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The parameterization method (PM) provides a broad theoretical and numerical foundation for computing invariant manifolds of dynamical systems. PM implements a change of variables in order to represent trajectories of a system of ordinary differential equations ``as simply as possible." In this paper we pursue a similar goal for stochastic oscillator systems. For planar nonlinear stochastic systems that are ``robustly oscillatory", we find a change of variables through which the dynamics are as simple as possible $\textit{in the mean}$. We prove existence and uniqueness of a deterministic vector field, the trajectories of which capture the local mean behavior of the stochastic oscillator. We illustrate the construction of such an ``effective vector field" for several examples, including a limit cycle oscillator perturbed by noise, an excitable system derived from a spiking neuron model, and a spiral sink with noise forcing (2D Ornstein-Uhlenbeck process). The latter examples comprise contingent oscillators that would not sustain rhythmic activity without noise forcing. Finally, we exploit the simplicity of the dynamics after the change of variables to obtain the effective diffusion constant of the resulting phase variable, and the stationary variance of the resulting amplitude (isostable) variable.

Understanding the co-evolution of super-massive black holes (SMBHs) and their host galaxies remains a key challenge of extragalactic astrophysics, particularly the earliest stages at high-redshift. However, studying SMBHs at high-redshift with cosmological simulations, is challenging due to the large volumes and high-resolution required. Through its innovative simulation strategy, the First Light And Reionisation Epoch Simulations (FLARES) suite of cosmological hydrodynamical zoom simulations allows us to simulate a much wider range of environments which contain SMBHs with masses extending to $M_{\bullet}>10^{9}\ M_{\odot}$ at $z=5$. In this paper, we use FLARES to study the physical properties of SMBHs and their hosts in the early Universe ($5\le\, z \le10$). FLARES predicts a sharply declining density with increasing redshift, decreasing by a factor of 100 over the range $z=5\to 10$. Comparison between our predicted bolometric luminosity function and pre-\emph{JWST} observations yield a good match. However, recent \emph{JWST} observations appear to suggest a larger contribution of SMBHs than previously observed, or predicted by FLARES. Finally, by using a re-simulation with AGN feedback disabled, we explore the impact of AGN feedback on their host galaxies. This reveals that AGN feedback results in a reduction of star formation activity, even at $z>5$, but only in the most massive galaxies. A deeper analysis reveals that AGN are also the cause of suppressed star formation in passive galaxies but that the presence of an AGN doesn't necessarily result in the suppression of star formation., Comment: 17 pages, 13 figures, to be submitted to the Open Journal of Astrophysics. The first two authors are joint primary authors. Updated with new observational constraints

Although the raison d'etre of the brain is the survival of the body, there are relatively few theoretical studies of closed-loop rhythmic motor control systems. In this paper we provide a unified framework, based on variational analysis, for investigating the dual goals of performance and robustness in powerstroke-recovery systems. We augment two previously published closed-loop motor control models by equipping each model with a performance measure based on the rate of progress of the system relative to a spatially extended external substrate -- such as progress relative to the ground for a locomotor task. The sensitivity measure quantifies the ability of the system to maintain performance in response to external perturbations. Motivated by a search for optimal design principles for feedback control achieving the complementary requirements of efficiency and robustness, we discuss the performance-sensitivity patterns of the systems featuring different sensory feedback architectures. In a paradigmatic half-center oscillator (HCO)-motor system, we observe that the excitation-inhibition property of feedback mechanisms determines the sensitivity pattern while the activation-inactivation property determines the performance pattern. Moreover, we show that the nonlinearity of the sigmoid activation of feedback signals allows the existence of optimal combinations of performance and sensitivity. In a detailed hindlimb locomotor system, we find that a force-dependent feedback can simultaneously optimize both performance and robustness, while length-dependent feedback variations result in significant performance-versus-sensitivity tradeoffs. Thus, this work provides an analytical framework for studying feedback control of oscillations in nonlinear dynamical systems, leading to several insights that have the potential to inform the design of control or rehabilitation systems., Comment: 48 pages, 17 figures, 3 tables

