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Sound location coding has been extensively studied at the central nucleus of the mammalian inferior colliculus (CNIC), supporting a population code. However, this population code has not been extensively characterized on the single-trial level with simultaneous recordings or at other anatomical regions like the dorsal cortex of inferior colliculus (DCIC), which is relevant for learning-induced experience dependent plasticity. To address these knowledge gaps, here we made in two complementary ways large-scale recordings of DCIC populations from awake mice in response to sounds delivered from 13 different frontal horizontal locations (azimuths): volumetric two-photon calcium imaging with ~700 cells simultaneously recorded at a relatively low temporal resolution, and high-density single-unit extracellular recordings with ~20 cells simultaneously recorded at a high temporal resolution. Independent of the method, the recorded DCIC population responses revealed substantial trial-to-trial variation (neuronal noise) which was significantly correlated across pairs of neurons (noise correlations) in the passively listening condition. Nevertheless, decoding analysis supported that these noisy response patterns encode sound location on the single-trial basis, reaching errors that match the discrimination ability of mice. The detected noise correlations contributed to minimize the error of the DCIC population code of sound azimuth. Altogether these findings point out that DCIC can encode sound location in a similar format to what has been proposed for CNIC, opening exciting questions about how noise correlations could shape this code in the context of cortico-collicular input and experience-dependent plasticity.

We demonstrate the effectiveness of seismic dense array surface wave focal spot imaging using USArray data from the western‐central United States. We study dispersion in the 60–310 s period range and assess the image quality of fundamental mode Rayleigh wave phase velocity maps. We apply isotropic spatial autocorrelation models to the time domain zero lag noise correlation wavefield data at distances of about one wavelength. Local estimates of the phase velocity, its uncertainty, and the regression quality imply overall better ZZ relative to ZR or RZ results. The extension of the depth resolution compared to passive surface wave tomography is demonstrated by the inversion of three clustered dispersion curves from different tectonic units. We observe anisotropic surface wave energy flux and the influence of body wave energy, but sensitivity tests at 60 s targeting the data range, correlation component, and processing choices show that the ZZ focal spots yield consistent high‐quality images compared to regional tomography results in the 60–150 s period range. In contrast, at 200–300 s the comparatively small scales of the imaged structures and the imperfect agreement with low‐resolution global tomography results highlight the persistent challenge to reconcile imaging results based on different data sources, theories, and techniques. Our study shows that surface wave focal spot imaging is an accurate, robust, local imaging approach. Better control over clean autocorrelation fields can further improve applications of this seismic imaging tool for increased resolution of the elastic structure below dense seismic arrays. Plain Language Summary: Seismic tomography is an established imaging method that estimates properties of the medium using information of the seismic waves that propagate between source and receiver. This concept is routinely applied to earthquake waves and also to waves that are reconstructed using seismic noise correlations, and has led to impressive high‐resolution images in areas with high seismic sensor density. Here we apply an alternative imaging approach that has been developed in ultrasound medical imaging to surface wave data from the dense seismic USArray covering the western‐central part of the contiguous United States. In contrast to tomography the focal spot method does not analyze propagating waves but properties of the spatial autocorrelation field. The seismic wave speed and potentially other medium properties are estimated at the location of each seismic sensor using data obtained at other dense array sensors that are closely spaced in terms of the wavelength. The focal spot imaging technique is elegant and simple to implement because it does not involve the solution of an inverse problem. In this work we demonstrate its effectiveness by reproducing images from available USArray tomography results. Key Points: The local Rayleigh wave speed can be estimated from the focal spot, the time domain spatial noise autocorrelation field at short distancesWe use USArray focal spots to image the elastic velocity structure in the 60−310 s period range and compare the results to tomographyClean seismic dense array focal spots can enhance vertical and lateral resolution and feature detection for improved imaging [ABSTRACT FROM AUTHOR]

Although much is known about how single neurons in the hippocampus represent an animal’s position, how circuit interactions contribute to spatial coding is less well understood. Using a novel statistical estimator and theoretical modeling, both developed in the framework of maximum entropy models, we reveal highly structured CA1 cell-cell interactions in male rats during open field exploration. The statistics of these interactions depend on whether the animal is in a familiar or novel environment. In both conditions the circuit interactions optimize the encoding of spatial information, but for regimes that differ in the informativeness of their spatial inputs. This structure facilitates linear decodability, making the information easy to read out by downstream circuits. Overall, our findings suggest that the efficient coding hypothesis is not only applicable to individual neuron properties in the sensory periphery, but also to neural interactions in the central brain. [ABSTRACT FROM AUTHOR]

The brain is an information processing machine and thus naturally lends itself to be studied using computational tools based on the principles of information theory. For this reason, computational methods based on or inspired by information theory have been a cornerstone of practical and conceptual progress in neuroscience. In this Review, we address how concepts and computational tools related to information theory are spurring the development of principled theories of information processing in neural circuits and the development of influential mathematical methods for the analyses of neural population recordings. We review how these computational approaches reveal mechanisms of essential functions performed by neural circuits. These functions include efficiently encoding sensory information and facilitating the transmission of information to downstream brain areas to inform and guide behavior. Finally, we discuss how further progress and insights can be achieved, in particular by studying how competing requirements of neural encoding and readout may be optimally traded off to optimize neural information processing.

A central goal of systems neuroscience is to understand how populations of sensory neurons encode and relay information to the rest of the brain. Three key quantities of interest are 1) how mean neural activity depends on the stimulus (sensitivity), 2) how neural activity (co)varies around the mean (noise correlations), and 3) how predictive these variations are of the subject’s behavior (choice probability). Previous empirical work suggests that both choice probability and noise correlations are affected by task training, with decision-related information fed back to sensory areas and aligned to neural sensitivity on a task-by-task basis. We used Utah arrays to record activity from populations of primary visual cortex (V1) neurons from two macaque monkeys that were trained to switch between two coarse orientation-discrimination tasks. Surprisingly, we find no evidence for significant trial-by-trial changes in noise covariance between tasks, nor do we find a consistent relationship between neural sensitivity and choice probability, despite recording from well-tuned task-sensitive neurons, many of which were histologically confirmed to be in supragranular V1, and despite behavioral evidence that the monkeys switched their strategy between tasks. Thus our data at best provide weak support for the hypothesis that trial-by-trial task-switching induces changes to noise correlations and choice probabilities in V1. However, our data agree with a recent finding of a single “choice axis” across tasks. They also raise the intriguing possibility that choice-related signals in early sensory areas are less indicative of task learning per se and instead reflect perceptual learning that occurs in highly overtrained subjects. NEW & NOTEWORTHY Converging evidence suggests that decision processes affect sensory neural activity, and this has informed numerous theories of neural processing. We set out to replicate and extend previous results on decision-related information and noise correlations in V1 of macaque monkeys. However, in our data, we find little evidence for a number of expected effects. Our null results therefore call attention to differences in task training, stimulus design, recording, and analysis techniques between our and prior studies. [ABSTRACT FROM AUTHOR]

