arXiv subjects

Harry Desmond

Publications and source records attributed to Harry Desmond.

At least 37 records · Page 2Linked to original sources

arXiv2026

Exhaustive Symbolic Integration: Integration by Differentiation and the Landscape of Symbolic Integrability

We introduce Exhaustive Symbolic Integration (ESI), a method that enumerates all symbolic functions up to a given complexity $k$ within a specified operator basis and determines which admit closed-form antiderivatives within the same class. This allows us to compute the "integrability fraction" $ρ(k)$ (the fraction of functions whose derivatives lie within the same class), which we do for five operator bases including combinations of rational functions, powers, exponentials, logarithms and trigonometric functions. We find that $ρ(k)$ declines at high complexity and that the operator basis has a dramatic effect -- in particular, adding the logarithm boosts $ρ(k)$ by a factor of $\sim$3 and produces or exacerbates a clear peak at $k=6$. We also deploy ESI as a novel integration algorithm, identifying three integrals that resist SymPy, Mathematica, RUBI, FriCAS, Maxima and Giac under all tested strategies. When an antiderivative can be found by multiple methods, ESI often returns the simplest form. These results reveal that the landscape of symbolic integrability is shaped primarily by the choice of operators, and that exhaustive enumeration can systematically discover integrable forms -- including novel ones -- that elude computer albegra systems.

cs.SC↗

arXiv2026

The functional form of galaxy and halo luminosity and mass functions

The galaxy luminosity and stellar mass function (LF, SMF), and halo mass function (HMF), are fundamental quantities in astrophysics and crucial inputs to a range of astrophysical and cosmological analyses. They are typically parametrised by fitting functions that have been chosen "by eye" to match observed or simulated data. We apply symbolic regression -- specifically the Exhaustive Symbolic Regression (ESR) algorithm -- to automate the search for optimal LF, SMF and HMF functional forms. ESR scores all functions up to a maximum complexity composed of a user-defined basis set of operators using the description length, an approximation to the Bayesian evidence that balances accuracy with complexity. We find many functions outperforming the Schechter and double Schechter functions for the LF and SMF, and that outperform the Press--Schechter and Warren/Tinker functions for the HMF. By additionally imposing "physicality checks" on functions' extrapolation and integration properties, we identify the optimal, low-complexity functional forms in terms of accuracy, simplicity and behaviour beyond the data range. As well as providing drop-in replacements for literature LF, SMF and HMF fitting functions, and identifying robust behaviour across well-fitting functions, we present a framework with which symbolic regression may be used to automate the discovery of optimal functions for any astrophysical dataset.

astro-ph.GA↗

arXiv2026

The Inefficiency of Genetic Programming for Symbolic Regression

We analyse the search behaviour of genetic programming for symbolic regression in practically relevant but limited settings, allowing exhaustive enumeration of all solutions. This enables us to quantify the success probability of finding the best possible expressions, and to compare the search efficiency of genetic programming to random search in the space of semantically unique expressions. This analysis is made possible by improved algorithms for equality saturation, which we use to improve the Exhaustive Symbolic Regression algorithm; this produces the set of semantically unique expression structures, orders of magnitude smaller than the full symbolic regression search space. We compare the efficiency of random search in the set of unique expressions and genetic programming. For our experiments we use two real-world datasets where symbolic regression has been used to produce well-fitting univariate expressions: the Nikuradse dataset of flow in rough pipes and the Radial Acceleration Relation of galaxy dynamics. The results show that genetic programming in such limited settings explores only a small fraction of all unique expressions, and evaluates expressions repeatedly that are congruent to already visited expressions.

cs.NE↗

arXiv2026

Renzo's rule revisited: A statistical study of galaxies' baryon - dark matter coupling