Phase reduction is an important tool for studying coupled and driven oscillators. The question of how to generalize phase reduction to stochastic oscillators remains actively debated. In this work, we propose a method to derive a self-contained stochastic phase equation of the form $d\vartheta = a_\vartheta(\vartheta)dt + \sqrt{2D_\vartheta(\vartheta)}\,dW_\vartheta(t)$ that is valid not only for noise-perturbed limit cycles, but also for noise-induced oscillations. We show that our reduction captures the asymptotic statistics of qualitatively different stochastic oscillators, and use it to infer their phase-response properties., Comment: 12 pages, 7 figures

We present detailed implementations of (a) binary stellar evolution (using binary_c) and (b) dust production and destruction into the cosmological semi-analytic galaxy evolution simulation, L-Galaxies. This new version of L-Galaxies is compared to a version assuming only single stars and to global and spatially-resolved observational data across a range of redshifts ($z$). We find that binaries have a negligible impact on the stellar masses, gas masses, and star formation rates of galaxies only if the total mass ejected by massive stars is unchanged. This is because massive stars determine the strength of supernova (SN) feedback, which in turn regulates galaxy growth. Binary effects, such as common envelope ejection and novae, affect carbon and nitrogen enrichment in galaxies, however heavier alpha elements are more affected by the choice of SN and wind yields. Unlike many other simulations, the new L-Galaxies reproduces observed dust-to-metal (DTM) and dust-to-gas (DTG) ratios at $z\sim{}0-4$. This is mainly due to shorter dust accretion timescales in dust-rich environments. However, dust masses are under-predicted at $z>4$, highlighting the need for enhanced dust production at early times in simulations, possibly accompanied by increased star formation. On sub-galactic scales, there is very good agreement between L-Galaxies and observed dust and metal radial profiles at $z=0$. A drop in DTM ratio is also found in diffuse, low-metallicity regions, contradicting the assumption of a universal value. We hope that this work serves as a useful template for binary stellar evolution implementations in other cosmological simulations in future., Comment: 19 pages, 10 figures. Submitted to MNRAS. Comments welcome!

This work investigates a case study of using physical-based sonification of Quadratic Unconstrained Binary Optimization (QUBO) problems, optimized by the Variational Quantum Eigensolver (VQE) algorithm. The VQE approximates the solution of the problem by using an iterative loop between the quantum computer and a classical optimization routine. This work explores the intermediary statevectors found in each VQE iteration as the means of sonifying the optimization process itself. The implementation was realised in the form of a musical interface prototype named Variational Quantum Harmonizer (VQH), providing potential design strategies for musical applications, focusing on chords, chord progressions, and arpeggios. The VQH can be used both to enhance data visualization or to create artistic pieces. The methodology is also relevant in terms of how an artist would gain intuition towards achieving a desired musical sound by carefully designing QUBO cost functions. Flexible mapping strategies could supply a broad portfolio of sounds for QUBO and quantum-inspired musical compositions, as demonstrated in a case study composition, "Dependent Origination" by Peter Thomas and Paulo Itaborai., Comment: Manuscript Accepted to the 2nd International Symposium on Quantum Computing and Musical Creativity (ISQCMC Berlin). Link: https://indico.desy.de/event/38609/page/4475-information

The quest to understand the nature of superconductivity in cuprates has spotlighted the pair density wave (PDW) -- a superconducting state characterized by a spatially modulated order parameter. Despite significant advances in understanding PDW properties, conclusively demonstrating its presence in systems pertinent to cuprate superconductors remains elusive. In this study, we present a systematic density-matrix renormalization group study to investigate the Emery model (or the three-band Hubbard model) on two-leg square cylinders with negative electron hopping term $t_{pp}$ between adjacent oxygen sites. Kinetic frustration - introduced by changing the sign of oxygen-oxygen hopping - leads to a much reduced Cu-Cu antiferromagnetic exchange along with an enlarged charge transfer energy that changes the local properties of the model. At light doping levels, our findings reveal a ground state remarkably consistent with a PDW, exhibiting mutually commensurate superconducting (SC), charge and spin density wave correlations. Intriguingly, the dominant SC pairing is observed between neighboring oxygen sites, diverging from the expected Cu sites in the positive $t_{pp}$ case. When the system incorporates moderate near-neighbor interactions, particularly an attractive $V_{pp}$ between adjacent oxygen sites, the SC correlations become quasi-long-ranged, accompanied by a pronounced divergence in the PDW susceptibility. When further increase the attractive $V_{pp}$, the system gives ways to an unconventional $d$-wave superconductivity., Comment: 7 pages, 6 figures

