A common issue faced by magnetic particle-based Lab-on-a-chip systems, e.g, for medical diagnostics, is the intrinsic fabrication-related polydispersity in particle sizes and magnetic properties. Therefore, to reduce this variation, it is prudent to integrate a pre-separation procedure for the particles into the overall workflow of the system. In this work, a concept for the controlled on-chip fractionation of micron-sized superparamagnetic beads (SPBs) is introduced, which is applicable for sorting magnetic particles according to their properties in a continuous operation mode. A specifically designed magnetic domain pattern is imprinted into an exchange-biased thin film system to generate a tailored magnetic stray field landscape (MFL), enabling lateral transport of SPBs when superposing the MFL with external magnetic field pulses. The domain pattern consists of parallel stripes with gradually increasing and decreasing width, resulting in a step-wise jumping motion of SPBs with increasing/decreasing jump distance. SPBs with different magnetophoretic mobilities, determined, among others, by the particle size and magnetic susceptibility, discontinue their lateral motion at different jump distances, i.e., different lateral positions on the substrate. Thorough analysis of the motion using optical microscopy and particle tracking revealed that an increasing stripe width not only leads to a larger jump distance but also to a lowered jump velocity. As a consequence, particles are spatially separated according to their magnetic and structural properties with a large throughput and time efficiency, as simultaneous sorting occurs for all particles present on the substrate using a constant sequence of short external field pulses.

Coreshell nanoparticles can combine optical features of different materials in a single nanostructure, which makes them interesting for many applications from biomedicine to energy harvesting. On the other hand, periodic arrays of plasmonic nanoparticles can exhibit topological phenomena such as topological edge states. Here we study periodic chains of Si@Ag coreshell nanoparticles. For this task, we combine the hybridization of surface plasmonic modes in complex nanostructures with the coupled electric dipole formalism employed for modelling the scattering of light by periodic arrays of small plasmonic nanoparticles. We propose treating coreshell nanoparticle as several coupled electric dipoles instead of just one and show how this is a more appropriate framework to study arrays of coreshell nanoparticles, which allows to build a one-to-one connection between the resonant modes of the nanoparticles and the dispersion bands of the system. Within this formalism, we show that a Su-Schrieffer-Heeger (SSH) chain of coreshell Si@Ag nanoparticles host multiple topological edge states pinned at the resonant frequencies of the coreshell nanoparticles.

The study of random landscapes has long relied on counting stationary points: metastable states and the barriers between them. However, this method is useless for describing flat regions, common in constraint satisfaction problems. We introduce a characterization of flat regions by counting the number of spheres that can be uniquely inserted into them, either by wedging spheres of fixed radius or by inscribing spheres of variable radius. The ratio of these counts constrains the topology of the solution space. We apply this characterization to the spherical perceptron and show the existence of at least two topological regimes.

We study the deformed supersymmetric quantum mechanics with a polynomial superpotential with $\hbar$ correction. In the minimal chamber, where all turning points are real and distinct, it was shown that the exact Wentzel--Kramers--Brillouin periods obey the ${\mathbb Z}_4$-extended thermodynamic Bethe ansatz (TBA) equations of the undeformed potential. By changing the energy parameter above/below the critical points, the turning points become complex, and the moduli are outside of the minimal chamber. We study the wall crossing of the ${\mathbb Z}_4$-extended TBA equations by this change of moduli and show that the ${\mathbb Z}_4$ structure is preserved after the wall crossing. In particular, the TBA equations for the cubic superpotential are studied in detail, where there are two chambers (minimal and maximal). At the maximally symmetric point in the maximal chamber, the TBA system becomes the two sets of the $D_3$-type TBA equations, which are regarded as the ${\mathbb Z}_4$ extension of the $A_3/{\mathbb Z}_2$-type TBA equation.

