Search

The analysis of neural power spectra plays a crucial role in understanding brain function and dysfunction. While recent efforts have led to the development of methods for decomposing spectral data, challenges remain in performing statistical analysis and group-level comparisons. Here, we introduce Bayesian Spectral Decomposition (BSD), a Bayesian framework for analysing neural spectral power. BSD allows for the specification, inversion, comparison, and analysis of parametric models of neural spectra, addressing limitations of existing methods. We first establish the face validity of BSD on simulated data and show how it outperforms an established method (\fooof{}) for peak detection on artificial spectral data. We then demonstrate the efficacy of BSD on a group-level study of EEG spectra in 204 healthy subjects from the LEMON dataset. Our results not only highlight the effectiveness of BSD in model selection and parameter estimation, but also illustrate how BSD enables straightforward group-level regression of the effect of continuous covariates such as age. By using Bayesian inference techniques, BSD provides a robust framework for studying neural spectral data and their relationship to brain function and dysfunction., Comment: 18 pages

The bright radio source, GLEAM J091734-001243 (hereafter GLEAM J0917-0012), was previously selected as a candidate ultra-high redshift (z>5) radio galaxy due to its compact radio size and faint magnitude (K(AB)=22.7). Its redshift was not conclusively determined from follow-up millimetre and near-infrared spectroscopy. Here we present new HST WFC3 G141 grism observations which reveal several emission lines including [NeIII]3867, [NeV]3426 and an extended (~4.8 kpc), [OII]3727 line which confirm a redshift of 3.004+/-0.001. The extended component of the [OII]3727 line is co-spatial with one of two components seen at 2.276 GHz in high resolution (60x20 mas) Long Baseline Array data, reminiscent of the alignments seen in local compact radio galaxies. The BEAGLE stellar mass (~2x10^11 Msun) and radio luminosity (L_500MHz}~10^28 W Hz^-1) put GLEAM J0917-0012 within the distribution of the brightest high-redshift radio galaxies at similar redshifts. However, it is more compact than all of them. Modelling of the radio jet demonstrates that this is a young, ~50 kyr old, but powerful, 10^39 W, compact steep spectrum radio source. The weak constraint on the active galactic nucleus bolometric luminosity from the [NeV]3426 line combined with the modelled jet power tentatively implies a large black hole mass, >10^9 Msun, and a low, advection-dominated accretion rate, an Eddington ratio <0.03. The [NeV]3426/[NeIII]3867 vs [OII]3727/[NeIII]3867 line ratios are most easily explained by radiative shock models with precursor photoionisation. Hence, we infer that the line emission is directly caused by the shocks from the jet and that this radio source is one of the youngest and most powerful known at cosmic noon. We speculate that the star-formation in GLEAM J0917-0012 could be on its way to becoming quenched by the jet., Comment: 16 pages, 7 figures, 4 tables, accepted for publication in PASA

We give a construction to build all digraphs with the property that every directed cycle has length three.

Non-custodial wallets are a type of cryptocurrency wallet wherein the owner has full control over the private keys and is solely responsible for managing and securing the digital assets that it contains. Unlike custodial wallets, which are managed by third parties, such as exchanges, non-custodial wallets ensure that funds are controlled exclusively by the end user. We characterise the difference between custodial and non-custodial wallets and examine their key features and related risks., Comment: 6 pages, 1 figure

Let G be an acyclic digraph, and let a, b, c, d be vertices, where a, b are sources, c, d are sinks, and every other vertex has in-degree and out-degree at least two. In 1985, Thomassen showed that there do not exist disjoint directed paths from a to c and from b to d, if and only if G can be drawn in a closed disc with a, b, c, d drawn in the boundary in order. We give a shorter proof.

We prove that for every complete graph $K_t$, all graphs $G$ with no induced subgraph isomorphic to a subdivision of $K_t$ have a stable subset of size at least $|G|/{\rm polylog}|G|$. This is close to best possible, because for $t\ge 6$, not all such graphs $G$ have a stable set of linear size, even if $G$ is triangle-free.

