Integration Time Window Research Articles

Strategies for motion- and respiration-robust estimation of fMRI intrinsic neural timescales

Abstract Intrinsic neural timescales (INT) reflect the time window of neural integration within a brain region and can be measured via resting-state fMRI (rs-fMRI). Despite the potential relevance of INT to cognition, brain organization, and neuropsychiatric illness, the influences of physiological artifacts on rs-fMRI INT have not been systematically considered. Two artifacts, head motion and respiration, pose serious issues in rs-fMRI studies. Here, we described their impact on INT estimation and tested the ability of two denoising strategies for mitigating these artifacts, high-motion frame censoring and global signal regression (GSR). We used a subset of the HCP Young Adult dataset with runs annotated for breathing patterns (Lynch et al., 2020) and at least one “clean” (reference) run that had minimal head motion and no respiration artifacts; other runs from the same participants (n = 46) were labeled as “non-clean.” We found that non-clean runs exhibited brain-wide increases in INT compared to their respective clean runs and that the magnitude of error in INT between non-clean and clean runs correlated with the amount of head motion. Importantly, effect sizes were comparable to INT effects reported in the clinical literature. GSR and high-motion frame censoring improved the similarity between INT maps from non-clean runs and their respective clean run. Using a pseudo-random frame-censoring approach, we uncovered a relationship between the amount of censored frames and both the mean INT and mean error, suggesting that frame censoring itself biases INT estimation. A group-level correction procedure reduced this bias and improved similarity between non-clean runs and their respective clean run. Based on our findings, we offer recommendations for rs-fMRI INT studies, which include implementing GSR and high-motion frame censoring with Lomb-Scargle interpolation of censored data, and performing group-level correction of the bias introduced by frame censoring.

A shared temporal window of integration across cognitive control and reinforcement learning paradigms: A correlational study.

Cognitive control refers to the ability to override prepotent response tendencies to achieve goal-directed behavior. On the other hand, reinforcement learning refers to the learning of actions through feedback and reward. Although cognitive control and reinforcement learning are often viewed as opposing forces in driving behavior, recent theories have emphasized possible similarities in their underling processes. With this study, we aimed to investigate whether a similar time window of integration could be observed during the learning of control on the one hand, and the learning rate in reinforcement learning paradigms on the other. To this end, we performed a correlational analysis on a large public dataset (n = 522) including data from two reinforcement learning tasks, i.e., a probabilistic selection task and a probabilistic Wisconsin Card Sorting Task (WCST), and data from a classic conflict task (i.e., the Stroop task). Results showed expected correlations between the time scale of control indices and learning rate in the probabilistic WCST. Moreover, the learning-rate parameters of the two reinforcement learning tasks did not correlate with each other. Together, these findings suggest a reliance on a shared learning mechanism between these two traditionally distinct domains, while at the same time emphasizing that value updating processes can still be very task-specific. We speculate that updating processes in the Stroop and WCST may be more related because both tasks require task-specific updating of stimulus features (e.g., color, word meaning, pattern, shape), as opposed to stimulus identity.

Study of Angular Resolution Using Imaging Atmospheric Cherenkov Technique

Angular resolution is crucial for the detailed study of gamma-ray sources and current Cherenkov telescopes (e.g., HESS, MAGIC, and VERITAS) that operate below tens of TeV. Several gamma-ray sources with a photon energy larger than 100 TeV have been revealed by the LHAASO in recent years; the angular resolution of the LHAASO is around 0.3∘. A gamma-ray detector with an angular resolution of less than 0.1∘ operating beyond 100 TeV is needed to study the detailed morphology of ultra-high-energy gamma-ray sources further. The cost-effectiveness is crucial for such large-area detectors. In this paper, the impact of telescope aperture, field of view, pixel size, optical point spread function, and signal integration time window on angular resolution is studied. These results can provide essential elements for the design of telescope arrays.

Seeing is believing: Larger Colavita effect in school-aged children with attention-deficit/hyperactivity disorder

Attention-deficit/hyperactivity disorder (ADHD) is a common neurodevelopmental disorder that leads to visually relevant compensatory activities and cognitive strategies in children. Previous studies have identified difficulties with audiovisual integration in children with ADHD, but the characteristics of the visual dominance effect when processing multisensory stimuli are not clear in children with ADHD. The current study used the Colavita paradigm to explore the visual dominance effect in school-aged children with ADHD. The results found that, compared with typically developing children, children with ADHD had a higher proportion of “visual–auditory” trials and a lower proportion of “simultaneous” trials. The study also found that the proportion of visual–auditory trials in children with ADHD decreased as their Swanson, Nolan, and Pelham–IV rating scale (SNAP-IV) inattention scores increased. The results showed that school-aged children with ADHD had a larger Colavita effect, which decreased with the severity of inattentive symptoms. This may be due to an overreliance on visual information and an abnormal integration time window. The connection between multisensory cognitive processing performance and clinical symptoms found in the current study provides empirical and theoretical support for the knowledge base of multisensory and cognitive abilities in disorders.

