Journal articles on the topic 'Potentiels de Hertz'

In this letter, a new form of electromagnetic-quantum equations is proposed. The electric and magnetic potentials are expressed through a single Hertz vector, and the systems of quantum and Maxwell equations are transformed into more compact integro-differential ones. These new forms are given for the Schrödinger, Pauli, Dirac and Klein–Gordon equations, and a practical way to calculate them by available software tools is considered.

A three-dimensional cell-based mechanical model of coronary artery tunica media is proposed. The model is composed of spherical cells forming a hexagonal close-packed lattice. Tissue anisotropy is taken into account by varying interaction forces with the direction of intercellular connection. Several cell-centre interaction potentials for repulsion and attraction are considered, including the Hertz contact model and its neo-Hookean extension, the Johnson–Kendall–Roberts model of adhesive contact, and a wormlike chain model. The model is validated against data from in vitro uni-axial tension tests performed on dissected strips of tunica media. The wormlike chain potential in combination with the neo-Hookean Hertz contact model produces stress–stretch curves which represent the experimental data very well.

The distributed network of receptors, neurons, and synapses in the somatosensory system efficiently processes complex tactile information. We used flexible organic electronics to mimic the functions of a sensory nerve. Our artificial afferent nerve collects pressure information (1 to 80 kilopascals) from clusters of pressure sensors, converts the pressure information into action potentials (0 to 100 hertz) by using ring oscillators, and integrates the action potentials from multiple ring oscillators with a synaptic transistor. Biomimetic hierarchical structures can detect movement of an object, combine simultaneous pressure inputs, and distinguish braille characters. Furthermore, we connected our artificial afferent nerve to motor nerves to construct a hybrid bioelectronic reflex arc to actuate muscles. Our system has potential applications in neurorobotics and neuroprosthetics.

Representations of the electromagnetic and the average velocity field for a cold magnetised plasma are derived in terms of scalar potential functions. These Hertz potentials are solutions of a coupled system of integro-differential equations of second Qrder. Different from other approaches, the analysis is carried out in the time domain and is therefore especially suited for the investigation of transient wave phenomena. Furthermore, the dielectric tensor operator of the plasma is derived. Mter solving the system of integro-differential equations for a special limiting case, the applicability of the method presented is demonstrated and generalisations are discussed.

After a review of the coupled Newton's equations for a small alignment of grains with a fixed reflecting end wall, the equations are put into block diagrams of Simulink. Simulink simulations are given for 6 grain systems for cubic and Hertz intergrain potentials. The expected granular solitary waves are seen in the simulations. The block diagrams hence convert a single impulse into a traveling energy bundle of fixed width. This work forms the necessary first step for the eventual realization of the mathematical system represented by the granular chain as a Very Large Scale Integrated (VLSI) circuit.

In this paper, we investigate the tunable characteristics of shock waves propagating in one-dimensional magnetic granular chains at various chain lengths and magnetic flux densities. According to the Hertz contact theory and Maxwell principle, a discrete element model with coupling elastic and field-induced interaction potentials of adjacent magnetic grains is proposed. We also present hard-sphere approximation analysis to describe the energy partitioning features of magnetic granular chains. The results demonstrate that, for a fixed magnetic field strength, when the chain length is greater than two times of the wave width of the solitary wave, the chain length has little effect on the output energy of the system; for a fixed chain length, the shock absorption and energy partitioning features of magnetic granular chains are remarkably influenced by varying magnetic flux densities. This study implies that the magnetic granular chain is potential to construct adaptive shock absorption components for impulse mitigation.

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 slow-wave components of the SEP whereas VFO typically were later and of smaller amplitude. Regular spiking (RS) cells exhibited vibrissa-evoked 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.

As part of the goal of developing wearable sensor technologies, we have continued the development of a headset system for monitoring activity across the primary motor cortex of the brain. Through the combination of electroencephalography (EEG) and near-infrared spectroscopy (NIRS), the headsets are capable of monitoring event-related potentials and hemodynamic activity, which are wirelessly transmitted to a computer for real-time processing to generate control signals for a motorized prosthetic limb or a virtual embodiment of one or more limbs. This paper focuses on recent observations that have been made regarding the frequency content of EEG data, which we believe is responsible for the high performance we have previously reported using artificial neural networks to infer user’s intentions. While the inference engine takes advantage of frequency content from 0-128 Hertz (Hz), distinct fluctuations in alpha (8-13 Hz), beta (13-30 Hz), and gamma (30-100 Hz) frequency bands are human-observable across varying upper limb motor exercises when observed at the group level. In addition to prosthetic limbs, this technology is continuing to be investigated for application in areas including pain treatment, robotic arm control, lie detection, and more general brain-computer interfaces.