We investigate a machine learning based classification of noise acting on a small quantum network with the aim of detecting spatial or multilevel correlations, and the interplay with Markovianity. We control a three-level system by inducing coherent population transfer exploiting different pulse amplitude combinations as inputs to train a feedforward neural network. We show that supervised learning can classify different types of classical dephasing noise affecting the system. Three non-Markovian (quasi-static correlated, anti-correlated and uncorrelated) and Markovian noises are classified with more than 99% accuracy. On the contrary, correlations of Markovian noise cannot be discriminated with our method. Our approach is robust to statistical measurement errors and retains its effectiveness for physical measurements where only a limited number of samples is available making it very experimental-friendly. Our result paves the way for classifying spatial correlations of noise in quantum architectures.

Sensory receptive fields are large enough that they can contain more than one perceptible stimulus. How, then, can the brain encode information about each of the stimuli that may be present at a given moment? We recently showed that when more than one stimulus is present, single neurons can fluctuate between coding one vs. the other(s) across some time period, suggesting a form of neural multiplexing of different stimuli (Caruso et al., 2018). Here, we investigate (a) whether such coding fluctuations occur in early visual cortical areas; (b) how coding fluctuations are coordinated across the neural population; and (c) how coordinated coding fluctuations depend on the parsing of stimuli into separate vs. fused objects. We found coding fluctuations do occur in macaque V1 but only when the two stimuli form separate objects. Such separate objects evoked a novel pattern of V1 spike count (‘noise’) correlations involving distinct distributions of positive and negative values. This bimodal correlation pattern was most pronounced among pairs of neurons showing the strongest evidence for coding fluctuations or multiplexing. Whether a given pair of neurons exhibited positive or negative correlations depended on whether the two neurons both responded better to the same object or had different object preferences. Distinct distributions of spike count correlations based on stimulus preferences were also seen in V4 for separate objects but not when two stimuli fused to form one object. These findings suggest multiple objects evoke different response dynamics than those evoked by single stimuli, lending support to the multiplexing hypothesis and suggesting a means by which information about multiple objects can be preserved despite the apparent coarseness of sensory coding.

Improvements in perception are frequently accompanied by decreases in correlated variability in sensory cortex. This relationship is puzzling because overall changes in correlated variability should minimally affect optimal information coding. We hypothesize that this relationship arises because instead of using optimal strategies for decoding the specific stimuli at hand, observers prioritize generality: a single set of neuronal weights to decode any stimuli. We tested this using a combination of multineuron recordings in the visual cortex of behaving rhesus monkeys and a cortical circuit model. We found that general decoders optimized for broad rather than narrow sets of visual stimuli better matched the animals’ decoding strategy, and that their performance was more related to the magnitude of correlated variability. In conclusion, the inverse relationship between perceptual performance and correlated variability can be explained by observers using a general decoding strategy, capable of decoding neuronal responses to the variety of stimuli encountered in natural vision.

UnlabelledAccurate sensory discrimination is commonly believed to require precise representations in the nervous system; however, neural stimulus responses can be highly variable, even to identical stimuli. Recent studies suggest that cortical response variability decreases during stimulus processing, but the implications of such effects on stimulus discrimination are unclear. To address this, we examined electrocorticographic cortical field potential recordings from the human nonprimary auditory cortex (superior temporal gyrus) while subjects listened to speech syllables. Compared with a prestimulus baseline, activation variability decreased upon stimulus onset, similar to findings from microelectrode recordings in animal studies. We found that this decrease was simultaneous with encoding and spatially specific for those electrodes that most strongly discriminated speech sounds. We also found that variability was predominantly reduced in a correlated subspace across electrodes. We then compared signal and variability (noise) correlations and found that noise correlations reduce more for electrodes with strong signal correlations. Furthermore, we found that this decrease in variability is strongest in the high gamma band, which correlates with firing rate response. Together, these findings indicate that the structure of single-trial response variability is shaped to enhance discriminability despite non-stimulus-related noise.Significance statementCortical responses can be highly variable to auditory speech sounds. Despite this, sensory perception can be remarkably stable. Here, we recorded from the human superior temporal gyrus, a high-order auditory cortex, and studied the changes in the cortical representation of speech stimuli across multiple repetitions. We found that neural variability is reduced upon stimulus onset across electrodes that encode speech sounds.

Distributed population codes are ubiquitous in the brain and pose a challenge to downstream neurons that must learn an appropriate readout. Here we explore the possibility that this learning problem is simplified through inductive biases implemented by stimulus-independent noise correlations that constrain learning to task-relevant dimensions. We test this idea in a set of neural networks that learn to perform a perceptual discrimination task. Correlations among similarly tuned units were manipulated independently of an overall population signal-to-noise ratio to test how the format of stored information affects learning. Higher noise correlations among similarly tuned units led to faster and more robust learning, favoring homogenous weights assigned to neurons within a functionally similar pool, and could emerge through Hebbian learning. When multiple discriminations were learned simultaneously, noise correlations across relevant feature dimensions sped learning, whereas those across irrelevant feature dimensions slowed it. Our results complement the existing theory on noise correlations by demonstrating that when such correlations are produced without significant degradation of the signal-to-noise ratio, they can improve the speed of readout learning by constraining it to appropriate dimensions. [ABSTRACT FROM AUTHOR]

Abstract Seismic signals can be extracted from ambient noise wavefields by the correlation technique. Recently, a prominent P‐type phase was observed from teleseismic noise correlations in the secondary microseism period band. The phase is named Pdmc in this paper, corresponding to its origin from the interference between the direct P waves transmitting through the deep mantle and the core (P and PKPab waves). We extract the phase by correlating noise records from two seismic networks in the Northern Hemisphere and locate the microseism sources that are efficient for the Pdmc construction in the South Pacific. We investigate the spatiotemporal links of the Pdmc signal with global oceanic waves and microseism sources. Interestingly, the correlation with wave height is higher in several regions surrounding the effective source region, rather than in the effective source region. The Pdmc amplitude is highly correlated with the power of the effective microseism sources. Also, it is apparently correlated with ineffective sources in the Southern Hemisphere and anticorrelated with sources in the Northern Hemisphere. We ascribe the correlation with the ineffective southern sources to the spatiotemporal interconnections of the southern sources. The anticorrelation with northern sources can be explained by the reverse seasonal patterns between the southern and northern sources and by that the northern sources impede the signal construction. The signal construction from noise correlations relies on the competition between the effective and ineffective sources, not just on the power of the effective sources. This principle should be valid in a general sense for noise‐derived signals.

