First-order Kernel Research Articles

Effect of Hydropneumatic Components Nonlinearities on the CRONE Suspension

This paper presents a fractional system composed of a sprung mass and a suspension device with fractional impedance (fractance for short). More precisely, this fractance is a fractional integrator. Practical realizations of this fractional integrator based on hydropneumatic RC cells are presented in a limited frequency band. The main objective of this paper is to analyze the influence of the hydropneumatic RC cell nonlinearities, which constitute the hydropneumatic networks of the CRONE suspension, on the stability degree robustness when varying the sprung mass. First, the achievement of a nonlinear validation model is emphasized, and then, a linear synthesis model is presented. These two models are used in the second part of this paper to analyze the obtained performances and to show the influence of the nonlinearities. This analysis of performances is made first from a qualitative standpoint using the functional domain of each Ri and Ci element and then from the quantitative standpoint using the Volterra series. In fact, the difference between the response of the nonlinear model and the one of the first-order kernel (which represents the linear response of the system) allows the determination of the influence of the nonlinearities on the dynamic behavior for a particular signal input. The results obtained show that the RC cell nonlinearities composing the hydropneumatic networks of the CRONE suspension do not modify the stability degree robustness versus sprung mass variations, thus extending in a nonlinear context this robustness that is present in the linear context.

Multifocal electroretinogram in normal emmetropic subjects: Correlation with optical coherence tomography

Aim of the Study:To establish the normative database for multifocal electroretinogram (mfERG) parameters in a normal emmetropic population. To correlate the data so obtained with the central macular thickness obtained using the optical coherence tomography (OCT) scan.Materials and Methods:mfERG data were obtained from 222 eyes of 111 emmetropic subjects. The amplitude (nv/deg2) and implicit times (ms) of the first-order kernel mfERG responses (N1, P1, and N2 waves) were obtained and grouped into five rings (Ring 1: Central 2°, Ring 2: 2–5°, Ring 3: 5–10°, Ring 4: 10–15°, Ring 5: >15°). The central macular thickness (CMT) was obtained using the macular thickness scan protocol of the OCT.Results:The mfERG data obtained were used to create a normative database. The amplitudes of the mfERG waves were maximum in the fovea and progressively decreased with increasing eccentricity (P = 0.0001). The latencies of the P1 and N2 waves were longest in the central ring and progressively shortened with eccentricity (P = 0.0001). No statistically significant correlations were observed between central ring 1 parameters and the CMT.Conclusion:This study establishes normative database for mfERG parameters in an emmetropic population. No statistically significant correlation was noted between CMT and mfERG parameters.

Modelling of nonlinear bridge aerodynamics and aeroelasticity: a convolution based approach

Innovative bridge decks exhibit nonlinear behaviour in wind tunnel studies which has placed increasing importance on the nonlinear bridge aerodynamics/aeroelasticity considerations for long-span bridges. The convolution scheme concerning the first-order kernels for linear analysis is reviewed, which is followed by an introduction to higher-order kernels for nonlinear analysis. A numerical example of a long- span suspension bridge is presented that demonstrates the efficacy of the proposed scheme.

The effect of pentobarbital sodium and propofol anesthesia on multifocal electroretinograms in rhesus macaques

We compared the suitability of pentobarbital sodium (PB) and propofol (PF) anesthetics for multifocal electroretinograms (mfERGs) in rhesus macaques. mfERGs were collected from 4 ocularly normal rhesus macaques. All animals were pre-anesthetized with intramuscular ketamine (10-15 mg/kg). Intravenous PB induction/maintenance levels were 15 mg/kg/2-10 mg/kg and for PF, 2-5 mg/kg/6-24 mg/kg/h. There were 3 testing sessions with PB anesthesia and 5-7 testing sessions with PF anesthesia. All PB sessions were carried out before PF. First-order (K1) and second-order (first slice) kernels (K2.1) response density amplitude (RDA), implicit time (IT), and root mean square signal-to-noise ratios (RMS SNR) of the low-frequency (LFC) and high-frequency (HFC) components were evaluated. The use of PF or PB anesthesia resulted in robust, replicable mfERGs in rhesus macaques; however, RMS SNR of K1 LFC in ring and quadrant analyses was significantly larger for PF than for PB. Additionally, K1 RDA under PF was significantly larger than under PB for N1, P1, and P2 components (ring and quadrant) and for N2 (quadrant). PF IT was significantly prolonged (<1 ms) relative to PB IT for N1, P1 (ring), and N1 (quadrant), while PB IT was significantly prolonged (0.8-4.2 ms) relative to PF IT for N2 and P2 (ring and quadrant). K1 HFC and K2.1 LFC did not differ significantly between PB and PF in the ring or quadrant analyses. The response differences found with PB and PF anesthesia likely arise from variable relative effects of the anesthetics on retinal γ-aminobutyric acid (GABA(A)) receptors, and in part, on glycine and on glutamate receptors. Given the advantages of a stable anesthetic plane with continuous intravenous infusion and a smoother, more rapid recovery, PF is an appealing alternative for mfERG testing in rhesus macaques.

