We propose a novel framework for robust dynamic games with nonlinear dynamics corrupted by state-dependent additive noise, and nonlinear agent-specific and shared constraints. Leveraging system-level synthesis (SLS), each agent designs a nominal trajectory and a causal affine error feedback law to minimize their own cost while ensuring that its own constraints and the shared constraints are satisfied, even under worst-case noise realizations. Building on these nonlinear safety certificates, we define the novel notion of a robustly constrained Nash equilibrium (RCNE). We then present an Iterative Best Response (IBR)-based algorithm that iteratively refines the optimal trajectory and controller for each agent until approximate convergence to the RCNE. We evaluated our method on simulations and hardware experiments involving large numbers of robots with high-dimensional nonlinear dynamics, as well as state-dependent dynamics noise. Across all experiment settings, our method generated trajectory rollouts which robustly avoid collisions, while a baseline game-theoretic algorithm for producing open-loop motion plans failed to generate trajectories that satisfy constraints.

We embed the perturbative Fock state of the Yang-Mills BV-multiplet in the vertex operator algebra of the path-integral for the $\mathcal{N}=2$ supersymmetric world line and evaluate the pull-back of the latter to an integral form on supermoduli space. Choosing a suitable Poincaré dual on the latter, we show that this integral form describes an extension of Yang-Mills theory. Upon projection back to the Fock space, we recover the Yang-Mills action from the world line. This furthermore gives an a priori justification for the construction of Yang-Mills equations of motion as emerging from deformations of the BRST differential.

Stellar substructures within tidal debris preserve information about their progenitor galaxies' properties, offering insights into hierarchical mass assembly. We examine a compact stellar system (CSS) around the nearby spiral galaxy NGC 7531, including the shell-like tidal debris. Our goals are to determine the nature of the CSS, reconstruct the accretion history, and understand how the large, diffuse shell-like structure formed. We present photometric measurements of the shell-like debris and CSS using DESI Legacy Imaging Survey (LS) data. We obtained Keck/LRIS spectroscopic data for the CSS to confirm its association with NGC 7531 and to derive its star formation history (SFH). Deep ($\sim$27.9 mag/arcsec$^{2}$) amateur telescope images enabled complete characterization of the tidal debris structure. We confirm the CSS is associated with NGC 7531. We rename it NGC 7531-UCD1, since its stellar mass ($3.7_{-0.7}^{+1.0}\times 10^6$ $\mathrm{M}_\odot$), half-light radius ($R_{h} = 0.13 \pm 0.05$ arcsec) and SFH place it as an ultra-compact dwarf galaxy (UCD). NGC 7531-UCD1 was likely a nuclear star cluster (NSC) that was tidally stripped into a UCD- this is further supported by the presence of tidal tails. We quantify the shell-like debris' mass as $M_\star\sim 3$--$11\times 10^8 M_\odot$, implying a merger mass ratio of ~300:1 to 10:1. Our amateur telescope images confirm new pieces of debris, previously unclear in the DESI LS images. N-body simulations reproduce the tidal features, requiring a near radial orbit of the progenitor with two pericentric passages. The first passage coincides with the measured star formation enhancement ~1 Gyr ago. Our findings agree with predictions about the NSC to UCD formation pathway via tidal stripping, and further confirm the presence of these objects outside of our Milky Way.

Studying coronal rain formation through thermal non-equilibrium (TNE) and thermal instability (TI) provides insights into coronal heating mechanisms. We analysed a quiescent coronal rain event using space-based observations from the High-Resolution Imager in Extreme Ultraviolet (\hrieuv) of Solar Orbiter (SolO), the Atmospheric Imaging Assembly (AIA) of the Solar Dynamics Observatory (SDO), and the Slit-Jaw Imager (SJI) from the Interface Region Imaging Spectrograph (IRIS) from November 1st, 2023. During the coronal rain shower, the coronal loop exhibits substantial EUV variability and structural changes. Rain clumps fell at $72-87$ km s$^{-1}$ with cool EUV absorbing core sizes of $\approx$600 km and densities of $\approx6\times10^{11}$ cm$^{-3}$ preceded by strong compressions. These mostly isothermal compressions suggest energy transfer into the rain, decelerating it and possibly reducing cooling rates -- consistent with accretion braking timescales. The shower carried microflare-level energy ($4.64\times10^{26}$ erg), with clumps producing impacts that reach the lower transition region and are visible across all EUV channels and in SJI 1400 Å. The impacts generated hot rebound flows ($10^{6.2}-10^{6.3} $K, $85-87$ km s$^{-1}$) that refilled and reheated the loop but carried less than $15\%$ of the clumps' kinetic energy. We detected steady footpoint heating signatures consistent with the TNE-TI scenario, with an estimated amplitude of $10^{-2\pm0.3}$ erg cm$^{-3}$ s$^{-1}$ and heating scale heights of $2-10$~Mm, matching active region values. Coronal rain may thus serve as both a template for accretion braking and a proxy for integrated heating driving TNE-TI cycles.

