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Neural circuits exhibit complex activity patterns, both spontaneously and evoked by external stimuli. Information encoding and learning in neural circuits depend on how well time-varying stimuli can control spontaneous network activity. We show that in firing-rate networks in the balanced state, external control of recurrent dynamics, i.e., the suppression of internally-generated chaotic variability, strongly depends on correlations in the input. A distinctive feature of balanced networks is that, because common external input is dynamically canceled by recurrent feedback, it is far more difficult to suppress chaos with common input into each neuron than through independent input. To study this phenomenon, we develop a non-stationary dynamic mean-field theory for driven networks. The theory explains how the activity statistics and the largest Lyapunov exponent depend on the frequency and amplitude of the input, recurrent coupling strength, and network size, for both common and independent input. We further show that uncorrelated inputs facilitate learning in balanced networks.

This article is part of the Physical Review Research collection titled Physics of Neuroscience. Recurrent networks are widely used as models of biological neural circuits and in artificial intelligence applications. Mean-field theory has been used to uncover key properties of recurrent network models such as the onset of chaos and their largest Lyapunov exponents, but quantities such as attractor dimension and Kolmogorov-Sinai entropy have thus far remained elusive. We calculate the complete Lyapunov spectrum of recurrent neural networks and show that chaos in these networks is extensive with a size-invariant Lyapunov spectrum and attractor dimensions much smaller than the number of phase space dimensions. The attractor dimension and entropy rate increase with coupling strength near the onset of chaos but decrease far from the onset, reflecting a reduction in the number of unstable directions. We analytically approximate the full Lyapunov spectrum using random matrix theory near the onset of chaos for strong coupling and discrete-time dynamics. We show that a generalized time-reversal symmetry of the network dynamics induces a point symmetry of the Lyapunov spectrum reminiscent of the symplectic structure of chaotic Hamiltonian systems. Temporally fluctuating input can drastically reduce both the entropy rate and the attractor dimension. We lay out a comprehensive set of controls for the accuracy and convergence of Lyapunov exponents. For trained recurrent networks, we find that Lyapunov spectrum analysis quantifies error propagation and stability achieved by different learning algorithms. Our methods apply to systems of arbitrary connectivity and highlight the potential of Lyapunov spectrum analysis as a diagnostic for machine learning applications of recurrent networks.

Abstract  First promising investigations of SU-8 removal experiments with a novel plasma etching technique are presented. The basic idea of this technique is to separate the highly effective generation of chemical radicals (e.g. oxygen radicals) using a traveling wave reactor (TWR) microwave source with water cooled plasma zone from the chemical reaction with the resist polymer. The etching tool operates in a remote and downstream mode with very high radical density allowing precise thermal management of the substrates on the chuck giving controlled process conditions without deviation in temperature, and generally preventing ion bombardment, at least resulting in gentle processing without jeopardizing the integrity of the metal structures. Very good removal of SU-8 with very few residues and very high etching rates up to 10 μm per minute are observed in first experiments which are offering chances to get even more than 20 μm per minute. The etching process is isotropic, and the rate stays stable during the whole removing process even for very thick films of 1 mm and more. First application examples of SU-8 removal are demonstrating the great potential of the presented microwave plasma based technique not only for the cleaning of metallic microparts but also for other more sensitive materials which is demonstrated by SU-8 removal from graphite X-ray mask substrates. [ABSTRACT FROM AUTHOR]

Abstract  In a close collaboration the team of Micromotion, micro resist technology, BESSY, and LSU-CAMD have successfully mastered the challenges of LIGA production of ultra-precision microparts for Micro Harmonic Drive® gears. The complementary expertise ranging from design and application know-how to process research and technical support resulted in high quality LIGA microparts and superior Micro Harmonic Drive® gears taking advantages of the free 2D design capability and material choice. It is also an excellent example that through contributions from partners with different background and expertise LIGA precision parts can be produced with high quality and yield and for a market competitive price. [ABSTRACT FROM AUTHOR]

Abstract LIGA is the basic idea of promising developments for the manufacturing of microelectromechanical system parts containing high aspect ratio microstructures. Aim of the work is a brief discussion of the starting-points for inline process inspection within a direct LIGA technology using deep X-ray lithography for the production of micromechanical gear wheels with critical dimensions of ?35??m width at ?1?mm height as well as to show methodic and technical measuring possibilities. Firstly, results of the determination of residual solvent content distribution within ultra-thick SU-8 films are shown obtained from refracted near field optical measurements. Furthermore, the capability of X-ray computer tomographic imaging is discussed and measurements for the determination of the three-dimensional shape of high aspect ratio microstructures are practically demonstrated with microscopic and interferometric optical methods. Finally, first results demonstrate the potential of the optical coherence tomography for several further important measurement tasks, among others, e.g. for the imaging of the distribution of mechanical stress at the resist?substrate interface. The results show that much information which is essential in the LIGA process can be achieved with recently available measurement methods. However, further development of non-destructive measurement techniques would be desirable for an effective inline process control of mass production of micromechanical parts. [ABSTRACT FROM AUTHOR]

Neuronal activity in the central nervous system varies strongly in time and across neuronal populations. It is a longstanding proposal that such fluctuations generically arise from chaotic network dynamics. Various theoretical studies predict that the rich dynamics of rate models operating in the chaotic regime can subserve circuit computation and learning. Neurons in the brain, however, communicate via spikes and it is a theoretical challenge to obtain similar rate fluctuations in networks of spiking neuron models. A recent study investigated spiking balanced networks of leaky integrate and fire (LIF) neurons and compared their dynamics to a matched rate network with identical topology, where single unit input-output functions were chosen from isolated LIF neurons receiving Gaussian white noise input. A mathematical analogy between the chaotic instability in networks of rate units and the spiking network dynamics was proposed. Here we revisit the behavior of the spiking LIF networks and these matched rate networks. We find expected hallmarks of a chaotic instability in the rate network: For supercritical coupling strength near the transition point, the autocorrelation time diverges. For subcritical coupling strengths, we observe critical slowing down in response to small external perturbations. In the spiking network, we found in contrast that the timescale of the autocorrelations is insensitive to the coupling strength and that rate deviations resulting from small input perturbations rapidly decay. The decay speed even accelerates for increasing coupling strength. In conclusion, our reanalysis demonstrates fundamental differences between the behavior of pulse-coupled spiking LIF networks and rate networks with matched topology and input-output function. In particular there is no indication of a corresponding chaotic instability in the spiking network.