When $H$ is a forest, the Gy\'arf\'as-Sumner conjecture implies that every graph $G$ with no induced subgraph isomorphic to $H$ and with bounded clique number has a stable set of linear size. We cannot prove that, but we prove that every such graph $G$ has a stable set of size $|G|^{1-o(1)}$. If $H$ is not a forest, there need not be such a stable set. Second, we prove that when $H$ is a ``multibroom'', there {\em is} a stable set of linear size. As a consequence, we deduce that all multibrooms satisfy a ``fractional colouring'' version of the Gy\'arf\'as-Sumner conjecture. Finally, we discuss extensions of our results to the multicolour setting.

A {\em $k$-kernel} in a digraph $G$ is a stable set $X$ of vertices such that every vertex of $G$ can be joined from $X$ by a directed path of length at most $k$. We prove three results about $k$-kernels. First, it was conjectured by Erd\H{o}s and Sz\'ekely in 1976 that every digraph $G$ with no source has a 2-kernel $|K|$ with $|K|\le |G|/2$. We prove this conjecture when $G$ is a ``split digraph'' (that is, its vertex set can be partitioned into a tournament and a stable set), improving a result of Langlois et al., who proved that every split digraph $G$ with no source has a 2-kernel of size at most $2|G|/3$. Second, the Erd\H{o}s-Sz\'ekely conjecture implies that in every digraph $G$ there is a 2-kernel $K$ such that the union of $K$ and its out-neighbours has size at least $|G|/2$. We prove that this is true if $V(G)$ can be partitioned into a tournament and an acyclic set. Third, in a recent paper, Spiro asked whether, for all $k\ge 3$, every strongly-connected digraph $G$ has a $k$-kernel of size at most about $|G|/(k+1)$. This remains open, but we prove that there is one of size at most about $|G|/(k-1)$.

We prove the existence of murmurations in the family of Maass forms of weight 0 and level 1 with their Laplace eigenvalue parameter going to infinity (i.e., correlations between the parity and Hecke eigenvalues at primes growing in proportion to the analytic conductor).

The fork is the tree obtained from the claw $K_{1,3}$ by subdividing one of its edges once, and the antifork is its complement graph. We give a complete description of all graphs that do not contain the fork or antifork as induced subgraphs., Comment: This is an old paper. It was published in 2020 in Discrete Math where it was awarded Editors' choice

We present deep near-infrared $K_{\rm s}$-band imaging for 35 of the 53 sources from the high-redshift ($z > 2$) radio galaxy candidate sample defined in Broderick et al. (2022). These images were obtained using the High-Acuity Widefield $K$-band Imager (HAWK-I) on the Very Large Telescope. Host galaxies are detected for 27 of the sources, with $K_{\rm s} \approx 21.6$$-$$23.0$ mag (2$''$ diameter apertures; AB). The remaining eight targets are not detected to a median $3\sigma$ depth of $K_{\rm s} \approx 23.3$ mag ($2''$ diameter apertures). We examine the radio and near-infrared flux densities of the 35 sources, comparing them to the known $z > 3$ powerful radio galaxies with 500-MHz radio luminosities $L_{500\,{\rm MHz}} > 10^{27}$ W Hz$^{-1}$. By plotting 150-MHz flux density versus $K_{\rm s}$-band flux density, we find that, similar to the sources from the literature, these new targets have large radio to near-infrared flux density ratios, but extending the distribution to fainter flux densities. Five of the eight HAWK-I deep non-detections have a median $3\sigma$ lower limit of $K_{\rm s} \gtrsim 23.8$ mag ($1.5''$ diameter apertures); these five targets, along with a further source from Broderick et al. (2022) with a deep non-detection ($K_{\rm s} \gtrsim 23.7$ mag; $3\sigma$; $2''$ diameter aperture) in the Southern H-ATLAS Regions $K_{\rm s}$-band Survey, are considered candidates to be ultra-high-redshift ($z > 5$) radio galaxies. The extreme radio to near-infrared flux density ratios ($>10^5$) for these six sources are comparable to TN J0924$-$2201, GLEAM J0856$+$0223 and TGSS J1530$+$1049, the three known powerful radio galaxies at $z > 5$. For a selection of galaxy templates with different stellar masses, we show that $z \gtrsim 4.2$ is a plausible scenario for our ultra-high-redshift candidates if the stellar mass $M_{\rm *} \gtrsim 10^{10.5}\,{\rm M}_\odot$. [abridged], Comment: 24 pages, 5 figures (one of which is a multi-page figure with 30 separate panels), 2 tables, accepted for publication in PASA