We present a systematic statistical analysis of an informal astrophysical phenomenon known as Renzo's rule (or Sancisi's law), which states that "for any feature in a galaxy's luminosity profile, there is a corresponding feature in the rotation curve, and vice versa." This is often posed as a challenge for the standard LCDM model while supporting alternative theories such as MOND. Indeed, we identify clear features in the dwarf spiral NGC 1560 -- a prime example for Renzo's rule -- and find correlation statistics which support Renzo's rule with a slight preference for MOND over LCDM halo fits. However, a broader analysis on galaxies in the SPARC database reveals an excess of features in rotation curves that lack clear baryonic counterparts, with correlation statistics deviating up to $3σ$ on average from that predicted by both MOND and LCDM haloes, challenging the validity of Renzo's rule. Thus we do not find clear evidence for Renzo's rule in present galaxy data overall. We additionally perform mock tests, which show that a definitive test of Renzo's rule is primarily limited by the lack of clearly resolved baryonic features in current galaxy data.

astro-ph.GA↗

arXiv2026

Comparing measures of the Hubble and BAO tensions in $Λ$CDM and possible solutions in $f(Q)$ gravity

We test whether $f(Q)$ symmetric teleparallel gravity theories can solve the Hubble tension consistently with DESI DR2 BAO. We consider three $f(Q)$ functional forms: logarithmic, exponential, and hyperbolic tangent. We extend these models by allowing a cosmological constant, and compare to phenomenological models with a flexible exponential, hyperbolic secant, and polynomial decay addition to the standard $Λ$CDM $H(z)$. We test these models against DESI DR2 BAO, CMB ($Planck$ 2018 + SPT-3G + ACT DR6), local $H_0$, and Cosmic Chronometer data. The logarithmic and hyperbolic tangent $f(Q)$ models do not provide an adequate solution, but the exponential model does. Furthermore, it slightly reduces the $(Ω_m, H_0 r_d)$ parameter space tension between CMB and BAO datasets to $2.56σ$, down from $2.65σ$ for $Λ$CDM. Although $Λ$CDM faces only $1.66σ$ tension in DESI data space, the $1σ$ higher tension in parameter space suggests a real anomaly. The models assisted by the cosmological constant perform slightly better still, at the cost of undermined theoretical motivation. They also perform poorly once local $H_0$ measurements are included. The phenomenological models fit all data reasonably well, yet the best-fitting models predict isotropically averaged BAO distances exceeding the DESI DR2 measurements at all redshifts. This highlights the difficulties of finding a theoretically motivated solution to the Hubble tension while remaining consistent with BAO data.

astro-ph.CO↗

arXiv2026

The causal structure of galactic astrophysics

Data-driven astrophysics currently relies on the detection and characterisation of correlations between objects' properties, which are then used to test physical theories that make predictions for them. This process fails to utilise information in the data that forms a crucial part of the theories' predictions, namely which variables are directly correlated (as opposed to accidentally correlated through others), the directions of these determinations, and the presence or absence of confounders that correlate variables in the dataset but are themselves absent from it. We propose to recover this information through causal discovery, a well-developed methodology for inferring the causal structure of datasets that is however almost entirely unknown to astrophysics. We develop a causal discovery algorithm suitable for large astrophysical datasets and illustrate it on $\sim$4.5$\times10^5$ nearby galaxies from the Nasa Sloan Atlas, demonstrating its ability to distinguish physical mechanisms that are degenerate on the basis of correlations alone.