• ABR thresholds were similar in mother vs. in virgin mice but latencies were shorter. • Evoked cortical responses were decreased in mothers compared to virgins. • Cortical response latencies were shorter in mothers than in virgins. • The MI per spike was higher in mothers than in virgins only for pup calls. • The noise correlations were lower in mothers than in virgins for all stimuli. A fundamental task for the auditory system is to process communication sounds according to their behavioral significance. In many mammalian species, pup calls became more significant for mothers than other conspecific and heterospecific communication sounds. To study the cortical consequences of motherhood on the processing of communication sounds, we recorded neuronal responses in the primary auditory cortex of virgin and mother C57BL/6 mice which had similar ABR thresholds. In mothers, the evoked firing rate in response to pure tones was decreased and the frequency receptive fields were narrower. The responses to pup and adult calls were also reduced but the amount of mutual information (MI) per spike about the pup call's identity was increased in mother mice. The response latency to pup and adult calls was significantly shorter in mothers. Despite similarly decreased responses to guinea pig whistles, the response latency, and the MI per spike did not differ between virgins and mothers for these heterospecific vocalizations. Noise correlations between cortical recordings were decreased in mothers, suggesting that the firing rate of distant neurons was more independent from each other. Together, these results indicate that in the most commonly used mouse strain for behavioral studies, the discrimination of pup calls by auditory cortex neurons is more efficient during motherhood. [ABSTRACT FROM AUTHOR]

A major goal in neuroscience is to estimate neural connectivity from large scale extracellular recordings of neural activity in vivo. This is challenging in part because any such activity is modulated by the unmeasured external synaptic input to the network, known as the common input problem. Many different measures of functional connectivity have been proposed in the literature, but their direct relationship to synaptic connectivity is often assumed or ignored. For in vivo data, measurements of this relationship would require a knowledge of ground truth connectivity, which is nearly always unavailable. Instead, many studies use in silico simulations as benchmarks for investigation, but such approaches necessarily rely upon a variety of simplifying assumptions about the simulated network and can depend on numerous simulation parameters. We combine neuronal network simulations, mathematical analysis, and calcium imaging data to address the question of when and how functional connectivity, synaptic connectivity, and latent external input variability can be untangled. We show numerically and analytically that, even though the precision matrix of recorded spiking activity does not uniquely determine synaptic connectivity, it is in practice often closely related to synaptic connectivity. This relation becomes more pronounced when the spatial structure of neuronal variability is jointly considered. [ABSTRACT FROM AUTHOR]

Understanding the neural code requires understanding how populations of neurons code information. Theoretical models predict that information may be limited by correlated noise in large neural populations. Nevertheless, analyses based on tens of neurons have failed to find evidence of saturation. Moreover, some studies have shown that noise correlations can be very small, and therefore may not affect information coding. To determine whether information-limiting correlations exist, we implanted eight Utah arrays in prefrontal cortex (PFC; area 46) of two male macaque monkeys, recording >500 neurons simultaneously. We estimated information in PFC about saccades as a function of ensemble size. Noise correlations were, on average, small (~10 -3). However, information scaled strongly sublinearly with ensemble size. After shuffling trials, destroying noise correlations, information was a linear function of ensemble size. Thus, we provide evidence for the existence of information-limiting noise correlations in large populations of PFC neurons. [ABSTRACT FROM AUTHOR]

Identifying the features of population responses that are relevant to the amount of information encoded by neuronal populations is a crucial step toward understanding population coding. Statistical features, such as tuning properties, individual and shared response variability, and global activity modulations, could all affect the amount of information encoded and modulate behavioral performance. We show that two features in particular affect information: the modulation of population responses across conditions (population signal) and the inverse population covariability along the modulation axis (projected precision). We demonstrate that fluctuations of these two quantities are correlated with fluctuations of behavioral performance in various tasks and brain regions consistently across 4 monkeys (1 female and 1 maleMacaca mulatta; and 2 maleMacacafascicularis). In contrast, fluctuations in mean correlations among neurons and global activity have negligible or inconsistent effects on the amount of information encoded and behavioral performance. We also show that differential correlations reduce the amount of information encoded in finite populations by reducing projected precision. Our results are consistent with predictions of a model that optimally decodes population responses to produce behavior. [ABSTRACT FROM AUTHOR]

Correlated electrical activity in neurons is a prominent characteristic of cortical microcircuits. Despite a growing amount of evidence concerning both spike-count and subthreshold membrane potential pairwise correlations, little is known about how different types of cortical neurons convert correlated inputs into correlated outputs. We studied pyramidal neurons and two classes of GABAergic interneurons of layer 5 in neocortical brain slices obtained from rats of both sexes, and we stimulated them with biophysically realistic correlated inputs, generated using dynamic clamp. We found that the physiological differences between cell types manifested unique features in their capacity to transfer correlated inputs. We used linear response theory and computational modeling to gain clear insights into how cellular properties determine both the gain and timescale of correlation transfer, thus tying single-cell features with network interactions. Our results provide further ground for the functionally distinct roles played by various types of neuronal cells in the cortical microcircuit. [ABSTRACT FROM AUTHOR]