An orientation of a given static graph is called transitive if for any three vertices $a,b,c$, the presence of arcs $(a,b)$ and $(b,c)$ forces the presence of the arc $(a,c)$. If only the presence of an arc between $a$ and $c$ is required, but its orientation is unconstrained, the orientation is called quasi-transitive. A fundamental result presented by Ghouila-Houri guarantees that any static graph admitting a quasi-transitive orientation also admits a transitive orientation. In a seminal work, Mertzios et al. introduced the notion of temporal transitivity in order to model information flows in simple temporal networks. We revisit the model introduced by Mertzios et al. and propose an analogous to Ghouila-Houri's characterization for the temporal scenario. We present a structure theorem that will allow us to express by a 2-SAT formula all the constraints imposed by temporal transitive orientations. The latter produces an efficient recognition algorithm for graphs admitting such orientations. Additionally, we extend the temporal transitivity model to temporal graphs having multiple time-labels associated to their edges and claim that the previous results hold in the multilabel setting. Finally, we propose a characterization of temporal comparability graphs via forbidden temporal ordered patterns.

We consider the problem of defining the field strength of abelian potentials when the spacetime is a Poisson manifold, within the groupoidal approach. The natural definition in terms of gauge invariant momenta is proved to be equivalent to covariant and invariant tensors of a local symplectic groupoid representing a symplectic realization of the Poisson manifold. A Poisson Chern-Simons model is then proposed and its equations of motion are shortly discussed.

We discuss photon rings around as well as shadows of Kerr black holes immersed in a swirling spacetime (KBHSU). We find that the spin-spin interaction between the angular momentum of the black hole and the swirling of the background leads to new interesting effects as it breaks the symmetry between the upper and lower hemispheres. We find that a pair of light rings exists for all values of the parameter space. Using a topological argument, we prove that there should be, indeed, two light rings and that, additionally, these light rings are unstable. In comparison to the Schwarzschild black hole immersed in a swirling universe, the light rings typically all possess different radii. Interestingly, as the value of the swirling parameter is increased at fixed angular momentum of the black hole the two disconnected patches of the ergoregions eventually merge. The light ring at this merger possesses no angular velocity (as measured by an observer at infinity) and is called a \textit{light point}. To our knowledge, this is the first time the existence of such a light point in a black hole space-time is reported. Finally, we also present the shadows of KBHSU for various parameter values and observe that, due to the presence of the swirling background, the shadows are twisted.

We investigate the open problem of the existence of genuinely unextendible product bases (GUPBs), that is, multipartite unextendible product bases (UPBs) which remain unextendible even with respect to biproduct vectors across all bipartitions of the parties. To this end, we exploit the well-known connection between UPBs and graph theory through orthogonality graphs and orthogonal representations, together with recent progress in this framework, and employ forbidden induced subgraph characterizations to single out the admissible local orthogonality graphs for GUPBs. Using this approach, we establish that GUPBs of size thirteen in three-qutrit systems-the smallest candidate GUPBs-do not exist. We further provide a partial characterization of graphs relevant to larger bases and systems with ququart subsystems.

The delay in arrival time of the multiple images of gravitationally lensed supernovae (glSNe) can be related to the present-day expansion rate of the universe, $H_{0}$. Despite their rarity, Rubin Observatory's Legacy Survey of Space and Time (Rubin-LSST) is expected to discover tens of galaxy-scale glSNe per year, many of which will not be resolved due to their compact nature. Follow-up from ground- and space-based telescopes will be necessary to estimate time delays to sufficient precision for meaningful $H_{0}$ constraints. We present the Glimpse model (GausSN Light curve Inference of Magnifications and Phase Shifts, Extended) that estimates time delays with resolved and unresolved observations together for the first time, while simultaneously accounting for dust and microlensing effects. With this method, we explore best follow-up strategies for glSNe observed by Rubin-LSST. For unresolved systems on the dimmest end of detectability by Rubin-LSST, having peak i-band magnitudes of 22-24 mag, the time delays are measured to as low as 0.7 day uncertainty with 6-8 epochs of resolved space-based observations in each of 4-6 optical and NIR filters. For systems of similar brightness that are resolved by ground-based facilities, time delays are consistently constrained to 0.5-0.8 day precision with 6 epochs in 4 optical and NIR filters of space-based observations or 8 epochs in 4 optical filters of deep ground-based observations. This work improves on previous time-delay estimation methods and demonstrates that glSNe time delays of $\sim10-20$ days can be measured to sufficient precision for competitive $H_{0}$ estimates in the Rubin-LSST era.

