Search

Importance: Many individuals with drug-resistant epilepsy continue to have seizures after resective surgery. Accurate identification of focal brain abnormalities is essential for successful neurosurgical intervention. Current clinical approaches to identify structural abnormalities for surgical targeting in epilepsy do not use diffusion-weighted MRI (dMRI), despite evidence that dMRI abnormalities are present in epilepsy and may relate to the epileptogenic zone. Objective: To investigate whether surgical resection of diffusion abnormalities relates to post-operative seizure freedom. Design: This retrospective case-control study was conducted between 2009 and 2022. Data were acquired at the National Hospital for Neurology and Neurosurgery, UK. Study participants included 200 individuals with drug-resistant focal epilepsy, who underwent resective surgery, and 97 healthy controls used as a normative baseline. Main Outcomes: Spatial overlap between diffusion abnormality clusters and surgical resection masks, and relation to post-surgical outcome. Results: Surgical resections overlapping with the largest abnormal cluster significantly correlated with sustained seizure freedom at 12 months (83% vs 55%; p<0.0001) and over five years (p<0.0001). Notably, resecting only a small proportion of the largest cluster was associated with better seizure outcomes than cases with no resection of this cluster (p=0.008). Furthermore, sparing the largest cluster but resecting other large clusters still improved seizure freedom rates compared to no overlap (p=0.03). Conclusions: Our results suggest that abnormal clusters, identified using dMRI, are integral to the epileptogenic network, and even a partial removal of such an abnormal cluster is sufficient to achieve seizure freedom. The study highlights the potential of incorporating dMRI into pre-surgical planning to improve outcomes in focal epilepsy.

Stage IV large scale structure surveys are promising probes of gravity on cosmological scales. Due to the vast model-space in the modified gravity literature, model-independent parameterisations represent useful and scalable ways to test extensions of $\Lambda$CDM. In this work we use a recently validated approach of computing the non-linear $3\times 2$pt observables in modified gravity models with a time-varying effective gravitational constant $\mu$ and a gravitational slip $\eta$ that is binned in redshift to produce Fisher forecasts for an LSST Y10-like survey. We also include in our modelling an effective nulling scheme for weak-lensing by applying the BNT transformation that localises the weak-lensing kernel enabling well-informed scale cuts. We show that the combination of improved non-linear modelling and better control of the scales that are modelled/cut yields high precision constraints on the cosmological and modified gravity parameters. We find that 4 redshift bins for $\mu$ of width corresponding to equal incremental $\Lambda$CDM growth is optimal given the state-of-the-art modelling and show how the BNT transformation can be used to mitigate the impact of small-scale systematic effects, such as baryonic feedback., Comment: 27 pages, 12 figures A few typos corrected and a couple of small changes made to the text to improve presentation of results, added missing reference. Comments welcome!

We provide a mode-sum prescription to directly compute the renormalized stress-energy tensor (RSET) for scalar fields in the Boulware vacuum. The method generalizes the recently developed extended coordinate method which was previously only applicable to Hartle-Hawking states. We exhibit the accuracy and efficiency of the method by calculating the RSET in sub-extremal and extremal Reissner-Nordstr\"om spacetimes. We find numerical evidence for the regularity of the RSET at the extremal horizon regardless of the field mass and its coupling. We employ our numerical results of the RSET to source the semi-classical Einstein equations, demonstrating that if the RSET is considered as a static perturbation, it will either de-extremalize the black hole, or convert it into a horizonless object., Comment: 21 pages, 6 figures

Anti-seizure medications (ASMs) are the mainstay of treatment for epilepsy, yet their effect on seizure spread is not fully understood. Higher ASM doses have been associated with shorter and less severe seizures. Our objective was to test if this effect was due to limiting seizure spread through early termination of otherwise unchanged seizures. We retrospectively examined intracranial EEG (iEEG) recordings in 15 subjects that underwent ASM tapering during pre-surgical monitoring. We estimated ASM plasma concentrations based on pharmaco-kinetic modelling. In each subject, we identified seizures that followed the same onset and initial spread patterns, but some seizures terminated early (truncated seizures), and other seizures continued to spread (continuing seizures). We compared ASM concentrations at the times of truncated seizures and continuing seizures. We found no substantial difference between ASM concentrations when truncated vs. continuing seizures occurred (Mean difference = 4%, sd = 29%, p=0.6). Our results indicate that ASM did not appear to halt established seizures in this cohort. Further research is needed to understand how ASM may modulate seizure duration and severity.