Both the global neuronal workspace (GNW) and integrated information theory (IIT) posit that highly complex and interconnected networks engender perceptual awareness. GNW specifies that activity recruiting frontoparietal networks will elicit a subjective experience, whereas IIT is more concerned with the functional architecture of networks than with activity within it. Here, we argue that according to IIT mathematics, circuits converging on integrative versus convergent yet non-integrative neurons should support a greater degree of consciousness. We test this hypothesis by analyzing a dataset of neuronal responses collected simultaneously from primary somatosensory cortex (SI) and ventral premotor cortex (vPM) in nonhuman primates presented with auditory, tactile, and audio-tactile stimuli as they are progressively anesthetized with propofol. We first describe the multisensory (audio-tactile) characteristics of SI and vPM neurons (mean and dispersion tendencies, as well as noise-correlations), and functionally label these neurons as convergent or integrative according to their spiking responses. Then, we characterize how these different pools of neurons behave as a function of consciousness. At odds with the IIT mathematics, results suggest that convergent neurons more readily exhibit properties of consciousness (neural complexity and noise correlation) and are more impacted during the loss of consciousness than integrative neurons. Last, we provide support for the GNW by showing that neural ignition (i.e., same trial coactivation of S1 and vPM) was more frequent in conscious than unconscious states. Overall, we contrast GNW and IIT within the same single-unit activity dataset, and support the GNW. [ABSTRACT FROM AUTHOR]

The fact that perception and behavior depend on the simultaneous and coordinated activity of neural populations is well established. Understanding encoding through neuronal population activity is however complicated by the statistical dependencies between the activities of neurons, which can be present in terms of both their mean (signal correlations) and their response variability (noise correlations). Here, we review the state of knowledge regarding population coding and the influence of correlated variability in the electrosensory pathways of the weakly electric fish Apteronotus leptorhynchus. We summarize known population coding strategies at the peripheral level, which are largely unaffected by noise correlations. We then move on to the hindbrain, where existing data from the electrosensory lateral line lobe (ELL) shows the presence of noise correlations. We summarize the current knowledge regarding the mechanistic origins of noise correlations and known mechanisms of stimulus dependent correlation shaping in ELL. We finish by considering future directions for understanding population coding in the electrosensory pathways of weakly electric fish, highlighting the benefits of this model system for understanding the origins and impact of noise correlations on population coding.

The fact that perception and behavior depend on the simultaneous and coordinated activity of neural populations is well established. Understanding encoding through neuronal population activity is however complicated by the statistical dependencies between the activities of neurons, which can be present in terms of both their mean (signal correlations) and their response variability (noise correlations). Here, we review the state of knowledge regarding population coding and the influence of correlated variability in the electrosensory pathways of the weakly electric fish Apteronotus leptorhynchus. We summarize known population coding strategies at the peripheral level, which are largely unaffected by noise correlations. We then move on to the hindbrain, where existing data from the electrosensory lateral line lobe (ELL) shows the presence of noise correlations. We summarize the current knowledge regarding the mechanistic origins of noise correlations and known mechanisms of stimulus dependent correlation shaping in ELL. We finish by considering future directions for understanding population coding in the electrosensory pathways of weakly electric fish, highlighting the benefits of this model system for understanding the origins and impact of noise correlations on population coding. [ABSTRACT FROM AUTHOR]

Understanding how cognitive processes affect the responses of sensory neurons may clarify the relationship between neuronal population activity and behavior. However, tools for analyzing neuronal activity have not kept up with technological advances in recording from large neuronal populations. Here, we describe prevalent hypotheses of how cognitive processes affect sensory neurons, driven largely by a model based on the activity of single neurons or pools of neurons as the units of computation. We then use simple simulations to expand this model to a new conceptual framework that focuses on subspaces of population activity as the relevant units of computation, uses comparisons between brain areas or to behavior to guide analyses of these subspaces, and suggests that population activity is optimized to decode the large variety of stimuli and tasks that animals encounter in natural behavior. This framework provides new ways of understanding the ever-growing quantity of recorded population activity data. [ABSTRACT FROM AUTHOR]

Correlated fluctuations of single neuron discharges, on a mesoscopic scale, decrease as a function of lateral distance in early sensory cortices, reflecting a rapid spatial decay of lateral connection probability and excitation. However, spatial periodicities in horizontal connectivity and associational input as well as an enhanced probability of lateral excitatory connections in the association cortex could theoretically result in nonmonotonic correlation structures. Here, we show such a spatially nonmonotonic correlation structure, characterized by significantly positive long-range correlations, in the inferior convexity of the macaque prefrontal cortex. This functional connectivity kernel was more pronounced during wakefulness than anesthesia and could be largely attributed to the spatial pattern of correlated variability between functionally similar neurons during structured visual stimulation. These results suggest that the spatial decay of lateral functional connectivity is not a common organizational principle of neocortical microcircuits. A nonmonotonic correlation structure could reflect a critical topological feature of prefrontal microcircuits, facilitating their role in integrative processes. [ABSTRACT FROM AUTHOR]

The circuit mechanisms behind shared neural variability (noise correlation) and its dependence on neural state are poorly understood. Visual attention is well-suited to constrain cortical models of response variability because attention both increases firing rates and their stimulus sensitivity, as well as decreases noise correlations. We provide a novel analysis of population recordings in rhesus primate visual area V4 showing that a single biophysical mechanism may underlie these diverse neural correlates of attention. We explore model cortical networks where top-down mediated increases in excitability, distributed across excitatory and inhibitory targets, capture the key neuronal correlates of attention. Our models predict that top-down signals primarily affect inhibitory neurons, whereas excitatory neurons are more sensitive to stimulus specific bottom-up inputs. Accounting for trial variability in models of state dependent modulation of neuronal activity is a critical step in building a mechanistic theory of neuronal cognition.

Noise correlations are a common feature of neural responses and have been observed in many cortical areas across different species. These correlations can influence information processing by enhancing or diminishing the quality of the neural code, but the origin of these correlations is still a matter of controversy. In this computational study we explore the hypothesis that noise correlations are the result of local recurrent excitatory and inhibitory connections. We simulated two-dimensional networks of adaptive spiking neurons with local connection patterns following Gaussian kernels. Noise correlations decay with distance between neurons but are only observed if the range of excitatory connections is smaller than the range of inhibitory connections (“Mexican hat” connectivity) and if the connection strengths are sufficiently strong. These correlations arise from a moving blob-like structure of evoked activity, which is absent if inhibitory interactions have a smaller range (“inverse Mexican hat” connectivity). Spatially structured external inputs fixate these blobs to certain locations and thus effectively reduce noise correlations. We further investigated the influence of these network configurations on stimulus encoding. On the one hand, the observed correlations diminish information about a stimulus encoded by a network. On the other hand, correlated activity allows for more precise encoding of stimulus information if the decoder has only access to a limited amount of neurons.