While the James Webb Space Telescope (JWST) now allows identifying quiescent galaxies (QGs) out to early epochs, the photometric selection of quiescent galaxy candidates (QGCs) and the derivation of key physical quantities are highly sensitive to the assumed star-formation histories (SFHs). We aim to quantify how the inclusion of JWST/MIRI data and different SFH models impacts the selection and characterisation of QGCs. We test the robustness of the physical properties inferred from the spectral energy distribution (SED) fitting, such as M*, age, star formation rate (SFR), and AV, and study how they impact the quiescence criteria of the galaxies across cosmic time. We perform SED fitting for ~13000 galaxies at z<6 from the CEERS/MIRI fields with up to 20 optical-mid infrared (MIR) broadband coverage. We implement three SFH prescriptions: flexible delayed, NonParametric, and extended Regulator. For each model, we compare results obtained with and without MIRI photometry and dust emission models. We evaluate the impact of these configurations on the number of candidate QGCs, selected based on rest UVJ colours, sSFR and main-sequence offset, and on their key physical properties such as M*, AV, and stellar ages. The number of QGCs selected varies significantly with the choice of SFH from 171 to 224 out of 13000 galaxies, depending on the model. This number increases to 222-327 when MIRI data are used (up to ~45% more QGCs). This enhancement is driven by improved constraints on dust attenuation and M*. We find a strong correlation between AV and M*, with massive galaxies (M*~10^11 M\odot) being 1.5-4.2 times more attenuated in magnitude than low-mass systems (M*~10^9 M\odot), depending on SFH. Regardless of the SFH assumption, ~13% of QGCs exhibit significant attenuation (AV > 0.5) in support of recent JWST studies challenging the notion that quiescent galaxies are uniformly dust-free.

We present memshare\footnote{The Software package is published as a CRAN package under https://CRAN.R-project.org/package=memshare, a package that enables shared memory multicore computation in R by allocating buffers in C++ shared memory and exposing them to R through ALTREP views. We compare memshare to SharedObject (Bioconductor) discuss semantics and safety, and report a 2x speedup over SharedObject with no additional resident memory in a column wise apply benchmark. Finally, we illustrate a downstream analytics use case: feature selection by mutual information in which densities are estimated per feature via Pareto Density Estimation (PDE). The analytical use-case is an RNA seq dataset consisting of N=10,446 cases and d=19,637 gene expressions requiring roughly n_threads * 10GB of memory in the case of using parallel R sessions. Such and larger use-cases are common in big data analytics and make R feel limiting sometimes which is mitigated by the addition of the library presented in this work.

We model the absorption of X-rays by gas obscuring the source and photoionized by it. We consider a broad range of column densities, including both Thomson-thin and Thomson-thick media. For the Thomson thin regime, we derive a simple criterion based on the source luminosity and spectrum, as well as the medium radius and column density, that distinguishes between the following cases: (i) The absorption can be modeled well by a neutral medium; (ii) The radiation ionizes its way through the medium, and no absorption is expected; and (iii) A detailed model is required because the column density inferred from modeling the absorption with a neutral gas is much lower than the actual column density, or because the absorption features cannot be fitted by a neutral absorber. We derive the criterion analytically using a toy model of hydrogen and oxygen and calibrate it for realistic compositions with metallicities in the range $Z/Z_{\odot}=0.01-50$, using \textsc{Cloudy}. We generalize the model to the Thomson-thick regime, where we consider, alongside photoabsorption, electron scattering, Compton heating, Comptonization, and photon degradation. In this case, the emergent spectrum depends on the boundary condition experienced by photons scattered back towards the source. We discuss the effect of a reflective boundary and a reprocessing boundary. We provide simple criteria for the expected absorption state and discuss additional effects that alter the spectrum. The main motivation for our modeling is X-ray emission from supernovae interacting with the circumstellar medium; however, we expect it to be useful for many other applications.

