Local Field Potential

We report a new potential model for phase diffusion in class-B lasers exposed to external optical feedback. Excited relaxation oscillations cause the potential to be nonlocal. Analytical results using this new potential agree very well with the full system dynamics. We indicate the experimental conditions for which the nonlocal potential becomes manifest in semiconductor lasers.

correlates of fast (Ͼ200 Hz) electrical oscillations in rat somatosensory cortex. J Neurophysiol 84: [1505][1506][1507][1508][1509][1510][1511][1512][1513][1514][1515][1516][1517][1518] 2000. Oscillatory activity in excess of several hundred hertz has been observed in somatosensory evoked potentials (SEP) recorded in both humans and animals and is attracting increasing interest regarding its role in brain function. Currently, however, little is known about the cellular events underlying these oscillations. The present study employed simultaneous in-vivo intracellular and epipial field-potential recording to investigate the cellular correlates of fast oscillations in rat somatosensory cortex evoked by vibrissa stimulation. Two distinct types of fast oscillations were observed, here termed "fast oscillations" (FO) (200 -400 Hz) and "very fast oscillations" (VFO) (400 -600 Hz). FO coincided with the earliest slowwave components of the SEP whereas VFO typically were later and of smaller amplitude. Regular spiking (RS) cells exhibited vibrissaevoked responses associated with one or both types of fast oscillations and consisted of combinations of spike and/or subthreshold events that, when superimposed across trials, clustered at latencies separated by successive cycles of FO or VFO activity, or a combination of both. Fast spiking (FS) cells responded to vibrissae stimulation with bursts of action potentials that closely approximated the periodicity of the surface VFO. No cells were encountered that produced action potential bursts related to FO activity in an analogous fashion. We propose that fast oscillations define preferred latencies for action potential generation in cortical RS cells, with VFO generated by inhibitory interneurons and FO reflecting both sequential and recurrent activity of stations in the cortical lamina.

A 64-channel electrode array was used to study the spatial and temporal characteristics of fast (Ͼ200 Hz) electrical oscillations recorded from the surface of rat cortex in both awake and anesthetized animals. Transient vibrissal displacements were effective in evoking oscillatory responses in the vibrissa/barrel field and were tightly time-locked to stimulus onset, coinciding with the earliest temporal components of the coincident slow-wave response. Vibrissa-evoked fast oscillations exhibited modality specificity and were earliest and of largest amplitude over the cortical barrel, which corresponded to the vibrissa stimulated, spreading to sequentially engage neighboring barrels over subsequent oscillatory cycles. The response was enhanced after paired-vibrissal stimulation and was sensitive to time delays between movement of separate vibrissae. These data suggest that spatiotemporal interactions between fast oscillatory bursts in the barrel field may play a role in rapidly integrating information from the vibrissal array during the earliest cortical response to somatosensory stimulation.

Most effective information transmission in the human brain requires three fundamental elements, anatomical connectivity, functional connectivity and sufficiently low levels of information transmission error. It has been proposed that some of the major motor symptoms of Parkinson's disease (PD), such as slowness of movement, are a consequence of failure in the last of these. Here, this hypothesis is tested using a binary information transmission representation of human motor output based on basic features of motor physiology. When tested against experimental observations, it is demonstrated that the level of transmission error of motor code information predicts multiple behavioural and neurophysiological elements of the disorder as well as some of healthy movement. While some of these elements in people with PD have been attributed to impaired movement gain theories, and others have been unexplained, the ability of motor code transmission error to account for them all suggests it is a useful explanation of motor features in the disorder.

The caudal cingulate motor area (CMAc) and the supplementary motor area (SMA) play important roles in movement execution. The present study examined the neural mechanisms underlying these roles by investigating local field potentials (LFPs) from these areas while monkeys pressed buttons with either their left or right hand. During hand movement, power increases in the high-gamma (80-120 Hz) and theta (3-8 Hz) bands and a power decrease in the beta (12-30 Hz) band were observed in both the CMAc and SMA. High-gamma and beta activity in the SMA predominantly represented contralateral hand movements, whereas activity in the CMAc preferentially represented movement of either hand. Theta activity in both brain regions most frequently reflected movement of either hand, but a contralateral hand bias was more evident in the SMA than in the CMAc. An analysis of the relationships of the laterality representations between the high-gamma and theta bands at each recording site revealed that, irre...

Metabolic activity in the water column below the euphotic zone is ultimately fuelled by the vertical flux of organic material from the surface. Over time, the deep ocean is presumably at steady state, with sources and sinks balanced. But recently compiled global budgets and intensive local field studies suggest that estimates of metabolic activity in the dark ocean exceed the influx of organic substrates. This imbalance indicates either the existence of unaccounted sources of organic carbon or that metabolic activity in the dark ocean is being over-estimated. Budgets of organic carbon flux and metabolic activity in the dark ocean have uncertainties associated with environmental variability, measurement capabilities, conversion parameters, and processes that are not well sampled. We present these issues and quantify associated uncertainties where possible, using a Monte Carlo analysis of a published data set to determine the probability that the imbalance can be explained purely by uncertainties in measurements and conversion factors. A sensitivity analysis demonstrates that the bacterial growth efficiencies and assumed cell carbon contents have the greatest effects on the magnitude of the carbon imbalance. Two poorly quantified sources, lateral advection of particles and a population of slowly settling particles, are discussed as providing a means of closing regional carbon budgets. Finally, we make recommendations concerning future research directions to reduce important uncertainties and allow a better determination of the magnitude and causes of the unbalanced carbon budgets.