Status epilepticus (SE) carries risks of morbidity and mortality. Experimental studies have implicated the entorhinal cortex in prolonged seizures; however, studies in large human cohorts are limited. We hypothesised that individuals with temporal lobe epilepsy (TLE) and a history of SE would have more severe entorhinal atrophy compared to others with TLE and no history of SE. 357 individuals with drug resistant temporal lobe epilepsy (TLE) and 100 healthy controls were scanned on a 3T MRI. For all subjects the cortex was segmented, parcellated, and the thickness calculated from the T1-weighted anatomical scan. Subcortical volumes were derived similarly. Cohen's d and Wilcoxon rank-sum tests respectively were used to capture effect sizes and significance. Individuals with TLE and SE had reduced entorhinal thickness compared to those with TLE and no history of SE. The entorhinal cortex was more atrophic ipsilaterally (d=0.51, p<0.001) than contralaterally (d=0.37, p=0.01). Reductions in ipsilateral entorhinal thickness were present in both left TLE (n=22:176, d=0.78, p<0.001), and right TLE (n=19:140, d=0.31, p=0.04), albeit with a smaller effect size in right TLE. Several other regions exhibited atrophy in individuals with TLE, but these did not relate to a history of SE. These findings suggest potential involvement or susceptibility of the entorhinal cortex in prolonged seizures.

Dating from the work of Neuts in the 1980s, the field of matrix-analytic methods has been developed to analyse discrete or continuous-time Markov chains with a two-dimensional state space in which the increment of a level variable is governed by an auxiliary phase variable. More recently, matrix-analytic techniques have been applied to general Markov additive models with a finite phase space. The basic assumption underlying these developments is that the process is skip-free (in the case of QBDs or fluid queues) or that it is one-sided, that is it is jump-free in one direction. From the Markov additive perspective, traditional matrix-analytic models can be viewed as special cases: for M/G/1 and GI/M/1-type Markov chains, increments in the level are constrained to be lattice random variables and for fluid queues, they have to be piecewise linear. In this paper we discuss one-sided lattice and non-lattice Markov additive processes in parallel. Results that are standard in one tradition are interpreted in the other, and new perspectives emerge. In particular, using three fundamental matrices, we address hitting, two-sided exit, and creeping probabilities., Comment: 38 pages

Magnetic resonance imaging (MRI) is a crucial tool to identify brain abnormalities in a wide range of neurological disorders. In focal epilepsy MRI is used to identify structural cerebral abnormalities. For covert lesions, machine learning and artificial intelligence algorithms may improve lesion detection if abnormalities are not evident on visual inspection. The success of this approach depends on the volume and quality of training data. Herein, we release an open-source dataset of preprocessed MRI scans from 442 individuals with drug-refractory focal epilepsy who had neurosurgical resections, and detailed demographic information. The MRI scan data includes the preoperative 3D T1 and where available 3D FLAIR, as well as a manually inspected complete surface reconstruction and volumetric parcellations. Demographic information includes age, sex, age of onset of epilepsy, location of surgery, histopathology of resected specimen, occurrence and frequency of focal seizures with and without impairment of awareness, focal to bilateral tonic-clonic seizures, number of anti-seizure medications (ASMs) at time of surgery, and a total of 1764 patient years of post-surgical follow up. Crucially, we also include resection masks delineated from post-surgical imaging. To demonstrate the veracity of our data, we successfully replicated previous studies showing long-term outcomes of seizure freedom in the range of around 50%. Our imaging data replicates findings of group level atrophy in patients compared to controls. Resection locations in the cohort were predominantly in the temporal and frontal lobes. We envisage our dataset, shared openly with the community, will catalyse the development and application of computational methods in clinical neurology.

We show how to efficiently sample the joint posterior of two non-covariant experiments with a large set of nuisance parameters. Specifically, we train an ensemble of normalizing flows to learn the the posterior distribution of both experiments. Once trained, we can use the flows to draw $\mathcal{O} (10^9)$ samples from the joint posterior of two independent cosmological measurements in seconds -- saving up to $\mathcal{O}(1)$ ton of $\text{CO}_2$ per Monte Carlo run. Using this new technique we find joint constraints between the Dark Energy Survey $3 \times 2$ point measurement, South Pole Telescope and Planck CMB lensing and a BOSS direct fit full shape analyses, for the first time. We find $\Omega_{\rm m} = 0.32^{+0.01}_{-0.01}$ and $S_8 = 0.79 ^ {+0.01}_ {-0.01}$. We release a public package called {\tt CombineHarvesterFlow} (https://github.com/pltaylor16/CombineHarvesterFlow) which performs these calculations., Comment: 10 pages, 6 figures. To be submitted to PRD

