Search

In the context of so much uncertainty with coronavirus variants and official mandate based on seemingly exaggerated predictions of gloom from epidemiologists, it is appropriate to consider a revised model of relative simplicity, because there can be dangers in developing models which endeavour to account for too many variables. Predictions and projections from any such models have to be in the context of relevant contingencies. The model presented here is based on relatively simple second order difference equations. The context here is as important as the content in that in many Western counties where the narrative currently seems more important than the truth, and the results of empirical science are valued more as a shield for politicians than a sword for protection of citizens.,,,,,,,,,,

An unusual alternating reflection method on conics is presented to evaluate inverse trigonometric and hyperbolic functions.

PLPHP (pyridoxal-phosphate homeostasis protein) deficiency is caused by biallelic pathogenic variants in PLPBP and is a rare cause of pyridoxine-responsive disorders. We describe three French-Canadian individuals with PLPHP deficiency, including one with unusual paroxysmal episodes lacking EEG correlation with a suspicious movement disorder, rarely reported in B6RDs. In addition, we review the clinical features and treatment responses of all 51 previously published individuals with PLPHP deficiency. Our case series underlines the importance of considering PLPBP mutations in individuals with partially B6-responsive seizures and highlights the presence of a founder effect in the French-Canadian population.

Orthoptic curves for the conics are well known. It is the Monge's circle for ellipse and hyperbola, and for parabola it is its directrix. These conics are level sets of quadratic functions in the plane. We consider level sets of quadratic functions in higher dimension, known as quadric hypersurfaces. For these hypersurfaces we present and study their orthoptic sets, which extend the idea of orthoptic curves for conics.

A simple standard problem in physics is the study of elastic collisions between elements of an ideal system, which consists of two point masses and a wall. Based on energy and momentum conservation laws, solving the problem consists in finding the intersection of a straight line with a conic. Relationships between the solutions are easily obtained if we consider the right (fundamental) basis to express the solutions. The geometric interpretation follows easily: moving from one point to another on a conic using directions given by this basis. With simple changes in variables, reflections and rotations appear clearly. Similarities with other phenomena such as Heron’s reflection principle in optics and Kepler’s second law of planetary motion are pointed out.

This paper is a survey of topics related to Hermite interpolation. In the first part we present the standard analysis of the Hermite interpolation problem. Existence, uniqueness and error formula are included. Then some computational aspects are studied including Leibnitz' formula and devided differences for monomials. Moreover continuity and differentiation properties of divided differences are analyzed. Finally we represent Hermite polynomial with respect to different basis and give links between them.

Objective: The distinction of hypersynchronous (HYP) and low-voltage fast (LVF) onset seizures in mesial temporal lobe epilepsy (MTLE) is well established, but classifying individual seizures and patients is often challenging. Experimental work indicates a strong association of HYP with fast ripples (250–500 Hz) and of LVF with ripples (80–250 Hz). We aimed to investigate whether analysis of high-frequency oscillations can be useful for characterizing the process of seizure generation in human MTLE patients. Methods: We retrospectively compared 19 HYP and 14 LVF onset clinical seizures from ten and six consecutive MTLE patients with a predominance of the respective pattern. Five-second intervals of stereotactic EEGs from the seizure onset zone were selected, each representing the onset of HYP and LVF, the corresponding pre-ictal periods and, after the large spikes of HYP onsets, the LVF-like pattern that frequently followed. Results: Pre-ictal fast ripple density and rate were higher for HYP than for LVF seizures (p .05). Fast ripple (p

Standard numerical differentiation rules that might be established by the method of undetermined coefficients are revisited. Best truncation error bounds are established by a direct method and by the method of integration by parts "backwards". A new method to increase the order of the truncation error using a primitive is presented. This approach leads to corrected numerical differentiation rules. Differentiation formulae and numerical tests are presented.