We devise a deterministic quantum algorithm to produce antisymmetric states of single-particle orbitals in the first quantization mapping. Unlike sorting-based antisymmetrization algorithms, which require ordered input states and high Clifford-gate overhead, our approach initializes the state of each particle independently. For a system of $η$ particles and $N$ single-particle states, our algorithm prepares antisymmetrized states of non-trivial localized (e.g., Hartree-Fock) orbitals using $O(η^2\sqrt{N})$ $T$-gates, outperforming alternative algorithms when $η\lesssim \sqrt{N}$. To achieve such scaling, we require $O(\sqrt{N})$ dirty ancilla qubits for intermediate calculations. Knowledge of the single-particle states to be antisymmetrized can be leveraged to further improve the efficiency of the circuit, and a measurement-based variant reduces gate cost by roughly a factor of two. We show example circuits for two- and three-particle systems and discuss the generalization to an arbitrary number of particles. For a specific three-particle example, we decompose the circuit into Clifford$+T$ gates and study the impact of noise on the prepared state.

We introduce a simple and efficient variation of the tangent-space excitation ansatz used to compute elementary excitation spectra of one-dimensional quantum lattice systems using matrix product states (MPS). A small basis for the excitation tensors is formed based on a single diagonalization analogous to a single site DMRG step but for multiple states. Once overlap and Hamiltonian matrix elements are found, obtaining the excitation for any momentum only requires diagonalization of a tiny matrix, akin to a non-orthogonal band-theory diagonalization. The approach is based on an infinite MPS description of the ground state, and we introduce an extremely simple alternative to variational uniform matrix product states (VUMPS) based on finite system DMRG. For the $S=1$ Heisenberg chain, our method -- site basis excitation ansatz (SBEA) -- efficiently produces the one-magnon dispersion with high accuracy. We also examine the role of MPS gauge choices, finding that not imposing a gauge condition -- leaving the basis nonorthogonal -- is crucial for the approach, whereas imposing a left-orthonormal gauge (as in prior work) severely hampers convergence. We also show how one can construct Wannier excitations, analogous to the Wannier functions of band theory, where one Wannier excitation, translated to all sites, can reconstruct the single magnon modes exactly for all momenta.

We estimate the impact of environmental law enforcement on violence in the Brazilian Amazon. The introduction of the Real-Time Deforestation Detection System (DETER), which enabled the government to monitor deforestation in real time and issue fines for illegal clearing, significantly reduced homicides in the region. To identify causal effects, we exploit exogenous variation in satellite monitoring generated by cloud cover as an instrument for enforcement intensity. Our estimates imply that the expansion of state presence through DETER prevented approximately 1,477 homicides per year, a 15\% reduction in homicides. These results show that a replicable environmental enforcement policy produces social benefits.

The presence of massive black holes (BHs) exceeding $10^9\,{\rm M}_{\odot}$ already at redshift $z > 6$ challenges standard models of BH growth. Super-Eddington (SE) accretion has emerged as a promising mechanism to solve this issue, yet its impact on early BH evolution in tailored numerical experiments remains largely unexplored. In this work, we investigate the growth of BH seeds embedded in a gas-rich, metal-poor protogalaxy at $z \sim 15$ using a suite of high-resolution hydrodynamical simulations that implement a slim-disc-based SE accretion model. We explored a broad parameter space, varying the initial BH mass, feedback efficiency, and spin. We find that SE accretion enables rapid growth in all cases, allowing BHs to accrete up to $10^5\,{\rm M}_{\odot}$ within a few $10^3$-$10^4$ years, independent of seed properties. Feedback regulates this process, both by depleting central gas and altering BH dynamics via star formation-driven potential fluctuations, yet even the strongest feedback regimes permit significantly greater growth than the Eddington-limited case. Growth stalls after less than $\sim$1 Myr due to local gas exhaustion, as no large-scale inflows are present in the adopted numerical setup. Our results show that SE accretion naturally leads to BHs that are overmassive relative to their host galaxy stellar content, consistent with JWST observations. We conclude that short low-duty-cycle SE episodes represent a viable pathway for assembling the most massive BHs observed at early cosmic times, even when starting from light seeds.