We study the parametrized complexity of fundamental relations between multidimensional subshifts, such as equality, conjugacy, inclusion, and embedding, for subshifts of finite type (SFTs) and effective subshifts. We build on previous work of E. Jeandel and P. Vanier on the complexity of these relations as two-input problems, by fixing one subshift as parameter and taking the other subshift as input. We study the impact of various dynamical properties related to periodicity, minimality, finite type, etc. on the computational properties of the parameter subshift, which reveals interesting differences and asymmetries. Among other notable results, we find choices of parameter that reach the maximum difficulty for each problem; we find nontrivial decidable problems for multidimensional SFT, where most properties are undecidable; and we find connections with recent work relating having computable language and being minimal for some property, showing in particular that this property may not always be chosen conjugacy-invariant.

Majorization inequalities have a long history, going back to Maclaurin and Newton. They were recently studied for several families of symmetric functions, including by Cuttler--Greene--Skandera (2011), Sra (2016), Khare--Tao (2021), McSwiggen--Novak (2022), and Chen--Sahi (2024+) among others. Here we extend the inequalities by these authors to Jack and Macdonald polynomials, and obtain conjectural characterizations of majorization and of weak majorization of the underlying partitions. We prove these characterizations for two variables. In fact, we upgrade -- and prove in the above cases -- the characterization of majorization, to containment of Jack and Macdonald differences lying in the Muirhead semiring.

We study 24 massive quiescent galaxies with $\log \textrm{M}_*/\textrm{M}_\odot > 10$ at $1 < z < 3$ with JWST/NIRSpec medium-resolution observations from the Early eXtragalactic Continuum and Emission Line Survey (EXCELS). We reconstruct their star formation histories and find that they have large bursts ($100\textrm{ M}_{\odot} \textrm{yr}^{-1} -1000 \textrm{ M}_{\odot} \textrm{yr}^{-1}$), followed by a rapid truncation of star formation. The number densities of the quenched galaxies in our sample that we predict underwent a submillimeter phase are consistent with submillimeter galaxies being the progenitors of our quenched population. The median post-starburst visibility time is $\sim600$ Myr, with more massive galaxies ($\log \textrm{M}_*/\textrm{M}_\odot > 10.7$) exhibiting shorter visibility times than lower mass galaxies. The range of quenching times -- defined as the time from the peak starburst to the time of quiescence -- found in this sample ($0.06-1.75$ Gyr) suggests multiple quenching pathways, consistent with previous studies. We do not see evidence for quenching mechanisms varying with redshift between $1<z<3$. We detect evidence for weak AGN activity in 4 out of the 8 galaxies with robust emission line detections, based on line ratio diagnostics. Our findings suggest that there are a diverse range of quenching mechanisms at cosmic noon, and support a scenario in which the primary quenching mechanisms are rapid ($<500$ Myr) following a starburst.

Quantum pseudo-telepathy games, such as the Mermin-Peres magic square and the doily game, theoretically allow players to win with unit probability when using entangled quantum strategies. We quantitatively characterize the quantum advantage in these games and compare it with violations of two Bell inequalities: the Clauser-Horne-Shimony-Holt and the Collins-Gisin inequalities. The analysis is restricted to two families of two-qubit states: modified Werner states and Bell-diagonal states. For each case, we identify and quantify the regions of quantum state space that exhibit either a quantum advantage or a Bell inequality violation, relative to the set of all entangled states. Within these families, the doily game captures a larger fraction of entangled states than the Mermin-Peres magic square game, though both are significantly more limited than the regions associated with Bell inequality violations. Although both approaches are fundamentally linked to quantum contextuality, our analysis of the examined two-qubit state families indicates that Bell inequalities are more effective at revealing entanglement, even if pseudo-telepathy games offer a more intuitive and conceptually appealing perspective.