Vagus Nerve Stimulation (VNS) is an established palliative treatment for drug resistant epilepsy. While effective for many patients, its mechanism of action is incompletely understood. Predicting individuals' response, or optimum stimulation parameters, is challenging. Computational modelling has informed other problems in epilepsy but, to our knowledge, has not been applied to VNS. We started with an established, four-population neural mass model (NMM), capable of reproducing the seizure-like dynamics of a thalamocortical circuit. We extended this to include 18 further neural populations, representing nine other brain regions relevant to VNS, with connectivity based on existing literature. We modelled stimulated afferent vagal fibres as projecting to the nucleus tractus solitarius (NTS), which receives input from the vagus nerve in vivo. Bifurcation analysis of a deterministic version of the model showed higher background NTS input made the model monostable at a fixed point (FP), representing normal activity, while lower inputs produce bistability between the FP and a limit cycle (LC), representing the seizure state. Adding noise produced transitions between seizure and normal states. This stochastic model spent decreasing time in the seizure state with increasing background NTS input, until seizures were abolished, consistent with the deterministic model. Simulated VNS stimulation, modelled as a 30 Hz square wave, was summed with the background input to the NTS and was found to reduce total seizure duration in a dose-dependent manner, similar to expectations in vivo. We have successfully produced an in silico model of VNS in epilepsy, capturing behaviour seen in vivo. This may aid understanding therapeutic mechanisms of VNS in epilepsy and provides a starting point to (i) determine which patients might respond best to VNS, and (ii) optimise individuals' treatments.

Normative models of brain structure estimate the effects of covariates such as age and sex using large samples of healthy controls. These models can then be applied to smaller clinical cohorts to distinguish disease effects from other covariates. However, these advanced statistical modelling approaches can be difficult to access, and processing large healthy cohorts is computationally demanding. Thus, accessible platforms with pre-trained normative models are needed. We present such a platform for brain morphology analysis as an open-source web application https://cnnplab.shinyapps.io/normativemodelshiny/, with six key features: (i) user-friendly web interface, (ii) individual and group outputs, (iii) multi-site analysis, (iv) regional and whole-brain analysis, (v) integration with existing tools, and (vi) featuring multiple morphology metrics. Using a diverse sample of 3,276 healthy controls across 21 sites, we pre-trained normative models on various metrics. We validated the models with a small clinical sample of individuals with bipolar disorder, showing outputs that aligned closely with existing literature only after applying our normative modelling. Further validation with a cohort of temporal lobe epilepsy showed agreement with previous group-level findings and individual-level seizure lateralisation. Finally, with the ability to investigate multiple morphology measures in the same framework, we found that biological covariates are better explained in specific morphology measures, and for clinical applications, only some measures are sensitive to the disease process. Our platform offers a comprehensive framework to analyse brain morphology in clinical and research settings. Validations confirm the superiority of normative models and the advantage of investigating a range of brain morphology metrics together.

Recent studies using four-point correlations suggest a parity violation in the galaxy distribution, though the significance of these detections is sensitive to the choice of simulation used to model the noise properties of the galaxy distribution. In a recent paper, we introduce an unsupervised learning approach which offers an alternative method that avoids the dependence on mock catalogs, by learning parity violation directly from observational data. However, the Convolutional Neural Network (CNN) model utilized by our previous unsupervised approach struggles to extend to more realistic scenarios where data is limited. We propose a novel method, the Neural Field Scattering Transform (NFST), which enhances the Wavelet Scattering Transform (WST) technique by adding trainable filters, parameterized as a neural field. We first tune the NFST model to detect parity violation in a simplified dataset, then compare its performance against WST and CNN benchmarks across varied training set sizes. We find the NFST can detect parity violation with $4\times$ less data than the CNN and $32\times$ less than the WST. Furthermore, in cases with limited data the NFST can detect parity violation with up to $6\sigma$ confidence, where the WST and CNN fail to make any detection. We identify that the added flexibility of the NFST, and particularly the ability to learn asymmetric filters, as well as the specific symmetries built into the NFST architecture, contribute to its improved performance over the benchmark models. We further demonstrate that the NFST is readily interpretable, which is valuable for physical applications such as the detection of parity violation.