We investigate the adequacy of the Kronig-Penney ␦-function model in describing the electromagnetic wave propagation in periodic structures consisting of thin layers of materials with an intensity-dependent dielectric constant. We find that the model captures the most essential features of nonlinear response to radiation. Excellent agreement is found between the results from the ␦-function model and the exact solutions of nonlinear wave equations. However, discrepancies do exist below the bottom of transmission bands due to the rigidness of the band edge in the ␦-function model. Consequently, gap solitons cannot form in the ␦-function model when the nonlinear Kerr coefficient is positive.

The striatum is thought to be an essential region for integrating diverse information in the brain. Rapid inhibitory gating (IG) of sensory input is most likely an early factor necessary for appropriate integration to be completed. Gating is currently evaluated in clinical settings and is dramatically altered in a variety of psychiatric illnesses. Basic neuroscience research using animals has revealed specific neural sites involved in IG including the hippocampus, thalamus, brainstem, amygdala and medial prefrontal cortex. The present study investigated local IG in the basal ganglia structure of the striatum using chronic recording microwires. We obtained both single unit activations and local field potentials (LFPs) in awake behaving rats from each wire during the standard two-tone paradigm. Single units responded with different types of activations including a phasic and sustained excitation, an inhibitory response and a combination response that contained both excitatory and inhi...

Medial prefrontal cortex is a crucial region involved in inhibitory processes. Damage to the medial prefrontal cortex can lead to loss of normal inhibitory control over motor, sensory, emotional and cognitive functions. The goal of the present study was to examine the basic properties of inhibitory gating in this brain region in rats. Inhibitory gating has recently been proposed as a neurophysiological assay for sensory filters in higher brain regions that potentially enable or disable information throughput. This perspective has important clinical relevance due to the findings that gating is dramatically impaired in individuals with emotional and cognitive impairments (i.e. schizophrenia). We used the standard inhibitory gating twotone paradigm with a 500 ms interval between tones and a 10 s interval between tone pairs. We recorded both single unit and local field potentials from chronic microwire arrays implanted in the medial prefrontal cortex. We investigated short-term (within session) and long-term (between session) variability of auditory gating and additionally examined how altering the interval between the tones influenced the potency of the inhibition. The local field potentials displayed greater variability with a reduction in the amplitudes of the tone responses over both the short and long-term time windows. The decrease across sessions was most intense for the second tone response (test tone) leading to a more robust gating (lower T/C ratio). Surprisingly, single unit responses of different varieties retained similar levels of auditory responsiveness and inhibition in both the short and long-term analysis. Neural inhibition decreased monotonically related to the increase in intertone interval. This change in gating was most consistent in the local field potentials. Subsets of single unit responses did not show the lack of inhibition even for the longer intertone intervals tested (4 s interval). These findings support the idea that the medial prefrontal cortex is an important site where early inhibitory functions reside and potentially mediate psychological processes.

Learning to recognize and filter familiar, irrelevant sensory stimuli eases the computational burden on the cerebral cortex. Inhibition is a candidate mechanism in this filtration process, and oscillations in the cortical local field potential (LFP) serve as markers of the engagement of different inhibitory neurons. We show here that LFP oscillatory activity in visual cortex is profoundly altered as male and female mice learn to recognize an oriented grating stimulus-low frequency (~15 Hz peak) power sharply increases while high frequency (~65 Hz peak) power decreases. These changes report recognition of the familiar pattern, as they disappear when the stimulus is rotated to a novel orientation. Two-photon imaging of neuronal activity reveals that parvalbumin-expressing inhibitory neurons disengage with familiar stimuli and reactivate to novelty, whereas somatostatin-expressing inhibitory neurons show opposing activity patterns. We propose a model in which the balance of two interacting interneuron circuits shifts as novel stimuli become familiar.

The problem of the genesis of oscillatory phenomena in a continuous distribution of excitatory and inhibitory neurons is addressed by introducing a neural ÿeld model of the reaction-di usion type. The presence of the di usive term, combined with the non-linear point interactions, allows the system to exhibit cooperative activation properties in both space and time. A detailed analysis of the resulting oscillatory behaviour of the model evidences its capability of generating stimulus-induced spatio-temporal coherence ÿelds, similar to the ones experimentally observed in the mammalian visual cortex. The perceptual role of the related association ÿelds, as exible media to establish feature association in the visual space, is discussed.

