The definition of the phase space of field theories in presence of boundaries of Cauchy surfaces requires a choice of boundary conditions or decay behaviour of those fields. Often these conditions are motivated in part by the decay behaviour of the initial data of known exact solutions. In the case of gauge field theories the initial data are not free but are subject to initial value constraints. Still, the decay behaviour is commonly specified for the kinematical, i.e. unconstrained phase space. This can lead to the following practical problem: The constraints are preferably solved for field variables on which they depend only algebraically, i.e. not involving derivatives, as otherwise one would need to solve partial differential equations. However, the specified decay behaviour may prevent from doing that. On the other hand, a precise specification of decay for all kinematical fields appears unnecessary because the decay of gauge degrees of freedom is not observable. Yet, knowledge of their decay is required as one needs to compute Poisson brackets on the kinematical phase space in order to define what gauge invariance means. Thus the interplay between the constraint structure and the decay properties of the kinematical phase space is complex. In this contribution we develop a reduced phase space induced approach to the decay problem. Upon specifying gauge conditions tailored to the algebraic structure of the constraints, these define a split of the kinematical phase space into gauge and true degrees of freedom. Then the decay conditions of the kinematical phase space is systematically parametrised by a choice of decay for just the true degrees of freedom (i.e. the reduced phase space), the decay of the gauge degrees of freedom then follows unambiguously from solving both the constraints and the gauge conditions.

Moire minibands in twisted homobilayer semiconductors can, under suitable approximations, be modeled as a pair of Landau levels with opposite Chern numbers. This provides a minimal model for searching novel topological states in a time-reversal-symmetric Hamiltonian. In this work, we investigate the effects of an external magnetic field in this model. We study the many-body ground state in the density-magnetic-field (n-B) plane along the dn/dB = \pm1/Phi0 Streda line with Hartree-Fock approximation. Away from charge neutrality, we find the Chern-insulating (incompressible) state is very robust while towards charge neutrality, we find a transition from incompressible phase to compressible phase as the interaction strength kappa decreases. Using time-dependent mean-field theory, we further analyze spin-flip excitations and find that the incompressible state along Streda line toward charge neutrality becomes unstable even at large kappa when magnetic field is sufficiently large. Finally, we solve the two-body problem in a given Landau level exactly where the two particles experience unequal magnetic fields using a new basis called center-of-charge basis. This basis allows any isotropic interaction to be parameterized by a single quantum number, the relative angular momentum, thereby extending the Haldane pseudopotentials to the unequal-magnetic-fields case. As the difference of the two magnetic fields varies, these pseudopotentials show a sequence of level crossings, leading to non-monotonic structure of pseudopotentials that is absent in ordinary Landau level systems. Our formulation provides a useful starting point for studying weak-field physics in moire flat bands, where magnetic Bloch-state basis becomes computationally impossible due to the large basis sizes.

In this paper, we present a laboratory study focused on the impact of post-quantum cryptography (PQC) algorithms on multiple layers of stateful HTTP over TLS transactions: the TCP handshake, the intermediate TCP-TLS layer, the TLS handshake, the intermediate TLS layer, and the HTTP application layer. To this end, we propose a laboratory architecture that emulates a real-world setup in which a load test of up to 100 transactions per second is sent to a load balancer, which in turn forwards them to a backend server that returns the responses. Each set of tests is executed using the TLS 1.3 key exchange groups as follows: traditional (or non-PQC), hybrid PQC and pure PQC. Each set of tests also varied the backend response size. Across more than thirty experiments, we performed data reduction and statistical analysis for each layer, to determine the specific impact of each algorithm (PQC and traditional) at every stage of the HTTP-over-TLS transaction.

We consider $(\infty,d)$-categories in the limit $d\to \infty$ via the core or localization functors that forget or invert higher non-invertible arrows, respectively. We compare the two resulting $(\infty,1)$-categories of $(\infty,\infty)$-categories and exhibit the localization-limit as a reflective localization of the core-limit. On the side, we study intermediate localizations that arise from notions of invertibility that only emerge at $d=\infty$ such as the one defined by coinduction.