The formation of charge density waves (CDW) is a long-standing open problem particularly in dimensions higher than one. Various observations in the vanadium antimonides discovered recently, such as the missing Kohn anomaly in the acoustic phonons or the latent heat at the transition $T_{\rm CDW}$ = 95 K , further underpin this notion. Here, we study the Kagome metal CsV$_3$Sb$_5$ using polarized inelastic light scattering. The electronic energy gap $2\Delta$ as derived from the redistribution of the continuum is much larger than expected from mean-field theory and reaches values above 20 for $2\Delta/k_{\rm B}T_{\rm CDW}$. The A$_{1g}$ phonon has a discontinuity at $T_{\rm CDW}$ and a precursor starting 20 K above $T_{\rm CDW}$. Density functional theory qualitatively reproduces the redistribution of the electronic continuum at the CDW transition and the phonon energies of the pristine and distorted structures. The linewidths of all A$_{1g}$ and E$_{2g}$ phonon lines including those emerging below $T_{\rm CDW}$ were analyzed in terms of anharmonic symmetric decay revealing strong phonon-phonon coupling. In addition, we observe two CDW amplitude modes (AMs): one in A$_{1g}$ symmetry and one in E$_{2g}$ symmetry. The temperature dependence of both modes deviates from the prediction of mean-field theory. The A$_{1g}$ AM displays an asymmetric Fano-type lineshape, suggestive of strong electron-phonon coupling. The asymmetric A$_{1g}$ AM, along with the discontinuity of the A$_{1g}$ phonon, the large phonon-phonon coupling parameters and the large gap ratio, indicate the importance of anharmonic strong phonon-phonon and electron-phonon coupling for the CDW formation in CsV$_3$Sb$_5$., Comment: 19 pages, 5 figures

A mechanical model and numerical method for structural membranes implied by all isosurfaces of a level-set function in a three-dimensional bulk domain are proposed. The mechanical model covers large displacements in the context of the finite strain theory and is formulated based on the tangential differential calculus. Alongside curved two-dimensional membranes embedded in three dimensions, also the simpler case of curved ropes (cables) in two-dimensional bulk domains is covered. The implicit geometries (shapes) are implied by the level sets and the boundaries of the structures are given by the intersection of the level sets with the boundary of the bulk domain. For the numerical analysis, the bulk domain is discretized using a background mesh composed by (higher-order) elements with the dimensionality of the embedding space. The elements are by no means aligned to the level sets, i.e., the geometries of the structures, which resembles a fictitious domain method, most importantly the Trace FEM. The proposed numerical method is a hybrid of the classical FEM and fictitious domain methods which may be labeled as "Bulk Trace FEM". Numerical studies confirm higher-order convergence rates and the potential for new material models with continuously embedded sub-structures in bulk domains., Comment: Article has been submitted to Comp. Methods Appl. Mech. Engrg

The history of reionisation is highly dependent on the ionising properties of high-redshift galaxies. It is therefore important to have a solid understanding of how the ionising properties of galaxies are linked to physical and observable quantities. In this paper, we use the First Light and Reionisation Epoch Simulations (FLARES) to study the Lyman-continuum (LyC, i.e. hydrogen-ionising) emission of massive ($M_*>10^8\,\mathrm{M_\odot}$) galaxies at redshifts $z=5-10$. We find that the specific ionising emissivity (i.e. intrinsic ionising emissivity per unit stellar mass) decreases as stellar mass increases, due to the combined effects of increasing age and metallicity. FLARES predicts a median ionising photon production efficiency (i.e. intrinsic ionising emissivity per unit intrinsic far-UV luminosity) of $\log_{10}(\xi_{\rm ion}\rm{/erg^{-1}Hz})=25.40^{+0.16}_{-0.17}$, with values spanning the range $\log_{10}(\xi_{\rm ion}\rm{/erg^{-1}Hz})=25-25.75$. This is within the range of many observational estimates, but below some of the extremes observed. We compare the production efficiency with observable properties, and find a weak negative correlation with the UV-continuum slope, and a positive correlation with the OIII equivalent width. We also consider the dust-attenuated production efficiency (i.e. intrinsic ionising emissivity per unit dust-attenuated far-UV luminosity), and find a median of $\log_{10}(\xi_{\rm ion}\rm{/erg^{-1}Hz})\sim25.5$. Within our sample of $M_*>10^8\,\mathrm{M_\odot}$ galaxies, it is the stellar populations in low mass galaxies that contribute the most to the total ionising emissivity. Active galactic nuclei (AGN) emission accounts for $10-20$ % of the total emissivity at a given redshift, and extends the LyC luminosity function by $\sim0.5$ dex., Comment: 19 pages, 17 figures, accepted for publication in MNRAS

