Variational log-Gaussian point-process methods for grid cells.

We present practical solutions to applying Gaussian-process (GP) methods to calculate spatial statistics for grid cells in large environments. GPs are a data efficient approach to inferring neural tuning as a function of time, space, and other variables. We discuss how to design appropriate kernels for grid cells, and show that a variational Bayesian approach to log-Gaussian Poisson models can be calculated quickly. This class of models has closed-form expressions for the evidence lower-bound, and can be estimated rapidly for certain parameterizations of the posterior covariance. We provide an implementation that operates in a low-rank spatial frequency subspace for further acceleration, and demonstrate these methods on experimental data.

Simultaneous representation of multiple time horizons by entorhinal grid cells and CA1 place cells.

Grid cells and place cells represent the spatiotemporal continuum of an animal's past, present, and future locations. However, their spatiotemporal relationship is unclear. Here, we co-record grid and place cells in freely foraging rats. We show that average time shifts in grid cells tend to be prospective and are proportional to their spatial scale, providing a nearly instantaneous readout of a spectrum of progressively increasing time horizons ranging hundreds of milliseconds. Average time shifts of place cells are generally larger compared to grid cells and also increase with place field sizes. Moreover, time horizons display nonlinear modulation by the animal's trajectories in relation to the local boundaries and locomotion cues. Finally, long and short time horizons occur at different parts of the theta cycle, which may facilitate their readout. Together, these findings suggest that population activity of grid and place cells may represent local trajectories essential for goal-directed navigation and planning.

Self-healing codes: How stable neural populations can track continually reconfiguring neural representations.

As an adaptive system, the brain must retain a faithful representation of the world while continuously integrating new information. Recent experiments have measured population activity in cortical and hippocampal circuits over many days and found that patterns of neural activity associated with fixed behavioral variables and percepts change dramatically over time. Such "representational drift" raises the question of how malleable population codes can interact coherently with stable long-term representations that are found in other circuits and with relatively rigid topographic mappings of peripheral sensory and motor signals. We explore how known plasticity mechanisms can allow single neurons to reliably read out an evolving population code without external error feedback. We find that interactions between Hebbian learning and single-cell homeostasis can exploit redundancy in a distributed population code to compensate for gradual changes in tuning. Recurrent feedback of partially stabilized readouts could allow a pool of readout cells to further correct inconsistencies introduced by representational drift. This shows how relatively simple, known mechanisms can stabilize neural tuning in the short term and provides a plausible explanation for how plastic neural codes remain integrated with consolidated, long-term representations.

Macro marine litter survey of sandy beaches along the Cox's Bazar Coast of Bay of Bengal, Bangladesh: Land-based sources of solid litter pollution.

Macro-sized marine litter (>2.5 cm) was collected, characterized, and enumerated along the Cox's Bazar Coast, Bangladesh. Marine litter abundance was converted to density (number of items/m2). Beach cleanliness was evaluated using the clean-coast index (CCI). Plastic polythene bags were the most abundant litter items, followed by plastic cups. Total marine litter abundance was 54,401 ± 184 items. Major sources of marine litter were from tourism, fishery and residential activities. Of 10 sites surveyed, two were classified as dirty, two were moderate, four were clean and two were very clean using the CCI. Marine litter pollution along the Cox's Bazar Coast represents a potential threat to coastal and marine environments. This baseline study will help to establish mitigation strategies that are urgently required to reduce marine litter pollution along the Cox's Bazar Coast.

The information theory of developmental pruning: Optimizing global network architectures using local synaptic rules.

During development, biological neural networks produce more synapses and neurons than needed. Many of these synapses and neurons are later removed in a process known as neural pruning. Why networks should initially be over-populated, and the processes that determine which synapses and neurons are ultimately pruned, remains unclear. We study the mechanisms and significance of neural pruning in model neural networks. In a deep Boltzmann machine model of sensory encoding, we find that (1) synaptic pruning is necessary to learn efficient network architectures that retain computationally-relevant connections, (2) pruning by synaptic weight alone does not optimize network size and (3) pruning based on a locally-available measure of importance based on Fisher information allows the network to identify structurally important vs. unimportant connections and neurons. This locally-available measure of importance has a biological interpretation in terms of the correlations between presynaptic and postsynaptic neurons, and implies an efficient activity-driven pruning rule. Overall, we show how local activity-dependent synaptic pruning can solve the global problem of optimizing a network architecture. We relate these findings to biology as follows: (I) Synaptic over-production is necessary for activity-dependent connectivity optimization. (II) In networks that have more neurons than needed, cells compete for activity, and only the most important and selective neurons are retained. (III) Cells may also be pruned due to a loss of synapses on their axons. This occurs when the information they convey is not relevant to the target population.