We introduce a novel Multi-Order Monte Carlo approach for uncertainty quantification in the context of multiscale time-dependent partial differential equations. The new framework leverages Implicit-Explicit Runge-Kutta time integrators to satisfy the asymptotic-preserving property across different discretization orders of accuracy. In contrast to traditional Multi-Level Monte Carlo methods, which require costly hierarchical re-meshing, our method constructs a multi-order hierarchy by varying both spatial and temporal discretization orders within the Monte Carlo framework. This enables efficient variance reduction while naturally adapting to the multiple scales inherent in the problem ensuring asymptotic consistency. The proposed method is particularly well-suited for hyperbolic systems with stiff relaxation, kinetic equations, and low Mach number flows, where standard Multi-Level Monte Carlo techniques often encounter computational challenges. Numerical experiments demonstrate that the novel Multi-Order Monte Carlo approach achieves substantial reduction of both error and variance while maintaining asymptotic consistency in the asymptotic limit.

Nonlinear scalar-tensor theories of gravity have been considered as candidates for dark matter and dark energy. Often, they possess screening mechanisms, which allow the fifth force mediated by the additional scalar degree(s) of freedom to evade detection from local experiments. Their classical behaviour is well studied, but their quantum nature is relatively unexplored. We outline a Green's function method for obtaining the leading-order quantum corrections to the classical symmetron field profile, in the vicinity of a spherically symmetric extended source, in the planar limit. For parameters that experiments had previously ruled out, our calculations indicate that the symmetron force may be weaker than the classical field suggests.

We present a semiclassical framework in which stress-tensor deformations of a quantum field theory (QFT) reorganize into a gravitational action evaluated at a metric saddle. The deformed partition function can be written as a gravitational path integral evaluated at the saddle, establishing a direct link between stress-tensor flows and gravitational dynamics. Two complementary routes arise: (i) from gravitational actions such as Einstein and Palatini, which map to stress-tensor deformations of a seed QFT; and (ii) from deformed QFTs such as generalized Nambu-Goto and $T\bar{T}$-like deformed models, which reconstruct the corresponding gravitational actions. Finally, in a free, massive scalar theory, we show that the one-loop effective action of the nonlocal deformation contains a local curvature term; its coefficient defines an induced Newton constant at a chosen renormalization scale, thereby demonstrating a bidirectional link between stress-tensor flows and classical gravity.

Extreme nitrogen enhancement relative to oxygen, recently found in very high-redshift galaxies, has been seen in local star-forming galaxies displaying high log(N/O) values ($\geq\!-1.1$) at relatively low O abundances, 12+log(O/H)$\leq$8. Understanding the physical origins of these extreme N-emitters at low redshifts enables us to better constrain chemical enrichment mechanisms that drove such high log(N/O) values in the early Universe. With direct N and O abundances derived for 944 SFGs with spectroscopic observational data from the Dark Energy Spectroscopic Instrument Data Release 1 (DESI DR1), we report the discovery of 19 extreme N-emitters at low-z (z$<$0.5). Our sample of N-emitters represents a five-fold increase in their known number at low-z with 12+log(O/H)$\leq$8, and statistically, $2.21\pm0.91$\% of DESI DR1 SFGs with reliable O and N abundances obtained directly, are extreme N-emitters. The sample spans a mass range of $\sim 10^7$--$10^{10}$~M$_{\odot}$ with 12+log(O/H) range of $\sim$7.1--8.2, and the N-emitter fraction is found to increase with increasing stellar mass and decreasing metallicity. The most extreme N-emitter in our sample has log(N/O)=$-0.53\pm0.13$, while also having the lowest 12+log(O/H)=$7.08\pm0.09$ and the highest stellar mass, log(M$_{*}$/M$_{\odot}$)=$9.95\pm0.13$ among our sample. With galactic chemical evolution models, we show that sustained N-enhancement by asymptotic giant branch stars, in conjunction with presence of outflows during the evolution of the galaxy, can well explain the high log(N/O) of low-z extreme N-emitters. While single starbursts with outflow are sufficient to explain lower-mass N-emitters, more massive ones require a dual starburst scenario where a secondary starburst is triggered by inflow of gas.