While our understanding of the way single neurons process chromatic stimuli in the early visual pathway has advanced significantly in recent years, we do not yet know how these cells interact to form stable representations of hue. Drawing on physiological studies, we offer a dynamical model of how the primary visual cortex tunes for color, hinged on intracortical interactions and emergent network effects. After detailing the evolution of network activity through analytical and numerical approaches, we discuss the effects of the model's cortical parameters on the selectivity of the tuning curves. In particular, we explore the role of the model's thresholding nonlinearity in enhancing hue selectivity by expanding the region of stability, allowing for the precise encoding of chromatic stimuli in early vision. Finally, in the absence of a stimulus, the model is capable of explaining hallucinatory color perception via a Turing-like mechanism of biological pattern formation., Comment: 21 pages, 15 figures

Using the First Light And Reionisation Epoch Simulations (${\rm F{\small LARES}}$), a suite of hydrodynamical simulations we explore the consequences of a realistic model for star--dust geometry on the observed properties of galaxies. We find that the UV attenuation declines rapidly from the central regions of galaxies, and bright galaxies have spatially extended star formation that suffers less obscuration than their fainter counterparts, demonstrating a non-linear relationship between the UV luminosity and the UV attenuation, giving a double power-law shape to the UVLF. Spatially distinct stellar populations within galaxies experience a wide range of dust attenuation due to variations in the dust optical depth along their line-of-sight; which can range from completely dust obscured to being fully unobscured. The overall attenuation curve of a galaxy is then a complex combination of various lines-of-sight within the galaxy. We explore the manifestation of this effect to study the reliability of line ratios to infer galaxy properties, in particular the Balmer decrement and the BPT diagram. We find the Balmer decrement predicted Balmer line attenuation to be higher (factor of $1$ to $\gtrsim10$) than expected from commonly used attenuation curves. The observed BPT line ratios deviate from their intrinsic values (median difference of 0.08 (0.02) and standard deviation of 0.2 (0.05) for log$_{10}$([N${\rm {\small II}}$]$\lambda 6585/$H$_{\alpha}$) (log$_{10}$([O${\rm {\small III}}$]$\lambda 5008/$H$_{\beta}$)). Finally, we explore the variation in observed properties (UV attenuation, UV slope and Balmer decrement) with viewing angle, finding average differences of $\sim0.3$ magnitudes in the UV attenuation., Comment: 17 pages, 13 figures. Published MNRAS. Data available at https://flaresimulations.github.io

Many systems in physics, chemistry and biology exhibit oscillations with a pronounced random component. Such stochastic oscillations can emerge via different mechanisms, for example linear dynamics of a stable focus with fluctuations, limit-cycle systems perturbed by noise, or excitable systems in which random inputs lead to a train of pulses. Despite their diverse origins, the phenomenology of random oscillations can be strikingly similar. Here we introduce a nonlinear transformation of stochastic oscillators to a new complex-valued function $Q^*_1(\textbf{x})$ that greatly simplifies and unifies the mathematical description of the oscillator's spontaneous activity, its response to an external time-dependent perturbation, and the correlation statistics of different oscillators that are weakly coupled. The function $Q^*_1(\textbf{x})$ is the eigenfunction of the Kolmogorov backward operator with the least negative (but non-vanishing) eigenvalue $\lambda_1=\mu_1+i\omega_1$. The resulting power spectrum of the complex-valued function is exactly given by a Lorentz spectrum with peak frequency $\omega_1$ and half-width $\mu_1$; its susceptibility with respect to a weak external forcing is given by a simple one-pole filter, centered around $\omega_1$; and the cross-spectrum between two coupled oscillators can be easily expressed by a combination of the spontaneous power spectra of the uncoupled systems and their susceptibilities. Our approach makes qualitatively different stochastic oscillators comparable, provides simple characteristics for the coherence of the random oscillation, and gives a framework for the description of weakly coupled oscillators.