Optimal Encoding in Stochastic Latent-Variable Models.

In this work we explore encoding strategies learned by statistical models of sensory coding in noisy spiking networks. Early stages of sensory communication in neural systems can be viewed as encoding channels in the information-theoretic sense. However, neural populations face constraints not commonly considered in communications theory. Using restricted Boltzmann machines as a model of sensory encoding, we find that networks with sufficient capacity learn to balance precision and noise-robustness in order to adaptively communicate stimuli with varying information content. Mirroring variability suppression observed in sensory systems, informative stimuli are encoded with high precision, at the cost of more variable responses to frequent, hence less informative stimuli. Curiously, we also find that statistical criticality in the neural population code emerges at model sizes where the input statistics are well captured. These phenomena have well-defined thermodynamic interpretations, and we discuss their connection to prevailing theories of coding and statistical criticality in neural populations.

Stable task information from an unstable neural population.

Over days and weeks, neural activity representing an animal's position and movement in sensorimotor cortex has been found to continually reconfigure or 'drift' during repeated trials of learned tasks, with no obvious change in behavior. This challenges classical theories, which assume stable engrams underlie stable behavior. However, it is not known whether this drift occurs systematically, allowing downstream circuits to extract consistent information. Analyzing long-term calcium imaging recordings from posterior parietal cortex in mice (Mus musculus), we show that drift is systematically constrained far above chance, facilitating a linear weighted readout of behavioral variables. However, a significant component of drift continually degrades a fixed readout, implying that drift is not confined to a null coding space. We calculate the amount of plasticity required to compensate drift independently of any learning rule, and find that this is within physiologically achievable bounds. We demonstrate that a simple, biologically plausible local learning rule can achieve these bounds, accurately decoding behavior over many days.

Too hot to handle: Unprecedented seagrass death driven by marine heatwave in a World Heritage Area.

The increased occurrence of extreme climate events, such as marine heatwaves (MHWs), has resulted in substantial ecological impacts worldwide. To date, metrics of thermal stress within marine systems have focussed on coral communities, and less is known about measuring stress relevant to other primary producers, such as seagrasses. An extreme MHW occurred across the Western Australian coastline in the austral summer of 2010-2011, exposing marine communities to summer seawater temperatures 2-5°C warmer than average. Using a combination of satellite imagery and in situ assessments, we provide detailed maps of seagrass coverage across the entire Shark Bay World Heritage Area (ca. 13,000 km2 ) before (2002 and 2010) and after the MHW (2014 and 2016). Our temporal analysis of these maps documents the single largest loss in dense seagrass extent globally (1,310 km2 ) following an acute disturbance. Total change in seagrass extent was spatially heterogeneous, with the most extensive declines occurring in the Western Gulf, Wooramel Bank and Faure Sill. Spatial variation in seagrass loss was best explained by a model that included an interaction between two heat stress metrics, the most substantial loss occurring when degree heating weeks (DHWm) was ≥10 and the number of days exposed to extreme sea surface temperature during the MHW (DaysOver) was ≥94. Ground truthing at 622 points indicated that change in seagrass cover was predominantly due to loss of Amphibolis antarctica rather than Posidonia australis, the other prominent seagrass at Shark Bay. As seawater temperatures continue to rise and the incidence of MHWs increase globally, this work will provide a basis for identifying areas of meadow degradation, or stability and recovery, and potential areas of resilience.

Neural field models for latent state inference: Application to large-scale neuronal recordings.