Effective policy and intervention strategies to combat human trafficking for child sexual exploitation material (CSEM) production require accurate prevalence estimates. Traditional Network Scale Up Method (NSUM) models often necessitate standalone surveys for each geographic region, escalating costs and complexity. This study introduces a partially pooled NSUM model, using a hierarchical Bayesian framework that efficiently aggregates and utilizes data across multiple regions without increasing sample sizes. We developed this model for a novel national survey dataset from the Philippines and we demonstrate its ability to produce detailed municipal-level prevalence estimates of trafficking for CSEM production. Our results not only underscore the model's precision in estimating hidden populations but also highlight its potential for broader application in other areas of social science and public health research, offering significant implications for resource allocation and intervention planning.

We present a multi-wavelength study on three new $z\sim5.6$ quasi stellar objects (QSOs) selected based on their radio and optical/near-infrared properties in publicly available surveys and then identified with dedicated spectroscopic observations. These are among the radio-brightest QSOs currently known at $z>5.5$, having $\rm R=S_{\rm 5GHz}/S_{\rm 4400A}>100$. In this work we present their identification and we also discuss their multi-wavelength properties (from the radio to the X-ray band) based on the detection in public surveys as well as dedicated radio and X-ray observations. The three sources present a wide range of properties, in terms of relative intensity and spectral shape, highlighting the importance of multi-wavelength observations in order to accurately characterise these high-$z$ objects. In particular, from our analysis we found one source, at $z=5.61$, that presents clear blazars properties (strong and flat radio and X-ray emission), making it one of the most distant currently known in this class. Moreover, from the fit of the optical/near-infrared photometric measurements with an accretion disc model, as well as the analysis of the CIV broad emission line in one case, we were able to estimate the mass and the accretion rate of the central black holes in these systems, finding $\rm M_{\rm BH}\sim1-10\times10^9$ M$_\odot$ accreting at a rate $\lambda_{\rm Edd}\sim0.1-0.2$. With this work we increase the number of very-high redshift radio-powerful QSOs characterised with multi-wavelength observations, essential in order to understand the evolution and the properties of this still poorly constrained class of sources., Comment: Submitted to A&A on July 4th

The advent of LLMs means that CUIs are cool again, but what isn't so cool is that we're doomed to use them alone. The one user, one account, one device paradigm has dominated the design of CUIs and is not going away as new conversational technologies emerge. In this provocation we explore some of the technical, legal, and design difficulties that seem to make multi-user CUIs so difficult to implement. Drawing inspiration from the ways that people manage messy group discussions, such as parliamentary and consensus-based paradigms, we show how LLM-based CUIs might be well suited to bridging the gap. With any luck, this might even result in everyone having to sit through fewer poorly run meetings and agonising group discussions - truly a laudable goal!, Comment: To appear in the proceedings of the 2024 ACM Conference on Conversational User Interfaces (CUI 24)

Honour based abuse covers a wide range of family abuse including female genital mutilation and forced marriage. Safeguarding professionals need to identify where abuses are happening in their local community to best support those at risk of these crimes and take preventative action. However, there is little local data about these kinds of crime. To tackle this problem, we ran comparative judgement surveys to map abuses at local level. In previous comparative judgement studies, participants reported fatigue associated with comparisons between areas with similar levels of abuse. Allowing for ties reduces fatigue, but increase the computational complexity when fitting the model. We designed an efficient Markov Chain Monte Carlo algorithm to fit the model, allowing for a wide range of prior distributions on the model parameters. Working with South Yorkshire Police and Oxford Against Cutting, we mapped the risk of honour based abuse at community level in two counties in the UK., Comment: 17 pages, 6 figures, submitted