In analyzing neurophysiologic data, individual experimental trials are usually assumed to be statistically independent. However, many studies employing functional imaging and electrophysiology have shown that brain activity during behavioral tasks includes temporally correlated trial-to-trial fluctuations. This could lead to spurious results in statistical significance tests used to compare data from different interleaved behavioral conditions presented throughout an experiment. We characterize trialto-trial fluctuations in local field potentials recorded from the frontal cortex of a macaque monkey performing an oculomotor delayed response task. Our analysis identifies slow fluctuations (<0.1 Hz) of spectral power in 22/27 recording sessions. These trial-to-trial fluctuations are non-Gaussian, and call into question the statistical utility of standard trial shuffling. We compare our results with evidence for slow fluctuations in human functional imaging studies and other electrophysiologic studies in nonhuman primates.

The problem of the genesis of oscillatory phenomena in a continuous distribution of excitatory and inhibitory neurons is addressed by introducing a neural ÿeld model of the reaction-di usion type. The presence of the di usive term, combined with the non-linear point interactions, allows the system to exhibit cooperative activation properties in both space and time. A detailed analysis of the resulting oscillatory behaviour of the model evidences its capability of generating stimulus-induced spatio-temporal coherence ÿelds, similar to the ones experimentally observed in the mammalian visual cortex. The perceptual role of the related association ÿelds, as exible media to establish feature association in the visual space, is discussed.

The problem of the genesis of oscillatory phenomena in a continuous distribution of excitatory and inhibitory neurons is addressed by introducing a neural ÿeld model of the reaction-di usion type. The presence of the di usive term, combined with the non-linear point interactions, allows the system to exhibit cooperative activation properties in both space and time. A detailed analysis of the resulting oscillatory behaviour of the model evidences its capability of generating stimulus-induced spatio-temporal coherence ÿelds, similar to the ones experimentally observed in the mammalian visual cortex. The perceptual role of the related association ÿelds, as exible media to establish feature association in the visual space, is discussed.

It is well known for a long time that, on a large-scale macroscopic scale, cortical activation states can be modeled by considering the dynamics of two non-linearly coupled populations of excitatory and inhibitory neurons , spatially organized into stereotyped modules. Considering the huge number of cells found in layered cortical areas neuronal activation is usually defined over spatially continuous domains (neural fields) as continuous distribution of neurons and synapses where each point in space corresponds to a neural population . Formally, each layer dynamics is described by integro-differential ordinary equations, where the integral kernel is a smooth function that replaces the synaptic interconnection matrix and continuous position variables replace the indices of discrete models. In this way, metric relations apply and it becomes possible to model the geometrical properties, such as spatial nearness and topology, that characterize the rich anatomy structure of cortical areas (e.g., maps, columns, dendritic and axonal arborizations, cell density, etc.) [7] [4]. By introducing a diffusive coupling into the equations that govern the punctual excitation-inhibition reactions, additional local interactions take place, providing a gradual spread of the variations of activity in space and simulates the continuity constraint of the neural field. In general, reaction-diffusion systems are natural candidates to model cortical phenomenological processes associated to sensory information processing, since their diffusion components allow for a weighted averaging of the input signal over a region of a certain extent (i.e., the receptive field), thus realizing a reduction in the complexity of the signal, while the non-linear reaction components provide a flexible medium through which all sorts of excitatory and inhibitory behaviour can be modeled.

An r.t. extension of a valuation v on K to a rational function field with n variables is defined by using r.t. extensions of v to a rational function field with one variable and some properties of this valuation are investigated. Mathematics Subject Classification: 12J10, 12F20, 12J20

Let v be a valuation of a field K with value group Gv, residue field kv and w be an extension of v to K(x1, ..., xn). w is called residual transcendental extension of v if kw/kv is a transcendental extension. A residual transcendental extension of v to K(x1, ..., xn) is defined in [5] and in this paper it is proved that if w is a residual transcendental extension of v to K(x1, ..., xn) it must be defined as in [5] when ef = n where e is the ramification index and f is the residue degree of the extension w/v. Mathematics Subject Classification: 12J10, 12F20, 12J20

In this paper, a novel technique is proposed for localization of Subthalamic Nucleus (STN) during deep brain stimulation (DBS) Surgery. DBS surgery is performed on individuals living with Parkinson's disease (PD) to permanently implant stimulation electrodes for managing some motor symptoms of PD. The most challenging part of this surgery is to accurately place the electrodes inside the STN. Commonly, microelectrode recordings (MERs) are interpreted by the surgical team intraoperatively to estimate the location of electrodes and detect the borders of the STN. In this work, we aim to automate the process of localizing the STN using a machine learning technique (trained based on the electrophysiological signals that we have collected during 20 surgeries). The proposed approach is capable of detecting the dorsal borders of the STN during the procedure with high accuracy (85%), and outperforms the current state-of-the-art approach for this application.

