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We construct neuron models from data by transferring information from an observed time series to the state variables and parameters of Hodgkin-Huxley models. When the learning period completes, the model will predict additional observations and its parameters uniquely characterise the complement of ion channels. However, the assimilation of biological data, as opposed to model data, is complicated by the lack of knowledge of the true neuron equations. Reliance on guessed conductance models is plagued with multi-valued parameter solutions. Here, we report on the distributions of parameters and currents predicted with intentionally erroneous models, over-specified models, and an approximate model fitting hippocampal neuron data. We introduce a recursive piecewise data assimilation (RPDA) algorithm that converges with near-perfect reliability when the model is known. When the model is unknown, we show model error introduces correlations between certain parameters. The ionic currents reconstructed from these parameters are excellent predictors of true currents and carry a higher degree of confidence, >95.5%, than underlying parameters, >53%. Unexpressed ionic currents are correctly filtered out even in the presence of mild model error. When the model is unknown, the covariance eigenvalues of parameter estimates are found to be a good gauge of model error. Our results suggest that biological information may be retrieved from data by focussing on current estimates rather than parameters.

Many neurological diseases originate in the dysfunction of cellular ion channels. Their diagnosis presents a challenge especially when alterations in the complement of ion channels are a priori unknown. Current approaches based on voltage clamps lack the throughput necessary to identify the mutations causing changes in electrical activity. Here, we introduce a single-shot method for diagnosing changes in the complement of ion channels from changes in the electrical activity of a cell. We developed data assimilation (DA) to estimate the parameters of individual ion channels and from these parameters reconstruct the ionic currents of hippocampal CA1 neurons to within 11% of their actual value. DA correctly predicts which ionic current is altered and by how much after we blocked the BK, SK, A and HCN channels with selective antagonists of known potency. We anticipate our assay will transform the treatment of neurological disease through comprehensive diagnosis and drug screening., Comment: 42 pages, 6 figures, 3 tables

Thermal electrons have gyroradii many orders of magnitude smaller than the finite width of a shock, thus need to be pre-accelerated before they can cross it and be accelerated by diffusive shock acceleration. One region where pre-acceleration may occur is the inner foreshock, which upstream electrons must pass through before any potential downstream crossing. In this paper, we perform a large scale particle-in-cell simulation that generates a single shock with parameters motivated from supernova remnants. Within the foreshock, reflected electrons excite the oblique whistler instability and produce electromagnetic whistler waves, which co-move with the upstream flow and as non-linear structures eventually reach radii of up to 5 ion-gyroradii. We show that the inner electromagnetic configuration of the whistlers evolves into complex non-linear structures bound by a strong magnetic field around 4 times the upstream value. Although these non-linear structures do not in general interact with co-spatial upstream electrons, they resonate with electrons that have been reflected at the shock. We show that they can scatter, or even trap, reflected electrons, confining around $0.8\%$ of the total upstream electron population to the region close to the shock where they can undergo substantial pre-acceleration. This acceleration process is similar to, yet approximately 3 times more efficient than, stochastic shock drift acceleration., Comment: 16 pages, 11 figures, accepted for publication in ApJ

To undergo diffusive shock acceleration, electrons need to be pre-accelerated to increase their energies by several orders of magnitude, else their gyro-radii are smaller than the finite width of the shock. In oblique shocks, where the upstream magnetic field orientation is neither parallel or perpendicular to the shock normal, electrons can escape to the shock upstream, modifying the shock foot to a region called the electron foreshock. To determine the pre-acceleration in this region, we undertake PIC simulations of oblique shocks while varying the obliquity and in-plane angles. We show that while the proportion of reflected electrons is negligible for $\theta_{\rm Bn} = 74.3^\circ$, it increases to $R \sim 5\%$ for $\theta_{\rm Bn} = 30^\circ$, and that, via the electron acoustic instability, these electrons power electrostatic waves upstream with energy density proportional to $R^{0.6}$ and a wavelength $\approx 2 \lambda_{\rm{se}}$, where $\lambda_{\rm{se}}$ is the electron skin length. While the initial reflection mechanism is typically a combination of shock surfing acceleration and magnetic mirroring, we show that once the electrostatic waves have been generated upstream they themselves can increase the momenta of upstream electrons parallel to the magnetic field. In $\lesssim 1\%$ of cases, upstream electrons are prematurely turned away from the shock and never injected downstream. In contrast, a similar fraction are re-scattered back towards the shock after reflection, re-interact with the shock with energies much greater than thermal, and cross into the downstream., Comment: Accepted for publication in ApJ. 15 pages, 15 figures