Upcoming deep galaxy surveys with JWST will probe galaxy evolution during the epoch of reionisation (EoR, $5\leq z\leq10$) over relatively compact areas (e.g. $\sim$ 300\,arcmin$^2$ for the JADES GTO survey). It is therefore imperative that we understand the degree of survey variance, to evaluate how representative the galaxy populations in these studies will be. We use the First Light And Reionisation Epoch Simulations (FLARES) to measure the galaxy bias of various tracers over an unprecedentedly large range in overdensity for a hydrodynamic simulation, and use these relations to assess the impact of bias and clustering on survey variance in the EoR. Star formation is highly biased relative to the underlying dark matter distribution, with the mean ratio of the stellar to dark matter density varying by a factor of 100 between regions of low and high matter overdensity (smoothed on a scale of 14$\,h^{-1}$cMpc). This is reflected in the galaxy distribution --the most massive galaxies are found solely in regions of high overdensity. As a consequence of the above, galaxies in the EoR are highly clustered, which can lead to large variance in survey number counts. For mean number counts $N\lesssim 100$ (1000), in a unit redshift slice of angular area 300\,arcmin$^2$ (1.4\,deg$^2$), the 2-sigma range in $N$ is roughly a factor of four (two). We present relations between the expected variance and survey area for different survey geometries; these relations will be of use to observers wishing to understand the impact of survey variance on their results., Comment: Accepted version. Thanks to the referee contains more extensive description of testing, comparison to online Cosmic Variance Calculator, and greater range of survey areas than the original submission

In the FLARES (First Light And Reionisation Epoch Simulations) suite of hydrodynamical simulations, we find the high redshift ($z>5$) intrinsic size-luminosity relation is, surprisingly, negatively sloped. However, after including the effects of dust attenuation we find a positively sloped UV observed size-luminosity relation in good agreement with other simulated and observational studies. In this work, we extend this analysis to probe the underlying physical mechanisms driving the formation and evolution of the compact galaxies driving the negative size-mass/size-luminosity relation. We find the majority of compact galaxies ($R_{1/2, \star}< 1 \mathrm{pkpc}$), which drive the negative slope of the size-mass relation, have transitioned from extended to compact sizes via efficient centralised cooling, resulting in high specific star formation rates in their cores. These compact stellar systems are enshrouded by non-star forming gas distributions as much as $100\times$ larger than their stellar counterparts. By comparing with galaxies from the EAGLE simulation suite, we find that these extended gas distributions `turn on' and begin to form stars between $z=5$ and $z=0$ leading to increasing sizes, and thus the evolution of the size-mass relation from a negative to a positive slope. This explicitly demonstrates the process of inside-out galaxy formation in which compact bulges form earlier than the surrounding discs.

Many natural and engineered systems can be modeled as discrete state Markov processes. Often, only a subset of states are directly observable. Inferring the conditional probability that a system occupies a particular hidden state, given the partial observation, is a problem with broad application. In this paper, we introduce a continuous-time formulation of the sum-product algorithm, which is a well-known discrete-time method for finding the hidden states' conditional probabilities, given a set of finite, discrete-time observations. From our new formulation, we can explicitly solve for the conditional probability of occupying any state, given the transition rates and observations within a finite time window. We apply our algorithm to a realistic model of the cystic fibrosis transmembrane conductance regulator (CFTR) protein for exact inference of the conditional occupancy probability, given a finite time series of partial observations., Comment: Accepted for publication in IEEE Transactions on Signal Processing