Central Retinal Function as Measured by the Multifocal Electroretinogram and Flicker Perimetry in Early Age-Related Macular Degeneration

To determine the retinal function in early age-related macular degeneration (AMD) assessed by the multifocal electroretinogram (mfERG) and flicker perimetry and to seek a relationship between local objective mfERG parameters and subjective flicker perimetry thresholds. mfERG and flicker perimetry were performed in 15 patients (15 eyes) with early AMD and 14 controls (14 eyes) of similar age. The mfERG P1 response amplitude density (nV/deg²) and P1 implicit time of the first-order kernel and the flicker thresholds of each concentric ring were analyzed. The relationship between individual mfERG responses and the corresponding individual flicker sensitivity outcomes was determined. The mfERG response amplitude of the central ring (ring 1) was significantly reduced in early AMD eyes compared with the controls (P = 0.009). No significant difference in mfERG amplitude between early AMD and control eyes was detected in the other rings. The mfERG implicit time was significantly increased in the early AMD eyes but only within the central four rings of 12°. A significant reduction in flicker sensitivity was also detected in early AMD eyes but only within the central 6°. There was a significant, moderate correlation (r = -0.477; P < 0.001) between local mfERG latency and flicker sensitivity from the same tested locations within the central 6°. There was a weak correlation (r = 0.200; P = 0.014) between mfERG amplitude and flicker sensitivity. Both mfERG and flicker perimetry show abnormal retinal function, but only in the very central macula, in early AMD. A novel relationship between mfERG and flicker sensitivity should enhance the clinical monitoring of disease progression.

Electrophysiological studies in newly onset type 2 diabetes without visible vascular retinopathy

The purpose of this study was to investigate the early alterations of retinal function, assessed with electrophysiology, in newly onset type 2 diabetes patients without vascular retinopathy. Seventeen patients with newly diagnosed type 2 diabetes (duration 7±3 months), without any vascular retinopathy in fundus photographs, were examined with full-field electroretinogram (ERG) and multifocal ERG (mfERG). The results were compared with those of age-matched subjects without diabetes. In the dark-adapted full-field ERG, the a-wave and the 30-Hz flicker implicit times were delayed in diabetes patients compared to controls, P=0.001 and P=0.020. In the first-order kernel of the mfERG, the first positive wave, P1, was delayed in all areas measured. The electrophysiological examinations demonstrate early alterations of retinal function characterised by a delayed a-wave implicit time in the dark-adapted full-field ERG, representing the rod signalling, and alterations in the multifocal ERG reflecting cone and/or postreceptoral function.

Investigation of the temporal properties of the retina using the m-sequence

The mfERG provides a topographic map of function of the retina and has been used in numerous studies to identify macular, paramacular and peripheral retinal dysfunction. This study investigates the changes in response due to the presentation rate of the stimulus. Twenty subjects gave informed consent to take part in the study, which had local regional ethical committee approval. Only a single hexagon of 8° diameter was presented to reduce ambiguity when identifying the higher-order kernels (HOK). Six rates were tested using a 60-Hz CRT monitor by introducing blank (black ~0 cd/m2) filler frames (FF). The rates tested were 0FF; 1FF; 2FF; 4FF; 7FF; and 14FF. The first-order kernel had largest responses to the slower stimuli (4FF and above). HOK had largest amplitudes at faster rates with the second-order kernel peaking at 1FF. At rates with 4FF and slower, the higher-order kernels were indiscernible above the noise.