Large-scale neural recording methods now allow us to observe large populations of identified single neurons simultaneously, opening a window into neural population dynamics in living organisms. However, distilling such large-scale recordings to build theories of emergent collective dynamics remains a fundamental statistical challenge. The neural field models of Wilson, Cowan, and colleagues remain the mainstay of mathematical population modeling owing to their interpretable, mechanistic parameters and amenability to mathematical analysis. Inspired by recent advances in biochemical modeling, we develop a method based on moment closure to interpret neural field models as latent state-space point-process models, making them amenable to statistical inference. With this approach we can infer the intrinsic states of neurons, such as active and refractory, solely from spiking activity in large populations. After validating this approach with synthetic data, we apply it to high-density recordings of spiking activity in the developing mouse retina. This confirms the essential role of a long lasting refractory state in shaping spatiotemporal properties of neonatal retinal waves. This conceptual and methodological advance opens up new theoretical connections between mathematical theory and point-process state-space models in neural data analysis.

Causes and consequences of representational drift.

The nervous system learns new associations while maintaining memories over long periods, exhibiting a balance between flexibility and stability. Recent experiments reveal that neuronal representations of learned sensorimotor tasks continually change over days and weeks, even after animals have achieved expert behavioral performance. How is learned information stored to allow consistent behavior despite ongoing changes in neuronal activity? What functions could ongoing reconfiguration serve? We highlight recent experimental evidence for such representational drift in sensorimotor systems, and discuss how this fits into a framework of distributed population codes. We identify recent theoretical work that suggests computational roles for drift and argue that the recurrent and distributed nature of sensorimotor representations permits drift while limiting disruptive effects. We propose that representational drift may create error signals between interconnected brain regions that can be used to keep neural codes consistent in the presence of continual change. These concepts suggest experimental and theoretical approaches to studying both learning and maintenance of distributed and adaptive population codes.

Autoregressive Point Processes as Latent State-Space Models: A Moment-Closure Approach to Fluctuations and Autocorrelations.

Modeling and interpreting spike train data is a task of central importance in computational neuroscience, with significant translational implications. Two popular classes of data-driven models for this task are autoregressive point-process generalized linear models (PPGLM) and latent state-space models (SSM) with point-process observations. In this letter, we derive a mathematical connection between these two classes of models. By introducing an auxiliary history process, we represent exactly a PPGLM in terms of a latent, infinite-dimensional dynamical system, which can then be mapped onto an SSM by basis function projections and moment closure. This representation provides a new perspective on widely used methods for modeling spike data and also suggests novel algorithmic approaches to fitting such models. We illustrate our results on a phasic bursting neuron model, showing that our proposed approach provides an accurate and efficient way to capture neural dynamics.

Climatic forcing and larval dispersal capabilities shape the replenishment of fishes and their habitat-forming biota on a tropical coral reef.

Fluctuations in marine populations often relate to the supply of recruits by oceanic currents. Variation in these currents is typically driven by large-scale changes in climate, in particular ENSO (El Nino Southern Oscillation). The dependence on large-scale climatic changes may, however, be modified by early life history traits of marine taxa. Based on eight years of annual surveys, along 150 km of coastline, we examined how ENSO influenced abundance of juvenile fish, coral spat, and canopy-forming macroalgae. We then investigated what traits make populations of some fish families more reliant on the ENSO relationship than others. Abundance of juvenile fish and coral recruits was generally positively correlated with the Southern Oscillation Index (SOI), higher densities recorded during La Niña years, when the ENSO-influenced Leeuwin Current is stronger and sea surface temperature higher. The relationship is typically positive and stronger among fish families with shorter pelagic larval durations and stronger swimming abilities. The relationship is also stronger at sites on the coral back reef, although the strongest of all relationships were among the lethrinids (r = .9), siganids (r = .9), and mullids (r = .8), which recruit to macroalgal meadows in the lagoon. ENSO effects on habitat seem to moderate SOI-juvenile abundance relationship. Macroalgal canopies are higher during La Niña years, providing more favorable habitat for juvenile fish and strengthening the SOI effect on juvenile abundance. Conversely, loss of coral following a La Niña-related heat wave may have compromised postsettlement survival of coral dependent species, weakening the influence of SOI on their abundance. This assessment of ENSO effects on tropical fish and habitat-forming biota and how it is mediated by functional ecology improves our ability to predict and manage changes in the replenishment of marine populations.

Phase reorganization leads to transient ß-LFP spatial wave patterns in motor cortex during steady-state movement preparation.