Maritime moving target detection and localisation technique for Global Navigation Satellite Signals‐based passive multistatic radar

AbstractThis article puts forward a ship target detection and localisation technique for GNSS‐based passive multistatic radar. The approach capitalises on the large spatial diversity offered by navigation satellite constellations to provide maritime awareness using short integration time windows, thus bypassing the shortcomings suffered by approaches relying on long dwells typically considered in satellite‐based passive radar systems. The proposed approach entirely operates on the Cartesian plane and it is able to provide in a single stage the detection and localisation of the target in the surveyed area. Theoretical and simulated performance analysis are provided to illustrate as the proposed approach can outperform conventional two‐stages (i.e. bistatic detection then localisation) procedures, with particular regard to the case of significant radar cross section scintillation, likely experienced in the system under consideration. The effectiveness of the approach has been verified via experimental data acquired in a few scenarios of interest comprising opportunistic targets belonging to different types.

Simple reconfigurable multiport photonic temporal N-differentiator and integrator based on dual-ring coupled Mach–Zehnder interferometer

At present, a high-order, reconfigurable photonic signal processor is very difficult to implement. A simple, reconfigurable photonic N-differentiator and integrator based on a unit of the dual-ring coupled Mach–Zehnder interferometer (DRMZI) is proposed first. The reconfigurability is achieved only by controlling the thermo-optic phase shifter (TO-PS) on the two improved micro-ring resonators. The device presents a wide fine-tunable differentiation order range from 0.2 ≤ N ≤ 1.7 reconfigured as a 2 × 2 differentiator after being optimized the TO-PS and the tunable couplers (TC). If it is reconfigured as an integrator, a first-order photonic temporal integrator with 16.1 GHz 3-dB bandwidth and integration time window 38.4 ps is achieved in our design. The 4 × 4 port DRMZI differential unit can be cascaded into k-stage to realize 0.2 × k ≤ N ≤ 1.7 × k order differential function, theoretically approaching any large order. At the same time, the differential signals can be successfully routed to different output ports by reconfiguring the optical path in the structure. The simulation results have shown that a two-stage 4 × 4 photonic temporal differentiator can perform more than two order differential operations, e.g., N = 2.4. Our research can provide a reference for chip-level large-scale integrated photonic processors.

What Is the Role of GABA Transporters in Seizures?

The brain utilizes γ‐aminobutyric acid (GABA) as its primary inhibitory neurotransmitter to control neuronal excitability and modulate the ongoing activity of neuronal ensembles. GABA controls the generation of membrane potential oscillations, which provide the time window for integration of synaptic inputs and generation of activity patterns in neuronal networks. These effects require a fine control of GABAA and GABAB receptor activation, which, in turn, depends on both the precise timing of GABA release from presynaptic terminals and GABA clearance from the extracellular space. GABA is synthesized in presynaptic terminals from glutamate via the glutamic acid decarboxylases 65 and 67 and is incorporated in synaptic vesicles via the vesicular GABA transporter, referred to as vesicular inhibitory amino-acid transporter (VIAAT) as it also mediates vesicular uptake of glycine1 (Figure). The clearance of GABA after release depends on its uptake by specific GABA transporters (GATs), including GAT-1, expressed predominantly in axons and presynaptic terminals, and GAT-3, expressed primarily in astrocytes.2,3 By controlling extracellular GABA levels, GATs have a major role in regulating tonic and phasic inhibition in the cerebral cortex, hippocampus, thalamus, and other areas.2,3 Experimental studies in mouse models indicate a major role of GATs in regulating cortical excitability and predisposition to seizures. Mutations affecting the GABA transporters have been linked to different seizure phenotypes. For example, loss of function mutations of the SLC6A1 gene encoding GAT-1 have been associated with epilepsy with myoclonic-atonic seizures and with absence seizures.4,5

Individual differences in alpha frequency are associated with the time window of multisensory integration, but not time perception

Previous research provides some preliminary evidence to link the temporal binding window, the time frame within which multisensory information from different sensory modalities is integrated, and time perception. In addition, alpha peak frequency has been proposed to be the neural mechanism for both processes. However, these links are not well established. Hence, the aim of the current study was to explore to what degree, if any, time perception, the temporal binding window and the alpha peak frequency are related. It was predicted that as the width of the temporal binding window increases the size of the filled duration illusion increases and the alpha peak frequency decreases. We observed a significant relationship between the temporal binding window and peak alpha frequency. However, time perception was not linked with either of these. These findings are discussed with respect to the possible underlying mechanisms of multisensory integration and time perception.