Anti-seizure medications (ASMs) are the primary treatment for epilepsy, yet medication tapering effects have not been investigated in a dose, region, and time-dependent manner, despite their potential impact on research and clinical practice. We examined over 3000 hours of intracranial EEG recordings in 32 subjects during long-term monitoring, of which 22 underwent concurrent ASM tapering. We estimated ASM plasma levels based on known pharmaco-kinetics of all the major ASM types. We found an overall decrease in the power of delta band activity around the period of maximum medication withdrawal in most (80%) subjects, independent of their epilepsy type or medication combination. The degree of withdrawal correlated positively with the magnitude of delta power decrease. This dose-dependent effect was strongly seen across all recorded cortical regions during daytime; but not in sub-cortical regions, or during night time. We found no evidence of differential effect in seizure onset, spiking, or pathological brain regions. The finding of decreased delta band power during ASM tapering agrees with previous literature. Our observed dose-dependent effect indicates that monitoring ASM levels in cortical regions may be feasible for applications such as medication reminder systems, or closed-loop ASM delivery systems. ASMs are also used in other neurological and psychiatric conditions, making our findings relevant to a general neuroscience and neurology audience.

Background: Understanding healthy human brain function is crucial to identify and map pathological tissue within it. Whilst previous studies have mapped intracranial EEG (icEEG) from non-epileptogenic brain regions, these maps do not consider the effects of age and sex. Further, most existing work on icEEG has often suffered from a small sample size due to this modality's invasive nature. Here, we substantially increase the subject sample size compared to existing literature, to create a multi-centre, normative map of brain activity which additionally considers the effects of age, sex and recording site. Methods: Using interictal icEEG recordings from n = 513 subjects originating from 15 centres, we constructed a normative map of non-pathological brain activity by regressing age and sex on relative band power in five frequency bands, whilst accounting for the site effect. Results: Recording site significantly impacted normative icEEG maps in all frequency bands, and age was a more influential predictor of band power than sex. The age effect varied by frequency band, but no spatial patterns were observed at the region-specific level. Certainty about regression coefficients was also frequency band specific and moderately impacted by sample size. Conclusion: The concept of a normative map is well-established in neuroscience research and particularly relevant to the icEEG modality, which does not allow healthy control baselines. Our key results regarding the site and age effect guide future work utilising normative maps in icEEG.

EEG slowing is reported in various neurological disorders including Alzheimer's, Parkinson's and Epilepsy. Here, we investigate alpha rhythm slowing in individuals with refractory temporal lobe epilepsy (TLE), compared to healthy controls, using scalp electroencephalography (EEG) and magnetoencephalography (MEG). We retrospectively analysed data from 17,(46) healthy controls and 22,(24) individuals with TLE who underwent scalp EEG and (MEG) recordings as part of presurgical evaluation. Resting-state, eyes-closed recordings were source reconstructed using the standardized low-resolution brain electrographic tomography (sLORETA) method. We extracted low (slow) 6-9 Hz and high (fast) 10-11 Hz alpha relative band power and calculated the alpha power ratio by dividing low (slow) alpha by high (fast) alpha. This ratio was computed for all brain regions in all individuals. Alpha oscillations were slower in individuals with TLE than controls (p<0.05). This effect was present in both the ipsilateral and contralateral hemispheres, and across widespread brain regions. Alpha slowing in TLE was found in both EEG and MEG recordings. We interpret greater low (slow)-alpha as greater deviation from health.

We study semi-classical particle production in non-singular bouncing cosmologies by employing the Unruh-DeWitt model of a particle detector propagating in this class of spacetimes. The scale factor for the bouncing cosmology is derived analytically and is inspired by the modified Friedmann equation employed in the loop quantum cosmology literature. We examine how the detector response varies with the free parameters in this model such as the equation of state during the contraction phase and the critical energy density during the bounce phase. We also investigate whether such a signature in the particle detector survives at late times., Comment: 27 pages, 11 figures. Minor revisions (v2)

A matching from a finite subset $A\subset\mathbb{Z}^n$ to another subset $B\subset\mathbb{Z}^n$ is a bijection $f : A \rightarrow B$ with the property that $a+f(a)$ never lies in $A$. A matching is called acyclic if it is uniquely determined by its multiplicity function. Alon et al. established the acyclic matching property for $\mathbb{Z}^n$, which was later extended to all abelian torsion-free groups. In a prior work, the authors of this paper settled the acyclic matching property for all abelian groups. The objective of this note is to explore a related concept, known as the weak acyclic matching property, within the context of abelian groups., Comment: Comments welcome

Many call centres are subject to service level agreements that stipulate that they must achieve targets in terms of the proportion of calls that are answered within a specified time. In order to manage a centre so that targets like these are met, we need to have a method of calculating the waiting time distributions experienced by customers. In this paper, we provide such a method for small call centres that employ skills-based routing. We first build the methodology for the single-skill case and then extend it to a multi-skill case. We model the call centre system as a continuous-time Markov chain and then make use of the Laplace transform to calculate the relevant quantities. We later demonstrate the use of this method to find the optimal routing policy in a certain class of policies.