Ultrafaint dwarf (UFD) galaxies are dominated by dark matter, the distribution of which may be inferred from the kinematics of that galaxy's stellar population. Star-by-star observations are available for the satellite UFD galaxies of the Milky Way, making them uniquely good laboratories in which to test cosmological predictions at the smallest scales. However, the kinematics of these galaxies are complicated by the presence of binary stars, which alter the stellar velocity distribution. In particular these binary stars increase the galaxy's stellar velocity dispersion, which is related to the total galactic mass by the virial theorem. Without correctly eliminating or accounting for binary stars we may therefore overestimate the masses of UFD galaxies or even confuse globular clusters for UFD galaxies. Here we write down the probability density function for the observed line-of-sight (LOS) velocity of a stellar population containing both visual and spectroscopic binary stars, which we then use to determine the effect of those binary stars on the observed LOS velocity dispersion. For the coldest UFD galaxies the fractional increase in LOS velocity dispersion is of order one and for the coldest globular clusters is of order 100. However, if the stellar initial mass function is bottom light, as it may be for UFD galaxies and globular clusters, then both of these values increase by half a dex.

We demonstrate here that a chain of Bilayer Graphene Quantum Dots (BLGQDs) can realize topological quantum matter by effectively simulating a spin-1 chain that hosts the Haldane phase within a specific range of parameters. We describe a chain of BLGQDs with two electrons per dot using an atomistic tight-binding model combined with exact diagonalization to solve the interacting few-electron problem. Coulomb interactions and valley-mixing effects are treated within a single microscopic framework, allowing us to systematically investigate spin and valley polarization transitions as functions of interaction strength and external tuning parameters. We calculate the low energy states for single and double QDs as a function of the number of electrons, identifying regimes of highly correlated multi-electron states. We confirm the presence of a spin-one ground state for two electrons. Then, we explore two coupled QDs with 4 electrons and extend the analysis to QD arrays. Using a mapping of the BLGQD chain to an effective bilinear-biquadratic (BLBQ) spin model, we demonstrate that BLGQD arrays can work as a quantum simulator for one-dimensional spin chains with emergent many-body topological phases.

Large Language Models are reshaping task automation, yet remain limited in complex, multi-step real-world tasks that require aligning with vague user intent and enabling dynamic user override. From a formative study with 12 participants, we found that end-users actively seek to shape task-oriented interfaces rather than relying on one-shot outputs. To address this, we introduce the human-agent co-generation paradigm, materialized in DuetUI. This LLM-empowered system unfolds alongside task progress through a bidirectional context loop-the agent scaffolds the interface by decomposing the task, while the user's direct manipulations implicitly steer the agent's next generation step. In a technical ablation study and a user study with 24 participants, DuetUI improved task efficiency and interface usability, supporting more seamless human-agent collaboration. Our contributions include the proposal of this novel paradigm, the design of a proof-of-concept DuetUI prototype embodying it, and empirical and technical insights from an initial evaluation of how this bidirectional loop may help align agents with human intent and inform future development.

Proximity ferroelectricity is a novel paradigm for inducing ferroelectricity in a non-ferroelectric polar material such as AlN or ZnO that are typically unswitchable with an external field below their dielectric breakdown field. When placed in direct contact with a thin switchable ferroelectric layer (such as Al1-xScxN or Zn1-xMgxO), they become a practically switchable ferroelectric. Using the thermodynamic Landau-Ginzburg-Devonshire theory, in this work we performed the finite element modeling of the polarization switching in the compositionally graded AlN-Al1-xScxN, ZnO-Zn1-xMgxO and MgO-Zn1-xMgxO structures sandwiched in both a parallel-plate capacitor geometry as well as in a sharp probe-planar electrode geometry. We reveal that the compositionally graded structure allows the simultaneous switching of spontaneous polarization in the whole system by a coercive field significantly lower than the electric breakdown field of unswitchable polar materials. The physical mechanism is the depolarization electric field determined by the gradient of chemical composition "x". The field lowers the steepness of the switching barrier in the otherwise unswitchable parts of the compositionally graded AlN-Al1-xScxN and ZnO-Zn1-xMgxO structures, while it induces a shallow double-well free energy potential in the MgO-like regions of compositionally graded MgO-Zn1-xMgxO structure. Proximity ferroelectric switching of the compositionally graded structures placed in the probe-electrode geometry occurs due to nanodomain formation under the tip. We predict that a gradient of chemical composition "x" significantly lowers effective coercive fields of the compositionally graded AlN-Al1-xScxN and ZnO-Zn1-xMgxO structures compared to the coercive fields of the corresponding multilayers with a uniform chemical composition in each layer.