Photonic RF and Microwave Integrator Based on a Transversal Filter With Soliton Crystal Microcombs

We demonstrate a photonic RF integrator based on an integrated soliton crystal microcomb source. By multicasting and progressively delaying the input RF signal using a transversal structure, the input RF signal is integrated discretely. Up to 81 wavelengths are provided by the microcomb source, which enable a large integration time window of 6.8 ns, together with a time resolution as fast as 84 ps. We perform signal integration of a diverse range of input RF signals including Gaussian pulses with varying time widths, dual pulses with varying time intervals and a square waveform. The experimental results show good agreement with theory. These results verify our microcomb-based integrator as a competitive approach for RF signal integration with high performance and potentially lower cost and footprint.

Distinct hierarchical alterations of intrinsic neural timescales account for different manifestations of psychosis.

Hierarchical perceptual-inference models of psychosis may provide a holistic framework for understanding psychosis in schizophrenia including heterogeneity in clinical presentations. Particularly, hypothesized alterations at distinct levels of the perceptual-inference hierarchy may explain why hallucinations and delusions tend to cluster together yet sometimes manifest in isolation. To test this, we used a recently developed resting-state fMRI measure of intrinsic neural timescale (INT), which reflects the time window of neural integration and captures hierarchical brain gradients. In analyses examining extended sensory hierarchies that we first validated, we found distinct hierarchical INT alterations for hallucinations versus delusions in the auditory and somatosensory systems, thus providing support for hierarchical perceptual-inference models of psychosis. Simulations using a large-scale biophysical model suggested local elevations of excitation-inhibition ratio at different hierarchical levels as a potential mechanism. More generally, our work highlights the robustness and utility of INT for studying hierarchical processes relevant to basic and clinical neuroscience.

Feed-forward recruitment of electrical synapses enhances synchronous spiking in the mouse cerebellar cortex.

In the cerebellar cortex, molecular layer interneurons use chemical and electrical synapses to form subnetworks that fine-tune the spiking output of the cerebellum. Although electrical synapses can entrain activity within neuronal assemblies, their role in feed-forward circuits is less well explored. By combining whole-cell patch-clamp and 2-photon laser scanning microscopy of basket cells (BCs), we found that classical excitatory postsynaptic currents (EPSCs) are followed by GABAA receptor-independent outward currents, reflecting the hyperpolarization component of spikelets (a synapse-evoked action potential passively propagating from electrically coupled neighbors). FF recruitment of the spikelet-mediated inhibition curtails the integration time window of concomitant excitatory postsynaptic potentials (EPSPs) and dampens their temporal integration. In contrast with GABAergic-mediated feed-forward inhibition, the depolarizing component of spikelets transiently increases the peak amplitude of EPSPs, and thus postsynaptic spiking probability. Therefore, spikelet transmission can propagate within the BC network to generate synchronous inhibition of Purkinje cells, which can entrain cerebellar output for driving temporally precise behaviors.

Audiovisual integration in depth: Modeling the effect of distance and stimulus effectiveness using the TWIN model

Integrating information across our various sensory modalities results in striking behavioral benefits. This integration depends on a variety of factors, among which are the effectiveness of the stimuli and the relative timing between them. Both of these factors physically vary as a function of the distance between stimuli and the observer: intensity decreases as a function of distance for both auditory and visual stimuli, while the relative timing of energy arriving at the sensory organs differs due to differing transmission speeds. As a result, the depth at which multisensory stimuli are presented is likely to be an important factor in the gain that is derived from integrating them. Here, we use a computational approach – the Time-Window-of Integration (TWIN) framework – to examine differences in simultaneity judgments and reaction times to audiovisual stimuli presented at two depths. Using the TWIN model, we tested whether the observed behavior could be explained solely on the basis of differences in peripheral processing times, on the basis of changes in the temporal binding window (TBW), or by a combination of both factors. The results indicated that a model allowing for different TBWs for near and far space best accounts for the observed data in the majority of participants. However, the best overall model (regardless of the number of parameters) was a model containing both distance-dependent peripheral processing times and TBWs. Interestingly, TBWs were found not to expand from near to far space, but rather to get smaller. Taken together, the results indicate that distance is an additional factor in multisensory integration, above its impact on relative timing and intensity.