In the Universe matter outside of stars and compact objects is mostly composed of collisionless plasma. The interaction of a supersonic plasma flow with an obstacle results in collisionless shocks that are often associated with intense nonthermal radiation and the production of cosmic ray particles. Motivated by simulations of non-relativistic high-Mach-number shocks in supernova remnants, we investigate the instabilities excited by relativistic electron beams in the extended foreshock of oblique shocks. The phase-space distributions in the inner and outer foreshock regions are derived with a Particle-in-Cell simulation of the shock and used as initial conditions for simulations with periodic boundary conditions to study their relaxation towards equilibrium. We find that the observed electron-beam instabilities agree very well with the predictions of a linear dispersion analysis: the electrostatic electron-acoustic instability dominates in the outer region of the foreshock, while the denser electron beams in the inner foreshock drive the gyroresonant oblique-whistler instability., Comment: accepted for publication in Physics of Plasmas. 14 pages, 12 figures

The current paradigm of cosmic ray (CR) origin states that the most part of galactic CRs is produced by supernova remnants. The interaction of supernova ejecta with the interstellar medium after supernova's explosions results in shocks responsible for CR acceleration via diffusive shock acceleration (DSA). We use particle-in-cell (PIC) simulations and a combined PIC-magnetohydrodynamic (PIC-MHD) technique to investigate whether DSA can occur in oblique high Mach number shocks. Using the PIC method, we follow the formation of the shock and determine the fraction of the particles that gets involved in DSA. Then, with this result, we use PIC-MHD simulations to model the large-scale structure of the plasma and the magnetic field surrounding the shock and find out whether or not the reflected particles can generate the upstream turbulence and trigger DSA. We find that the feasibility of this process in oblique shocks depends strongly on the Alfvenic Mach number, and the DSA process is more likely triggered at high Mach number shocks., Comment: Accepted for publication in ApJ

Building a visual overview of temporal event sequences with an optimal level-of-detail (i.e. simplified but informative) is an ongoing challenge - expecting the user to zoom into every important aspect of the overview can lead to missing insights. We propose a technique to build a multilevel overview of event sequences, whose granularity can be transformed across sequence clusters (vertical level-of-detail) or longitudinally (horizontal level-of-detail), using hierarchical aggregation and a novel cluster data representation Align-Score-Simplify. By default, the overview shows an optimal number of sequence clusters obtained through the average silhouette width metric - then users are able to explore alternative optimal sequence clusterings. The vertical level-of-detail of the overview changes along with the number of clusters, whilst the horizontal level-of-detail refers to the level of summarization applied to each cluster representation. The proposed technique has been implemented into a visualization system called Sequence Cluster Explorer (Sequen-C) that allows multilevel and detail-on-demand exploration through three coordinated views, and the inspection of data attributes at cluster, unique sequence, and individual sequence level. We present two case studies using real-world datasets in the healthcare domain: CUREd and MIMIC-III; which demonstrate how the technique can aid users to obtain a summary of common and deviating pathways, and explore data attributes for selected patterns., Comment: This is the author's version of the article to be published in IEEE Transactions on Visualization and Computer Graphics

Collisionless shocks are ubiquitous in the Universe and often associated with strong magnetic field. Here we use large-scale particle-in-cell simulations of non-relativistic perpendicular shocks in the high-Mach-number regime to study the amplification of magnetic field within shocks. The magnetic field is amplified at the shock transition due to the ion-ion two-stream Weibel instability. The normalized magnetic-field strength strongly correlates with the Alfv\'enic Mach number. Mock spacecraft measurements derived from PIC simulations are fully consistent with those taken in-situ at Saturn's bow shock by the Cassini spacecraft., Comment: Accepted to PRL. 7 pages, 4 figure

High Mach number collisionless shocks are found in planetary systems and supernova remnants (SNRs). Electrons are heated at these shocks to the temperature well above the Rankine-Hugoniot prediction. However processes responsible for electron heating are still not well understood. We use a set of large-scale Particle-In-Cell simulations of non-relativistic shocks in high Mach number regime to clarify the electron heating processes. The physics of these shocks is defined by ion reflection at the shock ramp. Further interaction of the reflected ions and the upstream plasma excites electrostatic Buneman and two-stream ion-ion Weibel instabilities. Electrons are heated via shock surfing acceleration, the shock potential, magnetic reconnection, stochastic Fermi scattering and the shock compression. The main contributor is the shock potential. Magnetic field lines are tangled due to the Weibel instability, which allows the parallel electron heating by the shock potential. The constrained model of the electron heating predicts the ion-to-electron temperature ratio within observed values at SNR shocks and in Saturn's bow shock., Comment: 10 pages, 3 figures