Background The 40-Hz auditory steady state response (40-Hz ASSR) provides a reliable marker of anesthetic-induced unconsciousness. Brain electric source analysis indicates that the 40-Hz ASSR arises from cortical and subcortical generators. The authors used source analysis to assess the effect of propofol anesthesia on the cerebral generators of the 40-Hz ASSR. They also examined the effect of propofol on two auditory evoked potentials of cortical origin: the N1 and the sustained potential. Methods Eleven healthy human volunteers were anesthetized with propofol given in target-concentration mode at the minimal concentration causing unconsciousness. The 40-Hz ASSR was recorded before, during, and after anesthesia. The source model consisted of five concurrently active generator dipoles: two in the contralateral auditory cortex (one tangentially oriented, one radially oriented), two in the ipsilateral auditory cortex (same orientations), and one in the midline brainstem. Results During anesthesia, the strength of the cortical and brainstem dipoles was reduced to the same extent (to 54% of baseline for the four cortical dipoles pooled vs. 53% for the brainstem dipole). Dipole strength during anesthesia was significantly less (P < 0.01) than during baseline and recovery for both cortical and brainstem dipoles. The N1 and sustained potential were no longer recordable during anesthesia. Conclusions The attenuation of the 40-Hz ASSR during propofol anesthesia results from a reduction of similar magnitude of the activity of the cortical and brainstem generators. The N1 and sustained potential are so profoundly attenuated during propofol anesthesia that they are no longer recordable from the scalp.

Some mathematical inconsistencies in the conventional form of Maxwell's equations extended by Lorentz for a single charge system are discussed. To surmount these in the framework of Maxwellian theory, a novel convection displacement current is considered as additional and complementary to the famous Maxwell displacement current. It is shown that this form of the Maxwell–Lorentz equations is similar to that proposed by Hertz for electrodynamics of bodies in motion. Original Maxwell's equations can be considered as a valid approximation for a continuous and closed (or going to infinity) conduction current. It is also proved that our novel form of the Maxwell–Lorentz equations is relativistically invariant. In particular, a relativistically invariant gauge for quasistatic fields has been found to replace the non-invariant Coulomb gauge. The new gauge condition contains the famous relationship between electric and magnetic potentials for one uniformly moving charge that is usually attributed to the Lorentz transformations. Thus, for the first time, using the convection displacement current, a physical interpretation is given to the relationship between the components of the four-vector of quasistatic potentials. A rigorous application of the new gauge transformation with the Lorentz gauge transforms the basic field equations into a pair of differential equations responsible for longitudinal and transverse fields, respectively. The longitudinal components can be interpreted exclusively from the standpoint of the instantaneous "action at a distance" concept and leads to necessary conceptual revision of the conventional Faraday–Maxwell field. The concept of electrodynamics dualism is proposed for self-consistent classical electrodynamics. It implies simultaneous coexistence of instantaneous long-range (longitudinal) and Faraday–Maxwell short-range (transverse) interactions that resembles in this aspect the basic idea of Helmholtz's electrodynamics.

Repetitive transcranial magnetic stimulation (rTMS) of human motor cortex can produce long-lasting changes in the excitability of excitatory and inhibitory neuronal networks. The effects of rTMS depend critically on stimulus frequency. The aim of our present study was to compare the effects of different rTMS protocols. We compared the aftereffects of 6 different rTMS protocols [paired associative stimulation at interstimulus intervals of 25 (PAS25) and 10 ms (PAS10); theta burst stimulation delivered as continuous (cTBS) or intermittent delivery pattern (iTBS); 1- and 5-Hz rTMS] on the excitability of stimulated and contralateral motor cortex in 10 healthy subjects. A pronounced increase of cortical excitability, evaluated by measuring the amplitude of motor evoked potentials (MEPs), was produced by iTBS (+56%) and PAS25 (+45%). Five-hertz rTMS did not produce a significant increase of MEPs. A pronounced decrease of cortical excitability was produced by PAS10 (−31%), cTBS (−29%), and 1-Hz rTMS (−20%). Short-interval intracortical inhibition was suppressed by PAS10. Cortical silent period duration was increased by 1-Hz stimulation. No significant effect was observed in the contralateral hemisphere. Head-to-head comparison of the different protocols enabled us to identify the most effective paradigms for modulating the excitatory and inhibitory circuits activated by TMS.