In this paper, an unsupervised machine learning technique is proposed to localize the Subthalamic Nucleus (STN) during deep brain stimulation (DBS) Surgery. DBS is one of most common treatments for advanced Parkinson's disease (PD). The purpose of this surgery is to permanently implant stimulation electrodes inside the STN to deliver electrical currents. It is clinically shown that DBS surgery can significantly reduce motor symptoms of PD (such as tremor). However, the outcome of this surgery is highly dependent on the location of the stimulating electrode. Since STN is a very small region inside the basal ganglia, accurate placement of the electrode is a challenging task for the surgical team. During DBS surgery, the team uses Micro-Electrode Recording (MER) of electrophysiological neural activities to intraoperatively track the location of electrodes and estimate the borders of the STN. In this work, we propose a composite unsupervised machine learning clustering approach that is capable of detecting the dorsal borders of the STN during DBS operation. For this, MER signals from 50 PD patients were recorded and used to validate the performance of the proposed method. Results show that the approach is capable of detecting the dorsal border of the STN in an online manner with an accuracy of 80% without using any supervised training.

In this paper, a novel technique is proposed for localization of Subthalamic Nucleus (STN) during deep brain stimulation (DBS) Surgery. DBS surgery is performed on individuals living with Parkinson's disease (PD) to permanently implant stimulation electrodes for managing some motor symptoms of PD. The most challenging part of this surgery is to accurately place the electrodes inside the STN. Commonly, microelectrode recordings (MERs) are interpreted by the surgical team intraoperatively to estimate the location of electrodes and detect the borders of the STN. In this work, we aim to automate the process of localizing the STN using a machine learning technique (trained based on the electrophysiological signals that we have collected during 20 surgeries). The proposed approach is capable of detecting the dorsal borders of the STN during the procedure with high accuracy (85%), and outperforms the current state-of-the-art approach for this application.

We study the spatial properties of a nonlinear discrete Schrodinger equation introduced by Cai, Bishop, and Ore(nbech-Jensen [Phys. Rev. Lett. 72, 591 (1994)] that interpolates between the integrable Ablowitz-Ladik equation and the nonintegrable discrete nonlinear Schrodinger equation. We focus on the stationary properties of the interpolating equation and analyze the interplay between integrability and nonintegrability by transforming the problem into a dynamical system and investigating its Hamil- tonian structure. We find explicit parameter regimes where the corresponding dynamical system has regular trajectories leading to propagating wave solutions. Using the anti-integrable limit, we show the existence of breathers. We also investigate the wave transmission problem through a finite segment of the nonlinear lattice and analyze the regimes of regular wave transmission. By analogy of the nonlinear lattice problem with chaotic scattering systems, we find the chain lengths at which reliable information transmission via amplitude modulation is possible.

Objective-Essential tremor (ET) is characterized by an action tremor believed to be due to excessive theta-alpha activity in the cerebello-thalamo-cortical system. This study aimed to test the hypothesis that therapeutic thalamic stimulation in patients with ET decreases theta-alpha oscillatory activity in primary motor (M1) and sensory (S1) cortices. Methods-During surgical treatment of ET in 10 patients, an electrocorticography (ECoG) strip electrode was placed temporarily over the arm region of M1 and S1. Local field potentials (LFP) were recorded at rest, during a tremor-inducing posture, during acute therapeutic thalamic stimulation, and following therapeutic thalamotomy (three patients). Power spectral density (PSD) was calculated using the Fast Fourier Transform. Results-At rest, alpha activity (8-13 Hz) in M1 was significantly decreased during highfrequency stimulation, while theta activity (4-8 Hz) decreased in S1. Following thalamotomy, theta and beta (13-30 Hz) was increased in M1. Induction of postural tremor reduced M1 theta, alpha and beta activity compared to the resting state. Conclusions-High-frequency thalamic deep brain stimulation (DBS) significantly reduces alpha oscillatory activity in the primary motor cortex of patients with ET, though this change is probably not critical for therapeutic efficacy. Significance-We demonstrate that ECoG can be effectively used to study the effect of subcortical stimulation on cortical oscillations.

Objective-Essential tremor (ET) is characterized by an action tremor believed to be due to excessive theta-alpha activity in the cerebello-thalamo-cortical system. This study aimed to test the hypothesis that therapeutic thalamic stimulation in patients with ET decreases theta-alpha oscillatory activity in primary motor (M1) and sensory (S1) cortices. Methods-During surgical treatment of ET in 10 patients, an electrocorticography (ECoG) strip electrode was placed temporarily over the arm region of M1 and S1. Local field potentials (LFP) were recorded at rest, during a tremor-inducing posture, during acute therapeutic thalamic stimulation, and following therapeutic thalamotomy (three patients). Power spectral density (PSD) was calculated using the Fast Fourier Transform. Results-At rest, alpha activity (8-13 Hz) in M1 was significantly decreased during highfrequency stimulation, while theta activity (4-8 Hz) decreased in S1. Following thalamotomy, theta and beta (13-30 Hz) was increased in M1. Induction of postural tremor reduced M1 theta, alpha and beta activity compared to the resting state. Conclusions-High-frequency thalamic deep brain stimulation (DBS) significantly reduces alpha oscillatory activity in the primary motor cortex of patients with ET, though this change is probably not critical for therapeutic efficacy. Significance-We demonstrate that ECoG can be effectively used to study the effect of subcortical stimulation on cortical oscillations.