astro-ph.GA↗

arXiv2026

The local void model for the Hubble and BAO tensions

The inconsistency between the locally inferred Hubble constant and the value inferred from the cosmic microwave background assuming the $Λ$CDM cosmological model has persisted, turning into an important problem. An emergent underlying trend is that this Hubble tension is driven by data confined to the very low-redshift Universe (typically $z < 0.15$). Most intermediate-redshift measurements remain mutually consistent with $H_0^\mathrm{CMB}$, the $Λ$CDM expectation anchored by the CMB. This Perspective examines if a large local void can explain the Hubble tension and its appearance only at low $z$. For an observer residing within a large underdensity, such as the Milky Way inside the claimed KBC void, gravitationally induced outflows and redshift can inflate the locally inferred recession scale $cz'$ despite having $H_0 = H_0^\mathrm{CMB}$. We summarise evidence suggestive of a local underdensity from multi-wavelength galaxy number counts, discuss the dynamical requirements implied by the amplitude of inferred bulk flows, and connect the solution to the emerging low-redshift BAO distance anomaly ($α_{\mathrm{iso}} < 1$). Previously published semi-analytic void models anticipated the observed redshift dependence of BAO deviations and predict a rapid convergence to CMB-consistent expansion for $z \gtrsim 0.2$, aligning with reconstructions of $H_0(z)$ from BAO plus uncalibrated Type Ia supernovae. We conclude by looking to future tests, including improved mapping of the local density and velocity field, fits to galaxy distance catalogues at the field level, kinematic Sunyaev-Zel'dovich constraints on coherent outflows, fast radio bursts, and the long-term prospect of redshift drift measurements as a direct probe of time-varying non-cosmological redshift contributions.

astro-ph.CO↗

arXiv2026

Revisiting the Great Attractor: The Local Group's streamline trajectory, cosmic velocity and dynamical fate

We revisit the Great Attractor using the Manticore-Local suite of digital twins of the nearby Universe. The Great Attractor concept has been proposed as an answer to three distinct questions: what sources the Local Group velocity in the cosmic microwave background frame, where present-day velocity streamlines converge, and where the Local Group is moving to. Addressing the original motivation of the Great Attractor -- explaining the Local Group cosmic velocity -- we find that mass within $155~h^{-1}\mathrm{Mpc}$ accounts for only ${\sim}72\%$ of that velocity magnitude with ${\sim}38\,°$ directional offset. We show that even in the purely linear regime convergence within this volume is not guaranteed, particularly when also accounting for small-scale contributions to the observer velocity; no single structure, including the proposed Great Attractor, would be expected to dominate the velocity budget. Streamline convergence is smoothing-scale-dependent, transitioning from Virgo at small scales through the Hydra--Centaurus region at intermediate scales to Shapley at large scales; at intermediate smoothing the convergence point lies near Abell 3565 with an asymmetric basin of mass $\log( M / (h^{-1} \mathrm{M}_\odot)) = 16.4 \pm 0.1$ that excludes Norma. To address the third question, we evolve the Manticore-Local realisations to scale factor $a = 10$ in a new Beyond-Present-Time simulation suite and identify the asymptotic future location of the Local Group. We find that the dominant motion is towards Virgo, but even it contributes at most one third of the Local Group velocity. Our results demonstrate that the classical Great Attractor is not a dynamically dominant structure but an artefact of the instantaneous velocity field, and that no single attractor is likely to account for the Local Group motion in the cosmic rest frame.

astro-ph.CO↗

arXiv2026

No evidence for p- or d-wave dark matter annihilation from local large-scale structure

If dark matter annihilates into standard model particles with a cross-section which is velocity dependent, then Local Group dwarf galaxies will not be the best place to search for the resulting gamma ray emission. A greater flux would be produced by more distant and massive halos, with larger velocity dispersions. We construct full-sky predictions for the gamma-ray emission from galaxy- and cluster-mass halos within $\sim 200 {\rm \, Mpc}$ using a suite of constrained $N$-body simulations ($\texttt{CSiBORG}$) based on the Bayesian Origin Reconstruction from Galaxies algorithm. Comparing to observations from the Fermi Large Area Telescope and marginalising over reconstruction uncertainties and other astrophysical contributions to the flux, we obtain constraints on the cross-section which are two (seven) orders of magnitude tighter than those obtained from dwarf spheroidals for $p$-wave ($d$-wave) annihilation. We find no evidence for either type of annihilation from dark matter particles with masses in the range $m_χ= 2-500{\rm \, GeV}/c^2$, for any channel. As an example, for annihilations producing bottom quarks with $m_χ= 10 {\rm \, GeV}/c^2$, we find $a_{1} < 2.4 \times 10^{-21} {\rm \, cm^3 s^{-1}}$ and $a_{2} < 3.0 \times 10^{-18} {\rm \, cm^3 s^{-1}}$ at 95% confidence, where the product of the cross-section, $σ$, and relative particle velocity, $v$, is given by $σv = a_\ell (v/c)^{2\ell}$ and $\ell=1, 2$ for $p$-, $d$-wave annihilation, respectively. Our bounds, although failing to exclude the thermal relic cross-section for velocity-dependent annihilation channels, are among the tightest to date.