Zusammenfassung. Koronaranomalien sind mit dem plötzlichen Herztod assoziiert. Manchmal ist er der erste und einzige Hinweis für eine Koronaranomalie. Aufgrund der potentiell letalen Folgen wird bei jungen Patienten mit typischen Thoraxschmerzen oder einer Synkope beim Sport versucht, eine Koronaranomalie mittels kardialer Bildgebung auszuschliessen. Viel häufiger ist die Koronaranomalie aber ein Zufallsbefund in der Abklärung von Patienten mit Verdacht auf eine koronare Herzkrankheit oder in der Vorbereitung von Patienten für eine Pulmonalvenenisolation mittels der Herz-CT-Untersuchung. Die Prävalenz der Koronaranomalie liegt an unserem Zentrum bei 2.6 %. Einige von ihnen – wie die Koronaranomalien, die dem gegenüberliegenden Sinus Valsalva entspringen (sogenannte ACAOS, anomalous coronary arteries originating from the opposite site of the sinus of Valsalva), Koronarfisteln oder das Bland-White-Garland Syndrom – gehen mit einem erhöhten kardiovaskulären Risiko einher. Eine weiterführende Abklärung der hämodynamischen Relevanz der Koronaranomalie ist in diesen Fällen empfohlen – unabhängig davon, ob es sich um die Verdachtsdiagnose oder einen Zufallsbefund handelt. Idealerweise wird eine Durchblutungsuntersuchung mittels der Single-Photon-Emissions-Computertomographie (SPECT) oder der Positronen-Emissions-Tomographie (PET) durchgeführt, die eine Fusion mit der Herz-CT-Untersuchung erlauben. In der Hybridbildgebung kann die Koronaranomalie dann einem minderdurchbluteten Areal zugeordnet werden und von einer allenfalls begleitenden koronaren Herzkrankheit abgegrenzt werden. Das Alter des Patienten, die klinische Präsentation und der Befund der Bildgebung sind entscheidend für das weitere therapeutische Vorgehen. Bei fehlenden prospektiv-randomisierten Studien sind die Therapie-Empfehlungen allerdings meist nur auf Expertenmeinungen gestützt und sollen im Einzelfall eingehend mit dem Patienten und in der kardiologisch-thoraxschirurgischen Konferenz besprochen werden.

Background Suppression of response to command commonly indicates unconsciousness and generally occurs at anesthetic concentrations that suppress or eliminate memory formation. The authors sought midlatency auditory evoked potential indices that successfully differentiated wakeful responsiveness and unconsciousness. Methods The authors correlated midlatency auditory evoked potential indices with anesthetic concentrations permitting and suppressing response in 22 volunteers anesthetized twice (5 days apart), with desflurane or propofol. They applied stepwise increases of 0.5 vol% end-tidal desflurane or 0.5 microg/ml target plasma concentration of propofol to achieve sedation levels just bracketing wakeful response. Midlatency auditory evoked potentials were recorded, and wakeful response was tested by asking volunteers to squeeze the investigator's hand. The authors measured latencies and amplitudes from raw waveforms and calculated indices from the frequency spectrum and the joint time-frequency spectrogram. They used prediction probability (PK) to rate midlatency auditory evoked potential indices and concentrations of end-tidal desflurane and arterial propofol for prediction of responsiveness. A PK value of 1.00 means perfect prediction and a PK of 0.50 means a correct prediction 50% of the time (e.g., by chance). Results The approximately 40-Hz power of the frequency spectrum predicted wakefulness better than all latency or amplitude indices, although not all differences were statistically significant. The PK values for approximately 40-Hz power were 0.96 during both desflurane and propofol anesthesia, whereas the PK values for the best-performing latency and amplitude index, latency of the Nb wave, were 0.86 and 0.88 during desflurane and propofol (P = 0.10 for -40-Hz power compared with Nb latency), and for the next highest, latency of the Pb wave, were 0.82 and 0.84 (P < 0.05). The performance of the best combination of amplitude and latency variables was nearly equal to that of approximately 40-Hz power. The approximately 40-Hz power did not provide a significantly better prediction than anesthetic concentration; the PK values for concentrations of desflurane and propofol were 0.91 and 0.94. Changes of 40-Hz power values of 20% (during desflurane) and 16% (during propofol) were associated with a change in probability of nonresponsiveness from 50% to 95%. Conclusions The approximately 40-Hz power index and the best combination of amplitude and latency variables perform as well as predictors of response to command during desflurane and propofol anesthesia as the steady-state concentrations of these anesthetic agents. Because clinical conditions may limit measurement of steady-state anesthetic concentrations, or comparable estimates of cerebral concentration, the approximately 40-Hz power could offer advantages for predicting wakeful responsiveness.

ZusammenfassungDie frühe Kindheit ist ein kritisches Alter für die Entwicklung von chronischer Adipositas. Die Anhäufung von Fettgewebe während der Entwicklung und Progression der frühen Adipositas im Kindesalter tritt sowohl durch Hypertrophie als auch Hyperplasie der Adipozyten im Fettgewebe auf. Dabei ist die derzeit verbreitete Hypothese, dass die Anzahl der Adipozyten in der Kindheit bestimmt wird und während des gesamten Lebens relativ konstant bleibt, obwohl bis zu einem gewissen Grad eine ständige Erneuerung von Adipozyten durch die Proliferation und Differenzierung von im Fettgewebe vorhandenen adipogenen Vorläuferzellen stattfindet. Adipositas ist bereits in der frühen Kindheit mit Störungen in der Biologie und Funktion des weißen Fettgewebes assoziiert, einschließlich der Adipozytenhypertrophie, lokalen und systemischen inflammatorischen Prozessen, einer Remodellierung der extrazellulären Matrix und Fibrose, verstärkter Proliferation von adipogenen Vorläuferzellen und Störungen in der Adipokinsekretion. Diese Veränderungen in der Biologie und Funktion des Fettgewebes sind potentiell ursächliche Faktoren, welche zur Entwicklung von Adipositas-assoziierten Begleiterkrankungen, wie Diabetes und Herz-Kreislauf-Erkrankungen, im späteren Leben beitragen.