Response variability, as measured by fluctuating responses upon repeated performance of trials, is a major component of neural responses, and its characterization is key to interpret high dimensional population recordings. Response variability and covariability display predictable changes upon changes in stimulus and cognitive or behavioral state, providing an opportunity to test the predictive power of models of neural variability. Still, there is little agreement on which model to use as a building block for population-level analyses, and models of variability are often treated as a subject of choice. We investigate two competing models, the doubly stochastic Poisson (DSP) model assuming stochasticity at spike generation, and the rectified Gaussian (RG) model tracing variability back to membrane potential variance, to analyze stimulus-dependent modulation of both single-neuron and pairwise response statistics. Using a pair of model neurons, we demonstrate that the two models predict similar single-cell statistics. However, DSP and RG models have contradicting predictions on the joint statistics of spiking responses. To test the models against data, we build a population model to simulate stimulus change-related modulations in pairwise response statistics. We use single-unit data from the primary visual cortex (V1) of monkeys to show that while model predictions for variance are qualitatively similar to experimental data, only the RG model's predictions are compatible with joint statistics. These results suggest that models using Poisson-like variability might fail to capture important properties of response statistics. We argue that membrane potential-level modeling of stochasticity provides an efficient strategy to model correlations. NEW & NOTEWORTHY Neural variability and covariability are puzzling aspects of cortical computations. For efficient decoding and prediction, models of information encoding in neural populations hinge on an appropriate model of variability. Our work shows that stimulus-dependent changes in pairwise but not in single-cell statistics can differentiate between two widely used models of neuronal variability. Contrasting model predictions with neuronal data provides hints on the noise sources in spiking and provides constraints on statistical models of population activity. [ABSTRACT FROM AUTHOR]

Noise correlations are a common feature of neural responses and have been observed in many cortical areas across different species. These correlations can influence information processing by enhancing or diminishing the quality of the neural code, but the origin of these correlations is still a matter of controversy. In this computational study we explore the hypothesis that noise correlations are the result of local recurrent excitatory and inhibitory connections. We simulated two-dimensional networks of adaptive spiking neurons with local connection patterns following Gaussian kernels. Noise correlations decay with distance between neurons but are only observed if the range of excitatory connections is smaller than the range of inhibitory connections ("Mexican hat" connectivity) and if the connection strengths are sufficiently strong. These correlations arise from a moving blob-like structure of evoked activity, which is absent if inhibitory interactions have a smaller range ("inverse Mexican hat" connectivity). Spatially structured external inputs fixate these blobs to certain locations and thus effectively reduce noise correlations. We further investigated the influence of these network configurations on stimulus encoding. On the one hand, the observed correlations diminish information about a stimulus encoded by a network. On the other hand, correlated activity allows for more precise encoding of stimulus information if the decoder has only access to a limited amount of neurons. [ABSTRACT FROM AUTHOR]

Neurons in the primate lateral prefrontal cortex (LPFC) encode working memory (WM) representations via sustained firing, a phenomenon hypothesized to arise from recurrent dynamics within ensembles of interconnected neurons. Here, we tested this hypothesis by using microelectrode arrays to examine spike count correlations (rsc) in LPFC neuronal ensembles during a spatial WM task. We found a pattern of pairwise rsc during WM maintenance indicative of stronger coupling between similarly tuned neurons and increased inhibition between dissimilarly tuned neurons. We then used a linear decoder to quantify the effects of the high-dimensional rsc structure on information coding in the neuronal ensembles. We found that the rsc structure could facilitate or impair coding, depending on the size of the ensemble and tuning properties of its constituent neurons. A simple optimization procedure demonstrated that near-maximum decoding performance could be achieved using a relatively small number of neurons. These WM-optimized subensembles were more signal correlation (rsignal)-diverse and anatomically dispersed than predicted by the statistics of the full recorded population of neurons, and they often contained neurons that were poorly WM-selective, yet enhanced coding fidelity by shaping the ensemble's rsc structure. We observed a pattern of rsc between LPFC neurons indicative of recurrent dynamics as a mechanism for WM-related activity and that the rsc structure can increase the fidelity of WM representations. Thus, WM coding in LPFC neuronal ensembles arises from a complex synergy between single neuron coding properties and multidimensional, ensemblelevel phenomena. [ABSTRACT FROM AUTHOR]

The study of the neural code aims at deciphering how the nervous system maps external stimuli into neural activity—the encoding phase—and subsequently transforms such activity into adequate responses to the original stimuli—the decoding phase. Several information-theoretical methods have been proposed to assess the relevance of individual response features, as for example, the spike count of a given neuron, or the amount of correlation in the activity of two cells. These methods work under the premise that the relevance of a feature is reflected in the information loss that is induced by eliminating the feature from the response. The alternative methods differ in the procedure by which the tested feature is removed, and the algorithm with which the lost information is calculated. Here we compare these methods, and show that more often than not, each method assigns a different relevance to the tested feature. We demonstrate that the differences are both quantitative and qualitative, and connect them with the method employed to remove the tested feature, as well as the procedure to calculate the lost information. By studying a collection of carefully designed examples, and working on analytic derivations, we identify the conditions under which the relevance of features diagnosed by different methods can be ranked, or sometimes even equated. The condition for equality involves both the amount and the type of information contributed by the tested feature. We conclude that the quest for relevant response features is more delicate than previously thought, and may yield to multiple answers depending on methodological subtleties.

Summary Neural responses in the visual cortex are variable, and there is now an abundance of data characterizing how the magnitude and structure of this variability depends on the stimulus. Current theories of cortical computation fail to account for these data; they either ignore variability altogether or only model its unstructured Poisson-like aspects. We develop a theory in which the cortex performs probabilistic inference such that population activity patterns represent statistical samples from the inferred probability distribution. Our main prediction is that perceptual uncertainty is directly encoded by the variability, rather than the average, of cortical responses. Through direct comparisons to previously published data as well as original data analyses, we show that a sampling-based probabilistic representation accounts for the structure of noise, signal, and spontaneous response variability and correlations in the primary visual cortex. These results suggest a novel role for neural variability in cortical dynamics and computations. [ABSTRACT FROM AUTHOR]