A mixed corrected symmetric SPH (MC-SSPH) method for computational dynamic problems

In this work, a mixed corrected symmetric smoothed particle hydrodynamics (MC-SSPH) method is proposed for solving the non-linear dynamic problems, and is extended to simulate the fluid dynamic problems. The proposed method is achieved by improving the conventional SPH, in which the constructed process is based on decomposing the high-order partial differential equation into multi-first-order partial differential equations (PDEs), correcting the particle approximations of the kernel and first-order kernel gradient of SPH under the concept of Taylor series, and finally making the obtained local matrix symmetric. For the purpose of verifying the validity and capacity of the proposed method, the Burgersʼ and modified KdV–Burgersʼ equations are solved using MC-SSPH and compared with other mesh-free methods. Meanwhile, the proposed MC-SSPH is further extended and applied to simulate free surface flows for better illustrating the special merit of particle method. All the numerical results agree well with available data, and demonstrate that the MC-SSPH method possesses the higher accuracy and better stability than the conventional SPH method, and the better flexibility and extended application than the other mesh-free methods.

Follow-up study on multifocal electroretinogram of acute and convalescence stage of Vogt-Koyanagi-Harada syndrome

Background Researches showed that multifocal electroretinogram （mfERG） is able to assess the retinal function in the eyes with acute Vogt-Koyanagi-Harada （VKH） syndrome. But the mfERG characteristics of convalescence stage of VKH are still below clear. Objective Present study was to compare and follow up the variation process of visual acuity and mfERG in acute and recovery stages of VKH syndrome. Methods This was a clinic-based retrospective study. Visual acuity, mfERG and fundus fluorescence angiography （FFA） were recorded from 35 eyes of 18 acute VKH cases. The period of follow-up in recovery stage lasted about 18 months with the repetitive recording results for 4 times. Results In this study,the visual acuity range in acute stage VKH was 0.01 to 1.0, and 91.4% （32/35 eyes） was below 0.6. Compared with normal control group, the visual acuity wassignificantly decreased （ P〈0. O1 ）. The response densities （amplitudes） of N,, PI waves of the first-order kernel were significantly lowed in all the 6 rings,and the implicit times of 1-4 rings of both waves were significantly prolonged in acute VKH eyes（P〈0.05 ）. The abnormalities of retinal function showed a regional difference at the posterior pole retina with the dominant change in the first ring,showing a cutting off 78% in the PI amplitude. The abnormal degree of mfERG was more serious as the the increase of retinal eccentricity. In 2 months of convalescence after glucocorticosteroids therapy, the range of visual acuity were 0. 1-1.2, and the amplitudes of N1 ,Pl of 1-2 rings were greatly elevated in comparison with acute on-set （P〈0.05）. However, there was still a remarkable difference in the amplitudes of from 1 through 6 rings,comparing with normal. The response density of Pl wave from whole recording region was only 44% of normal. Though the visual acuity was stable during the follow-up duration, a decreasing tendency in NI and PI amplitudes were seen. The implicit times of both wave shortened only in 1-3 rings in recovery stages of VKH （ P 〈 0. 05 ）. Conclusion VKH syndrome cause serious damage of posterior retinal function. Macular region is the site with greater retinal functional lesion and restore before and after medication. This hardly recovery of retinal function can last over one and half year, even satisfied visual acuity is stable after proper treatment. Key words: Vogt-Koyanagi-Harada syndrome; Visual acuity; Multifocal electroretinogram

Principal components′ analysis of multifocal electroretinogram in retinitis pigmentosa

Aims:To determine waveforms of multifocal electroretinogram (mfERG) in patients with retinitis pigmentosa (RP) contributing significantly to the overall retinal response by using principal components’ analysis.Settings and Design:Prospective, non-randomized, single-visit, observational, case-control study from a single tertiary ophthalmic center.Materials and Methods:Patients with various forms of RP underwent mfERG testing for a period of one year. The first-order kernel responses of RP cases were compared with concurrently recruited healthy controls.Statistical Analysis Used:Parametric data was analyzed using the unpaired t test for differences between the implicit time and amplitudes of cases and controls. Principal components’ analysis was done for each implicit time and amplitude in cases with RP using the Varimax rotation method.Results:From March 2006 to March 2007, 24 cases with typical RP (56%, 47 eyes) were included in the final analysis. Their mean age was 33.7 years (19-69 ± 15.5 years). Comparison of latencies and amplitudes among RP cases with log MAR acuity ≤ 0.18 and those > 0.18, revealed significant difference in the implicit time (P1) in Ring 2 only (P=0.028). Two components (predominently from Ring 1 and 2) each contributing 66.8% and 88.8% of the total variance in the data for latencies and amplitudes respectively, were seen.Conclusions:The first two rings of the mfERG contributed to the variance of waveforms in RP, irrespective of the visual acuity and poor visual field results.