The Neutrinos from Stored Muons (nuSTORM) facility will generate neutrino beams from both muon and meson decays in a storage ring, providing a neutrino flux known to the percent level. This unprecedented precision enables a rich physics programme, including high-precision tests of the Standard Model and searches for new phenomena. In this paper we demonstrate nuSTORM's sensitivity to key Standard Model processes such as, measurements of the weak mixing angle at low $Q^2$ and the rare process of neutrino trident production. We also show its powerful reach for a diverse range of beyond-the-Standard-Model scenarios, including eV-scale sterile neutrinos, Kaluza-Klein excitations from large extra dimensions and lepton flavour violation. Furthermore, nuSTORM can place significant constraints on heavy QCD axions and other axion-like particles produced in rare kaon decays. These capabilities establish nuSTORM as a powerful and complementary probe to long baseline experiments and collider searches.

Superconducting REBCO ($RE$Ba$_2$Cu$_3$O$_{7-x}$, where $RE$ is a rare earth, typically Y, Gd or Eu) electromagnets are useful for many applications like medical magnetic resonace imaging (MRI), nuclear magnetic resonance (NMR) spectroscopy, and magnets for particle accelerators and detectors. REBCO magnets are also the core of many nuclear fusion energy start-ups. In order to avoid permanent damage during operation, magnet design needs to take electro-thermal quench into account, which is due to unavoidable REBCO tape or magnet imperfections. However, most high-field magnet designs do not take superconducting screening currents into account. In this work, we show that it is essential to consider screening currents in magnet design, since they highly speed-up electrothermal quench propagation. Our study is based on detailed numerical modeling, based on the Minimum Electromagnetic Entropy Production (MEMEP) and Finite Differences (MEMEP-FD). Benchmarking with well-established Partial Element Equivalent Circuit (PEEC) model supports the correctness of MEMEP-FD. This work focusses on a 32 T all-superconducting magnet design and we analyze in detail the time evolution of electrothermal quench. Our findings will have an impact in the design of ultra-high-field magnets for NMR or user facilities, and possibly for other kinds of magnets, like those for fusion energy.

Quantum impurity models provide a central framework for correlated electron physics, with quantum dots enabling controlled experimental realizations. While their weak-coupling behavior is well understood through mappings to Kondo Hamiltonians, the opposite regime of highly transparent contacts has lacked a controlled theoretical description. Using the functional renormalization group (FRG), we resolve this regime for the three-channel charge Kondo device of Ref.~\cite{iftikhar2018}, benchmarking against conformal field theory by reproducing the universal zero-frequency conductance and, crucially, going beyond it to obtain the full frequency crossover of the conductance and the full temperature crossover of the impurity entropy, together with a continuous line of fixed points for interacting leads. These results establish FRG as a powerful nonperturbative tool for quantum impurity problems in regimes inaccessible to conventional approaches, with direct implications for mesoscopic experiments.

In this work, we address the problem of optimally placing a finite number of sensors within a given region so as to minimize the mean or maximal distance to the points of the domain. To tackle this natural geometric performance criterion, formulated in terms of distance functions, we combine tools from geometric analysis with a classical result of Varadhan, which provides an efficient approximation of the distance function via the solution of a simple elliptic PDE. The effectiveness of the proposed approach is demonstrated through illustrative numerical simulations.