The inquiry into identifying sets of monomials that can be eliminated from a generic homogeneous polynomial via a linear change of coordinates was initiated by E. K. Wakeford. This linear algebra problem prompted C. K. Fan and J. Losonczy to introduce the notion of acyclic matchings in the additive group $\mathbb{Z}^n$, subsequently extended to abelian groups by the latter author. Alon, Fan, Kleitman, and Losonczy established the acyclic matching property for $\mathbb{Z}^n$. This note aims to classify all abelian groups with respect to the acyclic matching property., Comment: Fixed some minor errors. To appear in Annals of Combinatorics

Recent measurements of the $4$-point correlation functions (4PCF) from spectroscopic surveys provide evidence for parity-violations in the large-scale structure of the Universe. If physical in origin, this could point to exotic physics during the epoch of inflation. However, searching for parity-violations in the 4PCF signal relies on a large suite of simulations to perform a rank test, or an accurate model of the 4PCF covariance to claim a detection, and this approach is incapable of extracting parity information from the higher-order $N$-point functions. In this work we present an unsupervised method which overcomes these issues, before demonstrating the approach is capable of detecting parity-violations in a few toy models using convolutional neural networks. This technique is complementary to the 4-point method and could be used to discover parity-violations in several upcoming surveys including DESI, Euclid and Roman., Comment: 8 pages. 5 figures. PRD Submitted

In this paper, we show how to calculate transient performance measures in models for small call centres that employ skills-based routing. In particular, we calculate the expected number of customer losses and call abandonments in a fixed time. We use the results to compare how call allocation policies can minimise the expected numbers of losses and abandonments, and make recommendations about which policies should be employed.

Delineation of seizure onset regions from EEG is important for effective surgical workup. However, it is unknown if their complete resection is required for seizure freedom, or in other words, if post-surgical seizure recurrence is due to incomplete removal of the seizure onset regions. Retrospective analysis of icEEG recordings from 63 subjects (735 seizures) identified seizure onset regions through visual inspection and algorithmic delineation. We analysed resection of onset regions and correlated this with post-surgical seizure control. Most subjects had over half of onset regions resected (70.7% and 60.5% of subjects for visual and algorithmic methods, respectively). In investigating spatial extent of onset or resection, and presence of diffuse onsets, we found no substantial evidence of association with post-surgical seizure control (all AUC<0.7, p>0.05). Seizure onset regions tends to be at least partially resected, however a less complete resection is not associated with worse post-surgical outcome. We conclude that seizure recurrence after epilepsy surgery is not necessarily a result of failing to completely resect the seizure onset zone, as defined by icEEG. Other network mechanisms must be involved, which are not limited to seizure onset regions alone.

Motivation: Characterising the changes in cortical morphology across the lifespan is fundamental for a range of research and clinical applications. Most studies to date have found a monotonic decrease in commonly used morphometrics, such as cortical thickness and volume, across the entire brain with increasing age. Any regional variations reported are subtle changes in the rate of decrease. However, these descriptions of morphological changes have been limited to a single length scale, or resolution. Here, we delineate the morphological changes associated with the healthy lifespan in multiscale morphometrics. Methods: Using MRI from subjects aged 6-88 years from NKI and CamCAN, we computed morphometrics at spatial scales ranging from 0.32 mm to 3 mm. We used generalised additive mixed models to account for site differences when extracting age trajectories. In a proof-of-principle application, we compared brain age estimations based on a single metric (pial surface area) computed at a single scale vs. multiple scales. Results: On the level of whole cortical hemispheres, lifespan trajectories show diverging and even opposing trends at different spatial scales, in contrast to the monotonic decreases of volume and thickness described so far. Pronounced regional differences between lobes also became apparent in scales over 0.7 mm. Using two complementary scales improved brain age estimates in RMSE by about 5 years. Conclusion: Our study provides a comprehensive multiscale description of lifespan effects on cortical morphology in an age range from 6-88 years. In future, this can be used as a normative model to compare individuals or cohorts, hence identifying morphological abnormalities. Our results reveal the complementary information contained in different spatial scales, suggesting that morphometrics should not be considered mere scalars, but functions of length scale.