Background and Aim: Cerebrovascular brain incidents especially brain aneurysm ruptures are a major cause of death and disability. Monitoring Somatosensory Evoked Potential (SSEP) and corresponding changes are used for identifying cerebral ischemia and predicting neuronal injuries during using temporary clips in brain aneurysm surgeries. This approach limits integrated performance evaluation for somatosensory and cortex paths. Methods and Materials/Patients: This clinical trial study was conducted on the patients who were candidate for anterior cerebral circulation aneurysm surgery during 2017-2018 in Rasul Akram Hospital. SSEP monitoring was performed related to the median nerve in the contralateral wrist to examine the Middle Cerebral Artery (MCA) and posterior tibialis nerve in the contralateral ankle to examine Anterior Cerebral Artery (ACA) during the surgery procedure. Incentive parameters with a power of 5 to 25 milliampere and corresponding duration of 0.2 milliseconds and waves with a frequency of 3.3 Hertz were registered. Before locating temporary clips, SSEP was extracted as a baseline from every patient and then recorded. Results: Totally 9 patients (9 aneurysms) were studied. Three of them were men and 6 patients women. The age of patients ranged 39-78 years. The clinical status of patients was assessed using the Hunt-Hess scale. Five cases were classified as grade 1, 2 cases as grade 2, and 2 cases as grade 3. Among 9 aneurysms, 7 cases were about A.com artery and 2 cases were in connection with MCA artery, having the size of 5 to 11 millimeters. Friedman test was applied to explore average latency change percentage and amplitude change percentage in 1st, 2nd, and 3rd minutes for the 1st, 2nd, and 3rd clips where the results were significantly different (P=0.050). Conclusion: Neuromonitoring can be used as an index for examining tissue perfusion level of the brain and help to prevent accidental ischemic injuries of the brain followed by temporary clipping.

A surface method of groundwater prospecting using nuclear magnetic resonance (NMR) in the Earth’s magnetic field is under study. The technique is employed for hydrogeological surveys down to a depth of about 100 m. The advantage of this method is that an NMR signal can be observed only in the presence of groundwater. A circular wire loop with a diameter of 100 m is laid out on the ground to excite and receive the NMR signal. An oscillating current with a rectangular pulse‐shape is passed through the loop, with the carrier‐frequency being equal to the proton‐resonance frequency in the Earth’s field. The excitation pulse is followed by a nuclear induction emf caused by the free Larmor precession in the Earth’s field. Of practical importance is the effect of the electrical conductivity of the ground on a groundwater NMR survey. Finite‐ground conductivity can result in induced currents that can screen the NMR signal. The calculations of NMR signals are based on the transformation of Maxwell’s equations in terms of magnetic Hertz potentials through use of the reciprocity principle. Groundwater NMR is measured with an instrument designed at the Institute of Chemical Kinetics and Combustion, Russian Academy of Science, Novosibirsk. Experiments were conducted in the Altay region of Russia. Both NMR‐signal amplitude and phase, were measured and compared with the calculated results for horizontally stratified media. Borehole logs and vertical‐resistivity profiles were also used for evaluation of results. The conductivity is shown to affect both phase and amplitude of the NMR signal at resistivities of a few to a few tens of ohm‐m depending on the depth of the water‐saturated layers. There is good agreement between calculated and experimental data. It is also established that the measurements of only NMR amplitude and phase are not sufficient for determining groundwater salinity.

Introduction: Dysphagia often occurs during Parkinson’s disease (PD) and can have severe consequences. Recently, neuromodulatory techniques have been used to treat neurogenic dysphagia. Here we aimed to compare the neurophysiological and swallowing effects of three different types of neurostimulation, 5 Hertz (Hz) repetitive transcranial magnetic stimulation (rTMS), 1 Hz rTMS and pharyngeal electrical stimulation (PES). Method: 12 PD patients with dysphagia were randomised to receive either 5 Hz rTMS, 1 Hz rTMS, or PES. In a cross-over design, patients were assigned to one intervention and received both real and sham stimulation. Patients received a baseline videofluoroscopic (VFS) assessment of their swallowing, enabling penetration aspiration scores (PAs) to be calculated for: thin fluids, paste, solids and cup drinking. Swallowing timing measurements were also performed on thin fluid swallows only. They then had baseline recordings of motor evoked potentials (MEPs) from both pharyngeal and (as a control) abductor pollicis brevis (APB) cortical areas using single-pulse TMS. Subsequently, the intervention was administered and post interventional TMS recordings were taken at 0 and 30 minutes followed by a repeat VFS within 60 minutes of intervention. Results: All interventions were well tolerated. Due to lower than expected recruitment, statistical analysis of the data was not undertaken. However, with respect to PAs swallowing timings and MEP amplitudes, there was visual separation in a positive direction between active and sham groups for all interventions. Conclusion: PES, 5 Hz rTMS and 1 Hz rTMS are tolerable interventions in PD related dysphagia. Due to small patient numbers no definitive conclusions could be drawn from the data with respect to individual interventions improving swallowing function and comparative effectiveness between interventions. Larger future studies are needed to further explore the efficacy of these neuromodulatory treatments in Parkinson’s Disease associated dysphagia.