The energy coupling efficiency of active galactic nucleus (AGN) outbursts is known to differ significantly with factors including the jet kinetic power, duration of the outburst, and properties of the host galaxy cluster. As such, constraints on their jet power and lifetime functions are crucial to quantify the role of kinetic-mode AGN feedback on the evolution of galaxies since $z \sim 1$. In this work, we address this issue by measuring the energetics of a sample of 79 low-redshift (0.02 $< z <$ 0.2) remnant radio galaxies compiled from large-sky radio surveys - these objects uniquely probe the full duration of an AGN outburst. The jet kinetic power and outburst duration of each remnant are determined using the RAiSE dynamical model based on the surface brightness distribution observed in multi-frequency radio images. We compare the energetics constrained for this sample to those predicted for mock radio source populations - with various intrinsic functions for jet power and lifetime distributions - to correct for sample selection biases imposed on our sample. The intrinsic jet power and lifetime functions that yield a selection-biased mock population most similar to our observed sample are found using Bayesian inference. Our analysis places robust constraints on assumed power-law indices for the intrinsic jet power and lifetime functions: $p(Q)\propto Q^{-1.49\pm0.07}$ and $p(t_{\mathrm{on}})\propto t_{\mathrm{on}}^{-0.97\pm0.12}$ respectively. We discuss the implication of these findings for feedback-regulated accretion and the self-regulating nature of jet activity. The methodology proposed in this work can be extended to active radio galaxies in future studies., Comment: 19 pages, 9 figures, 2 tables; submitted to MNRAS

We prove that a graph does not contain as a minor a graph formed by 0-, 1-, 2- or 3-summing $k$ copies of $K_5$ or $K_{3,3}$, if and only if it has bounded genus.

A graph is a ``$k$-Kuratowski graph'' if it has exactly $k$ components, each isomorphic to $K_5$ or to $K_{3,3}$. We prove that if a graph $G$ contains no $k$-Kuratowski graph as a minor,then there is a set $X$ of boundedly many vertices such that $G\setminus X$ can be drawn in a (possibly disconnected) surface in which no $k$-Kuratowski graph can be drawn.

We present a multi-wavelength analysis, from the radio to the X-ray band, of the redshift $z=6.44$ VIK J2318$-$31 radio-loud (RL) quasi stellar object (QSO), one of the most distant currently known in this class. The work is based on newly obtained (uGMRT, ATCA, Chandra) as well as archival (GNIRS and X-Shooter) dedicated observations that have not been published yet. Based on the observed X-ray and radio emission, its relativistic jets are likely young and misaligned from our line of sight. Moreover, we can confirm, with simultaneous observations, the presence of a turnover in the radio spectrum at $\nu_{\rm peak} \sim 650$ MHz which is unlikely to be associated with self-synchrotron absorption. From the NIR spectrum we derived the mass of the central black hole, M$_{\rm BH}=8.1^{+6.8}_{-5.6} \times 10^8 {\rm M_{\odot}}$, and the Eddington ratio, $\lambda_{\rm EDD} = 0.8^{+0.8}_{-0.6}$, using broad emission lines as well as an accretion disc model fit to the continuum emission. Given the high accretion rate, the presence of a $\sim$8$\times$10$^8$ M$_\odot$ black hole at $z=6.44$ can be explained by a seed black hole ($\sim$10$^{4}$ M$_\odot$) that formed at $z\sim25$, assuming a radiative efficiency $\eta_{\rm d}\sim0.1$. However, by assuming $\eta_{\rm d}\sim0.3$, as expected for jetted systems, the mass observed would challenge current theoretical models of black hole formation., Comment: Accepted for publication on A&A the 22nd April 2024