Similar activity patterns may arise from model neural networks with distinct coupling properties and individual unit dynamics. These similar patterns may, however, respond differently to parameter variations and, specifically, to tuning of inputs that represent control signals. In this work, we analyze the responses resulting from modulation of a localized input in each of three classes of model neural networks that have been recognized in the literature for their capacity to produce robust three-phase rhythms: coupled fast-slow oscillators, near-heteroclinic oscillators, and threshold-linear networks. Triphasic rhythms, in which each phase consists of a prolonged activation of a corresponding subgroup of neurons followed by a fast transition to another phase, represent a fundamental activity pattern observed across a range of central pattern generators underlying behaviors critical to survival, including respiration, locomotion, and feeding. To perform our analysis, we extend the recently developed local timing response curve (lTRC), which allows us to characterize the timing effects due to perturbations, and we complement our lTRC approach with model-specific dynamical systems analysis. Interestingly, we observe disparate effects of similar perturbations across distinct model classes. Thus, this work provides an analytical framework for studying control of oscillations in nonlinear dynamical systems, and may help guide model selection in future efforts to study systems exhibiting triphasic rhythmic activity., Comment: 49 pages, 21 figures, 8 tables

Passive galaxies are ubiquitous in the local universe, and various physical channels have been proposed that lead to this passivity. To date, robust passive galaxy candidates have been detected up to $z \leqslant 5$, but it is still unknown if they exist at higher redshifts, what their relative abundances are, and what causes them to stop forming stars. We present predictions from the First Light And Reionisation Epoch Simulations (FLARES), a series of zoom simulations of a range of overdensities using the EAGLE code. Passive galaxies occur naturally in the EAGLE model at high redshift, and are in good agreement with number density estimates from HST and early JWST results at $3 \leqslant z \leqslant 5$. Due to the unique FLARES approach, we extend these predictions to higher redshifts, finding passive galaxy populations up to $z \sim 8$. Feedback from supermassive black holes is the main driver of passivity, leading to reduced gas fractions and star forming gas reservoirs. We find that passive galaxies at $z \geqslant 5$ are not identified in the typical UVJ selection space due to their still relatively young stellar populations, and present new rest--frame selection regions. We also present NIRCam and MIRI fluxes, and find that significant numbers of passive galaxies at $z \geqslant 5$ should be detectable in upcoming wide surveys with JWST. Finally, we present JWST colour distributions, with new selection regions in the observer--frame for identifying these early passive populations., Comment: 21 pages, 20 figures. Accepted to MNRAS

The star formation and metal enrichment histories of galaxies - at any epoch - constitute one of the key properties of galaxies, and their measurement is a core aim of observational extragalactic astronomy. The lack of deep rest-frame optical coverage at high-redshift has made robust constraints elusive, but this is now changing thanks to the \emph{James Webb Space Telescope (JWST)}. In preparation for the constraints provided by \emph{JWST} we explore the star formation and metal enrichment histories of galaxies at $z=5-13$ using the First Light And Reionisation Epoch Simulations (FLARES) suite. Built on the EAGLE model, the unique strategy of FLARES allows us to simulate a wide range of stellar masses (and luminosities) and environments. While we predict significant redshift evolution of average ages and specific star formation rates our core result is a mostly flat relationship of age and specific star formation rate with stellar mass. We also find that galaxies in this epoch predominantly have strongly rising star formation histories, albeit with the magnitude dropping with redshift and stellar mass. In terms of chemical enrichment we predict a strong stellar mass - metallicity relation present at $z=10$ and beyond alongside significant $\alpha$-enhancement. Finally, we find no environmental dependence of the relationship between age, specific star formation rate, or metallicity with stellar mass., Comment: To be submitted to MNRAS. Comments welcome

With its exquisite sensitivity, wavelength coverage, and spatial and spectral resolution, the James Webb Space Telescope is poised to revolutionise our view of the distant, high-redshift ($z>5$) Universe. While Webb's spectroscopic observations will be transformative for the field, photometric observations play a key role in identifying distant objects and providing more comprehensive samples than accessible to spectroscopy alone. In addition to identifying objects, photometric observations can also be used to infer physical properties and thus be used to constrain galaxy formation models. However, inferred physical properties from broadband photometric observations, particularly in the absence of spectroscopic redshifts, often have large uncertainties. With the development of new tools for forward modelling simulations it is now routinely possible to predict observational quantities, enabling a direct comparison with observations. With this in mind, in this work, we make predictions for the colour evolution of galaxies at $z=5-15$ using the FLARES: First Light And Reionisation Epoch Simulations cosmological hydrodynamical simulation suite. We predict a complex evolution, driven predominantly by strong nebular line emission passing through individual bands. These predictions are in good agreement with existing constraints from Hubble and Spitzer as well as some of the first results from Webb. We also contrast our predictions with other models in the literature: while the general trends are similar we find key differences, particularly in the strength of features associated with strong nebular line emission. This suggests photometric observations alone should provide useful discriminating power between different models., Comment: 10 pages, 9 figures, accepted for publication in MNRAS