Zirpel, Lance, William R. Lippe, and Edwin W Rubel. Activity-dependent regulation of [Ca2+]i in avian cochlear nucleus neurons: roles of protein kinases A and C and relation to cell death. J. Neurophysiol. 79: 2288–2302, 1998. Neurons of the cochlear nucleus, nucleus magnocellularis (NM), of young chicks require excitatory afferent input from the eighth nerve for maintenance and survival. One of the earliest changes seen in NM neurons after deafferentation is an increase in intracellular calcium concentration ([Ca2+]i). This increase in [Ca2+]i is due to loss of activation of metabotropic glutamate receptors (mGluR) that activate second-messenger cascades involved in [Ca2+]i regulation. Because mGluRs are known to act via the phospholipase C and adenylate cyclase signal transduction pathways, the goal of this study was to determine the roles of protein kinases A (PKA) and C (PKC) activities in the regulation of NM neuron [Ca2+]i by eighth nerve stimulation. Additionally, we sought to determine the relationship between increased [Ca2+]i and cell death as measured by propidium iodide incorporation. [Ca2+]i of individual NM neurons in brain stem slices was monitored using fura-2 ratiometric fluorescence imaging. NM field potentials were monitored in experiments in which the eighth nerve was stimulated. Five hertz orthodromic stimulation maintained NM neuron [Ca2+]i at ∼110 nM for 180 min. In the absence of stimulation, NM neuron [Ca2+]i increased steadily to a mean of 265 nM by 120 min. This increase was attenuated by superfusion of PKC activators phorbol-12,13-myristate acetate (100 nM) or dioctanoylglycerol (50 μM) and by activators of PKA: 1 mM 8-bromoadenosine-3′,5′-cyclophosphate sodium (8-Br-cAMP), 50 μM forskolin or 100 μM Sp-adenosine 3′,5′-cyclic monophosphothioate triethylamine. Inhibition of PKA (100 μM Rp-cAMPS) or PKC (50 nM bisindolymaleimide or 10 μM U73122) during continuous orthodromic stimulation resulted in an increase in NM neuron [Ca2+]i that exceeded 170 and 180 nM, respectively, by 120 min. Nonspecific kinase inhibition with 1 μM staurosporine during stimulation resulted in an [Ca2+]i increase that was greater in magnitude than that seen with either PKA or PKC inhibition alone, equal to that seen in the absence of stimulation, but much smaller than that seen with inhibition of mGluRs. In addition, manipulations that resulted in a [Ca2+]i increase ≥250 nM resulted in an increase in number and percentage of propidium iodide-labeled NM neurons. These results suggest that eighth nerve activity maintains [Ca2+]i of NM neurons at physiological levels in part via mGluR-mediated activation of PKA and PKC and that increases in [Ca2+]i due to activity deprivation or interruption of the PKA and PKC [Ca2+]i regulatory mechanisms are predictive of subsequent cell death.

AbstractIn this publication, the Luneberg integrals are revisited and the conditions of the using of such integrals have been recalled. Additivity law of Luneberg’s integrals and the link with the Frenel kernel for the propagation are discussed. By means of the definition of the Luneberg’s integrals, the propagation of a vectorial electromagnetic field (Hertz potentials) is developed and a new approach of the computation have been proposed based on Zernike polynomials. With this new approach simulations of holograms is illustrated in the case of the digital in-line holography with an opaque disk.

ABSTRACTIn conductivity spectroscopy, ionic conductivities of solid electrolytes are measured continuously from a few Hertz up to the mid-infrared, i.e., in a frequency range covering more than twelve decades. In this paper we present experimental conductivity spectra of various cryst alline and glassy ionic conductors. Tracing the characteristic patterns of the spectra back to their generic processes provides a powerful means for probing the motion of the ions on atomic scales of space and time. The technique is particularly useful for exploring the single-particle potentials felt by the ions and, hence, for elucidating details of the surrounding structure. In our examples we discuss widths, anisotropies, and geometrical arrangements of sites in crystals as well as the existence of non-equivalent sites in glass.

This review article is a guide to work that uses the method of separation of variables for problems that occur in general relativity. The main emphasis is on recent progress in the solution of important systems of equations such as Dirac’s equation, Maxwell’s equations and the gravitational perturbation (or spin 2) equations. Recent advances and established results for these equations in Kerr black hole and Robertson—Walker space-time backgrounds form the central theme of the discussion. These two important physical examples also illustrate some of the difficulties in a theory of solution by separation of variables methods for systems of equations. Other aspects of this subject such as solutions of the Rarita-Schwinger equation (spin 3 2 ) and the role of generalized Hertz potentials are also discussed.