HermesD is a high-rate, low-power wireless transmission system to aid research in neural prosthetic systems for motor disabilities and basic motor neuroscience. It is the third generation of our "Hermes systems" aimed at recording and transmitting neural activity from brain-implanted electrode arrays. This system supports the simultaneous transmission of 32 channels of broadband data sampled at 30 ks/s, 12 b/sample, using frequency-shift keying modulation on a carrier frequency adjustable from 3.7 to 4.1 GHz, with a link range extending over 20 m. The channel rate is 24 Mb/s and the bit stream includes synchronization and error detection mechanisms. The power consumption, approximately 142 mW, is low enough to allow the system to operate continuously for 33 h, using two 3.6-V/1200-mAh Li-batteries. The transmitter was designed using off-the-shelf components and is assembled in a stack of three 28 mm 28-mm boards that fit in a 38 mm 38 mm 51-mm aluminum enclosure, a significant size reduction over the initial version of HermesD. A 7-dBi circularly polarized patch antenna is used as the transmitter antenna, while on the receiver side, a 13-dBi circular horn antenna is employed. The advantages of using circularly polarized waves are analyzed and confirmed by indoor measurements. The receiver is a stand-alone device composed of several submodules and is interfaced to a computer for data acquisition and processing. It is based on the superheterodyne architecture and includes automatic frequency control that keeps it optimally tuned to the transmitter frequency. The HermesD communications performance is shown through bit-error rate measurements and eye-diagram plots. The Manuscript

Several studies have shown that memory consolidation relies partly on interactions between sensory and limbic areas. The functional loop formed by the olfactory system and the hippocampus represents an experimentally tractable model that can provide insight into this question. It had been shown previously that odor-learning associated beta band oscillations (15–30 Hz) of the local field potential in the rat olfactory system are enhanced with criterion performance, but it was unknown if these involve networks beyond the olfactory system. We recorded local field potentials from the olfactory bulb (OB) and dorsal and ventral hippocampus during acquisition of odor discriminations in a go/no-go task. These regions showed increased beta oscillation power during odor sampling, accompanied by a coherence increase in this frequency band between the OB and both hippocampal subfields. This coherence between the OB and the hippocampus increased with the onset of the first rule transfer to a new...

Synchronization of neuronal discharges has been hypothesized to play a role in defining cell assemblies representing particular constellations of stimulus features. In many systems and species, synchronization is accompanied by an oscillatory response modulation at frequencies in the γ-band. The cellular mechanisms underlying these phenomena of synchronization and oscillatory patterning have been studied mainly in vitro due to the difficulty in designing a direct in vivo assay. With the prospect of using conditional genetic manipulations of cortical network components, our objective was to test whether the mouse would meet the criteria to provide a model system for the study of γ-band synchrony. Multi-unit and local field potential recordings were made from the primary visual cortex of anesthetized C57BL/6J mice. Neuronal responses evoked by moving gratings, bars, and random dot patterns were analyzed with respect to neuronal synchrony and temporal patterning. Oscillations at γ-freq...

As an application of Roberts' cohomology (net cohomology), we prove the completeness of the DHR sectors of the local observables of the model in the title, detailed in . This result is achieved via the triviality of the net 1 -cohomology, with values in the local fields, enhancing the Roberts' methods to the case of anyonic Weyl nets, not satisfying the split property. We take advantage of using different causal index sets for the nets involved. The presence of anyonic commutation relations is treated introducing the notion of nets graded by a generic group, and the related properties of graded locality and graded duality. As a further result, we obtain the description of twisted and untwisted sectors of the model as two symmetric subcategories of a W * -braided category, whose objects are the same as the dual category of the compact Abelian group of the gauge symmetry. The work also furnish some hints for the analysis of the sector structure of generic models on different spacetimes.

The present work tackles the existence of local gauge symmetries in the setting of Algebraic Quantum Field Theory (AQFT). The net of causal loops, previously introduced by the authors, is a model independent construction of a covariant net of local C*-algebras on any 4-dimensional globally hyperbolic space-time, aimed to capture structural properties of any reasonable quantum gauge theory. Representations of this net can be described by causal and covariant connection systems, and local gauge transformations arise as maps between equivalent connection systems. The present paper completes these abstract results, realizing QED as a representation of the net of causal loops in Minkowski space-time. More precisely, we map the quantum electromagnetic field Fμν, not free in general, into a representation of the net of causal loops and show that the corresponding connection system and the local gauge transformations find a counterpart in terms of Fμν.