Selective attention allows organisms to extract behaviorally relevant information while ignoring distracting stimuli that compete for the limited resources of their central nervous systems. Attention is highly flexible, and it can be harnessed to select information based on sensory modality, within-modality feature(s), spatial location, object identity, and/or temporal properties. In this review, we discuss the body of work devoted to understanding mechanisms of selective attention in the somatosensory system. In particular, we describe the effects of attention on tactile behavior and corresponding neural activity in somatosensory cortex. Our focus is on neural mechanisms that select tactile stimuli based on their location on the body (somatotopic-based attention) or their sensory feature (feature-based attention). We highlight parallels between selection mechanisms in touch and other sensory systems and discuss several putative neural coding schemes employed by cortical populations to signal the behavioral relevance of sensory inputs. Specifically, we contrast the advantages and disadvantages of using a gain vs. spike-spike correlation code for representing attended sensory stimuli. We favor a neural network model of tactile attention that is composed of frontal, parietal, and subcortical areas that controls somatosensory cells encoding the relevant stimulus features to enable preferential processing throughout the somatosensory hierarchy. Our review is based on data from noninvasive electrophysiological and imaging data in humans as well as single-unit recordings in nonhuman primates. [ABSTRACT FROM AUTHOR]

The ability to distinguish between elements of a sensory neuron's activity that are stimulus independent versus driven by the stimulus is critical for addressing many questions in systems neuroscience. This is typically accomplished by measuring neural responses to repeated presentations of identical stimuli and identifying the trial-variable components of the response as noise. In awake primates, however, small "fixational" eye movements (FEMs) introduce uncontrolled trial-to-trial differences in the visual stimulus itself, potentially confounding this distinction. Here, we describe novel analytical methods that directly quantify the stimulus-driven and stimulusindependent components of visual neuron responses in the presence of FEMs. We apply this approach, combined with precise model-based eye tracking, to recordings from primary visual cortex (V1), finding that standard approaches that ignore FEMs typically miss more than half of the stimulus-driven neural response variance, creating substantial biases in measures of response reliability. We show that these effects are likely not isolated to the particular experimental conditions used here, such as the choice of visual stimulus or spike measurement time window, and thus will be a more general problem for V1 recordings in awake primates. We also demonstrate that measurements of the stimulus-driven and stimulus-independent correlations among pairs of V1 neurons can be greatly biased by FEMs. These results thus illustrate the potentially dramatic impact of FEMs on measures of signal and noise in visual neuron activity and also demonstrate a novel approach for controlling for these eye-movement-induced effects. [ABSTRACT FROM AUTHOR]

The ability to discriminate between similar sensory stimuli relies on the amount of information encoded in sensory neuronal populations. Such information can be substantially reduced by correlated trial-to-trial variability. Noise correlations have been measured across a wide range of areas in the brain, but their origin is still far from clear. Here we show analytically and with simulations that optimal computation on inputs with limited information creates patterns of noise correlations that account for a broad range of experimental observations while at same time causing information to saturate in large neural populations. With the example of a network of V1 neurons extracting orientation from a noisy image, we illustrate to our knowledge the first generative model of noise correlations that is consistent both with neurophysiology and with behavioral thresholds, without invoking suboptimal encoding or decoding or internal sources of variability such as stochastic network dynamics or cortical state fluctuations. We further show that when information is limited at the input, both suboptimal connectivity and internal fluctuations could similarly reduce the asymptotic information, but they have qualitatively different effects on correlations leading to specific experimental predictions. Our study indicates that noise at the sensory periphery could have a major effect on cortical representations in widely studied discrimination tasks. It also provides an analytical framework to understand the functional relevance of different sources of experimentally measured correlations. [ABSTRACT FROM AUTHOR]

The natural world presents us with a rich and ever-changing sensory landscape containing diverse stimuli that constantly compete for representation in the brain. When the brain selects a stimulus as the highest priority for attention, it differentially enhances the representation of the selected, "target" stimulus and suppresses the processing of other, distracting stimuli. A stimulus may be selected for attention while it is still present in the visual scene (predictive selection) or after it has vanished (post hoc selection). We present a biologically inspired computational model that accounts for the prioritized processing of information about targets that are selected for attention either predictively or post hoc. Central to the model is the neurobiological mechanism of "selective disinhibition" - the selective suppression of inhibition of the representation of the target stimulus. We demonstrate that this mechanism explains major neurophysiological hallmarks of selective attention, including multiplicative neural gain, increased inter-trial reliability (decreased variability), and reduced noise correlations. The same mechanism also reproduces key behavioral hallmarks associated with target-distracter interactions. Selective disinhibition exhibits several distinguishing and advantageous features over alternative mechanisms for implementing target selection, and is capable of explaining the effects of selective attention over a broad range of real-world conditions, involving both predictive and post hoc biasing of sensory competition and decisions. [ABSTRACT FROM AUTHOR]

Recent analysis of evoked activity recorded across different brain regions and tasks revealed a marked decrease in noise correlations and trial-by-trial variability. Given the importance of correlations and variability for information processing within the rate coding paradigm, several mechanisms have been proposed to explain the reduction in these quantities despite an increase in firing rates. These models suggest that anatomical clusters and/or tightly balanced excitation-inhibition can generate intrinsic network dynamics that may exhibit a reduction in noise correlations and trial-by-trial variability when perturbed by an external input. Such mechanisms based on the recurrent feedback crucially ignore the contribution of feedforward input to the statistics of the evoked activity. Therefore, we investigated how statistical properties of the feedforward input shape the statistics of the evoked activity. Specifically, we focused on the effect of input correlation structure on the noise correlations and trial-by-trial variability. We show that the ability of neurons to transfer the input firing rate, correlation, and variability to the output depends on the correlations within the presynaptic pool of a neuron, and that an input with even weak within-correlations can be sufficient to reduce noise correlations and trial-by-trial variability, without requiring any specific recurrent connectivity structure. In general, depending on the ongoing activity state, feedforward input could either increase or decrease noise correlation and trial-by-trial variability. Thus, we propose that evoked activity statistics are jointly determined by the feedforward and feedback inputs. [ABSTRACT FROM AUTHOR]