Previous studies on the origin and properties of spatial patterns in motor cortex ß-local field potential (ß-LFP) oscillations have focused on planar traveling waves. However, it is unclear 1) whether ß-LFP waves are limited to plane waves, or even 2) whether they are propagating waves of excito-excitatory activity, i.e., primarily traveling waves in excitable media; they could reflect, instead, reorganization in the relative phases of transient oscillations at different spatial sites. We addressed these two problems in ß-LFPs recorded via microelectrode arrays implanted in three adjacent motor cortex areas of nonhuman primates during steady-state movement preparation. Our findings are fourfold: 1) ß-LFP wave patterns emerged as transient events, despite stable firing rates of single neurons concurrently recorded during the same periods. 2) ß-LFP waves showed a richer variety of spatial dynamics, including rotating and complex waves. 3) ß-LFP wave patterns showed no characteristic wavelength, presenting instead a range of scales with global zero-lag phase synchrony as a limiting case, features surprising for purely excito-excitatory waves but consistent with waves in coupled oscillator systems. 4) Furthermore, excito-excitatory traveling waves induced by optogenetic stimulation in motor cortex showed, in contrast, a characteristic wavelength and reduced phase synchrony. Overall, ß-LFP wave statistics differed from those of induced traveling waves in excitable media recorded under the same microelectrode array setup. Our findings suggest phase reorganization in neural coupled oscillators contribute significantly to the origin of transient ß-LFP spatial dynamics during preparatory steady states and outline important constraints for spatially extended models of ß-LFP dynamics in motor cortex. NEW & NOTEWORTHY We show that a rich variety of transient ß-local field potential (ß-LFP) wave patterns emerge in motor cortex during preparatory steady states, despite stable neuronal firing rates. Furthermore, unlike optogenetically induced traveling waves, ß-LFP waves showed no characteristic wavelength, presenting instead a range of scales with global phase synchrony as a limiting case. Overall, our statistical analyses suggest that transient phase reorganization in neural coupled oscillators, beyond purely excito-excitatory traveling waves, contribute significantly to the origin of motor cortex ß-LFP wave patterns.

Dissociation between sustained single-neuron spiking and transient ß-LFP oscillations in primate motor cortex.

Determining the relationship between single-neuron spiking and transient (20 Hz) ß-local field potential (ß-LFP) oscillations is an important step for understanding the role of these oscillations in motor cortex. We show that whereas motor cortex firing rates and beta spiking rhythmicity remain sustained during steady-state movement preparation periods, ß-LFP oscillations emerge, in contrast, as short transient events. Single-neuron mean firing rates within and outside transient ß-LFP events showed no differences, and no consistent correlation was found between the beta oscillation amplitude and firing rates, as was the case for movement- and visual cue-related ß-LFP suppression. Importantly, well-isolated single units featuring beta-rhythmic spiking (43%, 125/292) showed no apparent or only weak phase coupling with the transient ß-LFP oscillations. Similar results were obtained for the population spiking. These findings were common in triple microelectrode array recordings from primary motor (M1), ventral (PMv), and dorsal premotor (PMd) cortices in nonhuman primates during movement preparation. Although beta spiking rhythmicity indicates strong membrane potential fluctuations in the beta band, it does not imply strong phase coupling with ß-LFP oscillations. The observed dissociation points to two different sources of variation in motor cortex ß-LFPs: one that impacts single-neuron spiking dynamics and another related to the generation of mesoscopic ß-LFP signals. Furthermore, our findings indicate that rhythmic spiking and diverse neuronal firing rates, which encode planned actions during movement preparation, may naturally limit the ability of different neuronal populations to strongly phase-couple to a single dominant oscillation frequency, leading to the observed spiking and ß-LFP dissociation.NEW & NOTEWORTHY We show that whereas motor cortex spiking rates and beta (~20 Hz) spiking rhythmicity remain sustained during steady-state movement preparation periods, ß-local field potential (ß-LFP) oscillations emerge, in contrast, as transient events. Furthermore, the ß-LFP phase at which neurons spike drifts: phase coupling is typically weak or absent. This dissociation points to two sources of variation in the level of motor cortex beta: one that impacts single-neuron spiking and another related to the generation of measured mesoscopic ß-LFPs.

Optogenetic Stimulation Shifts the Excitability of Cerebral Cortex from Type I to Type II: Oscillation Onset and Wave Propagation.