A theory is proposed for the component of the Casimir-like force that arises between bodies embedded in a macroscopic quantum damped oscillator. When the oscillator's parameters depend on the distance between the bodies, the oscillator-induced Casimir-like force is generally determined by a broad spectral range extending to high frequencies, limited by the frequency dispersion of the damping function. Here it is shown that there is a large class of systems in which the low-frequency range dominates the forces. This allows for the use of the Ohmic approximation, which is crucial for extending the theory to the lumped element description of fluctuation-induced forces in electrical circuits. Estimates of the circuit-induced Casimir-Lifshitz force suggest that under certain conditions it can be identified experimentally due to its dependence on various circuit elements.

The long-term rates of change of all the Keplerian orbital elements of a two-body system acted upon by a remote massive pointlike object are analytically worked out, to the Newtonian quadrupolar level, without any restriction either on the orbital eccentricity and inclination of the disturbed pair or the position of the distant perturber. The latter is considered fixed during the average over one orbital revolution of the inner binary by means of which its orbital perturbations are calculated. The results are presented in a compact form that facilitates a straightforward application to the case of the supermassive black hole-or megapyknon-M87$^\ast$. In principle, the presence of another distant intermediate-mass black hole may concur to cause the observed jet precession, assumed tightly coupled with the accretion disk. Such a possibility is ruled out by the exclusion plots in the parameter space obtained with the approach presented here.

Higher lying excited states beyond S1 and T1 are widely recognized in many photophysical systems, including thermally activated delayed fluorescence (TADF). However, their explicit and quantitative impact on photophysical observables such as photoluminescence quantum yields (PLQY) and lifetimes is difficult to be attained experimentally and it has not been systematically assessed within a fully ab initio kinetic modeling framework. To address this gap, we developed KinLuv, a multistate excited state kinetic model that includes higher lying excited states (S2, T2) and all possible monomolecular interconversion processes between all the electronic states, whose rate constants were computed using Fermi golden rule explicitly including the Herzberg Teller (HT) vibronic coupling effect. We applied KinLuv to prototypical multi resonance TADF (MRTADF) emitters and their derivatives, as well as other representative organic chromophores, demonstrating its broad applicability across diverse photophysical playgrounds beyond TADF. The resulting simulations quantitatively reproduce key experimental observables, including PLQY and prompt and delayed fluorescence lifetimes. Beyond its predictive power, the present results establish clear criteria for identifying when higher lying excited states influence the excited state decay and when simplified models remain adequate. This framework enables rational selection of minimal kinetic models that balance physical insight with numerical robustness, with direct implications for the in silico design of high performance organic emitters.

It has been proposed that measurements of scattering times ($τ$) from fast radio bursts (FRB) may be used to infer the FRB host dispersion measure (DM) and its redshift. This approach relies on the existence of a correlation between $τ$ and DM within FRB hosts such as that observed for Galactic pulsars. We assess the measurability of a $τ- $DM$_{\rm host}$ relation through simulated observations of FRBs within the ASKAP/CRAFT survey, taking into account instrumental effects. We show that even when the FRB hosts intrinsically follow the $τ- $DM relation measured for pulsars, this correlation cannot be inferred from FRB observations; this limitation arises mostly from the large variance around the average cosmic DM value given by the Macquart relation, the variance within the $τ- $DM relation itself, and observational biases against large $τ$ values. We argue that theoretical relations have little utility as priors on redshift, e.g., for purposes of galaxy identification, and that the recent lack of an observed correlation between scattering and DM in the ASKAP/CRAFT survey is not unexpected, even if our understanding of a $τ- $DM$_{\rm host}$ relation is correct.

