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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