With the coincident detection of a gamma-ray flare and a neutrino from the blazar TXS 0506+056, Active Galactic Nuclei (AGN) have been put into focus as possible sources of the diffuse neutrino flux. We present a space and time-resolved model of the high-energy particle emission of a plasmoid assumed to travel along the axis of an AGN jet at relativistic speed. This was achieved by modifying the publicly available CRPropa (version 3.1+) propagation framework which in our work is capable of being applied to source physics on sub-kpc scales. The propagation of a population of primary protons is modelled in a purely turbulent magnetic field and we take into account interactions of these protons with photons scattered from the accretion disc, synchrotron radiation emitted by ambient relativistic electrons, as well with themselves and with other ambient matter. Our model produces a PeV-neutrino flare caused mainly by photo-hadronic interactions of primaries with the accretion disc field. Secondary high-energy gamma-rays partly attenuate with the ambient photon fields whose combined optical depths achieve their minimal opacity for photons of around 10 TeV. Thus, our model is well capable of producing neutrino flares with a significantly reduced emission of gamma-rays in jets with a hadronic jet component which in the future can be fit to specific AGN flare scenarios., Comment: 19 pages, 7 figures, accepted by MNRAS on 01 June 2020 for publication

Time series analysis allows for the determination of the Power Spectral Density (PSD) and Probability Density Function (PDF) for astrophysical sources. The former of these illustrates the distribution of power at various timescales, typically taking a power-law form, while the latter characterises the distribution of the underlying stochastic physical processes, with Gaussian and lognormal functional forms both physically motivated. In this paper, we use artificial time series generated using the prescription of Timmer & Koenig to investigate connections between the PDF and PSD. PDFs calculated for these artificial light curves are less likely to be well described by a Gaussian functional form for steep (<-1) PSD spectral indices due to weak non-stationarity. Using the Fermi LAT monthly light curve of the blazar PKS2155-304 as an example, we prescribe and calculate a false positive rate which indicates how likely the PDF is to be attributed an incorrect functional form. Here, we generate large numbers of artificial light curves with intrinsically normally distributed PDFs and with statistical properties consistent with observations. These are used to evaluate the probabilities that either Gaussian or lognormal functional forms better describe the PDF. We use this prescription to show that PKS2155-304 requires a high prior probability of having a normally distributed PDF, P(G) >= 0.82, for the calculated PDF to prefer a Gaussian functional form over a lognormal. We present possible choices of prior and evaluate the probability that PKS2155-304 has a lognormally distributed PDF for each., Comment: 14 pages, 13 figures, accepted for publication in MNRAS

Order of magnitude variability has been observed in the blazar sub-class of Active Galactic Nuclei on minute timescales. These high-energy flares are often difficult to explain with shock acceleration models due to the small size of the inferred emitting region, with recent particle-in-cell (PIC) simulations showing that magnetic reconnection is a promising alternative mechanism. Here, we present a macroscopic emission model physically motivated by PIC simulations, where the energy for particle acceleration originates from the reconnecting magnetic field. We track the radial growth and relative velocity of a reconnecting plasmoid, modelling particle acceleration and radiative losses from synchrotron and synchrotron self-Compton (SSC) emission. To test the viability of magnetic reconnection as the mechanism behind rapid blazar flares we simultaneously fit our model to the observed light-curve and SED from the 2016 TeV flare of BL Lacertae. We find generally that, without considering external photons, reconnecting plasmoids are unable to produce Compton-dominant TeV flares and so cannot reproduce the observations due to overproduction of synchrotron emission. Additionally, problematically large plasmoids, comparable in size to the entire jet radius, are required to emit sufficient SSC gamma-rays to be observable. However, our plasmoid model can reproduce the rapid TeV lightcurve of the flare, demonstrating that reconnection is able to produce rapid, powerful TeV flares on observed timescales. We conclude that while reconnection can produce SSC flares on the correct timescales, the primary source of TeV emission cannot be SSC and the size of plasmoids required may be implausibly large., Comment: Replaced with accepted version. Contains additional figures and considers the effect of a magnetic guide field

Classical Novae were revealed as a surprise source of gamma-rays in Fermi LAT observations. During the first 8 years since the LAT was launched, 6 novae in total have been detected to > 5 sigma in gamma-rays, in contrast to the 69 discovered optically in the same period. We attempt to resolve this discrepancy by assuming all novae are gamma-ray emitters, and assigning peak one-day fluxes based on a flat distribution of the known emitters to a simulated population. To determine optical parameters, the spatial distribution and magnitudes of bulge and disc novae in M31 are scaled to the Milky Way, which we approximate as a disc with a 20 kpc radius and elliptical bulge with semi major axis 3 kpc and axis ratios 2:1 in the xy plane. We approximate Galactic reddening using a double exponential disc with vertical and radial scale heights of r_d = 5 kpc and z_d = 0.2 kpc, and demonstrate that even such a rudimentary model can easily reproduce the observed fraction of gamma-ray novae, implying that these apparently rare sources are in fact nearby and not intrinsically rare. We conclude that classical novae with m_R < 12 and within ~8 kpc are likely to be discovered in gamma-rays using the Fermi LAT., Comment: Accepted by MNRAS, 10 pages, 7 figures