The tight relationship between infrared luminosity (L$_\mathrm{TIR}$) and 1.4 GHz radio continuum luminosity (L$_\mathrm{1.4GHz}$) has proven useful for understanding star formation free from dust obscuration. Infrared emission in star-forming galaxies typically arises from recently formed, dust-enshrouded stars, whereas radio synchrotron emission is expected from subsequent supernovae. By leveraging the wealth of ancillary far-ultraviolet - far-infrared photometry from the Deep Extragalactic VIsible Legacy Survey (DEVILS) and Galaxy and Mass Assembly (GAMA) surveys, combined with 1.4 GHz observations from the MeerKAT International GHz Tiered Extragalactic Exploration (MIGHTEE) survey and Deep Investigation of Neutral Gas Origins (DINGO) projects, we investigate the impact of timescale differences between far-ultraviolet - far-infrared and radio-derived star formation rate (SFR) tracers. We examine how the SED-derived star formation histories (SFH) of galaxies can be used to explain discrepancies in these SFR tracers, which are sensitive to different timescales. Galaxies exhibiting an increasing SFH have systematically higher L$_\mathrm{TIR}$ and SED-derived SFRs than predicted from their 1.4 GHz radio luminosity. This indicates that insufficient time has passed for subsequent supernovae-driven radio emission to accumulate. We show that backtracking the SFR(t) of galaxies along their SED-derived SFHs to a time several hundred megayears prior to their observed epoch will both linearise the SFR-L$_\mathrm{1.4GHz}$ relation and reduce the overall scatter. The minimum scatter in the SFR(t)-L$_\mathrm{1.4GHz}$ is reached at 200 - 300 Myr prior, consistent with theoretical predictions for the timescales required to disperse the cosmic ray electrons responsible for the synchrotron emission., Comment: 23 pages, 13 figures, 2 tables. Accepted for publication in MNRAS

The Single Instruction, Multiple Thread (SIMT) paradigm of GPU programming does not support the branching nature of a parton shower algorithm by definition. However, modern GPUs are designed to schedule threads with diverging processes independently, allowing them to handle such branches. With regular thread synchronisation and careful treatment of the individual steps, one can simulate a parton shower on a GPU. We present a Sudakov veto algorithm designed to simulate parton branching on multiple events in parallel. We also release a CUDA C++ program that generates matrix elements, showers partons and computes jet rates and event shapes for LEP at 91.2 GeV on a GPU. To benchmark its performance, we also provide a near-identical C++ program designed to simulate events serially on a CPU. While the consequences of branching are not absent, we demonstrate that a GPU can provide the throughput of a many-core CPU. As an example, we show that the time taken to shower 10^6 events on one NVIDIA TESLA V100 GPU is equivalent to that of 295 Intel Xeon E5-2620 CPU cores., Comment: 23 pages, 9 figures

In 1972, Mader showed that every graph without a 3-connected subgraph is 4-degenerate and thus 5-colorable}. We show that the number 5 of colors can be replaced by 4, which is best possible., Comment: 13 pages

It was conjectured, independently by two sets of authors, that for all integers $k,d\ge 1$ there exists $\ell>0$, such that if $S,T$ are subsets of vertices of a graph $G$, then either there are $k$ paths between $S,T$, pairwise at distance at least $d$, or there is a set $X\subseteq V(G)$ with $|X|\le k-1$ such that every path between $S,T$ contains a vertex with distance at most $\ell$ from some member of $X$. The result is known for $k\le 2$, but we will show that it is false for all $k\ge 3$, even if $G$ is constrained to have maximum degree at most three. We also give a proof of the result when $k=2$ that is simpler than the previous proofs.

AI assistants such as Alexa, Google Assistant, and Siri, are making their way into the healthcare sector, offering a convenient way for users to access different healthcare services. Trust is a vital factor in the uptake of healthcare services, but the factors affecting trust in voice assistants used for healthcare are under-explored and this specialist domain introduces additional requirements. This study explores the effects of different functional, personal, and risk factors on trust in and adoption of healthcare voice AI assistants (HVAs), generating a partial least squares structural model from a survey of 300 voice assistant users. Our results indicate that trust in HVAs can be significantly explained by functional factors (usefulness, content credibility, quality of service relative to a healthcare professional), together with security, and privacy risks and personal stance in technology. We also discuss differences in terms of trust between HVAs and general-purpose voice assistants as well as implications that are unique to HVAs., Comment: 37 pages. This is a preprint of the paper accepted for the 27th ACM Conference on Computer-Supported Cooperative Work and Social Computing (CSCW'24)