In 1977 he became a visiting assistant professor at Ohio State University. He became a tenure-track assistant professor the following year and moved up through the ranks, staying at OSU throughout the rest of his career. But he always kept a busy traveling schedule, making regular visits to both Strasbourg and Israel, where he had active collaborations for many years. He became professor emeritus at OSU in 2008 and passed away in 2012. The primary focus of Steve's research was automorphic forms, automorphic representations,

This paper introduces Neural Oscillation Signature Theory (NOST), a theoretical framework proposing that cognitive states can be inferred from linguistic output because neural oscillatory patterns systematically shape language production. The framework integrates established findings from cognitive neuroscience-particularly research on neural oscillations and their role in memory, attention, executive function, and emotional regulation-with insights from psycholinguistics regarding the cognitive processes underlying language production. The central theoretical claim is that the statistical properties of linguistic output (lexical, syntactic, semantic, temporal, and prosodic features) carry extractable information about the neural oscillatory configuration present during language generation. This paper articulates five core theoretical propositions, derives specific testable hypotheses organized by oscillatory frequency band, proposes the NOST Information Principle as a formal statement of the framework's foundational assumption, introduces the concept of Psychological Lense-Thirring Precession as a model for tracking cognitive integration dynamics, and discusses implications for cognitive assessment. The framework is offered as a theoretical contribution warranting empirical investigation rather than an established finding.

Objective: High frequency oscillations (HFOs) recorded from intracranial electrodes during epileptiform discharges have been proposed as a biomarker of epileptic brain sites and may also be a useful feature for seizure forecasting, with mixed results. Currently, pathological subclasses of HFOs have been defined primarily by frequency characteristics. Despite this, there has been limited investigation into the spatial context of HFOs with recruitment of local cortex into seizure discharging. We sought to further understand the biophysical underpinnings of ictal HFOs. Methods: Here we examine ictal HFOs from multi-scale electrophysiological recordings during spontaneous human rhythmic onset seizures. We compare features of ictal discharges in both the seizure core and penumbra, as defined by multiunit activity patterns. Results: We show marked differences in spectral features, unit coupling, and information theoretic characteristics of HFOs during ictal discharges before and after loc...

Energy loss of slow charged particles in a degenerate electron gas is calculated on the basis of the dielectric theory. The influence of dynamic local field correction is examined. A straightforward extension of this theory to problems that exceed the validity of the first Born approximation is discussed.

Focal cortical dysplasias (FCDs) are a common cause of brain seizures and are often associated with intractable epilepsy. Here we evaluated aberrant brain neurophysiology in an in vivo mouse model of FCD induced by neonatal freeze lesions (FLs) to the right cortical hemisphere (near S1). Linear multi-electrode arrays were used to record extracellular potentials from cortical and subcortical brain regions near the FL in anesthetized mice (5-13 months old) followed by 24 h cortical EEG recordings. Results indicated that FL animals exhibit a high prevalence of spontaneous spike-wave discharges (SWDs), predominately during sleep (EEG), and an increase in the incidence of hyper-excitable burst/suppression activity under general anesthesia (extracellular recordings, 0.5-3.0% isoflurane). Brief periods of burst activity in the local field potential (LFP) typically presented as an arrhythmic pattern of increased theta-alpha spectral peaks (4-12 Hz) on a background of low-amplitude delta act...

A common feature across neuropsychiatric disorders is inability to discontinue an action or thought once it has become detrimental. Reversal learning, a hallmark of executive control, requires plasticity within cortical, striatal and limbic circuits and is highly sensitive to disruption of N-methyl-D -aspartate receptor (NMDAR) function. In particular, selective deletion or antagonism of GluN2B containing NMDARs in cortical regions including the orbitofrontal cortex (OFC), promotes maladaptive perseveration. It remains unknown whether GluN2B functions to maintain local cortical activity necessary for reversal learning, or if it exerts a broader influence on the integration of neural activity across cortical and subcortical systems. To address this question, we utilized in vivo electrophysiology to record neuronal activity and local field potentials (LFP) in the orbitofrontal cortex and dorsal striatum (dS) of mice with deletion of GluN2B in neocortical and hippocampal principal cells while they performed touchscreen reversal learning. Reversal impairment produced by corticohippocampal GluN2B deletion was paralleled by an aberrant increase in functional connectivity between the OFC and dS. These alterations in coordination were associated with alterations in local OFC and dS firing activity. These data demonstrate highly dynamic patterns of cortical and striatal activity concomitant with reversal learning, and reveal GluN2B as a molecular mechanism underpinning the timing of these processes.

A common feature across neuropsychiatric disorders is inability to discontinue an action or thought once it has become detrimental. Reversal learning, a hallmark of executive control, requires plasticity within cortical, striatal and limbic circuits and is highly sensitive to disruption of N-methyl-D -aspartate receptor (NMDAR) function. In particular, selective deletion or antagonism of GluN2B containing NMDARs in cortical regions including the orbitofrontal cortex (OFC), promotes maladaptive perseveration. It remains unknown whether GluN2B functions to maintain local cortical activity necessary for reversal learning, or if it exerts a broader influence on the integration of neural activity across cortical and subcortical systems. To address this question, we utilized in vivo electrophysiology to record neuronal activity and local field potentials (LFP) in the orbitofrontal cortex and dorsal striatum (dS) of mice with deletion of GluN2B in neocortical and hippocampal principal cells while they performed touchscreen reversal learning. Reversal impairment produced by corticohippocampal GluN2B deletion was paralleled by an aberrant increase in functional connectivity between the OFC and dS. These alterations in coordination were associated with alterations in local OFC and dS firing activity. These data demonstrate highly dynamic patterns of cortical and striatal activity concomitant with reversal learning, and reveal GluN2B as a molecular mechanism underpinning the timing of these processes.

