Pattern Formation in the Early Universe

Systems that exhibit pattern formation are typically driven and dissipative. In the early universe, parametric resonance can drive explosive particle production called preheating. The fields that are populated then decay quantum mechanically if their particles are unstable. Thus, during preheating, a driven-dissipative system exists. We have shown previously that pattern formation can occur in two dimensions in a self-coupled inflaton system undergoing parametric resonance. In this paper, we provide evidence of pattern formation for more realistic initial conditions in both two and three dimensions. In the one-field case, we have the novel interpretation that these patterns can be thought of as a network of domain walls. We also show that the patterns are spatio-temporal, leading to a distinctive, but probably low-amplitude peak in the gravitational wave spectrum. In the context of a two-field model, we discuss putting power from resonance into patterns on cosmological scales, in particular to explain the observed excess power at 100 h^{-1}Mpc, but why this seems unlikely in the absence of a period of post-preheating inflation. Finally we note our model is similar to that of the decay of DCCs and therefore pattern formation may also occur at RHIC and LHC.Comment: 9 pages, 11 figure

A Pulse-Gated, Predictive Neural Circuit

Recent evidence suggests that neural information is encoded in packets and may be flexibly routed from region to region. We have hypothesized that neural circuits are split into sub-circuits where one sub-circuit controls information propagation via pulse gating and a second sub-circuit processes graded information under the control of the first sub-circuit. Using an explicit pulse-gating mechanism, we have been able to show how information may be processed by such pulse-controlled circuits and also how, by allowing the information processing circuit to interact with the gating circuit, decisions can be made. Here, we demonstrate how Hebbian plasticity may be used to supplement our pulse-gated information processing framework by implementing a machine learning algorithm. The resulting neural circuit has a number of structures that are similar to biological neural systems, including a layered structure and information propagation driven by oscillatory gating with a complex frequency spectrum.Comment: This invited paper was presented at the 50th Asilomar Conference on Signals, Systems and Computer

Graded, Dynamically Routable Information Processing with Synfire-Gated Synfire Chains

Coherent neural spiking and local field potentials are believed to be signatures of the binding and transfer of information in the brain. Coherent activity has now been measured experimentally in many regions of mammalian cortex. Synfire chains are one of the main theoretical constructs that have been appealed to to describe coherent spiking phenomena. However, for some time, it has been known that synchronous activity in feedforward networks asymptotically either approaches an attractor with fixed waveform and amplitude, or fails to propagate. This has limited their ability to explain graded neuronal responses. Recently, we have shown that pulse-gated synfire chains are capable of propagating graded information coded in mean population current or firing rate amplitudes. In particular, we showed that it is possible to use one synfire chain to provide gating pulses and a second, pulse-gated synfire chain to propagate graded information. We called these circuits synfire-gated synfire chains (SGSCs). Here, we present SGSCs in which graded information can rapidly cascade through a neural circuit, and show a correspondence between this type of transfer and a mean-field model in which gating pulses overlap in time. We show that SGSCs are robust in the presence of variability in population size, pulse timing and synaptic strength. Finally, we demonstrate the computational capabilities of SGSC-based information coding by implementing a self-contained, spike-based, modular neural circuit that is triggered by, then reads in streaming input, processes the input, then makes a decision based on the processed information and shuts itself down

Observations and modeling of the surface seiches of Lake Tahoe, USA

A rich array of spatially complex surface seiche modes exists in lakes. While the amplitude of these oscillations is often small, knowledge of their spatio-temporal characteristics is valuable for understanding when they might be of localized hydrodynamic importance. The expression and impact of these basin-scale barotropic oscillations in Lake Tahoe are evaluated using a finite-element numerical model and a distributed network of ten high-frequency nearshore monitoring stations. Model-predicted nodal distributions and periodicities are confirmed using the presence/absence of spectral power in measured pressure signals, and using coherence/phasing analysis of pressure signals from stations on common and opposing antinodes. Surface seiches in Lake Tahoe have complex nodal distributions despite the relative simplicity of the basin morphometry. Seiche amplitudes are magnified on shallow shelves, where they occasionally exceed 5 cm; elsewhere, amplitudes rarely exceed 1 cm. There is generally little coherence between surface seiching and littoral water quality. However, pressure–temperature coherence at shelf sites suggests potential seiche-driven pumping. Main-basin seiche signals are present in attached marinas, wetlands, and bays, implying reversing flows between the lake and these water bodies. On the shallow sill connecting Emerald Bay to Lake Tahoe, the fundamental main-basin seiche combines with a zeroth-mode harbor seiche to dominate the cross-sill flow signal, and to drive associated temperature fluctuations. Results highlight the importance of a thorough descriptive understanding of the resonant barotropic oscillations in any lake basin in a variety of research and management contexts, even when the magnitude of these oscillations tends to be small