Analysis of multifocal electroretinogram first-order kernel P(1) wave in anisometropic amblyopia

To investigate the features of the multifocal electroretinogram (mfERG) first-order kernel P(1) wave in anisometropic amblyopic eyes. mfERG of fifteen anisometropic amblyopic eyes and their normal control eyes were recorded with ROLAND RETIscan visual evoked response system, the mean amplitude density and eclipse period of the P(1) wave were analyzed and compared between the amblyopic and normal eyes with t-test. The P(1) wave amplitude density of mfERG first-order kernel in amblyopic eyes (164.7 ± 73.1) nV×deg(-2) was significantly attenuated in the central region of the visual field as compared with that of the control eyes (227.0 ± 61.3) nV×deg(-2) (t = 2.554, P = 0.016). The eclipse period of the amblyopic eyes (30.3 ± 4.3) ms was shorter than that of the control eyes (34.4 ± 3.2) ms (t = 2.92, P = 0.007). The significant change of the multifocal electroretinogram (mfERG) first-order kernel P(1) wave may reflect the abnormality of the retinal on-bipolar cells function and the visual information transmission, whether the P(1) wave could be used as an objective index of amblyopic eyes is a promising research topic.

Evaluation of focal retinal function using multifocal electroretinography in patients with X-linked retinoschisis

Objective: To evaluate focal retinal function in patients presenting with features of X-linked retinoschisis (XLRS), with the use of multifocal electroretinography (mfERG). Design: Consecutive observational case-control study. Participants: Eighteen eyes of 9 patients who presented to the retina clinic of Sankara Nethralaya from 2005 to 2008. Methods: XLRS was diagnosed clinically and corroborated with full-field electroretinogram (ffERG), mfERG, and optical coherence tomography. ffERG and mfERG recordings were done with VERIS 5.2.2X according to International Society for Clinical Electrophysiology of Vision standards. The mfERG stimulus consisted of 103 hexagons flickered at a 75 Hz frame rate, subtended 35° horizontally and 31° vertically at a viewing distance of 53 cm. The amplitudes and implicit times of ffERG and first-order kernels of mfERG were analyzed and compared with those of the controls. Results: P1 and N1 amplitudes were reduced and P1 and N1 implicit times were prolonged significantly in patients with XLRS, compared with controls. Conclusions: mfERG helps estimate focal retinal function in patients with XLRS.

Minor effect of blue-light filtering on multifocal electroretinograms

To assess the impact of blue-light filtering on retinal processing to evaluate potential side effects of these filters on visual function at the neural level. Department of Ophthalmology, Otto-von-Guericke-University Magdeburg, Magdeburg, Germany. Cohort study. Multifocal electroretinograms (ERGs) were recorded monocularly after pupil dilation in pseudophakic patients with a colorless intraocular lens (IOL) under 2 conditions: (1) stimulus perception through a yellow-tinted filter with the filter characteristics of the AF-1 YA-60BB IOL (blue-light filter) and (2) stimulus perception through a neutral filter that homogeneously attenuates the effective stimulus intensity like the blue-light filter independent of the wavelength. First-order kernel multifocal ERGs were extracted at 61 visual field locations and averaged for 5 stimulus eccentricities. Amplitudes and implicit times were determined for the multifocal ERG components N1 (first negative deflection), N2 (second negative deflection), and P1 (first positive deflection). The study evaluated 20 patients. Typical multifocal ERGs were obtained for both conditions at all eccentricities. There were no significant differences in amplitudes or implicit times between the 2 conditions except for a slight P1 amplitude enhancement (6.9%) with the blue-light filter at an intermediate eccentricity (P = .003). The bipolar cell-dominated multifocal ERG was largely unaffected by short-term effects of blue-light filtering. The induced change in the spectral composition of the stimulus did not significantly alter the activity at the input stage of the visual system, specifically the retinal network comprising photoreceptors, horizontal cells, and bipolar cells.