Young and Older Adults Differ in Integration of Sensory Cues for Vertical Perception.

Introduction The subjective visual vertical (SVV) measures the perception of a person's spatial orientation relative to gravity. Weighted central integration of vestibular, visual, and proprioceptive inputs is essential for SVV perception. Without any visual references and minimal proprioceptive contribution, the static SVV reflects balance of the otolith organs. Normal aging is associated with bilateral and progressive decline in otolith organ function, but age-dependent effects on SVV are inconclusive. Studies on sensory reweighting for visual vertical and multisensory integration strategies reveal age-dependent differences, but most studies have included elderly participants in comparison to younger adults. The aim of this study was to compare young adults with older adults, an age group younger than the elderly. Methods Thirty-three young and 28 older adults (50–65 years old) adjusted a tilted line accurately to their perceived vertical. The rod's final position from true vertical was recorded as tilt error in degrees. For otolithic balance, visual vertical was recorded in the dark without any visual references. The rod and frame task (RFT) with tilted disorienting visual frames was used for creating visuovestibular conflict. We adopted Nyborg's analysis method to derive the rod and frame effect (RFE) and trial-to-trial variability measures. Rod alignment times were also analyzed. Results There was no age difference in signed tilts of SVV without visual reference. There was an age effect on RFE and on overall trial-to-trial variability of rod tilt, with older adults displaying larger frame effects and greater variability in rod tilts. Alignment times were longer in the tilted-frame conditions for both groups and in the older adults compared to their younger counterparts. The association between tilt accuracy and tilt precision was significant for older adults only during visuovestibular conflict, revealing an increase in RFE with an increase in tilt variability. Correlation of σSVV, which represents vestibular input precision, with RFE yielded exactly the same contribution of σSVV to the variance in RFE for both age groups. Conclusions Older adults have balanced otolithic input in an upright position. Increased reliance on visual cues may begin at ages younger than what is considered elderly. Increased alignment times for older adults may create a broader time window for integration of relevant and irrelevant sensory information, thus enhancing their multisensory integration. In parallel with the elderly, older adults may differ from young adults in their integration of sensory cues for visual vertical perception.

Effect of music training and art training on letters-speech sounds audiovisual integration in college students

Objective To investigate the effects of music training and art training on the audiovisual integration of letters-speech sounds in college students. Method Visual letters and auditory speech sounds were used to conduct a discrimination task test in music students, art students and ordinary college students (n=30 for each group). SPSS17.0 was used to conduct ANOVA and Race model analysis on reaction time and hit rate. Results (1) Reaction time: the results showed that the interaction between group and stimulus type was significant(F=7.89, P<0.01). The simple effect analysis found that all the participants reacted faster to consistent audiovisual(letters B and speech B) stimuli in comparison to unimodal stimuli, and the redundant signal effect occured.(2) Race model analysis showed that the time window of audiovisual integration were 120-130 ms in the music group, 130-190 ms in the art group, and 120-170 ms in the general group(P<0.01). The positive area (pAUC) under the Race model curve of the music group(18.95) was significantly smaller than that of the art group(159.43) and the general group(125.01)(P<0.01), and there was no significant difference between the art group and the general group(P=0.13). Conclusion Music training has a regulating effect on the integration of letters and speech sounds, while art training has no significant effect on it. Key words: Audiovisual integration; The redundant signal effect; Race model; Music training; Art training

Design of a Miniaturized Broadband Silicon Hybrid Plasmonic Temporal Integrator for Ultrafast Optical Signal Processing

A fractional-order silicon hybrid plasmonic temporal integrator with considerably wide full-width at half- maximum (FWHM) bandwidth of ∼1 THz, higher than the previously reported photonic temporal integrators, and noticeably compact footprint of ∼5 μm × 3 μm is proposed. The presented plasmonic temporal integrator is implemented based on a double-ring add-drop resonator structure with ring radii of 1.5 μm. The 3-D finite-difference time-domain (3D-FDTD) simulation results show that the fractional-order of the integrator is 0.64 and it is capable of processing the ultrashort pulses with the duration of 450 fs. The integration time window is estimated as 520 fs, while the achieved energy efficiency is as high as −1.92 dB. The compact size and wide bandwidth of the proposed integrator makes it suitable for ultrafast optical signal processing applications. As an example, the functionality of the designed integrator for solving ordinary differential equations (ODEs) is investigated.