Aperiodic activity is a physiologically distinct component of the electrophysiological power spectrum. It is suggested to reflect the balance of excitation and inhibition in the brain, within selected frequency bands. However, the impact of recurrent seizures on aperiodic activity remains unknown, particularly in patients with severe bilateral seizures. Here, we hypothesised greater aperiodic abnormality in the epileptogenic zone, in patients with focal to bilateral tonic clonic (FBTC) seizures, and earlier age of seizure onset. Pre-operative magnetoencephalography (MEG) recordings were acquired from 36 patients who achieved complete seizure freedom (Engel I outcome) post-surgical resection. A normative whole brain map of the aperiodic exponent was computed by averaging across subjects for each region in the hemisphere contralateral to the side of resection. Selected regions of interest were then tested for abnormality using deviations from the normative map in terms of z-scores. Resection masks drawn from postoperative structural imaging were used as an approximation of the epileptogenic zone. Patients with FBTC seizures had greater abnormality compared to patients with focal onset seizures alone in the resection volume (p=0.003, area under the ROC curve = 0.78 ). Earlier age of seizure onset was correlated with greater abnormality of the aperiodic exponent in the resection volume (correlation coefficient = -0.3, p= 0.04)) as well as the whole cortex (rho = -0.33, p=0.03). The abnormality of the aperiodic exponent did not significantly differ between the resected and non-resected regions of the brain. Abnormalities in aperiodic components relate to important clinical characteristics such as severity and age of seizure onset. This suggests the potential use of the aperiodic band power component as a marker for severity of epilepsy.

Identifying abnormal electroencephalographic activity is crucial in diagnosis and treatment of epilepsy. Recent studies showed that decomposing brain activity into periodic (oscillatory) and aperiodic (trend across all frequencies) components may illuminate drivers of changes in spectral activity. Using iEEG data from 234 subjects, we constructed a normative map and compared this with a separate cohort of 63 patients with refractory focal epilepsy being considered for neurosurgery. The normative map was computed using three approaches: (i) relative complete band power, (ii) relative band power with the aperiodic component removed (iii) the aperiodic exponent. Corresponding abnormalities were also calculated for each approach in the separate patient cohort. We investigated the spatial profiles of the three approaches, assessed their localizing ability, and replicated our findings in a separate modality using MEG. The normative maps of relative complete band power and relative periodic band power had similar spatial profiles. In the aperiodic normative map, exponent values were highest in the temporal lobe. Abnormality estimated through the complete band power robustly distinguished between good and bad outcome patients. Neither periodic band power nor aperiodic exponent abnormalities distinguished seizure outcome groups. Combining periodic and aperiodic abnormalities improved performance, similar to the complete band power approach. Our findings suggest that sparing cerebral tissue that generates abnormalities in either periodic or aperiodic activity may lead to a poor surgical outcome. Both periodic and aperiodic abnormalities are necessary to distinguish patient outcomes, with neither sufficient in isolation. Future studies could investigate whether periodic or aperiodic abnormalities are affected by the cerebral location or pathology.

Chronobiological rhythms, such as the circadian rhythm, have long been linked to neurological disorders, but it is currently unknown how pathological processes affect the expression of biological rhythms in the brain. Here, we use the unique opportunity of long-term, continuous intracranially recorded EEG from 38 patients (totalling 6338 hours) to delineate circadian (daily) and ultradian (minute to hourly) rhythms in different brain regions. We show that functional circadian and ultradian rhythms are diminished in pathological tissue, independent of regional variations. We further demonstrate that these diminished rhythms are persistent in time, regardless of load or occurrence of pathological events. These findings provide evidence that brain pathology is functionally associated with persistently diminished chronobiological rhythms in vivo in humans, independent of regional variations or pathological events. Future work interacting with, and restoring, these modulatory chronobiological rhythms may allow for novel therapies.

In traditional priority queues, we assume that every customer upon arrival has a fixed, class-dependent priority, and that a customer may not commence service if a customer with a higher priority is present in the queue. However, in situations where a performance target in terms of the tails of the class-dependent waiting time distributions has to be met, such models of priority queueing may not be satisfactory. In fact, there could be situations where high priority classes easily meet their performance target for the maximum waiting time, while lower classes do not. Here, we are interested in the stationary distribution at the times of commencement of service of this maximum priority process. Until now, there has been no explicit expression for this distribution. We construct a mapping of the maximum priority process to a tandem fluid queue, which enables us to find expressions for this stationary distribution. We derive the results for the stationary distribution of the maximum priority process at the times of the commencement of service., Comment: The Eleventh International Conference on Matrix-Analytic Methods in Stochastic Models (MAM11), 2022, Seoul, Republic of Korea

In this paper, we consider a quantum scalar field propagating on the Reissner-Nordstr\"om black hole spacetime. We compute the renormalized stress-energy tensor for the field in the Hartle-Hawking, Boulware and Unruh states. When the field is in the Hartle-Hawking state, we renormalize using the recently developed ``extended coordinate'' prescription. This method, which relies on Euclidean techniques, is very fast and accurate. Once, we have renormalized in the Hartle-Hawking state, we compute the stress-energy tensor in the Boulware and Unruh states by leveraging the fact that the difference between stress-energy tensors in different quantum states is already finite. We consider a range of coupling constants and masses for the field and a range of electric charge values for the black hole, including near-extreme values. Lastly, we compare these results with the analytic approximations available in the literature., Comment: 18 pages, 4 figures