We consider uniqueness results for meromorphic functions $f:{\mathbb C} \to \widehat{\mathbb C}$ such that for certain values $a\in {\mathbb C}$ the implication $f(z)=a \Rightarrow f'(z)=a$ holds, i.e. that $f$ and $f'$ share values {\it partially}. In particular, we give a result for four partially shared values.

Binary black holes (BBHs) forming in the accretion disks of active galactic nuclei (AGNs) represent a promising channel for gravitational-wave production. BBHs are often assumed to form at migration traps, i.e. radial locations where the Type I migration of embedded stellar-mass black holes (BHs) transitions from outwards to inwards. In this work, we test this assumption by explicitly simulating the radial migration of BH pairs in AGN disks under different torque prescriptions, including thermal effects and the switch to Type II migration. We map where and when binaries form as a function of supermassive BH (SMBH) mass, disk viscosity, and migrating BH mass. We find that, for SMBH masses below $10^8 M_\odot$, the majority of pair-up events occur near migration traps ($\gtrsim 80\%$). In contrast, for higher SMBH masses, differential migration dominates and off-trap pair-ups can prevail. Certain disk configurations (e.g., $α= 0.01$, $M_\bullet < 10^6 M_\odot$) present a significant overdensity of pair-ups even in the absence of traps due to traffic-jam accumulations where the gamma profile changes slope sharply. We also investigate hierarchical BBH formation, showing that higher-generation pair-ups cluster more tightly around trap or traffic-jam radii. Our results provide realistic prescriptions for BBH pair-up locations and timescales, highlighting the limitations of assuming fixed BBH formation sites.

Upcoming ground and space-based surveys are poised to illuminate low surface brightness tidal features, providing a new observable connection to dark matter physics. From imaging of tidal debris, the morphology of stellar streams can be used to infer the geometry of dark matter halos. In this paper, we develop a generative approach, X-Stream, which translates stream imaging into constraints on the radial density profile of dark matter halos--from the inner region out to the virial radius. Using the GPU-accelerated code streamsculptor, we generate thousands of stream realizations in trial gravitational potentials and apply nested sampling with a custom objective function to explore viable regions of parameter space. We find that multiple stellar streams can be used to constrain the entire radial density profile of a halo, including both its inner and outer density slopes. These constraints provide a test for alternatives to cold dark matter, such as self-interacting dark matter, which predicts cored density profiles. From cosmological simulations, the outer density slope is expected to correlate with merger histories though remains underexplored observationally. With ongoing and upcoming missions such as Euclid, the Rubin Observatory, ARRAKIHS, and the Nancy Grace Roman Space Telescope, X-Stream will enable detailed mapping of dark matter for thousands of galaxies across a wide range of redshifts and halo masses.

We theoretically identify observable consequences of spatial and spin symmetries on the dynamics of a small XXZ quantum simulator. Our proposed protocol relies on the choice of suitable initial states, and involves the measurement scheme whose experimental implementation is the simplest. We analyze a system of $N=2n=6$ to $12$ particles, trapped in a planar geometry comprised of two rings which exhibits point group symmetry $D_{nh}$. The particles represent effective spins whose interaction is described by the XXZ or Heisenberg Hamiltonian. The system is prepared in an initial state which is sitewise-factorized and invariant under all spatial symmetries, it evolves for a given time, after which the $z$-components of all $N$ spins are measured. We show that symmetries dictate (i) the qualitative behaviour of the measurement probabilities as a function of the evolution time, and (ii) the number of measurement results with different probabilities. We highlight the role of a twofold rotation of all spins. We also demonstrate that, in larger systems, the collapse of the initial state may be observed.

We study two-neutrino double-beta decay ($2νββ$) into first-excited $0^+_2$ states of nuclei used in $ββ$ decay experiments, including $^{76}$Ge, $^{82}$Se, $^{130}$Te, and $^{136}$Xe. We calculate the corresponding nuclear matrix elements (NMEs) within the nuclear shell model, using various Hamiltonians that describe well the spectroscopy of the initial and final nuclei. We evaluate the next-to-leading order (NLO) long-range NMEs recently introduced within chiral effective field theory, keeping three terms in the expansion of the energy denominator. In most cases, NLO contributions to the half-life are below 5%, but they can significantly increase due to cancellations in the leading-order Gamow-Teller NME. A detailed analysis in terms of nuclear deformation, including triaxiality, indicates that larger deformation differences between the initial and final states generally lead to smaller NMEs, but the seniority structure of the states also plays a relevant role. The lower range of our predicted half-lives, with uncertainties dominated by the nuclear Hamiltonian used, are slightly longer than the current experimental limit in $^{76}$Ge and consistent with the very recent half-life indication in $^{82}$Se.