We explore the radial distribution of satellite galaxies in groups in the Galaxy and Mass Assembly (GAMA) survey and the IllustrisTNG simulations. Considering groups with masses $12.0 \leq \log_{10} (\mathcal{M}_h / h^{-1} \mathrm{M}_{\odot}) < 14.8$ at $z<0.267$, we find a good agreement between GAMA and a sample of TNG300 groups and galaxies designed to match the GAMA selection. Both display a flat profile in the centre of groups, followed by a decline that becomes steeper towards the group edge, and normalised profiles show no dependence on group mass. Using matched satellites from TNG and dark matter-only TNG-Dark runs we investigate the effect of baryons on satellite radial location. At $z=0$, we find that the matched subhaloes from the TNG-Dark runs display a much flatter radial profile: namely, satellites selected above a minimum stellar mass exhibit both smaller halo-centric distances and longer survival times in the full-physics simulations compared to their dark-matter only analogues. We then divide the TNG satellites into those which possess TNG-Dark counterparts and those which do not, and develop models for the radial positions of each. We find the satellites with TNG-Dark counterparts are displaced towards the halo centre in the full-physics simulations, and this difference has a power-law behaviour with radius. For the `orphan' galaxies without TNG-Dark counterparts, we consider the shape of their radial distribution and provide a model for their motion over time, which can be used to improve the treatment of satellite galaxies in semi-analytic and semi-empirical models of galaxy formation., Comment: 20 pages, 22 figures. MNRAS, version after referee report

Motor systems show an overall robustness, but because they are highly nonlinear, understanding how they achieve robustness is difficult. In many rhythmic systems, robustness against perturbations involves response of both the shape and the timing of the trajectory. This makes the study of robustness even more challenging. To understand how a motor system produces robust behaviors in a variable environment, we consider a neuromechanical model of motor patterns in the feeding apparatus of the marine mollusk \textit{Aplysia californica} \citep{shaw2015,lyttle2017}. We established in \citep{WGCT2021} the tools for studying combined shape and timing responses of limit cycle systems under sustained perturbations and here apply them to study robustness of the neuromechanical model against increased mechanical load during swallowing. Interestingly, we discover that nonlinear biomechanical properties confer resilience by immediately increasing resistance to applied loads. In contrast, the effect of changed sensory feedback signal is significantly delayed by the firing rates' hard boundary properties. Our analysis suggests that sensory feedback contributes to robustness in swallowing primarily by shifting the timing of neural activation involved in the power stroke of the motor cycle (retraction). This effect enables the system to generate stronger retractor muscle forces to compensate for the increased load, and hence achieve strong robustness. The approaches that we are applying to understanding a neuromechanical model in \textit{Aplysia}, and the results that we have obtained, are likely to provide insights into the function of other motor systems that encounter changing mechanical loads and hard boundaries, both due to mechanical and neuronal firing properties., Comment: 26 pages, 13 figures

Density dependence is important in the ecology and evolution of microbial and cancer cells. Typically, we can only measure net growth rates, but the underlying density-dependent mechanisms that give rise to the observed dynamics can manifest in birth processes, death processes, or both. Therefore, we utilize the mean and variance of cell number fluctuations to separately identify birth and death rates from time series that follow stochastic birth-death processes with logistic growth. Our method provides a novel perspective on stochastic parameter identifiability, which we validate by analyzing the accuracy in terms of the discretization bin size. We apply our method to the scenario where a homogeneous cell population goes through three stages: (1) grows naturally to its carrying capacity, (2) is treated with a drug that reduces its carrying capacity, and (3) overcomes the drug effect to restore its original carrying capacity. In each stage, we disambiguate whether it happens through the birth process, death process, or some combination of the two, which contributes to understanding drug resistance mechanisms. In the case of limited data sets, we provide an alternative method based on maximum likelihood and solve a constrained nonlinear optimization problem to identify the most likely density dependence parameter for a given cell number time series. Our methods can be applied to other biological systems at different scales to disambiguate density-dependent mechanisms underlying the same net growth rate.