Incoming signals interact with rich, ongoing population activity dynamics in cortical circuits. These intrinsic dynamics are the consequence of interactions among local excitatory and inhibitory neurons and affect inter-region communication and information coding. It is unclear whether specializations in the patterns of interactions among excitatory and inhibitory neurons underlie systematic differences in activity dynamics across the cortex. Here, in mice, we compare the functional interactions among somatostatin (SOM)-expressing inhibitory interneurons and the rest of the neural population in auditory cortex (AC), a sensory region of the cortex, and posterior parietal cortex (PPC), an association region. The spatial structure of shared variability among SOM and non-SOM neurons differs across regions: correlations decay rapidly with distance in AC but not in PPC. However, in both regions, activity of SOM neurons is more highly correlated than non-SOM neurons' activity. Our results imply both generalization and specialization in the functional structure of inhibitory subnetworks across the cortex. [Display omitted] • In vivo imaging of somatostatin inhibitory neurons in auditory and parietal cortices • SOM neurons in both regions form highly coordinated subnetworks • The spatial scale of shared variability across neurons is wider in parietal cortex Khoury et al. show that somatostatin-expressing interneurons form highly coordinated subnetworks in both sensory and association cortices. However, the spatial scale of these subnetworks is significantly broader in association cortex relative to sensory cortex, implying area-specific specialization in the structure of inhibitory subnetworks. [ABSTRACT FROM AUTHOR]

Sensory function is mediated by interactions between external stimuli and intrinsic cortical dynamics that are evident in the modulation of evoked responses by cortical state. A number of recent studies across different modalities have demonstrated that the patterns of activity in neuronal populations can vary strongly between synchronized and desynchronized cortical states, i.e., in the presence or absence of intrinsically generated up and down states. Here we investigated the impact of cortical state on the population coding of tones and speech in the primary auditory cortex (A1) of gerbils, and found that responses were qualitatively different in synchronized and desynchronized cortical states. Activity in synchronized A1 was only weakly modulated by sensory input, and the spike patterns evoked by tones and speech were unreliable and constrained to a small range of patterns. In contrast, responses to tones and speech in desynchronized A1 were temporally precise and reliable across trials, and different speech tokens evoked diverse spike patterns with extremely weak noise correlations, allowing responses to be decoded with nearly perfect accuracy. Restricting the analysis of synchronized A1 to activity within up states yielded similar results, suggesting that up states are not equivalent to brief periods of desynchronization. These findings demonstrate that the representational capacity of A1 depends strongly on cortical state, and suggest that cortical state should be considered as an explicit variable in all studies of sensory processing. [ABSTRACT FROM AUTHOR]

Low-threshold M currents are mediated by the Kv7 family of potassium channels. Kv7 channels are important regulators of spiking activity, having a direct influence on the firing rate, spike time variability, and filter properties of neurons. How Kv7 channels affect the joint spiking activity of populations of neurons is an important and open area of study. Using a combination of computational simulations and analytic calculations, we show that the activation of Kv7 conductances reduces the covariability between spike trains of pairs of neurons driven by common inputs. This reduction is beyond that explained by the lowering of firing rates and involves an active cancellation of common fluctuations in the membrane potentials of the cell pair. Our theory shows that the excess covariance reduction is due to a Kv7-induced shift from low-pass to band-pass filtering of the single neuron spike train response. Dysfunction of Kv7 conductances is related to a number of neurological diseases characterized by both elevated firing rates and increased network-wide correlations. We show how changes in the activation or strength of Kv7 conductances give rise to excess correlations that cannot be compensated for by synaptic scaling or homeostatic modulation of passive membrane properties. In contrast, modulation of Kv7 activation parameters consistent with pharmacological treatments for certain hyperactivity disorders can restore normal firing rates and spiking correlations. Our results provide key insights into how regulation of a ubiquitous potassium channel class can control the coordination of population spiking activity. [ABSTRACT FROM AUTHOR]

The primary visual cortex is an excellent model system for investigating how neuronal populations encode information, because of well-documented relationships between stimulus characteristics and neuronal activation patterns. We used two-photon calcium imaging data to relate the performance of different methods for studying population coding (population vectors, template matching, and Bayesian decoding algorithms) to their underlying assumptions. We show that the variability of neuronal responses may hamper the decoding of population activity, and that a normalization to correct for this variability may be of critical importance for correct decoding of population activity. Second, by comparing noise correlations and stimulus tuning we find that these properties have dissociated anatomical correlates, even though noise correlations have been previously hypothesized to reflect common synaptic input. We hypothesize that noise correlations arise from large non-specific increases in spiking activity acting on many weak synapses simultaneously, while neuronal stimulus response properties are dependent on more reliable connections. Finally, this paper provides practical guidelines for further research on population coding and shows that population coding cannot be approximated by a simple summation of inputs, but is heavily influenced by factors such as input reliability and noise correlation structure. [ABSTRACT FROM AUTHOR]

As multi-electrode and imaging technology begin to provide us with simultaneous recordings of large neuronal populations, new methods for modelling such data must also be developed. We present a model of responses to repeated trials of a sensory stimulus based on thresholded Gaussian processes that allows for analysis and modelling of variability and covariability of population spike trains across multiple time scales. The model framework can be used to specify the values of many different variability measures including spike timing precision across trials, coefficient of variation of the interspike interval distribution, and Fano factor of spike counts for individual neurons, as well as signal and noise correlations and correlations of spike counts across multiple neurons. Using both simulated data and data from different stages of the mammalian auditory pathway, we demonstrate the range of possible independent manipulations of different variability measures, and explore how this range depends on the sensory stimulus. The model provides a powerful framework for the study of experimental and surrogate data and for analyzing dependencies between different statistical properties of neuronal populations. [ABSTRACT FROM AUTHOR]

Abstract: While techniques for retrieval of seismic velocities from wavelet arrival times in ambient noise correlations are now well established, interpretation of wavelet amplitudes remains unsatisfactory. It is clear that such amplitudes contain information on seismic attenuation, but they are also affected by ambient noise intensity, site amplification, and any nonlinear preprocessing that may have been applied to the noise signals. Disentangling these many factors in order to reliably recover seismic attenuation is challenging. It is argued here that noise intensity, while rarely isotropic or homogeneous, may nevertheless be modeled by a radiative transfer equation. It is then shown that this recognition sufficiently constrains the noise intensity that we may hope to fit measured correlation amplitudes to models for spatially varying attenuation and site amplification factors. One-bit preprocessing, it is shown, is not compatible with such fits except in the special case of spatially constant noise intensity. An alternative procedure for accelerating convergence is suggested. Numerical simulations for a case of homogeneous attenuation and homogeneous seismic velocity are presented in support of the assertions. Attenuation, site factors, and noise intensity are successfully retrieved from correlations of numerically simulated imperfectly diffuse waves measured on a linear array of sensors. [Copyright &y& Elsevier]