Evaluation of functional integrity of the retinohypothalamic tract in advanced glaucoma using multifocal electroretinography and light-induced melatonin suppression

The aim of the study was to investigate the survival of melanopsin-expressing retinal ganglion cells (mRGCs) and the functional integrity of the retinohypothalamic tract in patients with bilateral advanced glaucomatous optic neuropathy by measuring the neuroendocrine light response of the pineal gland. Nine patients with bilateral advanced primary open-angle glaucoma (glaucoma group) and nine normal control subjects (control group) were included in this pilot observational, prospective, case-control study. The best-corrected visual acuity logMAR, standard automated perimetry mean deviation, and the retinal nerve fiber layer thickness determined by optical coherence tomography and multifocal electroretinography were used to evaluate the changes. Melatonin was analyzed in the saliva by radioimmunoassay before and after exposure to bright light (600 lux) for 60 min at night. The advanced glaucoma group did not have any significant nocturnal melatonin suppression after exposure to bright light (14.28 ± 3.07 pg/ml pre-light melatonin concentration vs. 15.22 ± 3.56 pg/ml after light exposure; p = 0.798) unlike the marked melatonin suppression in the control group (22.43 ± 4.37 pg/ml pre-light melatonin concentration vs. 11.25 ± 1.89 pg/ml after light exposure; p < 0.002). Response density estimates by the scalar product amplitude measure for the interval 0–80 ms of the first-order kernel responses were similar in both groups, indicating that outer retinal function was significantly unchanged in the glaucoma group (5.95 ± 0.54 nV/dg^2) compared with the control group (6.20 ± 0.22 nV/dg^2) ( p = 0.689). Our findings are consistent with the interpretation that the rhythmic secretion of melatonin was affected in advanced glaucoma, suggesting that attention should be paid to non-image-forming visual functions, such as control of circadian rhythm and the clinical impact in patients with glaucoma.

Basilar-membrane responses to broadband noise modeled using linear filters with rational transfer functions.

Basilar-membrane responses to white Gaussian noise were recorded using laser velocimetry at basal sites of the chinchilla cochlea with characteristic frequencies near 10 kHz and first-order Wiener kernels were computed by cross correlation of the stimuli and the responses. The presence or absence of minimum-phase behavior was explored by fitting the kernels with discrete linear filters with rational transfer functions. Excellent fits to the kernels were obtained with filters with transfer functions including zeroes located outside the unit circle, implying nonminimum-phase behavior. These filters accurately predicted basilar-membrane responses to other noise stimuli presented at the same level as the stimulus for the kernel computation. Fits with all-pole and other minimum-phase discrete filters were inferior to fits with nonminimum-phase filters. Minimum-phase functions predicted from the amplitude functions of the Wiener kernels by Hilbert transforms were different from the measured phase curves. These results, which suggest that basilar-membrane responses do not have the minimum-phase property, challenge the validity of models of cochlear processing, which incorporate minimum-phase behavior.

3-D visualizations of coastal bathymetry by utilization of airborne TOPSAR polarized data

Multi-frequency C and L bands in the TOPSAR data have been utilized to reconstruct three-dimensional (3-D) bathymetry pattern. The main objective of this study is to utilize fuzzy arithmetic to reduce the errors arising from speckle in synthetic aperture radar (SAR) data when constructing ocean bathymetry from polarized SAR data. In doing so, two 3-D surface models, the Volterra algorithm and a fuzzy B-spline (FBS) algorithm, which construct a global topological structure between the data points, were used to support an approximation to the real surface. Volterra algorithm was used to express the non-linearity of TOPSAR data intensity gradient based on the action balance equation (ABC). In this context, a first-order kernel of Volterra algorithm was used to express ABC equation. The inverse of Volterra algorithm then performed to simulate 2-D current velocities from CVV and LHH band. Furthermore, the 2-D continuity equation then used to estimate the water depth. In order to reconstruct 3-D bathymetry pattern, the FBS has been performed to water depth information which was estimated from 2-D continuity equation. The best reconstruction of coastal bathymetry of the test site in Kuala Terengganu, Malaysia, was obtained with polarized L and C bands SAR acquired with HH and VV polarizations, respectively. With 10 m spatial resolution of TOPSAR data, bias of –0.004 m, the standard error mean of 0.023 m, r 2 value of 0.95, and 90% confidence intervals in depth determination was obtained with LHH band.