We introduce the theory of inscribed $v$-sheaves, a differentiable extension of the theory of diamonds and $v$-sheaves with internal tangent bundles that are often relative inscribed Banach-Colmez spaces, then apply this theory to the study of $p$-adic periods. In particular, we construct natural inscribed versions of the Hodge and Hodge-Tate period maps and their lattice refinements for de Rham torsors, then compute the derivatives of these period maps in terms of classical structures in $p$-adic Hodge theory. These torsors include infinite level global Shimura varieties and infinite level local Shimura varieties, and for these spaces we also give another moduli-theoretic construction of the inscribed structure; the construction in the local Shimura case applies more generally to the non-minuscule moduli of mixed characterisic local shtukas with one leg. The key new ingredients in our study of inscribed structures on $p$-adic Lie group torsors over smooth rigid varieties over a $p$-adic field are the Liu-Zhu period map, a refinement of the Hodge period map whose derivative is the geometric Sen morphism/canonical Higgs field, and a closely related exact tensor functor from $\mathbb{Q}_p$-local systems to a category of twistor bundles on the relative thickened Fargues-Fontaine curve. These new structures are only visible after passing to the inscribed setting. We also discuss some possible implications of our computations in the vein of ``differential topology for diamonds."

We study the stability of steady-state solutions of the Wave-Kinetic Equations for acoustic waves. Combining theoretical analysis and numerical simulations, we characterise the time evolution of small isotropic perturbations for both 2D and 3D equilibrium Rayleigh-Jeans and non-equilibrium Kolmogorov-Zakharov solutions. In particular, we show that the stability of these solutions is ensured by different mechanisms.

We present a novel method of combining kinematic models obtained at multiple spatial resolution levels in a self-consistent manner. The MHONGOOSE survey has mapped atomic hydrogen emission in $30$ nearby dwarf and spiral galaxies. Each galaxy is imaged at multiple resolution levels with unprecedented dynamic range in spatial resolution (from $\sim 10''$ to $ 90''$) and HI sensitivity, with the latter varying by almost a factor of $30$ across all resolution scales. We use radial weighting functions to combine kinematic models from all resolution levels. The weights are derived from the residuals of model fits to a set of observations of synthetic model galaxies with known rotation curves and geometries. We obtain combined (weighted and smoothed) inclination and position angle profiles for each galaxy. These suppress the sharp, often unphysical radial fluctuations arising in single-resolution profiles. We then fit the rotation speed and velocity dispersion profiles at each resolution level with the geometric profiles fixed to the combined profiles, finally combining these using the same weighting and smoothing approach. The combined rotation curves utilise all of the available information and have smaller typical systematic errors compared to those obtained using a single resolution level, particularly near the centres and outer edges of models. This initial demonstration is promising; there is scope to further refine the process to use such information-rich observations to their full potential.

Persistent wealth inequality, where a small fraction of the population accumulates most resources while the majority remains economically vulnerable, is a widespread phenomenon. We investigate its underlying mechanisms using an agent-based Yard-Sale model that incorporates two complementary features: transaction rules that favor poorer agents, representing social protection policies, and an economic growth process with explicit wealth redistribution. Our results reveal that social protection plays a dominant role in reducing inequality, while redistribution primarily serves to reintegrate excluded agents. These findings suggest that social protection policies, that is, targeted mechanisms favoring economically vulnerable agents, may have a substantially greater impact on reducing inequality than redistribution driven solely by economic growth. We also find that both the shape of the wealth distributions and the resulting inequality levels are strongly influenced by the underlying distribution of individual risk, highlighting the importance of considering agent heterogeneity when modeling economic dynamics.

Wealth inequality remains a critical socioeconomic challenge, driven by systemic dynamics and self-reinforcing mechanisms that amplify the economic imbalances. Simplified models from statistical physics provide valuable insights into the fundamental mechanisms governing wealth distribution. In this study, we extend the Yard-Sale model -- a minimal kinetic exchange framework -- to investigate how limiting risk in economic transactions affects inequality. While previous research demonstrates that such models naturally lead to wealth concentration, we introduce a mechanism that restricts the maximum risk agents can assume during exchanges. Numerical simulations reveal that this modification fosters more equitable wealth distributions and significantly reduces extreme disparities. These findings highlight the importance of individual-level constraints in shaping systemic outcomes, offering new perspectives on promoting economic balance.