Enhanced Thalamocortical Synaptic Transmission and Dysregulation of the Excitatory-Inhibitory Balance at the Thalamocortical Feedforward Inhibitory Microcircuit in a Genetic Mouse Model of Migraine.

Migraine is a complex brain disorder, characterized by attacks of unilateral headache and global dysfunction in multisensory information processing, whose underlying cellular and circuit mechanisms remain unknown. The finding of enhanced excitatory, but unaltered inhibitory, neurotransmission at intracortical synapses in mouse models of familial hemiplegic migraine (FHM) suggested the hypothesis that dysregulation of the excitatory-inhibitory balance in specific circuits is a key pathogenic mechanism. Here, we investigated the thalamocortical (TC) feedforward inhibitory microcircuit in FHM1 mice of both sexes carrying a gain-of-function mutation in CaV2.1. We show that TC synaptic transmission in somatosensory cortex is enhanced in FHM1 mice. Due to similar gain of function of TC excitation of layer 4 excitatory and fast-spiking inhibitory neurons elicited by single thalamic stimulations, neither the excitatory-inhibitory balance nor the integration time window set by the TC feedforward inhibitory microcircuit was altered in FHM1 mice. However, during repetitive thalamic stimulation, the typical shift of the excitatory-inhibitory balance toward excitation and the widening of the integration time window were both smaller in FHM1 compared with WT mice, revealing a dysregulation of the excitatory-inhibitory balance, whereby the balance is relatively skewed toward inhibition. This is due to an unexpected differential effect of the FHM1 mutation on short-term synaptic plasticity at TC synapses on cortical excitatory and fast-spiking inhibitory neurons. Our findings point to enhanced transmission of sensory, including trigeminovascular nociceptive, signals from thalamic nuclei to cortex and TC excitatory-inhibitory imbalance as mechanisms that may contribute to headache, increased sensory gain, and sensory processing dysfunctions in migraine.SIGNIFICANCE STATEMENT Migraine is a complex brain disorder, characterized by attacks of unilateral headache and by global dysfunction in multisensory information processing, whose underlying cellular and circuit mechanisms remain unknown. Here we provide insights into these mechanisms by investigating thalamocortical (TC) synaptic transmission and the function of the TC feedforward inhibitory microcircuit in a mouse model of a rare monogenic migraine. This microcircuit is critical for gating information flow to cortex and for sensory processing. We reveal increased TC transmission and dysregulation of the cortical excitatory-inhibitory balance set by the TC feedforward inhibitory microcircuit, whereby the balance is relatively skewed toward inhibition during repetitive thalamic activity. These alterations may contribute to headache, increased sensory gain, and sensory processing dysfunctions in migraine.

Evolutionary Elongation of the Time Window of Integration in Auditory Cortex: Macaque vs. Human Comparison of the Effects of Sound Duration on Auditory Evoked Potentials.

The auditory cortex integrates auditory information over time to obtain neural representations of sound events, the time scale of which critically affects perception. This work investigated the species differences in the time scale of integration by comparing humans and monkeys regarding how their scalp-recorded cortical auditory evoked potentials (CAEPs) decrease in amplitude as stimulus duration is shortened from 100 ms (or longer) to 2 ms. Cortical circuits tuned to processing sounds at short time scales would continue to produce large CAEPs to brief sounds whereas those tuned to longer time scales would produce diminished responses. Four peaks were identified in the CAEPs and labeled P1, N1, P2, and N2 in humans and mP1, mN1, mP2, and mN2 in monkeys. In humans, the N1 diminished in amplitude as sound duration was decreased, consistent with the previously described temporal integration window of N1 (>50 ms). In macaques, by contrast, the mN1 was unaffected by sound duration, and it was clearly elicited by even the briefest sounds. Brief sounds also elicited significant mN2 in the macaque, but not the human N2. Regarding earlier latencies, both P1 (humans) and mP1 (macaques) were elicited at their full amplitudes even by the briefest sounds. These findings suggest an elongation of the time scale of late stages of human auditory cortical processing, as reflected by N1/mN1 and later CAEP components. Longer time scales of integration would allow neural representations of complex auditory features that characterize speech and music.

Differential sustained and transient temporal processing across visual streams.