Abstract: The aim of this article is to investigate a possible way to improve ambient noise tomography by expanding the data base of useful cross-correlation measurements. We show that the curvelet transform makes it possible to compute synthetic noise correlations by simulating directly seismic ambient noise using the spectral element method. These synthetic correlations can in turn be used to identify surface waves and overtones even on correlations having a signal to noise ratio much lower than one. We hope that the possibility to compute SEM synthetic correlations and to extract more information from correlations will be useful to improve ambient noise tomography and monitoring. [Copyright &y& Elsevier]

Cortical circuits perform the computations underlying rapid perceptual decisions within a few dozen milliseconds with each neuron emitting only a few spikes. Under these conditions, the theoretical analysis of neural population codes is challenging, as the most commonly used theoretical tool-Fisher information-can lead to erroneous conclusions about the optimality of different coding schemes. Here we revisit the effect of tuning function width and correlation structure on neural population codes based on ideal observer analysis in both a discrimination and a reconstruction task. We show that the optimal tuning function width and the optimal correlation structure in both paradigms strongly depend on the available decoding time in a very similar way. In contrast, population codes optimized for Fisher information do not depend on decoding time and are severely suboptimal when only few spikes are available. In addition, we use the neurometric functions of the ideal observer in the classification task to investigate the differential coding properties of these Fisher-optimal codes for fine and coarse discrimination. We find that the discrimination error for these codes does not decrease to zero with increasing population size, even in simple coarse discrimination tasks. Our results suggest that quite different population codes may be optimal for rapid decoding in cortical computations than those inferred from the optimization of Fisher information. [ABSTRACT FROM AUTHOR]

Abstract: A temporal analysis of the noise of a H2RG detector is performed in view of the calibration of a dedicated setup. The implication on the noise performance of the subtraction of the reference output is described, and we extend the correlation method to groups of several pixels to derive the ratio of the interpixel capacitance to the pixel capacitance of a detector. We find . All measurements are consistent to a sub-percent accuracy and provide a calibration of our setup. [Copyright &y& Elsevier]

Abstract: In this proceeding, we address the possibility of studying one-dimensional physics experimentally using optical lattices. These are periodic potentials created by laser fields in clouds of ultra-cold dilute atomic systems. We concentrate on the case of fermionic isotopes and study Luttinger liquid physics. In particular, we compare different regimes of spin coherence. We will argue that these systems are experimentally very attractive thanks to high degree of tunabilty and control, thus constituting an ideal laboratory for realizing model strongly correlated systems. [Copyright &y& Elsevier]

Cortical processing of task-relevant information enables recognition of behaviorally meaningful sensory events. It is unclear how task-related information is represented within cortical networks by the activity of individual neurons and their functional interactions. Here, we use two-photon imaging to record neuronal activity from the primary auditory cortex of mice during a pure-tone discrimination task. We find that a subset of neurons transiently encode sensory information used to inform behavioral choice. Using Granger causality analysis, we show that these neurons form functional networks in which information transmits sequentially. Network structures differ for target versus non-target tones, encode behavioral choice, and differ between correct versus incorrect behavioral choices. Correct behavioral choices are associated with shorter communication timescales, larger functional correlations, and greater information redundancy. In summary, specialized neurons in primary auditory cortex integrate task-related information and form functional networks whose structures encode both sensory input and behavioral choice. [Display omitted] • Aberrant attentional gain in auditory cortex reflects incorrect decision making • Task-relevant information is transiently encoded by individual neurons • Neuronal network structures with task-relevant information encode behavioral choice • Networked neurons communicate task-relevant information redundantly Francis et al. find that, as mice perform an auditory discrimination task, cortical neurons form functional networks in which task-relevant information transmits sequentially between neurons. Network structures encode behavioral choice, and correct behavioral choices are associated with shorter communication timescales, larger functional correlations, and greater information redundancy between neurons. [ABSTRACT FROM AUTHOR]

Decoding the activity of a population of neurons is a fundamental problem in neuroscience. A key aspect of this problem is determining whether correlations in the activity, i.e., noise correlations, are important. If they are important, then the decoding problem is high dimensional: decoding algorithms must take the correlational structure in the activity into account. If they are not important, or if they play a minor role, then the decoding problem can be reduced to lower dimension and thus made more tractable. The issue of whether correlations are important has been a subject of heated debate. The debate centers around the validity of the measures used to address it. Here, we evaluate three of the most commonly used ones: synergy, ΔIshuffled, and ΔI. We show that synergy and ΔIshuffled are confounded measures: they can be zero when correlations are clearly important for decoding and positive when they are not. In contrast, ΔI is not confounded. It is zero only when correlations are not important for decoding and positive only when they are; that is, it is zero only when one can decode exactly as well using a decoder that ignores correlations as one can using a decoder that does not, and it is positive only when one cannot decode as well. Finally, we show that ΔI has an information theoretic interpretation; it is an upper bound on the information lost when correlations are ignored. [ABSTRACT FROM AUTHOR]

Neurons are known to respond to external stimuli in a noisy manner. This response variability is often correlated across the neural population. However, the functional role of these noise correlations is still unclear. In this paper, Fisher information is used to analyze the effects of noise correlations on the accuracy with which a neural population encodes a stimulus. The existence of limited-range correlations of the type found in cortical tissue yields a saturation of the Fisher information content as a function of the population size only for an additive noise model. We also show that random variability in the correlation coefficient within a neural population can considerably improve the average encoding quality. This means that diversity in the correlations, as found empirically, could be exploited for improving stimulus representation. [Copyright &y& Elsevier]

This paper describes the use of an InGaAs-InP photoheterojunction bipolar transistor (photo-HBT) for millimeter-wave generation and digital modulation. Optical mixing of two coherent signals generates the carrier, and a digital drive signal to the base is used for the modulation. We describe an advanced large signal model of the photo-HBT that takes into account distributed effects at high frequencies and all noise sources, including optical amplifier noise and noise correlations due to the high operation frequency and the nonlinear mixing processes. The model enables one to predict carrier-to-noise ratio dependence on frequency, optical power, and the transistor operating point. Frequency- and time-domain responses of the modulated millimeter- wave carrier and bit error rates are also calculated. Experiments at 10 and 45 GHz with modulation rates ranging between 50 Mb/s and 2.5 Gb/s were performed, and a superb fit to the calculated responses is found [ABSTRACT FROM PUBLISHER]