astro-ph.CO↗

arXiv2026

Testing cosmic anisotropy with cluster scaling relations

We test claims of large-scale anisotropy in the local expansion rate using cluster scaling relations as distance indicators. Using a Bayesian forward model, we jointly fit the X-ray luminosity--temperature (LT) and thermal Sunyaev-Zel'dovich--temperature (YT) relations, marginalising over the latent cluster distances and modelling selection effects as well as peculiar velocities. The latter are modelled using reconstructions of the local peculiar velocity field where we self-consistently account for possible anisotropic redshift--distance relations via an approximate scheme. This treatment proves crucial to the inferred anisotropy and breaks the degeneracy between anisotropy in scaling relation normalisations and underlying cosmological anisotropy. We apply our method to 312 clusters at $z \lesssim 0.2$, testing dipolar, quadrupolar and general (pixelised) anisotropy models. Bayesian model selection finds no more than weak evidence for any anisotropic model. For dipole models, we obtain upper limits of $δH_0 / H_0 < 3.2\%$ and bulk flow magnitude $< 1300\,\mathrm{km\,s^{-1}}$. Our results contrast with previous claims of statistically significant anisotropy from the same data, which we attribute to our principled forward modelling of both redshifts and scaling relation observables through latent distances and our treatment of the impact of anisotropic redshift--distance relations when modelling the local peculiar velocity field. Our work highlights the importance of accurately modelling peculiar velocities when testing isotropy with distance indicators, and motivates the further development of reconstructions that self-consistently treat large-scale deviations from the Hubble flow.

astro-ph.CO↗

arXiv2026

Clustering properties of the CatWISE2020 quasar catalogue and their impact on the cosmic dipole anomaly

The cosmic dipole anomaly -- the observation of a significant mismatch between the dipole observed in the matter distribution and that expected given the kinematic interpretation of the cosmic microwave background dipole -- poses a serious challenge to the Cosmological Principle upon which the standard model of cosmology rests. Measurements of the dipole ($\ell=1$) in a given sample crucially depend on having control over other large-scale power ($\ell > 1$) so as to avoid biases, in particular those potentially caused by correlations among multipoles during fitting, and those by local source clustering. Currently, the most powerful catalogue that exhibits the cosmic dipole anomaly is the sample of 1.6~million mid-infrared quasars derived from CatWISE2020. We therefore analyse clustering properties of this catalogue by performing an inference analysis of large-scale multipoles in real space, and by computing its angular power spectrum on small scales to test for convergence with $Λ$CDM. After accounting for the known trend of the quasar number counts with ecliptic latitude, we find that any other large-scale power is consistent with noise, find no evidence for the presence of an octupole ($\ell=3$) in the data, and quantify the clustering dipole's proportion to be marginal. Our results therefore reaffirm the anomalously high dipole in the distribution of quasars.

astro-ph.CO↗

arXiv2026

The galaxy-environment connection revealed by constrained simulations

The evolution of galaxies is known to be connected to their position within the large-scale structure and their local environmental density. We investigate the relative importance of these using the underlying dark matter density field extracted from the Constrained Simulations in BORG (CSiBORG) suite of constrained cosmological simulations. We define cosmic web environment through both dark matter densities averaged on a scale up to 16 Mpc/h, and through cosmic web location identified by applying DisPerSE to the CSiBORG haloes. We correlate these environmental measures with the properties of observed galaxies in large surveys using optical data (from the NASA-Sloan Atlas) and 21-cm radio data (from ALFALFA). We find statistically significant correlations between environment and colour, neutral hydrogen gas (HI) mass fraction, star formation rate and Sérsic index. Together, these correlations suggest that bluer, star forming, HI rich, and disk-type galaxies tend to reside in lower density areas, further from filaments, while redder, more elliptical galaxies with lower star formation rates tend to be found in higher density areas, closer to filaments. We find analogous trends with the quenching of galaxies, but notably find that the quenching of low mass galaxies has a greater dependence on environment than the quenching of high mass galaxies. We find that the relationship between galaxy properties and the environmental density is stronger than that with distance to filament, suggesting that environmental density has a greater impact on the properties of galaxies than their location within the larger-scale cosmic web.