Parkinson's disease (PD) is characterized by aberrant discharge patterns and exaggerated oscillatory activity within basal ganglia-thalamocortical circuits. We have previously observed substantial alterations in spike and local field potential (LFP) activities recorded in the thalamic parafascicular nucleus (PF) and motor cortex (M1), respectively, of hemiparkinsonian rats during rest or catching movements. This study explored whether the mutual effects of the PF and M1 depended on the amplitude and phase relationship in their identified neuron spikes or group rhythmic activities. Microwire electrode arrays were paired and implanted in the PF and M1 of rats with unilateral dopaminergic cell lesions. The results showed that the identified PF neurons exhibited aberrant cell type-selective firing rates and preferential and excessive phase-locked firing to cortical LFP oscillations mainly at 12-35 Hz (beta frequencies), consistent with the observation of identified M1 neurons with ongoi...

Disruption of the function of the primary motor cortex (M1) is thought to play a critical role in motor dysfunction in Parkinson’s disease (PD). Detailed information regarding the specific aspects of M1 circuits that become abnormal is lacking. We recorded single units and local field potentials (LFPs) of M1 neurons in unilateral 6-hydroxydopamine (6-OHDA) lesion rats and control rats to assess the impact of dopamine (DA) cell loss during rest and a forelimb reaching task. Our results indicated that M1 neurons can be classified into two groups (putative pyramidal neurons and putative interneurons) and that 6-OHDA could modify the activity of different M1 subpopulations to a large extent. Reduced activation of putative pyramidal neurons during inattentive rest and reaching was observed. In addition, 6-OHDA intoxication was associated with an increase in certain LFP frequencies, especially those in the beta range (broadly defined here as any frequency between 12 and 35 Hz), which beco...

We prove the generalized induction equation and the generalized local induction equation (GLIE), which replaces the commonly used local induction approximation (LIA) to simulate the dynamics of vortex lines and thus superfluid turbulence. We show that the LIA is, without in fact any approximation at all, a general feature of the velocity field induced by any length of a curved vortex filament. Specifically, the LIA states that the velocity field induced by a curved vortex filament is asymmetric in the binormal direction. Up to a potential term, the induced incompressible field is given by the Biot-Savart integral, where we recall that there is a direct analogy between hydrodynamics and magnetostatics. Series approximations to the Biot-Savart integrand indicate a logarithmic divergence of the local field in the binormal direction. While this is qualitatively correct, LIA lacks metrics quantifying its small parameters. Regardless, LIA is used in vortex filament methods simulating the self-induced motion of quantized vortices. With numerics in mind, we represent the binormal field in terms of incomplete elliptic integrals, which is valid for R 3 . From this and known expansions we derive the GLIE, asymptotic for local field points. Like the LIA, generalized induction shows a persistent binormal deviation in the local-field but unlike the LIA, the GLIE provides bounds on the truncated remainder. As an application, we adapt formulae from vortex filament methods to the GLIE for future use in these methods. Other examples we consider include vortex rings, relevant for both superfluid 4 He and Bose-Einstein condensates.

In parts I and II, we determined which faithful irreducible representations $V$ of a simple linear algebraic group $G$ are generically free for Lie($G$), i.e., which $V$ have an open subset consisting of vectors whose stabilizer in Lie($G$) is zero, with some assumptions on the characteristic of the field. This paper settles the remaining cases, which are of a different nature because Lie($G$) has a more complicated structure and there need not exist general dimension bounds of the sort that exist in good characteristic.

Subthalamic nucleus (STN) deep brain stimulation (DBS) is an established treatment for the motor symptoms of Parkinson&#39;s disease (PD). However, the mechanisms of action of DBS are unknown. Random temporal patterns of DBS are less effective than regular DBS, but the neuronal basis for this dependence on temporal pattern of stimulation is unclear. Using a rat model of PD, we quantified the changes in behavior and single-unit activity in globus pallidus externa and substantia nigra pars reticulata during high-frequency STN DBS with different degrees of irregularity. Although all stimulus trains had the same average rate, 130-Hz regular DBS more effectively reversed motor symptoms, including circling and akinesia, than 130-Hz irregular DBS. A mixture of excitatory and inhibitory neuronal responses was present during all stimulation patterns, and mean firing rate did not change during DBS. Low-frequency (7-10 Hz) oscillations of single-unit firing times present in hemiparkinsonian ra...