Constant optogenetic stimulation targeting both pyramidal cells and inhibitory interneurons has recently been shown to elicit propagating waves of gamma-band (40-80 Hz) oscillations in the local field potential of non-human primate motor cortex. The oscillations emerge with non-zero frequency and small amplitude-the hallmark of a type II excitable medium-yet they also propagate far beyond the stimulation site in the manner of a type I excitable medium. How can neural tissue exhibit both type I and type II excitability? We investigated the apparent contradiction by modeling the cortex as a Wilson-Cowan neural field in which optogenetic stimulation was represented by an external current source. In the absence of any external current, the model operated as a type I excitable medium that supported propagating waves of gamma oscillations similar to those observed in vivo. Applying an external current to the population of inhibitory neurons transformed the model into a type II excitable medium. The findings suggest that cortical tissue normally operates as a type I excitable medium but it is locally transformed into a type II medium by optogenetic stimulation which predominantly targets inhibitory neurons. The proposed mechanism accounts for the graded emergence of gamma oscillations at the stimulation site while retaining propagating waves of gamma oscillations in the non-stimulated tissue. It also predicts that gamma waves can be emitted on every second cycle of a 100 Hz oscillation. That prediction was subsequently confirmed by re-analysis of the neurophysiological data. The model thus offers a theoretical account of how optogenetic stimulation alters the excitability of cortical neural fields.

Contribution of LFP dynamics to single-neuron spiking variability in motor cortex during movement execution.

Understanding the sources of variability in single-neuron spiking responses is an important open problem for the theory of neural coding. This variability is thought to result primarily from spontaneous collective dynamics in neuronal networks. Here, we investigate how well collective dynamics reflected in motor cortex local field potentials (LFPs) can account for spiking variability during motor behavior. Neural activity was recorded via microelectrode arrays implanted in ventral and dorsal premotor and primary motor cortices of non-human primates performing naturalistic 3-D reaching and grasping actions. Point process models were used to quantify how well LFP features accounted for spiking variability not explained by the measured 3-D reach and grasp kinematics. LFP features included the instantaneous magnitude, phase and analytic-signal components of narrow band-pass filtered (δ,θ,α,ß) LFPs, and analytic signal and amplitude envelope features in higher-frequency bands. Multiband LFP features predicted single-neuron spiking (1ms resolution) with substantial accuracy as assessed via ROC analysis. Notably, however, models including both LFP and kinematics features displayed marginal improvement over kinematics-only models. Furthermore, the small predictive information added by LFP features to kinematic models was redundant to information available in fast-timescale (<100 ms) spiking history. Overall, information in multiband LFP features, although predictive of single-neuron spiking during movement execution, was redundant to information available in movement parameters and spiking history. Our findings suggest that, during movement execution, collective dynamics reflected in motor cortex LFPs primarily relate to sensorimotor processes directly controlling movement output, adding little explanatory power to variability not accounted by movement parameters.

Environmental influences on kelp performance across the reproductive period: an ecological trade-off between gametophyte survival and growth?

Most kelps (order Laminariales) exhibit distinct temporal patterns in zoospore production, gametogenesis and gametophyte reproduction. Natural fluctuations in ambient environmental conditions influence the intrinsic characteristics of gametes, which define their ability to tolerate varied conditions. The aim of this work was to document seasonal patterns in reproduction and gametophyte growth and survival of Ecklonia radiata (C. Agardh) J. Agardh in south-western Australia. These results were related to patterns in local environmental conditions in an attempt to ascertain which factors explain variation throughout the season. E. radiata was fertile (produced zoospores) for three and a half months over summer and autumn. Every two weeks during this time, gametophytes were grown in a range of temperatures (16-22 °C) in the laboratory. Zoospore densities were highly variable among sample periods; however, zoospores released early in the season produced gametophytes which had greater rates of growth and survival, and these rates declined towards the end of the reproductive season. Growth rates of gametophytes were positively related to day length, with the fastest growing recruits released when the days were longest. Gametophytes consistently survived best in the lowest temperature (16 °C), yet exhibited optimum growth in higher culture temperatures (20-22 °C). These results suggest that E. radiata releases gametes when conditions are favourable for growth, and E. radiata gametophytes are tolerant of the range of temperatures observed at this location. E. radiata releases the healthiest gametophytes when day length and temperature conditions are optimal for better germination, growth, and sporophyte production, perhaps as a mechanism to help compete against other species for space and other resources.