astro-ph.GA↗

arXiv2026

Testing subhalo abundance matching with galaxy kinematics

The rotation velocities of disc galaxies trace dark matter halo structure, providing direct constraints on the galaxy--halo connection. We construct a Bayesian forward model to connect the dark matter halo population predicted by $Λ$CDM with an observed sample of disc galaxies (SPARC) through their maximum rotation velocities. Our approach combines a subhalo abundance matching scheme (accounting for assembly bias) with a parameterised halo response to galaxy formation. When assuming no correlation between selection in the SPARC survey and halo properties, reproducing the observed velocities requires strong halo expansion, low abundance matching scatter ($<0.15$ dex at $1σ$) and a halo proxy that strongly suppresses the stellar masses in satellite haloes. This is in clear tension with independent clustering constraints. Allowing for SPARC-like galaxies to preferentially populate low $\Vmax$ haloes at fixed virial mass greatly improves the goodness-of-fit and resolves these tensions: the preferred halo response shifts to mild contraction, the abundance matching scatter increases to $\sint = 0.19^{+0.13}_{-0.11}$ dex and the proxy becomes consistent with clustering. However, the inferred selection threshold is extreme, implying that SPARC galaxies occupy the lowest ${\sim}16$ per cent of the $\Vmaxhalo$ distribution at fixed $\Mvir$. Moreover, even with selection, the inferred scatter remains in statistical disagreement with the low-mass clustering constraints, which are most representative of the SPARC galaxies in our sample. Our analysis highlights the advantage of augmenting clustering-based constraints on the galaxy--halo connection with kinematics and suggests a possible tension using current data.

astro-ph.GA↗

arXiv2026

Symbolically regressing dark matter halo profiles using weak lensing

The structure of dark matter haloes is often described by radial density profiles motivated by cosmological simulations. These are typically assumed to have a fixed functional form (e.g. NFW), with some free parameters that can be constrained with observations. However, relying on simulations has the disadvantage that the resulting profiles depend on the dark matter model and the baryonic physics implementation, which are highly uncertain. Instead, we present a method to constrain halo density profiles directly from observations. This is done using a symbolic regression algorithm called Exhaustive Symbolic Regression (ESR). ESR searches for the optimal analytic expression to fit data, combining both accuracy and simplicity. We apply ESR to a sample of 149 galaxy clusters from the HSC-XXL survey to identify which functional forms perform best across the entire sample of clusters. We identify density profiles that statistically outperform NFW under a minimum-description-length criterion. Within the radial range probed by the weak-lensing data ($R \sim 0.3 - 3$ h$^{-1}$ Mpc), the highest-ranked ESR profiles exhibit shallow inner behaviour and a maximum in the density profile. As a practical application, we show how the best-fitting ESR models can be used to obtain enclosed mass estimates. We find masses that are, on average, higher than those derived using NFW, highlighting a source of potential bias when assuming the wrong density profile. These results have important knock-on effects for analyses that utilise clusters, for example cosmological constraints on $σ_8$ and $Ω_m$ from cluster abundance and clustering. Beyond the HSC dataset, the method is readily applicable to any data constraining the dark matter distribution in galaxies and galaxy clusters, such as other weak lensing surveys, galactic rotation curves, or complementary probes.