We present a rigorous spectral programme connecting the Z 210 primorial lattice of the DUST framework to the Riemann Hypothesis (RH). Starting from the observation that primes are precisely the residue classes surviving an infinite primorial sieve, we construct the tower of finite groups G n = (Z/P n # Z) * whose inverse limit G ∞ is a profinite group carrying a canonical self-adjoint convolution operator H on ℓ 2 (G ∞). We prove: (i) self-adjointness of H via the Kato-Rellich theorem, giving σ(H) ⊂ R; (ii) an exact trace formula on each finite level via Poisson summation on the compact abelian group G n ; (iii) a spectral duality theorem k ↔ P n #k from character conjugation; and (iv) numerical verification that the Z 210 operator eigenvalue ordering achieves Spearman rank correlation 1.0000 with the first 48 Riemann zero heights. We then construct the primorial Cayley graph: the adjacency operator of Cay(G n , S n) where S n consists of prime residues. By the Lubotzky-Phillips-Sarnak theorem (1988), this graph is Ramanujan if and only if the Generalised Riemann Hypothesis (GRH) holds for the associated Dirichlet L-functions. The Riemann Hypothesis is therefore equivalent to the statement that the primorial Cayley graphs form a tower of Ramanujan expanders. We verify this at level n = 4 (Z 210 : largest non-trivial eigenvalue 5.500 < 2 √ 10 ≈ 6.325) and provide three families of falsifiable predictions.

A Galois scaffold is defined to be a variant of a normal basis that allows for an easy determination of valuation and thus has implications for the questions of the Galois module structure. We introduce a class of elementary abelian p-extensions of local function fields of characteristic p, which we call one-dimensional and which should be considered no more complicated than cyclic degree p extensions, and show that they, just as cyclic degree p extensions, possess a Galois scaffold.

Objective: The brain operates via generation, transmission and integration of neuronal signals and most neurological disorders are related to perturbation of these processes. Neurostimulation by Focused Ultrasound (FUS) is a promising technology with potential to rival other clinically-used techniques for the investigation of brain function and treatment of numerous neurological diseases. The purpose of this study was to characterize spatial and temporal aspects of causal electrophysiological signals directly stimulated by short, single pulses of focused ultrasound (FUS) on ex vivo mouse hippocampal brain slices. Approach: MicroElectrode Arrays (MEA) are used to study the spatio-temporal dynamics of extracellular neuronal activities both at the single neuron and neural networks scales. Hence, MEAs provide an excellent platform for characterization of electrical activity generated, modulated and transmitted in response to FUS exposure. In this study, a novel mixed FUS/MEA platform was designed for the spatio-temporal description of the causal responses generated by single 1.78 MHz FUS pulses in ex vivo mouse hippocampal brain slices. Main results: Our results show that FUS pulses can generate local field potentials (LFPs), sustained by synchronized neuronal post-synaptic potentials, and reproducing network activities. LFPs induced by FUS stimulation were found to be repeatable to consecutive FUS pulses though exhibiting a wide range of amplitudes (50 -600 µV), durations (20 -200 ms), and response delays (10 -60 ms). Moreover, LFPs were spread across the hippocampal slice following single FUS pulses thus demonstrating that FUS may be capable of stimulating different neural structures within the hippocampus. Significance: Current knowledge on neurostimulation by ultrasound describes neuronal activity generated by trains of repetitive ultrasound pulses. This novel study details the causal neural responses produced by single-pulse FUS neurostimulation while illustrating the distribution and propagation properties of this neural activity along major neural pathways of the hippocampus.

Cortical oscillations within or across brain regions play fundamental roles in sensory, motor, and memory functions. It can be altered by neuromodulations such as repetitive transcranial magnetic stimulation (rTMS) and pharmacological manipulations such as ketamine. However, the neurobiological basis of the effects of rTMS and ketamine, as well as their interactions, on cortical oscillations is not understood. In this study, we developed and applied a rodent model that enabled simultaneous rTMS treatment, pharmacological manipulations, and invasive electrophysiological recordings, which is difficult in humans. Specifically, a miniaturized C-shaped coil was designed and fabricated to deliver focal subthreshold rTMS above the primary somatosensory (S1) and motor (M1) cortex in rats. Multi-electrode arrays (MEA) were implanted to record local field potentials (LFPs) and single unit activities. A novel form of synchronized activities, poly population spikes (PPS), was discovered as the ...

We show how certain N-dimensional dynamical systems are able to exploit the full instability capabilities of their fixed points to do Hopf bifurcations and how such a behavior produces complex time evolutions based on the nonlinear combination of the oscillation modes that emerged from these bifurcations. For really different oscillation frequencies, the evolutions describe robust wave form structures, usually periodic, in which selfsimilarity with respect to both the time scale and system dimension is clearly appreciated. For closer frequencies, the evolution signals usually appear irregular but are still based on the repetition of complex wave form structures. The study is developed by considering vector fields with a scalar-valued nonlinear function of a single variable that is a linear combination of the N dynamical variables. In this case, the linear stability analysis can be used to design N-dimensional systems in which the fixed points of a saddle-node pair experience up to NϪ1 Hopf bifurcations with preselected oscillation frequencies. The secondary processes occurring in the phase region where the variety of limit cycles appear may be rather complex and difficult to characterize, but they produce the nonlinear mixing of oscillation modes with relatively generic features.