Abstract Objective A vast network involving the nodules and overlying cortices is believed to be responsible for the epileptogenicity in gray matter heterotopia with multiple nodules, which often associated with difficult‐to‐treat epilepsy. We sought to determine if functional magnetic resonance imaging (fMRI) could detect internodular functional connectivity (FC), and if this connectivity reflects an actual synchronized neuronal activity and partakes in epileptogenicity. Methods We studied 16 epilepsy patients with multiple heterotopic nodules; eight underwent subsequent intracerebral EEG. We examined the internodular FC using fMRI and its correspondence with internodular synchrony of intracerebral interictal activity. We then compared the spreading speed of ictal activity between connected and unconnected nodules; and the FC among possible combinations of nodule pairs in terms of their involvement at seizure onset. Results Seventy nodules were studied: 83% have significant connection to at least one other nodule. Among the 49 pairs studied with intracerebral EEG, (1) synchronized interictal activity is more prevalent in fMRI‐connected pairs (P

Background: Epilepsy surgery failure is not uncommon, with several explanations having been proposed. In this series, we detail cases of epilepsy surgery failure subsequently attributed to insular involvement. Methods: We retrospectively identified patients investigated at the epilepsy monitoring units of two Canadian tertiary care centers (2004–2020). Included patients were adults who had undergone epilepsy surgeries with recurrence of seizures post-operatively and who were subsequently determined to have an insular epileptogenic focus. Clinical, electrophysiological, neuroimaging, and surgical data were synthesized. Results: We present 14 patients who demonstrated insular epileptic activity post-surgery-failure as detected by intracranial EEG, MEG, or seizure improvement after insular resection. Seven patients had manifestations evoking possible insular involvement prior to their first surgery. Most patients (8/14) had initial surgeries targeting the temporal lobe. Seizure recurrence ranged from the immediate post-operative period to one year. The main modality used to determine insular involvement was MEG (8/14). Nine patients underwent re-operations that included insular resection; seven achieved a favorable post-operative outcome (Engel I or II). Conclusions: Our series suggests that lowering the threshold for suspecting insular epilepsy may be necessary to improve epilepsy surgery outcomes. Detecting insular epilepsy post-surgery-failure may allow for re-operations which may lead to good outcomes.

Sleep spindles and K-complexes (KCs) are a hallmark of N2 sleep. While the functional significance of spindles is comparatively well investigated, there is still ongoing debate about the role of the KC: it is unclear whether it is a cortical response to an arousing stimulus (either external or internal) or whether it has sleep-promoting properties. Invasive intracranial EEG recordings from individuals with drug-resistant epilepsy offer a unique opportunity to study in-situ human brain physiology. To better understand the function of the KC, we aimed to (i) investigate the intracranial correlates of spontaneous scalp KCs, and (ii) compare the intracranial activity of scalp KCs associated or not with arousals. Whole-night recordings from adults with drug-resistant focal epilepsy who underwent combined intracranial-scalp EEG for pre-surgical evaluation at the Montreal Neurological Institute between 2010 and 2018 were selected. KCs were visually marked in the scalp and categorized according to the presence of microarousals: (i) Pre-microarousal KCs; (ii) KCs during an ongoing microarousal; and (iii) KCs without microarousal. Power in different spectral bands was computed to compare physiological intracranial EEG activity at the time of scalp KCs relative to the background, as well as to compare microarousal subcategories. A total of 1198 scalp KCs selected from 40 subjects were analyzed, resulting in 32,504 intracranial KC segments across 992 channels. Forty-seven percent of KCs were without microarousal, 30% were pre-microarousal, and 23% occurred during microarousals. All scalp KCs were accompanied by widespread cortical increases in delta band power (0.3–4 ​Hz) relative to the background: the highest percentages were observed in the parietal (60–65%) and frontal cortices (52–58%). Compared to KCs without microarousal, pre-microarousal KCs were accompanied by increases (66%) in beta band power (16–30 ​Hz) in the motor cortex, which was present before the peak of the KC. In addition, spatial distribution of spectral power changes following each KC without microarousal revealed that certain brain regions were associated with increases in delta power (25–62%) or decreases in alpha/beta power (11–24%), suggesting a sleep-promoting pattern, whereas others were accompanied by increases of higher frequencies (12–27%), suggesting an arousal-related pattern. This study shows that KCs can be generated across widespread cortical areas. Interestingly, the motor cortex shows awake-like EEG activity before the onset of KCs followed by microarousals. Our findings also highlight region-specific sleep- or arousal-promoting responses following KCs, suggesting a dual role for the human KC.