Our aim in this paper is to deal with integrability of maximal functions for Herz–Morrey spaces on the unit ball with variable exponent$p_{1}(\cdot )$approaching$1$and for double phase functionals$\unicode[STIX]{x1D6F7}_{d}(x,t)=t^{p_{1}(x)}+a(x)t^{p_{2}}$, where$a(x)^{1/p_{2}}$is nonnegative, bounded and Hölder continuous of order$\unicode[STIX]{x1D703}\in (0,1]$and$1/p_{2}=1-\unicode[STIX]{x1D703}/N>0$. We also establish Sobolev type inequality for Riesz potentials on the unit ball.

Background: Audiology clinics have many tools available to evaluate auditory and vestibular complaints. However, many tools lack established normative ranges across the life span. We conducted this study to establish reference ranges across the life span for audiology/ vestibular measures commonly used to evaluate patients with traumatic brain injury. Materials and Methods: In this repeated measures study, 75 adults, ages 18-65 years, without a history of traumatic brain injury, underwent robust auditory/vestibular evaluations three times over six months, including rotational chair, videonystagmography, computerized dynamic posturography, vestibular evoked myogenic potentials, and retinal fundoscopy. Results: Age effect was notable for transient evoked otoacoustic emissions, pure-tone audiometry, auditory brainstem response, auditory middle latency response, and auditory-steady state response at 4000 hertz (Hz). Older participants (50-65 years) were more likely to have delayed latency horizontal saccades, positional nystagmus, slowed lower-extremity motor control responses, and delayed latency ocular vestibular evoked myogenic potentials. Low to mid-frequency horizontal (0.003-4 Hz) and mid-frequency vertical (1-3 Hz) vestibulo-ocular reflex, otolith-mediated reflexes, dynamic visual acuity and balance measures were generally not influenced by age. Females had larger static subjective visual testing offset angles, longer cervical vestibular evoked myogenic potential P1 latency, faster velocity horizontal saccades, and quicker motor control latency for large backward translations than age-matched males. Conclusion: These reference ranges can be used to discern impairment within the auditory and vestibular pathway following traumatic brain injury in young to middle-aged adults.