We confirm a conjecture of Fox, Pach, and Suk, that for every $d>0$, there exists $c>0$ such that every $n$-vertex graph of VC-dimension at most $d$ has a clique or stable set of size at least $n^c$. This implies that, in the language of model theory, every graph definable in NIP structures has a clique or anti-clique of polynomial size, settling a conjecture of Chernikov, Starchenko, and Thomas. Our result also implies that every two-colourable tournament satisfies the tournament version of the Erd\H{o}s-Hajnal conjecture, which completes the verification of the conjecture for six-vertex tournaments. The result extends to uniform hypergraphs of bounded VC-dimension as well. The proof method uses the ultra-strong regularity lemma for graphs of bounded VC-dimension proved by Lov\'asz and Szegedy and the method of iterative sparsification introduced by the authors in an earlier paper., Comment: 11 pages, minor revisions

We prove the Erd\H{o}s-Hajnal conjecture for the five-vertex path $P_5$; that is, there exists $c>0$ such that every $n$-vertex graph with no induced $P_5$ has a clique or stable set of size at least $n^c$. This completes the verification of the Erd\H{o}s-Hajnal property of all five-vertex graphs. Indeed, we show a stronger statement, that $P_5$ satisfies the polynomial version of a theorem of R\"odl. To achieve this, we combine simple probabilistic and structural ideas with the iterative sparsification framework introduced in the series., Comment: 15 pages

This paper presents the inaugural investigation of beyond the Standard Model (BSM) radiation processes, framed as a generalized, process- and model-independent parton shower algorithm within Herwig 7, based on direct translations of Universal FeynRules Output (UFO) constructed via Herwig's ufo2herwig module. Leveraging the fact that shower kinematics are dictated by the spins of involved particles, we calculate comprehensive helicity-dependent branching kernels for all feasible splittings of scalars, fermions, and vector bosons, tailored to Herwig 7's angular-ordering (AO) parton shower algorithm. Utilizing these kernels, we derive BSM splitting functions in the quasi-collinear limit, ensuring compatibility with the Standard Model (SM) and supersymmetry (SUSY) splitting functions when analogous parameter conditions are applied. These newly derived functions have been integrated into the Herwig 7 event generator framework. Comparative analyses with fixed-order matrix element calculations show good agreement for single radiation events. Moreover, the results showcase the influence of BSM radiation at the Large Hadron Collider (LHC) and envisage its implications for future collider endeavours. This research augments our comprehension of BSM radiation effects, with significant bearings on present and prospective collider-based inquiries.

We demonstrate the importance of radio selection in probing heavily obscured galaxy populations. We combine Evolutionary Map of the Universe (EMU) Early Science data in the Galaxy and Mass Assembly (GAMA) G23 field with the GAMA data, providing optical photometry and spectral line measurements, together with Wide-field Infrared Survey Explorer (WISE) infrared (IR) photometry, providing IR luminosities and colours. We investigate the degree of obscuration in star forming galaxies, based on the Balmer decrement (BD), and explore how this trend varies, over a redshift range of 0

A new release of the Monte Carlo event generator Herwig (version 7.3) has been launched. This iteration encompasses several enhancements over its predecessor, version 7.2. Noteworthy upgrades include: the implementation of a process-independent electroweak angular-ordered parton shower integrated with QCD and QED radiation; a new recoil scheme for initial-state radiation improving the behaviour of the angular-ordered parton shower; the incorporation of the heavy quark effective theory to refine the hadronization and decay of excited heavy mesons and heavy baryons; a dynamic strategy to regulate the kinematic threshold of cluster splittings within the cluster hadronization model; several improvements to the structure of the cluster hadronization model allowing for refined models; the possibility to extract event-by-event hadronization corrections in a well-defined way; the possibility of using the string model, with a dedicated tune. Additionally, a new tuning of the parton shower and hadronization parameters has been executed. This article discusses the novel features introduced in version 7.3.0., Comment: 10 pages, 3 figures. Herwig is available from https://herwig.hepforge.org