Malaria is a parasitic disease, transmitted by mosquito vectors. Plasmodium vivax presents particular challenges for disease control, in light of an undetectable reservoir of latent parasites (hypnozoites) within the host liver. Superinfection, which is driven by temporally proximate mosquito inoculation and/or hypnozoite activation events, is an important feature of P. vivax. Here, we present a model of hypnozoite accrual and superinfection for P. vivax. To couple host and vector dynamics, we construct a density-dependent Markov population process with countably many types, for which disease extinction is shown to occur almost surely. We also establish a functional law of large numbers, taking the form of an infinite-dimensional system of ordinary differential equations that can also be recovered under the hybrid approximation or a standard compartment modelling approach. Recognising that the subset of these equations that models the infection status of human hosts has precisely the same form as the Kolmogorov forward equations for a Markovian network of infinite server queues with an inhomogeneous batch arrival process, we use physical insight into the evolution of the latter to write down a time-dependent multivariate generating function for the solution. We use this characterisation to collapse the infinite-compartment model into a single integrodifferential equation (IDE) governing the intensity of mosquito-to-human transmission. Through a steady state analysis, we recover a threshold phenomenon for this IDE in terms of a bifurcation parameter $R_0$, with the disease-free equilibrium shown to be uniformly asymptotically stable if $R_0<1$ and an endemic equilibrium solution emerging if $R_0>1$. Our work provides a theoretical basis to explore the epidemiology of P. vivax, and introduces a general strategy for constructing tractable population-level models of malarial superinfection.

Intracranial EEG (iEEG) is the gold standard technique for epileptogenic zone (EZ) localisation, but requires a hypothesis of which tissue is epileptogenic, guided by qualitative analysis of seizure semiology and other imaging modalities such as magnetoencephalography (MEG). We hypothesised that if quantifiable MEG band power abnormalities were sampled by iEEG, then patients' post-resection seizure outcome were better. Thirty-two individuals with neocortical epilepsy underwent MEG and iEEG recordings as part of pre-surgical evaluation. Interictal MEG band power abnormalities were derived using 70 healthy controls as a normative baseline. MEG abnormality maps were compared to electrode implantation, with the spatial overlap of iEEG electrodes and MEG abnormalities recorded. Finally, we assessed if the implantation of electrodes in abnormal tissue, and resection of the strongest abnormalities determined by MEG and iEEG explained surgical outcome. Intracranial electrodes were implanted in brain tissue with the most abnormal MEG findings in individuals that were seizure-free post-resection (T=3.9, p=0.003). The overlap between MEG abnormalities and iEEG electrodes distinguished outcome groups moderately well (AUC=0.68). In isolation, the resection of the strongest MEG and iEEG abnormalities separated surgical outcome groups well (AUC=0.71, AUC=0.74 respectively). A model incorporating all three features separated outcome groups best (AUC=0.80). Intracranial EEG is a key tool to delineate the EZ and help render patients seizure-free after resection. We showed that data-driven abnormalities derived from interictal MEG recordings have clinical value and may help guide electrode placement in individuals with neocortical epilepsy. Finally, our predictive model of post-operative seizure-freedom, which leverages both MEG and iEEG recordings, may aid patient counselling of expected outcome., Comment: 22 pages, 6 figures

Successful epilepsy surgery depends on localising and resecting cerebral abnormalities and networks that generate seizures. Abnormalities, however, may be widely distributed across multiple discontiguous areas. We propose spatially constrained clusters as candidate areas for further investigation, and potential resection. We quantified the spatial overlap between the abnormality cluster and subsequent resection, hypothesising a greater overlap in seizure-free patients. Thirty-four individuals with refractory focal epilepsy underwent pre-surgical resting-state interictal MEG recording. Fourteen individuals were totally seizure free (ILAE 1) after surgery and 20 continued to have some seizures post-operatively (ILAE 2+). Band power abnormality maps were derived using controls as a baseline. Patient abnormalities were spatially clustered using the k-means algorithm. The tissue within the cluster containing the most abnormal region was compared with the resection volume using the dice score. The proposed abnormality cluster overlapped with the resection in 71% of ILAE 1 patients. Conversely, an overlap only occurred in 15% of ILAE 2+ patients. This effect discriminated outcome groups well (AUC=0.82). Our novel approach identifies clusters of spatially similar tissue with high abnormality. This is clinically valuable, providing (i) a data-driven framework to validate current hypotheses of the epileptogenic zone localisation or (ii) to guide further investigation., Comment: 16 pages, 3 figures