<h1 align="left"><span style="font-family: Times New Roman;"><span style="font-size: medium;">1. Introduction.</span><span style="font-size: medium;"> </span><span style="font-size: medium;">Research using the event-related potential (ERP) technique has provided many important insights into the neural mechanisms associated with language comprehension. The integration of lexico-semantic information is associated with an increased centro-parietal negativity between 300-500 ms known as the N400 (Kutas & Federmeier, 2011; Kutas & Hillyard 1980). Morphosyntactic integration is associated with an early left anterior negativity (LAN) maximal around 200-500 ms, followed by a late posterior positivity (P600) maximal between 500 and 800 ms (see Kutas, Van Petten & Kluender (2005) for review). The P600, in absence of early negativity, is also elicited by well-formed sentences that present increased difficulty due to temporary ambiguity (i.e. garden-paths; Gouvea, Phillips, Kazanina & Poeppel, 2010; Osterhout, Holcomb & Swinney, 1994). The use of ERP as a means of indexing the different neural mechanisms associated with language processing is contingent on the assumption that all neurologically normal, native speakers show consistent responses to sentence stimuli such that the grand averaged ERPs reflect effects that are manifest uniformly across individuals. This notion was recently challenged by Tanner and Van Hell (2014). In their innovative study, they showed that, although in the grand mean syntactic violations elicited a classic biphasic LAN/P600 response, most participants either showed an N400 or a P600 rather than a biphasic response. Given the topographical distribution of the effects for each group, they concluded that the LAN often found for syntactic violations in grand mean analyses is the result of the distributed negativity in some subjects being neutralized or minimized by the right lateralized positivity in the others such that only the left anterior negativity remains. Response dominance did not, however, predict acceptability judgment accuracy, nor did it correlate with measures of working memory (WM) and executive control. </span></span></h1><p align="left"><span style="font-family: Times New Roman;">The individual differences in N400/P600 response dominance observed by Tanner and Van Hell (2014) lead to interesting questions regarding other contexts which tend to elicit these potentials. Garden-path sentences are known to elicit P600 effects in absence of early effects but there is some variability (Friederici, Mecklinger, Spencer, Steinhauer & Donchin, 2001; Gouvea et al., 2010; Horberg, Koptjevskaja-Tamm & Kallionen, 2013; Matzke, Mai, Nager, Russeler & Munte, 2002; Vos, Gunter, Schriefers & Friederici, 2001). This variablity could suggest the possibility of individual differences in response profiles, as Tanner and Van Hell (2014) found for syntactic violations. </span></p><p align="left"><span style="font-family: Times New Roman;">One known source of variability in garden-path effects for both P600s and comprehension accuracy is working memory capacity (WMC). High WMC individuals show greater P600 effects for garden-path sentences compared to low WMC individuals (Friederici, Steinhauer, Mecklinger, & Meyer, 1998). High WMC individuals also show reduced garden-path effects in comprehension accuracy such that they have better comprehension accuracy for garden-paths (Just & Carpenter, 1992). Lower comprehension accuracy in low WMC individuals indicates they are more likely to arrive at “Good Enough” interpretations (Ferreira, Bailey & Ferraro, 2002) in which the faithful interpretation of the sentence is not adopted. </span></p><p align="left"><span style="font-family: Times New Roman;">In the current study we applied the RDI analysis to the ERPs associated with garden-path sentences in order to determine (1) if participants’ N400/P600 dominance for garden-path sentences will fall into a continuum such that there will be a continuous distribution of N400 and P600 effect magnitudes with negative correlations between them, (2) if response dominance will predict comprehension accuracy, and (3), if so, is that effect reducible to individual differences in WMC.</span></p><p align="left"><span style="font-family: Times New Roman; font-size: small;"> </span></p><p align="left"><span style="font-family: Times New Roman; font-size: small;"> </span></p><p align="left"><strong><span style="font-family: Times New Roman;">2. Methods.</span></strong></p><p align="left"><span style="font-family: Times New Roman;">2.1. Participants.<strong> </strong>Data were collected from 62 right handed participants, 25 of which were excluded due to eligibility issues, technical issues, noncompliance, or excessive artifacts. As a result, 37 participants (20 female) between the ages of 18 and 35 (<em>M</em> = 21.6, <em>SD</em> = 3.21) were included in the analysis. All participants were right-handed, neurologically normal, native speakers of English with normal or corrected-to-normal vision, and none had had started learning a second language before age 12.</span></p><p align="left"><span style="font-family: Times New Roman;">2.2. Sentence Stimuli<strong> </strong>This experiment used the same control and garden-path sentences as O’Rourke & Colflesh (2014) (based on Gouvea et al., 2010). See sentences (1) and (2) for examples of garden-path and control sentences, respectively.</span></p><ol><li><p>The patient met the doctor and the nurse with the white dress <span style="text-decoration: underline;">showed</span> the chart during the meeting.</p></li><li><p>The patient met the doctor while the nurse with the white dress <span style="text-decoration: underline;">showed</span> the chart during the meeting.</p></li></ol><p align="left"><span style="font-family: Times New Roman;">There were 36 sentences per condition and an additional 288 sentences including fillers and conditions not presented herein. Fifty percent of the sentences were followed by a yes/no comprehension question. </span></p><p align="left"><span style="font-family: Times New Roman;">2.3. Complex Span Tasks. As indices of WMC, three complex span tasks were used in the current study: reading span (Daneman & Carpenter, 1980; Unsworth, Heitz, Schrock & Engle, 2005), operation span (Unsworth, et al., 2005), and symmetry span (Unsworth, Redick, Heitz, Broadway, & Engle, 2009). In the reading span task participants were presented with a series of sentences and asked to indicate, via button press, if the sentence they read made sense. After each sentence they were then presented with a letter that they were to remember for later recall. At the end of the sequence, they had to recall the letters in serial order. Their score reflects the total number of letters recalled in the correct serial position out of a total of 75 items. Operation span was identical to reading span as described above except instead of making sense judgments on sentences, participants had to read math problems involving two operations, one addition/subtraction and one multiplication/division, and verify if the solution provided was correct. Symmetry Span (Engle, 2005) is a complex span task like the aforementioned tasks, but it uses visuospatial stimuli. Participants were presented with a series of 8x8 black and white grids and asked to indicate, via button press, whether the design was vertically symmetrical. After each symmetry judgment they were presented with a 4x4 grid with a square filled in red that they were asked to remember for later recall. At the end of the sequence, participants had to recall the position of the red squares, in the order in which they appeared. The maximum score was 42.