Voice applications (voice apps) are a key element in Voice Assistant ecosystems such as Amazon Alexa and Google Assistant, as they provide assistants with a wide range of capabilities that users can invoke with a voice command. Most voice apps, however, are developed by third parties - i.e., not by Amazon/Google - and they are included in the ecosystem through marketplaces akin to smartphone app stores but with crucial differences, e.g., the voice app code is not hosted by the marketplace and is not run on the local device. Previous research has studied the security and privacy issues of voice apps in the wild, finding evidence of bad practices by voice app developers. However, developers' perspectives are yet to be explored. In this paper, we report a qualitative study of the experiences of voice app developers and the challenges they face. Our findings suggest that: 1) developers face several risks due to liability pushed on to them by the more powerful voice assistant platforms, which are linked to negative privacy and security outcomes on voice assistant platforms; and 2) there are key issues around monetization, privacy, design, and testing rooted in problems with the voice app certification process. We discuss the implications of our results for voice app developers, platforms, regulators, and research on voice app development and certification., Comment: To be presented at USENIX Security 2024

There may exist stellar-mass binary black holes (BBH) which merge while orbiting nearby a supermassive black hole (SMBH). In such a triple system, the SMBH will modulate the gravitational waveform of the BBH through orbital Doppler shift and de Sitter precession of the angular momentum. Future space-based GW observatories focused on the milli- and decihertz band will be uniquely poised to observe these waveform modulations, as the GW frequency from stellar-mass BBHs varies slowly in this band while modulation effects accumulate. In this work, we apply the Fisher information matrix formalism to estimate how well space-borne GW detectors can measure properties of BBH+SMBH hierarchical triples using the GW from orbiting BBH. We extend previous work by considering the more realistic case of an eccentric orbit around the SMBH, and notably include the effects of orbital pericenter precession. We find that for detector concepts such as LISA, B-DECIGO, and TianGO, we can extract the SMBH mass and semimajor axis of the orbit with a fractional uncertainty below the 0.1% level over a wide range of triple system parameters. Furthermore, we find that the effects of pericenter precession and orbital eccentricity significantly improve our ability to measure this system. We also find that while LISA could measure these systems, the decihertz detector concepts B-DECIGO and TianGO would enable better sensitivity to the triple's parameters., Comment: 12 pages (main text excluding references and appendices), 11 figures, submitted to PRD

This paper presents the results of 475 hours of interferometric observations with the Australia Telescope Compact Array towards the Spiderweb protocluster at \(z=2.16\). We search for large, extended molecular gas reservoirs among 46 previously detected CO(1-0) emitters, employing a customised method we developed. Based on the CO emission images and position-velocity diagrams, as well as the ranking of sources using a binary weighting of six different criteria, we have identified 14 robust and 7 tentative candidates that exhibit large extended molecular gas reservoirs. These extended reservoirs are defined as having sizes greater than 40 kpc or super-galactic scale. This result suggests a high frequency of extended gas reservoirs, comprising at least \(30 \%\) of our CO-selected sample. An environmental study of the candidates is carried out based on N-th nearest neighbour and we find that the large molecular gas reservoirs tend to exist in denser regions. The spatial distribution of our candidates is mainly centred on the core region of the Spiderweb protocluster. The performance and adaptability of our method are discussed. We found 13 (potentially) extended gas reservoirs located in nine galaxy (proto)clusters from the literature. We noticed that large extended molecular gas reservoirs surrounding (normal) star-forming galaxies in protoclusters are rare. This may be attributable to the lack of observations low-J CO transitions and the lack of quantitative analyses of molecular gas morphologies. The large gas reservoirs in the Spiderweb protocluster are a potential source of the intracluster medium seen in low redshift Virgo- or Coma-like galaxy clusters., Comment: 25 pages, 16 figures. Accepted for publication in MNRAS