A normative electrographic activity map could be a powerful resource to understand normal brain function and identify abnormal activity. Here, we present a normative brain map using scalp EEG in terms of relative band power. In this exploratory study we investigate its temporal stability, its similarity to other imaging modalities, and explore a potential clinical application. We constructed scalp EEG normative maps of brain dynamics from 17 healthy controls using source-localised resting-state scalp recordings. We then correlated these maps with those acquired from MEG and intracranial EEG to investigate their similarity. Lastly, we use the normative maps to lateralise abnormal regions in epilepsy. Spatial patterns of band powers were broadly consistent with previous literature and stable across recordings. Scalp EEG normative maps were most similar to other modalities in the alpha band, and relatively similar across most bands. Towards a clinical application in epilepsy, we found abnormal temporal regions ipsilateral to the epileptogenic hemisphere. Scalp EEG relative band power normative maps are spatially stable across time, in keeping with MEG and intracranial EEG results. Normative mapping is feasible and may be potentially clinically useful in epilepsy. Future studies with larger sample sizes and high-density EEG are now required for validation., Comment: 4 figures

When investigating suitability for surgery, people with drug-refractory focal epilepsy may have intracranial EEG (iEEG) electrodes implanted to localise seizure onset. Diffusion-weighted magnetic resonance imaging (dMRI) may be acquired to identify key white matter tracts for surgical avoidance. Here, we investigate whether structural connectivity abnormalities, inferred from dMRI, may be used in conjunction with functional iEEG abnormalities to aid localisation and resection of the epileptogenic zone (EZ), and improve surgical outcomes in epilepsy. We retrospectively investigated data from 43 patients with epilepsy who had surgery following iEEG. Twenty five patients (58%) were free from disabling seizures (ILAE 1 or 2) at one year. For all patients, T1-weighted and diffusion-weighted MRIs were acquired prior to iEEG implantation. Interictal iEEG functional, and dMRI structural connectivity abnormalities were quantified by comparison to a normative map and healthy controls respectively. First, we explored whether the resection of maximal (dMRI and iEEG) abnormalities related to improved surgical outcomes. Second, we investigated whether the modalities provided complementary information for improved prediction of surgical outcome. Third, we suggest how dMRI abnormalities may be useful to inform the placement of iEEG electrodes as part of the pre-surgical evaluation using a patient case study. Seizure freedom was 15 times more likely in those patients with resection of maximal dMRI and iEEG abnormalities (p=0.008). Both modalities were separately able to distinguish patient outcome groups and when combined, a decision tree correctly separated 36 out of 43 (84%) patients based on surgical outcome. Structural dMRI could be used in pre-surgical evaluations, particularly when localisation of the EZ is uncertain, to inform personalised iEEG implantation and resection., Comment: 5 figures

In this paper, we consider the occupancy distribution for an open network of infinite server queues with multivariate batch arrivals following a non-homogeneous Poisson process, and general service time distributions. We derive a probability generating function for the transient occupancy distribution of the network, and prove that it is necessary and sufficient for ergodicity that the expected occupancy time for each batch be finite. Further, we recover recurrence relations for the transient probability mass function formulated in terms of a distribution obtained by compounding the batch size with a multinomial distribution.

Objective: Identifying abnormalities in interictal intracranial EEG, by comparing patient data to a normative map, has shown promise for the localisation of epileptogenic tissue and prediction of outcome. The approach typically uses short interictal segments of around one minute. However, the temporal stability of findings has not been established. Methods: Here, we generated a normative map of iEEG in non-pathological brain tissue from 249 patients. We computed regional band power abnormalities in a separate cohort of 39 patients for the duration of their monitoring period (0.92-8.62 days of iEEG data, mean 4.58 days per patient, over 4,800 hours recording). To assess the localising value of band power abnormality, we computed DRS - a measure of how different the surgically resected and spared tissue were in terms of band power abnormalities - over time. Results: In each patient, band power abnormality was relatively consistent over time. The median DRS of the entire recording period separated seizure free (ILAE = 1) and not seizure free (ILAE > 1) patients well (AUC = 0.69). This effect was similar interictally (AUC = 0.69) and peri-ictally (AUC = 0.71). Significance: Our results suggest that band power abnormality DRS, as a predictor of outcomes from epilepsy surgery, is a relatively robust metric over time. These findings add further support for abnormality mapping of neurophysiology data during presurgical evaluation.