, equilibrium thermal fluctuations associated with the eigenmodes have been observed to nullify the zeroth-order shear near the rational surface through the induced second-order eddy current, and, in turn, give rise to the formation of magnetic islands which cause rapid electron energy transport in the region. The theoretical verification of the observed behavior is discussed.

A comprehensive analysis of the stability properties of the appropriate kinetically generalized form of MHD ballooning modes, together with the usual trapped-particle drift modes, is presented. The calculations are fully electromagnetic and include the complete dynamics associated with compressional ion acoustic waves. Trapped-particle effects, together with all forms of collisionless dissipation, are taken into account without approximations. The influence of collisions is estimated with a model Krook operator. Results from the application of this analysis to realistic tokamak operating conditions indicate that unstable short-wavelength modes with significant growth rates can extend from β = 0 to values above the upper ideal-MHD critical beta associated with the 'second stability regime'. Since the maximum growth rates of the relevant modes appear to vary gradually with beta, these results support a 'soft' beta-limit picture involving a continuous (rather than abrupt or 'hard') modification of anomalous transport already present in low-beta tokamaks. However, at higher beta the increasing dominance of the electromagnetic component of the perturbations indicated by these calculations could also imply significantly different transport scaling properties.

Bean-shaped configurations favorable for high ..beta.. discharges have been investigated in the Princeton Beta Experiment (PBX) tokamak. Strongly indented bean-shaped plasmas have been successfully formed, and beta values of over 5% have been obtained with 5 MW of injected neutral beam power. These high beta discharges still lie in the first stability regime for ballooning modes, and MHD stability analysis implicates the external kink as responsible for the present ..beta.. limit.

The model ballooning mode equation of Connor, Hastie and Taylor for large-aspect-ratio circular tokamaks is analysed in the limit of large pressure gradient, and corresponding expressions for stability boundaries are derived. In particular, it is found that for fixed radial wavenumbers infinite sequences of unstable bands exist and that minimizing over the radial wavenumbers leads to asymptotic merging between the neighbouring bands, which significantly modifies the second stability boundary compared with that for zero radial wavenumber.

Extensive numerical studies of ideal-MHD instabilities have been carried out to gain insight into the parametric dependence of critical β's in tokamaks. The large number of interrelated equilibrium quantities involved in establishing a critical β has demanded a careful, systematic survey in order to isolate this dependence. The results of this survey establish the scaling with geometrical quantities including aspect ratio, elongation, and triangularity in the parameter regimes appropriate to both current and reactor-sized plasmas. A moderate dependence on the pressure profile and a strong variation with the current profile is found. The principal result is that, for aspect ratio R/a ≈ 3, critical β's are of the order of 2% for circular cross-sections and 5% for plasmas with elongation K ≈2; somewhat higher values could be achieved with more optimal shaping. Finally, sequences of equilibria have been analysed to compare critical β as a function of toroidal mode number n. It is concluded that the infinite-n analytic ballooning theory provides a sufficient condition for ideal-MHD internal-mode stability. Low-n free-boundary modes appear to set a lower limit.

Magnetohydrodynamic instabilities limit the material that can be contained in a tokamak. The nature of the dangerous kink and ballooning modes is investigated for a typical configuration. In high-beta systems the most dangerous instabilities are ballooning modes that form large convective cells concentrated in regions of unfavorable magnetic field-line curvature.

A nonvariational approach for determining the ideal MHD stability of axisymmetric toroidal confinement systems is presented. The code (NOVA) employs cubic B -spline finite elements and Fourier expansion in a general flux coordinate (ψ, φ, ζ) system. At least as much accuracy and faster convergence were obtained in comparison with the existing variational PEST and ERATO codes which employ linear finite elements. This nonvariational approach benchmarked here on the ideal MHD problem is a prelude to a future extended version applicable to problems having non-Hermitian eigenmode equations where variational energy principles cannot be obtained.

A study of the MHD stability properties of bean-shaped tokamak plasmas is presented. For ballooning modes, while increased indentation gives larger stable-beta configurations, the existence and accessibility of the second stable region are sensitive to the pressure and safety factor profiles. The second stable region appears at lower beta values for large aspect ratio and moderately high q-values. Finite-Larmor-radius kinetic effects can significantly improve the stability properties. For low-q ( 1) operation, long-wavelength (n ~ 2, 3) internal-pressure-driven modes occur at modest βp values and accessibility to higher beta operation is unlikely. Indentation modifies the nature of the usually vertical axisymmetric instability, but the mode can be passively stabilized by placing highly conducting plates near the tips of the plasma bean. At constant q, indentation has a stabilizing effect on tearing modes.