How do high-level visual regions process the temporal aspects of our visual experience? While the temporal sensitivity of early visual cortex has been studied with fMRI in humans, temporal processing in high-level visual cortex is largely unknown. By modeling neural responses with millisecond precision in separate sustained and transient channels, and introducing a flexible encoding framework that captures differences in neural temporal integration time windows and response nonlinearities, we predict fMRI responses across visual cortex for stimuli ranging from 33 ms to 20 s. Using this innovative approach, we discovered that lateral category-selective regions respond to visual transients associated with stimulus onsets and offsets but not sustained visual information. Thus, lateral category-selective regions compute moment-to-moment visual transitions, but not stable features of the visual input. In contrast, ventral category-selective regions process both sustained and transient components of the visual input. Our model revealed that sustained channel responses to prolonged stimuli exhibit adaptation, whereas transient channel responses to stimulus offsets are surprisingly larger than for stimulus onsets. This large offset transient response may reflect a memory trace of the stimulus when it is no longer visible, whereas the onset transient response may reflect rapid processing of new items. Together, these findings reveal previously unconsidered, fundamental temporal mechanisms that distinguish visual streams in the human brain. Importantly, our results underscore the promise of modeling brain responses with millisecond precision to understand the underlying neural computations.

Multisensory Integration and Exogenous Spatial Attention: A Time-window-of-integration Analysis.

Although it is well documented that occurrence of an irrelevant and nonpredictive sound facilitates motor responses to a subsequent target light appearing nearby, the cause of this "exogenous spatial cuing effect" has been under discussion. On the one hand, it has been postulated to be the result of a shift of visual spatial attention possibly triggered by parietal and/or cortical supramodal "attention" structures. On the other hand, the effect has been considered to be due to multisensory integration based on the activation of multisensory convergence structures in the brain. Recent RT experiments have suggested that multisensory integration and exogenous spatial cuing differ in their temporal profiles of facilitation: When the nontarget occurs 100-200 msec before the target, facilitation is likely driven by crossmodal exogenous spatial attention, whereas multisensory integration effects are still seen when target and nontarget are presented nearly simultaneously. Here, we develop an extension of the time-window-of-integration model that combines both mechanisms within the same formal framework. The model is illustrated by fitting it to data from a focused attention task with a visual target and an auditory nontarget presented at horizontally or vertically varying positions. Results show that both spatial cuing and multisensory integration may coexist in a single trial in bringing about the crossmodal facilitation of RT effects. Moreover, the formal analysis via time window of integration allows to predict and quantify the contribution of either mechanism as they occur across different spatiotemporal conditions.

The Firing Rate Speed Code of Entorhinal Speed Cells Differs across Behaviorally Relevant Time Scales and Does Not Depend on Medial Septum Inputs.

The firing rate of speed cells, a dedicated subpopulation of neurons in the medial entorhinal cortex (MEC), is correlated with running speed. This correlation has been interpreted as a speed code used in various computational models for path integration. These models consider firing rate to be linearly tuned by running speed in real-time. However, estimation of firing rates requires integration of spiking events over time, setting constraints on the temporal accuracy of the proposed speed code. We therefore tested whether the proposed speed code by firing rate is accurate at short time scales using data obtained from open-field recordings in male rats and mice. We applied a novel filtering approach differentiating between speed codes at multiple time scales ranging from deciseconds to minutes. In addition, we determined the optimal integration time window for firing-rate estimation using a general likelihood framework and calculated the integration time window that maximizes the correlation between firing rate and running speed. Data show that these time windows are on the order of seconds, setting constraints on real-time speed coding by firing rate. We further show that optogenetic inhibition of either cholinergic, GABAergic, or glutamatergic neurons in the medial septum/diagonal band of Broca does not affect modulation of firing rates by running speed at each time scale tested. These results are relevant for models of path integration and for our understanding of how behavioral activity states may modulate firing rates and likely information processing in the MEC.SIGNIFICANCE STATEMENT Path integration is the most basic form of navigation relying on self-motion cues. Models of path integration use medial septum/diagonal band of Broca (MSDB)-dependent MEC grid-cell firing patterns as the neurophysiological substrate of path integration. These models use a linear speed code by firing rate, but do not consider temporal constraints of integration over time for firing-rate estimation. We show that firing-rate estimation for speed cells requires integration over seconds. Using optogenetics, we show that modulation of firing rates by running speed is independent of MSDB inputs. These results enhance our understanding of path integration mechanisms and the role of the MSDB for information processing in the MEC.