</span></p><p align="left"><span style="font-family: Times New Roman;">2.5. Procedure.<strong> </strong>Electroencephalographic (EEG) data was recorded using the Electrical Geodesics Inc. (EGI) Hydrocel 256 channel system while participants performed the sentence processing task. Sentences were presented word-by-word and participants responded to the comprehension questions with a button press. Data was collected over two sessions. Upon completion of the sentence processing task, participants performed the working memory assessments.</span></p><p align="left"><span style="font-family: Times New Roman;">2.6. Data Analysis. Upon completion of pre-processing and averaging, ERPs were computed for each individual for each experimental condition for a 1500 ms interval time-locked to the presentation of the critical verb (“showed” in the examples above) relative to a 200 ms pre-stimulus baseline. The following time windows were considered in the analysis of P600 effects: 300-500, 500-700 and 700-900 ms. The analyses were performed on midline and dorsal and electrodes. The midline electrodes were divided into anterior (FPZ, AFZ, FZ, FCZ, CZ) and posterior (CPZ, 90, PZ, POZ, OZ) sections. The dorsal electrodes were grouped by anterior-posterior (AP) location and hemisphere: Left anterior (FP1, AF3, F1, F3, FC3, C3), right anterior (FP2, AF4, F2, F4, FC4, C3), left posterior (CP3, CP1, P1, P3, P1, PO3, O1) and right posterior (CP4, CP1, P4, P2, PO4, O2). Sentence type effects in the ERP data were assessed in the dorsal regions with multiple three-way analysis of variance (ANOVA) (Sentence Type x AP x Hemisphere) and in the midline electrodes with a two-way ANOVA (Sentence Type x AP). RDI was then calculated using Tanner & Van Hell (2014)’s formula, using the same centro-parietal region of interest and time windows. Participants were divided into groups according to response dominance (N400 or P600). An analysis of covariance (ANCOVA) was run with garden-path comprehension accuracy as the dependent variable, RDI group as the independent variable and average, standardized WM score (average z-score for the three measures) as the covariate.</span></p><p align="left"><strong><span style="font-family: Times New Roman;">3. Results. </span></strong></p><p align="left"><span style="font-family: Times New Roman;">3.1. Sentence Type Effects.<strong> </strong>Accuracy for garden-path sentences (<em>M</em> = 68.3%, <em>SD</em> = 14.4) was significantly lower than control sentences (<em>M</em> = 73.6%, <em>SD</em> = 11.4; <em>F</em>(1,36) = 6.13, <em>p</em> < .05, <em>η<sub>p</sub><sup>2</sup></em> = .15). In the ERP data, garden-path sentences (compared to controls) showed a significant interaction of Type and AP over midline sites in the 500-700 and 700-900 ms time windows (<em>F</em>(1,36) = 4.18, <em>p</em> < .05, <em>η<sub>p</sub><sup>2</sup></em> = .10 and <em>F</em>(1,36) = 6.02, <em>p</em> < .05, <em>η<sub>p</sub><sup>2</sup></em> = .14, respectively) such that garden-paths elicited greater positivity than control sentences over posterior sites. Simple comparisons showed significant effects of type in posterior areas in both the 500-700 (<em>F</em>(1,36) = 4.14, <em>p</em> < .05, <em>η<sub>p</sub><sup>2</sup></em> = .10) and 700-900 time windows (<em>F</em>(1,36) = 4.93, <em>p</em> < .05, <em>η<sub>p</sub><sup>2</sup></em> = .12). There were no effects in the anterior sites. </span></p><p align="left"><span style="font-family: Times New Roman;">3.2. RDI Analysis.<strong> </strong>Analysis of N400 and P600 effect magnitudes for garden path sentences showed a strong negative correlation (<em>r</em>(32) = -.90; <em>p</em> < .001). The data suggest a continuum between strong N400 and P600 dominance. Participants were divided into groups based on RDI values (negative values indicating N400 dominance and positive indicating P600 dominance). A total of 18 participants were N400 dominant and 19 were P600 dominant. </span></p><p align="left"><span style="font-family: Times New Roman;">Prior to running the ANCOVA, it was necessary to determine that the covariates affected the dependent variable equally across the two groups. In the entire sample, there was a significant correlation between average complex span score and garden-path comprehension accuracy (<em>r</em>(32) = .52, p < .01). Each RDI group showed positive correlations (N400 dominant, <em>r</em>(14) = .63; P600 dominant, <em>r</em>(16) = .48). Using a Fisher transformation (Fisher, 1915), the difference between the group correlations was not significant (<em>z</em> = .6, <em>p</em> > .50). </span></p><p align="left"><span style="font-family: Times New Roman;">The ANCOVA showed that there was a significant effect of Response Dominance on GP Comprehension Accuracy after controlling for WMC, F(1,31) = 4.45, p < .05, <em>η<sub>p</sub><sup>2</sup></em> =.13) such that P600 dominant individuals had greater accuracy. Complex span performance accounted for a significant amount of variance (F(1,31) = 13.8, p < .005, <em>η<sub>p</sub><sup>2</sup></em> = .31).</span></p><p align="left"><span style="font-family: Times New Roman;"><strong>4. Discussion. </strong>The current study found evidence of distinct neural response profiles which were not apparent in the grand averaged data in neurologically normal, native English speakers during the processing of garden-path sentences and this individual differences measure predicted comprehension performance. The key finding of the current study is the effect of response dominance on behavioral performance. Response dominance emerged as an effective predictor of comprehension accuracy such that P600 dominant participants had better comprehension accuracy for garden-path sentences. The results of the ANCOVA show that response dominance is not a proxy for WMC but rather a distinct individual difference measure. This suggests that cognitive capacity alone does not limit the individual’s ability to resolve garden-paths. Response dominance may, instead, indicate the engagement of specific parsing strategies. The results of the current study extend the utility of Tanner and Van Hell (2014)’s RDI as an individual difference to the processing of the garden-path sentences showing that individuals in the sample exhibited distinct response profiles (either N400 or P600 dominant). While future research will reveal the neurocognitive underpinnings of response dominance, the findings of the current study establish this individual difference measure as a means of predicting behavior from neural activity. </span></p>