Ideal and resistive MHD equations for the shear Alfven waves are studied in a low-β toroidal model by employing the high-n ballooning formalism. The ion sound effects are neglected. For an infinite shear slab, the ideal MHD model gives rise to acontinuous spectrum of real frequencies and discrete eigenmodes (Alfven-Landau modes) with complex frequencies. With toroidal coupling effects due to nonuniform toroidal magnetic field, the continuum is broken up into small continuum bands and new discrete toroidal eigenmodes can exist inside the continuum gaps. Unstable ballooning eigenmodes are also introduced by the bad curvature when β > βc. The resistivity (η) can be considered perturbatively for the ideal modes. In addition, four branches of resistive modes are induced by the resistivity: (1) resistive entropy modes which are stable with frequencies going to zero with resistivity as η 1 3 ; (2) tearing modes which are stable (Δ′ η 3 5 ; (3) resistive periodic shear Alfven waves which approach the finite frequency end points of the continuum bands as η 1 2 ; and (4) resistive ballooning modes which are purely growing with growth rate proportional to η 1 3 β 2 3 as η → 0 and β → 0.

We propose a means by which the theory of drift instabilities can be extended to plasmas of arbitrary β. We then concentrate on the drift Alfven instability driven by an electron temperature gradient, proposed by Coroniti and Kennel (1970) to be a source of Pi 1 micropulsations on auroral lines of force. Even at relatively low β the full finite β theory differs considerably from previous low β theories and produces better agreement with observation.

Stability criteria for localized instabilities for both ideal and resistive models are derived and evaluated for general axisymmetric configurations. A numerical scheme for determining the spectrum in these configurations is developed. Application is made to the special case of an elliptical cylindrical plasma column, with finite pressure and length, carrying a uniform axial current. (auth)

Neutral-beam current-drive experiments in the DIII-D tokamak with a single null poloidal divertor are described. A plasma current of 0.34 MA has been sustained by neutral beams alone, and the energy confinement is of $H$-mode quality. Poloidal $\ensuremath{\beta}$ values reach 3.5 without disruption or coherent magnetic activity suggesting that these plasmas may be entering the second stability regime.

A rearrangement of the divertor coils in PDX will enable a test in 1984 of the MHD stability properties of deeply indented bean-shaped plasmas. The goal is a beta of 10%. Indentation is expected to counter the deterioration of MHD stability against pressure driven modes that is occasioned by the larger aspect ratios typical of anticipated reactor oriented devices. Indeed, as shown by M. Chance et al., indentation may offer direct access to the second region of stability for ballooning modes, and numerical analyses with PEST show the internal kink to be stabilized completely with even relatively modest indentation. The internal kink is implicated in the loss of beam ions in PDX. In this report the theoretical basis for the forthcoming experiment, and the design considerations underlying the modification from PDX to PBX, are described in detail. Additional theoretical material, including an analysis of particle orbits in an indented tokamak plasma, is appended.

A study of the MHD stability properties of bean-shaped tokamak plasmas is presented. For ballooning modes, while increased indentation gives larger ..beta.. stable configurations, the existence and accessibility of the second stable region is sensitive to the pressure and safety factor profiles. The second stable region appears at lower ..beta.. values for large aspect ratio and moderately high q-values. Finite-Larmor-radius (FLR) kinetic effects can significantly improve the stability properties. For low q (< 1) operation, long wavelength (n approx. 2,3) internal pressure driven modes occur at modest ..beta../sub p/ values and accessibility to higher ..beta.. operation is unlikely. Indentation modifies the nature of the usually vertical axisymmetric instability, but the mode can be passively stabilized by placing highly conducting plates near to the tips of the plasma bean. At constant q, indentation has a stabilizing effect on tearing modes.

High-..beta.. experiments, in medium to high-q tokamak plasmas, exhibit a temporal ..beta.. saturation and collapse. This behavior has been attributed to ballooning, ideal kink, or tearing modes. In PBX, a unique diagnostic capability allowed studies of the relation between MHD and energy loss for neutral-beam-heated (

In the absence of a conducting wall, typical spheromak plasmas are unstable to tilting and/or shifting modes. The effects of the cross-sectional shape, aspect ratio, and the location of a conducting wall on the stability of these modes are investigated. A circular cross-section (b/a ~ 1) configuration with a flux hole δ = 0.5 (aspect ratio R/a = 2) will will be stabilized by an ellipsoidal wall of mean separation of 1.3 minor radii from the plasma.