astro-ph.CO↗

arXiv2025

Introduction to Symbolic Regression in the Physical Sciences

Symbolic regression (SR) has emerged as a powerful method for uncovering interpretable mathematical relationships from data, offering a novel route to both scientific discovery and efficient empirical modelling. This article introduces the Special Issue on Symbolic Regression for the Physical Sciences, motivated by the Royal Society discussion meeting held in April 2025. The contributions collected here span applications from automated equation discovery and emergent-phenomena modelling to the construction of compact emulators for computationally expensive simulations. The introductory review outlines the conceptual foundations of SR, contrasts it with conventional regression approaches, and surveys its main use cases in the physical sciences, including the derivation of effective theories, empirical functional forms and surrogate models. We summarise methodological considerations such as search-space design, operator selection, complexity control, feature selection, and integration with modern AI approaches. We also highlight ongoing challenges, including scalability, robustness to noise, overfitting and computational complexity. Finally we emphasise emerging directions, particularly the incorporation of symmetry constraints, asymptotic behaviour and other theoretical information. Taken together, the papers in this Special Issue illustrate the accelerating progress of SR and its growing relevance across the physical sciences.

cs.LG↗

arXiv2025

Constraining Fifth Forces using the Local Distance Ladder: Implications for the Hubble Tension

We revisit the local distance ladder measurement of the Hubble constant in models where gravity is modified by a fifth force, an additional long-range interaction. In many such theories the force is screened; suppressed in dense environments but potentially active in galaxies used for distance calibration. We model this environmental dependence using three quantities that characterize each galaxy's large-scale gravitational environment: the external gravitational potential $Φ$, acceleration $a$, and curvature $K$. Our baseline analysis recalibrates the SH0ES-team's Cepheid-supernova distance ladder, incorporating the fifth force via its impact on the Cepheid period-luminosity relation. Across models, a fifth force is strongly constrained, with posteriors concentrated around a null result. The inferred Hubble constant is $H_0 = 73.1 \pm 1.0 \, \mathrm{km/s/Mpc}$, retaining the Hubble tension at $>5 \, σ$. As an additional test, we incorporate four independent Tip of the Red Giant Branch (TRGB) distance datasets into a joint Cepheid-TRGB-supernova calibration. These combined analyses further constrain the magnitude of fifth-force effects. Taken together, our results show that, across the class of screened fifth-force models we analyze, the calibration of the local distance ladder remains essentially unchanged, leaving the Hubble tension intact.

astro-ph.CO↗

arXiv2025

Astrophysical Tests of Dark Matter Self-Interactions

Self-interacting dark matter (SIDM) arises generically in scenarios for physics beyond the Standard Model that have dark sectors with light mediators or strong dynamics. The self-interactions allow energy and momentum transport through halos, altering their structure and dynamics relative to those produced by collisionless dark matter. SIDM models provide a promising way to explain the diversity of galactic rotation curves, and they form a predictive and versatile framework for interpreting astrophysical phenomena related to dark matter. This review provides a comprehensive explanation of the physical effects of dark matter self-interactions in objects ranging from galactic satellites (dark and luminous) to clusters of galaxies and the large-scale structure. The second major part describes the methods used to constrain SIDM models including current constraints, with the aim of advancing tests with upcoming galaxy surveys. This part also provides a detailed review of the unresolved small-scale structure formation issues and concrete ways to test simple SIDM models. The review is rounded off by a discussion of the theoretical motivation for self-interactions, degeneracies with baryonic and gravitational effects, extensions to the single-component elastic-interactions SIDM framework, and future observational and theoretical prospects.

astro-ph.CO↗

arXiv2025

The Cosmological Dipole in Tilted Anisotropic Universes

There is tentative evidence for a mismatch between the rest frames of matter and the cosmic microwave background, the "quasar dipole anomaly". We consider such a dipole in tilted anisotropic models, for a range of scenarios and sources: spatial curvature, cosmic heat flux, large scale electromagnetic fields and a Khronon field. Crucially, we determine the ancillary effects on other cosmological observables in each of these models and we show that, apart from the case of the Khronon field, it is unlikely that one can obtain a dipole with the amplitude that is being observed unless one considers additional exotica.

astro-ph.CO↗