The James Webb Space Telescope (JWST) is set to transform many areas of astronomy, one of the most exciting is the expansion of the redshift frontier to $z>10$. In its first year alone JWST should discover hundreds of galaxies, dwarfing the handful currently known. To prepare for these powerful observational constraints, we use the First Light And Reionisation Epoch (FLARES) simulations to predict the physical and observational properties of the $z>10$ population of galaxies accessible to JWST. This is the first time such predictions have been made using a hydrodynamical model validated at low redshift. Our predictions at $z=10$ are broadly in agreement with current observational constraints on the far-UV luminosity function and UV continuum slope $\beta$, though the observational uncertainties are large. We note tension with recent constraints $z\sim 13$ from Harikane et al. 2022 - compared to these constraints, FLARES predicts objects with the same space density should have an order of magnitude lower luminosity, though this is mitigated slightly if dust attenuation is negligible in these systems. Our predictions suggest that in JWST's first cycle alone, around $600$ galaxies should be identified at $z>10$, with the first small samples available at $z>13$., Comment: Submitted to MNRAS 20/04/2022

We present the intrinsic and observed sizes of galaxies at $z\geq5$ in the First Light And Reionisation Epoch Simulations (FLARES). We employ the large effective volume of FLARES to produce a sizeable sample of high redshift galaxies with intrinsic and observed luminosities and half light radii in a range of rest frame UV and visual photometric bands. This sample contains a significant number of intrinsically ultra-compact galaxies in the far-UV (1500 angstrom), leading to a negative intrinsic far-UV size-luminosity relation. However, after the inclusion of the effects of dust these same compact galaxies exhibit observed sizes that are as much as 50 times larger than those measured from the intrinsic emission, and broadly agree with a range of observational samples. This increase in size is driven by the concentration of dust in the core of galaxies, heavily attenuating the intrinsically brightest regions. At fixed luminosity we find a galaxy size redshift evolution with a slope of $m=1.21-1.87$ depending on the luminosity sample in question, and we demonstrate the wavelength dependence of the size-luminosity relation which will soon be probed by the Webb Space Telescope.

Generalizing the application of machine learning models to situations where the statistical distribution of training and test data are different has been a complex problem. Our contributions in this paper are threefold: (1) we introduce an anchored-based Out of Distribution (OOD) Regression Mixup algorithm, leveraging manifold hidden state mixup and observation similarities to form a novel regularization penalty, (2) we provide a first of its kind, high resolution Distributed Acoustic Sensor (DAS) dataset that is suitable for testing OOD regression modelling, allowing other researchers to benchmark progress in this area, and (3) we demonstrate with an extensive evaluation the generalization performance of the proposed method against existing approaches, then show that our method achieves state-of-the-art performance. Lastly, we also demonstrate a wider applicability of the proposed method by exhibiting improved generalization performances on other types of regression datasets, including Udacity and Rotation-MNIST datasets., Comment: TII Accepted Version

May and Leonard (SIAM J. Appl. Math 1975) introduced a three-species Lotka-Volterra type population model that exhibits heteroclinic cycling. Rather than producing a periodic limit cycle, the trajectory takes longer and longer to complete each "cycle", passing closer and closer to unstable fixed points in which one population dominates and the others approach zero. Aperiodic heteroclinic dynamics have subsequently been studied in ecological systems (side-blotched lizards; colicinogenic E. coli), in the immune system, in neural information processing models ("winnerless competition"), and in models of neural central pattern generators. Yet as May and Leonard observed "Biologically, the behavior (produced by the model) is nonsense. Once it is conceded that the variables represent animals, and therefore cannot fall below unity, it is clear that the system will, after a few cycles, converge on some single population, extinguishing the other two." Here, we explore different ways of introducing discrete stochastic dynamics based on May and Leonard's ODE model, with application to ecological population dynamics, and to a neuromotor central pattern generator system. We study examples of several quantitatively distinct asymptotic behaviors, including total extinction of all species, extinction to a single species, and persistent cyclic dominance with finite mean cycle length., Comment: 21 pages, 6 figures