Hubs of brain networks are brain regions exhibiting denser connections than others, promoting long-range communication. Studies suggested the reorganization of hubs in epilepsy. The patterns of connector hub abnormalities specific to mesial temporal lobe epilepsy (mTLE) are unclear. We wish to quantify connector hub abnormalities in mTLE and identify epilepsy-related resting state networks involving abnormal connector hubs. A recently developed sparsity-based analysis of reliable k-hubness (SPARK) allowed us to address this question by using resting state functional MRI in 20 mTLE patients and 17 healthy controls. Handling the multicollinearity of functional networks, SPARK measures a new metric of hubness by counting the number (k) of networks involved in each voxel, and identifies which networks are actually associated to each connector hub. This measure provides new information about the network architecture involving connector hubs and a realistic range of k-hubness. We quantified the disruption and emergence of connector hubs in individual epileptic subjects and assessed the lateralization of networks involving connector hubs. In mTLE, we found pathological disruptions of normal connector hubs in the mTL and within the default mode network. Right mTLE had remarkably higher emergence of new connector hubs in the mTL than left mTLE. Different patterns of lateralization of the salience network involving the abnormal hippocampus were found in right versus left mTLE. The temporal, cerebellar, default mode, subcortical and motor networks also contributed to the lateralization of hippocampal networks. We finally observed an asymmetrical connector hub reorganization and overall regularization of epilepsy-related resting state networks in mTLE, characterized by the disruption of distant connections and the emergence of local connections. Keywords: Mesial temporal lobe epilepsy, Connector hub, Network regularization, Sparse dictionary learning, Resting state fMRI

Mixture problems are basic but important problems in Operations Research. In this paper we consider variants of the basic linear mixture problem and indicate mathematical links between them.

Objective: The stage of sleep is a known modulator of high-frequency oscillations (HFOs). For instance, high amplitude slow waves during NREM sleep and the subtypes of REM sleep were shown to contribute to a better separation between physiological and pathological HFOs. This study investigated rates and spatial spread of the different HFO types (physiological and pathological ripples in the 80–250 Hz frequency band, and fast ripples above 250 Hz) depending on time spent in sleep across the different sleep cycles. Methods: Fifteen patients with focal pharmaco-resistant epilepsy underwent one night of video-polysomnography during chronic intracranial EEG recording for presurgical epilepsy evaluation. The HFO rate and spread across the different sleep cycles were determined with an automatic HFO detector. We built models to explain the observed rate and spread based on time in sleep and other variables i.e. sleep stage, delta band and sigma band activity, and slow wave amplitude. Statistical significance of the different variables was determined by a model comparison using the Akaike information criterion. Results: The rate of HFOs depends significantly on the accumulated time of sleep. As the night advanced, the rate of pathological ripples and fast ripples decreased during NREM sleep (up to 15% per hour spent in the respective sleep stages), while the rate of physiological ripples increased during REM sleep (8% per hour spent in REM sleep). Interestingly, the stage of sleep but not the sleep cycle determined the extent of spread of HFOs, showing a larger field during NREM sleep and a more restricted field during REM sleep. Conclusion: The different dependence with sleep time for physiological and pathological ripples is in keeping with their distinct underlying generating mechanisms. From a practical point of view, the first sleep cycle seems to be best suitable for studying HFOs in epilepsy, given that the contrast between physiological and pathological ripple rates is largest during this time.

Objective: To explore the relationship between functional connectivity and presence of interictal epileptic discharges (IEDs) in different brain regions in intracranial EEG (iEEG). Methods: We studied 38 focal epilepsy patients who underwent simultaneous EEG/fMRI scanning and subsequent intracerebral stereo-EEG investigation. In EEG/fMRI analysis, IEDs with different spatial distributions were considered independent studies and IED-related maximal BOLD responses were evaluated. Studies with iEEG electrodes inside the maximal responses were selected and divided into three groups: Studies with 1. distinct maximal BOLD highly concordant with seizure-onset-zone (SOZ); 2. Moderate maximal BOLD concordant with SOZ; 3. maximal BOLD discordant with SOZ. Using maximal BOLD as seed, its functionally connected zone (FCZ) was determined. IED rates in iEEG channels inside and outside the FCZ were compared in the three groups. The effect of laterality and distance between channels and maximal BOLD, and correlation between functional connectivity values and IED rates were analyzed. Results: Thirty-six studies in 25 patients were included. IED rates of intracranial EEG channels inside the FCZ were significantly higher than outside in Group 1 (p = 2.6×10−6) and Group 2 (p = 1.2×10−3) and the inside-outside difference remained after regressing distance and laterality factors. In Group 1, connectivity values were significantly correlated with IED rates in channels inside the FCZ (p