Probabilistic concurrent systems are foundational models for modern mobile computing. In this paper, a unifying approach to probabilistic testing equivalences is proposed. With the help of a new distribution-based semantics for probabilistic models and a probabilistic testing framework with respect to process predicates, the internal characterization and the external characterization for testing equivalences are studied. The latter characterization can be viewed as the generalization of the classical fair/should equivalence and may equivalence. These equivalences are shown to be congruences. A thorough comparison between these equivalences and probabilistic bisimilarities is carried out. The techniques introduced in this paper can be easily extended to other probabilistic concurrent models. To showcase this flexibility, a case study is carried out on the pCSP model.

Let $S=K[x_1,\ldots,x_n]$ be the ring of polynomials in $n$ variables over an arbitrary field $K$. Given a finitely generated multigraded module $M$, its Stanley length, denoted by $\operatorname{slength}(M)$, is the minimal length of a Stanley decomposition of $M$. Let $I\subset S$ be a monomial ideal, minimally generated by $m$ monomials. We give an upper bound for $\operatorname{slength}(I)$, in terms of its minimal monomial generators. Also, we give precise formulas for $\operatorname{slength}(I)$, if $n=2$ or $m=2$. Also, we show that if $I$ has linear quotients, then $\operatorname{slength}(I)=m$, and the converse holds in some special cases.

This paper presents a terrestrial localization system based on 5G infrastructure as a viable alternative to GNSS, particularly in scenarios where GNSS signals are obstructed or unavailable. It discusses network planning aimed at enabling positioning as a primary service, in contrast to the traditional focus on communication services in terrestrial networks. Building on a network infrastructure optimized for positioning, the paper proposes a system that leverages carrier phase (CP) ranging in combination with trilateration to localize the user within the network when at least three base stations (BSs) provide line-of-sight (LOS) conditions. Achieving accurate CP-based positioning requires addressing three key challenges: integer ambiguity resolution, LOS/NLOS link identification, and localization under obstructed LOS conditions. To this end, the system employs a multi-carrier CP approach, which eliminates the need for explicit integer ambiguity estimation. Additionally, a deep learning model is developed to identify NLOS links and exclude them from the trilateration process. In cases where LOS is obstructed and CP ranging becomes unreliable, the system incorporates an error-state extended Kalman filter to fuse complementary data from other sensors, such as inertial measurement units (IMUs) and cameras. This hybrid approach enables robust tracking of moving users across diverse channel conditions. The performance of the proposed terrestrial positioning system is evaluated using the real-world KITTI dataset, featuring a moving vehicle in an urban environment. Simulation results show that the system can achieve a positioning error of less than 5 meters in the KITTI urban scenario--comparable to that of public commercial GNSS services--highlighting its potential as a resilient and accurate solution for GNSS-denied environments.

The spatial distribution of the zeros of the spectrogram is significantly altered when a signal is added to white Gaussian noise. The zeros tend to delineate the support of the signal, and deterministic structures form in the presence of interference, as if the zeros were trapped. While sophisticated methods have been proposed to detect signals as holes in the pattern of spectrogram zeros, few formal arguments have been made to support the delineation and trapping effects. Through detailed computations for simple toy signals, we show that two basic mathematical arguments, the intensity of zeros and Rouché's theorem, allow discussing delineation and trapping, and the influence of parameters like the signal-to-noise ratio. In particular, interfering chirps, even nearly superimposed, yield an easy-to-detect deterministic structure among zeros.

We characterize weighted modulation spaces (data space) for which the heat semigroup $e^{-tL}f$ converges pointwise to the initial data $f$ as time $t$ tends to zero. Here $L$ stands for the standard Laplacian $-Δ$ or Hermite operator $H=-Δ+|x|^2$ on the Euclidean space. This is the first result on pointwise convergence with data in a weighted modulation spaces (which do not coincide with weighted Lebesgue spaces). We also prove that the Hardy-Littlewood maximal operator operates on certain modulation spaces. This may be of independent interest. We have highlighted several open questions that arise naturally from our findings.