Memory effects for the heat conductivity of random suspensions of spheres

The presence of a particulate phase defines the effective response of a suspension to changes of the average heat flux. Using the random-point approximation we show that within the first order in the concentration, one needs to solve the problem for the temperature field created by a single inclusion in a matrix subject to an unsteady temperature gradient at infinity. We solve this problem by means of Laplace transform and use the solution as the first-order kernel in the functional expansion. From this kernel, we find the statistical average for the heat flux, which turns out to be a memory integral of the spatially averaged time-dependent temperature gradient. Thus, we discover that the constructive relationship between the average flux and averaged temperature gradient is not local in time, but rather involves a convolution integral that represents the memory due to the heterogeneity of the system. This is a novel result, which inter alia gives a rigorous justification to the usage of generalizations of the heat conduction law involving fractional time derivatives. The decay of the kernel is very close to t −1/2 for dimensionless times lesser than one and abruptly changes to t −3/2 for larger times.

Serial multifocal electroretinograms during long-term elevation and reduction of intraocular pressure in non-human primates

The purpose of this study was to evaluate the relationship between elevations of intraocular pressure (IOP) and the multifocal electroretinogram (mfERG) in non-human primates. Experimental glaucoma was induced in 4 rhesus and 4 cynomolgus monkeys by laser trabecular meshwork destruction (LTD) in one eye. To evaluate the contribution of ganglion cells to mfERG changes, one monkey of each species had previously underwent unilateral optic nerve transection (ONT). After >or=44 weeks of elevation, the IOP was reduced by trabeculectomy in 2 non-transected animals. In the intact (non-transected) animals, there was an increase in the amplitude of the early mfERG waveforms (N1 and P1) of the first-order kernel (K1) throughout the period of IOP elevation in all of the rhesus, but not all of the cynomolgus monkeys. A species difference was also present as a decrease of the second-order kernel, first slice (K2.1) in all of the cynomolgus monkeys but only in 1 of the rhesus monkeys (the 1 with the ONT). Similar IOP effects on the mfERG were seen in the ONT animals. Surgical lowering of IOP resulted in a return of the elevated K1 amplitudes to baseline levels. However, the depressed K2.1 RMS in the cynomolgus monkeys did not recover. These results demonstrate species-specific changes in cone-driven retinal function during periods of elevated IOP. These IOP-related effects can occur in the absence of retinal ganglion cells and may be reversible.

System characterization of neuronal excitability in the hippocampus and its relevance to observed dynamics of spontaneous seizure-like transitions

Most forms of epilepsy are marked by seizure episodes that arise spontaneously. The low-magnesium/high-potassium (low-Mg2+/high-K+) experimental model of epilepsy is an acute model that produces spontaneous, recurring seizure-like events (SLEs). To elucidate the nature of spontaneous seizure transitions and their relationship to neuronal excitability, whole-cell recordings from the intact hippocampus were undertaken in vitro, and the response of hippocampal CA3 neurons to Gaussian white noise injection was obtained before and after treatment with various concentrations of low-Mg2+/high-K+ solution. A second-order Volterra kernel model was estimated for each of the input–output response pairs. The spectral energy of the responses was also computed, providing a quantitative measure of neuronal excitability. Changes in duration and amplitude of the first-order kernel correlated positively with the spectral energy increase following treatment with low-Mg2+/high-K+ solution, suggesting that variations in neuronal excitability are coded by the system kernels, in part by differences to the profile of the first-order kernel. In particular, kernel duration was more sensitive than amplitude to changes in spectral energy, and correlated more strongly with kernel area. An oscillator network model of the hippocampal CA3 was constructed to investigate the relationship of kernel duration to network excitability, and the model was able to generate spontaneous, recurrent SLEs by increasing the duration of a mode function analogous to the first-order kernel. Results from the model indicated that disruption to the dynamic balance of feedback was responsible for seizure-like transitions and the observed intermittency of SLEs. A physiological candidate for feedback imbalance consistent with the network model is the destabilizing interaction of extracellular potassium and paroxysmal neuronal activation. Altogether, these results (1) validate a mathematical model for epileptiform activity in the hippocampus by quantifying and subsequently correlating its behavior with an experimental, in vitro model of epilepsy; (2) elucidate a possible mechanism for epileptogenesis; and (3) pave the way for control studies in epilepsy utilizing the herein proposed experimental and mathematical setup.

A class of asymptotically normal degenerate quasi U-statistics

Some quasi U-statistics, unlike other variants of U-statistics, arising in distance based tests for homogeneity of groups, have first-order stationary kernels of degree 2, and yet they enjoy asymptotic normality under suitable hypotheses of invariance. Central limit theorems for a more general class of quasi U-statistics with possibly higher order stationarity (and degree) are formulated with the aid of appropriate martingale (array) characterizations as well as permutational invariance structures.