Multi-dye theranostic nanoparticle platform for bioimaging and cancer therapy.

BACKGROUND: Theranostic nanomaterials composed of fluorescent and photothermal agents can both image and provide a method of disease treatment in clinical oncology. For in vivo use, the near-infrared (NIR) window has been the focus of the majority of studies, because of greater light penetration due to lower absorption and scatter of biological components. Therefore, having both fluorescent and photothermal agents with optical properties in the NIR provides the best chance of improved theranostic capabilities utilizing nanotechnology. METHODS: We developed nonplasmonic multi-dye theranostic silica nanoparticles (MDT-NPs), combining NIR fluorescence visualization and photothermal therapy within a single nanoconstruct comprised of molecular components. A modified NIR fluorescent heptamethine cyanine dye was covalently incorporated into a mesoporous silica matrix and a hydrophobic metallo-naphthalocyanine dye with large molar absorptivity was loaded into the pores of these fluorescent particles. The imaging and therapeutic capabilities of these nanoparticles were demonstrated in vivo using a direct tumor injection model. RESULTS: The fluorescent nanoparticles are bright probes (300-fold enhancement in quantum yield versus free dye) that have a large Stokes shift (>110 nm). Incorporation of the naphthalocyanine dye and exposure to NIR laser excitation results in a temperature increase of the surrounding environment of the MDT-NPs. Tumors injected with these NPs are easily visible with NIR imaging and produce significantly elevated levels of tumor necrosis (95%) upon photothermal ablation compared with controls, as evaluated by bioluminescence and histological analysis. CONCLUSION: MDT-NPs are novel, multifunctional nanomaterials that have optical properties dependent upon the unique incorporation of NIR fluorescent and NIR photothermal dyes within a mesoporous silica platform.

Fractionated photothermal antitumor therapy with multidye nanoparticles.

PURPOSE: Photothermal therapy is an emerging cancer treatment paradigm which involves highly localized heating and killing of tumor cells, due to the presence of nanomaterials that can strongly absorb near-infrared (NIR) light. In addition to having deep penetration depths in tissue, NIR light is innocuous to normal cells. Little is known currently about the fate of nanomaterials post photothermal ablation and the implications thereof. The purpose of this investigation was to define the intratumoral fate of nanoparticles (NPs) after photothermal therapy in vivo and characterize the use of novel multidye theranostic NPs (MDT-NPs) for fractionated photothermal antitumor therapy. METHODS: The photothermal and fluorescent properties of MDT-NPs were first characterized. To investigate the fate of nanomaterials following photothermal ablation in vivo, novel MDT-NPs and a murine mammary tumor model were used. Intratumoral injection of MDT-NPs and real-time fluorescence imaging before and after fractionated photothermal therapy was performed to study the intratumoral fate of MDT-NPs. Gross tumor and histological changes were made comparing MDT-NP treated and control tumor-bearing mice. RESULTS: The dual dye-loaded mesoporous NPs (ie, MDT-NPs; circa 100 nm) retained both their NIR absorbing and NIR fluorescent capabilities after photoactivation. In vivo MDT-NPs remained localized in the intratumoral position after photothermal ablation. With fractionated photothermal therapy, there was significant treatment effect observed macroscopically (P = 0.026) in experimental tumor-bearing mice compared to control treated tumor-bearing mice. CONCLUSION: Fractionated photothermal therapy for cancer represents a new therapeutic paradigm enabled by the application of novel functional nanomaterials. MDT-NPs may advance clinical treatment of cancer by enabling fractionated real-time image guided photothermal therapy.

A model for the origin and properties of flicker-induced geometric phosphenes.

We present a model for flicker phosphenes, the spontaneous appearance of geometric patterns in the visual field when a subject is exposed to diffuse flickering light. We suggest that the phenomenon results from interaction of cortical lateral inhibition with resonant periodic stimuli. We find that the best temporal frequency for eliciting phosphenes is a multiple of intrinsic (damped) oscillatory rhythms in the cortex. We show how both the quantitative and qualitative aspects of the patterns change with frequency of stimulation and provide an explanation for these differences. We use Floquet theory combined with the theory of pattern formation to derive the parameter regimes where the phosphenes occur. We use symmetric bifurcation theory to show why low frequency flicker should produce hexagonal patterns while high frequency produces pinwheels, targets, and spirals.