We extend the theory of infinite-exponent partition relations to arbitrary linear order types, with a particular focus on the real number line. We give a complete classification of all consistent partition relations on the real line with countably infinite exponents, and a characterisation of the statement "no uncountable-exponent partition relations hold on the real line", working throughout in ZF without the Axiom of Choice.

BaCd2P2 (BCP) has been recently identified as a new solar absorber with promising optoelectronic properties. This work demonstrates that, despite having a low precursor purity (98.90% to 99.95%), synthesized BCP samples exhibit a promising photoconductive carrier lifetime up to 300 ns, an implied open-circuit voltage exceeding 1 V, and photoluminescence quantum yield in the order of 0.2%, comparable to a high-purity single-crystalline GaAs wafer. To better understand the underlying mechanisms of BCP's promising properties, its tolerance to intrinsic defects and extrinsic impurities is investigated using first-principles defect modeling and compared with that of the well-studied GaAs. The results show that the nonradiative recombination rates induced by dominant deep-level intrinsic antisite defects are lower in BCP than in GaAs under typical growth conditions. Further exploration of the impact of transition metal impurities in the raw materials used to make BCP and impurities introduced during its synthesis shows that most of these do not form deep-level nonradiative recombination centers. As an impurity-tolerant counterpart of GaAs, BCP demonstrates great potential to improve the cost-to-performance ratio of photovoltaics.

In this paper, we study a class of quasilinear elliptic equations involving both local and nonlocal operators with variable exponents. The problem exhibits singular nonlinearities along with a subcritical superlinear growth term and a parameter $λ$. We study the existence of multiple solutions with the help of variational methods by restricting the associated energy functional on appropriate subsets of the Nehari manifold. Using the topological index and the structure of the fibering maps, we analyse a key splitting property of the associated Nehari manifold. This decomposition allows us to establish the existence of two distinct solutions. Additionally, we establish the $L^\infty$-bound for the solutions.

High-throughput characterization often requires estimating parameters and model dimension from experimental data of limited quantity and quality. Such data may result in an ill-posed inverse problem, where multiple sets of parameters and model dimensions are consistent with available data. This ill-posed regime may render traditional machine learning and deterministic methods unreliable or intractable, particularly in high-dimensional, nonlinear, and mixed continuous and discrete parameter spaces. To address these challenges, we present a Bayesian framework that hybridizes several Markov chain Monte Carlo (MCMC) sampling techniques to estimate both parameters and model dimension from sparse, noisy data. By integrating sampling for mixed continuous and discrete parameter spaces, reversible-jump MCMC to estimate model dimension, and parallel tempering to accelerate exploration of complex posteriors, our approach enables principled parameter estimation and model selection in data-limited regimes. We apply our framework to a specific ill-posed problem in quantum information science: recovering the locations and hyperfine couplings of nuclear spins surrounding a spin-defect in a semiconductor from sparse, noisy coherence data. We show that a hybridized MCMC method can recover meaningful posterior distributions over physical parameters using an order of magnitude less data than existing approaches, and we validate our results on experimental measurements. More generally, our work provides a flexible, extensible strategy for solving a broad class of ill-posed inverse problems under realistic experimental constraints.

We explore the finite-density phase diagram of the single-flavour Gross-Neveu-Wilson (GNW) model using matrix product state (MPS) simulations. At zero temperature and along the symmetry line of the phase diagram, we find a sequence of inhomogeneous ground states that arise through a real-space version of the mechanism of Hilbert-space fragmentation. For weak interactions, doping the symmetry-protected topological (SPT) phase of the GNW model leads to localized charges or holes at periodic arrangements of immobile topological defects separating the fragmented subchains: a topological crystal. Increasing the interactions, we observe a transition into a parity-broken phase with a pseudoscalar condensate displaying a modulated periodic pattern. This soliton lattice is a sequence of topological charges corresponding to anti-kinks, which also bind the doped fermions at their respective centers. Out of this symmetry line, we show that quasi-spiral profiles appear with a characteristic wavevector set by the density $k = 2πρ$, providing non-perturbative evidence for chiral spirals beyond the large-N limit. These results demonstrate that various exotic inhomogeneous phases can arise in lattice field theories, and motivate the use of quantum simulators to confirm such QCD-inspired phenomena in future experiments.