We propose a system of differential equations modeling the competition between two obligate mutualistic species for a single nutrient in a chemostat. Each species promotes the growth of the other, and growth occurs only in the presence of its partner. The three-dimensional model incorporates interspecific density-dependent growth functions and distinct removal rates. We perform a mathematical analysis by characterizing the multiplicity of equilibria and deriving conditions for their existence and stability. Using MatCont, we construct numerical operating diagrams in the parameter space of dilution rate and input substrate concentration, providing a global view of the qualitative dynamics of the system. One-parameter bifurcation diagrams with respect to the input substrate then reveal a variety of dynamical transitions, including saddle-node, Hopf, limit point of cycles LPC, period-doubling PD, and homoclinic bifurcations. When mortality is included, the system exhibits a richer dynamical repertoire than in the mortality-free case, with stable and unstable periodic orbits, tri-stability between equilibria and limit cycles, and several codimension-two bifurcations, including Bogdanov-Takens (BT), cusp of cycles (CPC), resonance points (R1 and R2), and generalized Hopf GH points. These features allow coexistence not only around positive equilibria but also along stable limit cycles, reflecting more realistic ecological dynamics. In contrast, neglecting mortality restricts coexistence to equilibria only. Overall, this study highlights the critical role of mortality in shaping complex dynamics in obligate mutualism, producing multistability and oscillatory coexistence patterns that may better represent natural microbial or ecological systems.

We modify the Double Machine Learning estimator to broaden its applicability to macroeconomic time-series settings. A deterministic cross-fitting step, termed Reverse Cross-Fitting, leverages the time-reversibility of stationary series to improve sample utilization and efficiency. We detail and prove the conditions under which the estimator is asymptotically valid. We then demonstrate, through simulations, that its performance remains valid in realistic finite samples and is robust to model misspecification and violations of assumptions, such as heteroskedasticity. In high dimensions, predictive metrics for tuning nuisance learners do not generally minimize bias in the causal score. We propose a calibration rule targeting a "Goldilocks zone", a region of tuning parameters that delivers stable, partialled-out signals and reduced small-sample bias. Finally, we apply our procedure to residualized Local Projections to estimate the dynamic effects of a rise in Tier 1 regulatory capital. The results underscore the usefulness of the methodology for inference in macroeconomic applications.

Decorated square-kagome quantum antiferromagnets provide a natural setting in which strong frustration, lattice decoration, and spin-orbit-induced anisotropy compete on comparable energy scales. Here we show that in Na$_6$Cu$_7$BiO$_4$(PO$_4$)$_4$Cl$_3$ the coupling ($J_{10}$) which links the decorating Cu(3) sites to the square-kagome backbone, stabilizes the gapped quantum-paramagnetic regime, while symmetry-allowed Dzyaloshinskii-Moriya (DM) interactions systematically suppress the minimum spinon gap $Δ_{\mathrm{spinon}}$ and drive the system toward magnetic condensation. To establish this, we combine ab initio calculation of the DM vectors with a generalized Schwinger-boson self-consistent mean-field theory that treats singlet and triplet hopping/pairing channels on equal footing. As a benchmark, the isotropic square-kagome Heisenberg model exhibits four competing low-energy saddle points distinguished by their Wilson-loop fluxes and by characteristic static and dynamical structure-factor fingerprints. A minimal DM perturbation does not qualitatively reshape this competing landscape, but already enhances the tendency towards order. For the realistic decorated Hamiltonian, finite-size scaling of $Δ_{\mathrm{spinon}}$ together with momentum-resolved structure factors identifies $J_{10}$ (exchange with decorating Cu) as the control parameter of the gapped regime and shows that the full symmetry-allowed DM pattern shifts the system further toward condensation. Our results place Na$_6$Cu$_7$BiO$_4$(PO$_4$)$_4$Cl$_3$ in close proximity to a magnetic instability and provide experimentally testable predictions for anisotropy-enhanced soft modes in decorated square-kagome materials.

We present TreeON, a novel neural-based framework for reconstructing detailed 3D tree point clouds from sparse top-down geodata, using only a single orthophoto and its corresponding Digital Surface Model (DSM). Our method introduces a new training supervision strategy that combines both geometric supervision and differentiable shadow and silhouette losses to learn point cloud representations of trees without requiring species labels, procedural rules, terrestrial reconstruction data, or ground laser scans. To address the lack of ground truth data, we generate a synthetic dataset of point clouds from procedurally modeled trees and train our network on it. Quantitative and qualitative experiments demonstrate better reconstruction quality and coverage compared to existing methods, as well as strong generalization to real-world data, producing visually appealing and structurally plausible tree point cloud representations suitable for integration into interactive digital 3D maps. The codebase, synthetic dataset, and pretrained model are publicly available at https://angelikigram.github.io/treeON/.

Platform trials allow treatment arms to enter and exit over time while maintaining a shared control arm, yielding concurrent and non-concurrent controls (NCC). Pooling NCC is often motivated as a strategy to improve statistical efficiency, but it is unclear which estimand is targeted, what assumptions justify identification and estimation, and when precision gains are achievable; these questions are further complicated by time-to-event/survival data. Motivated by the Adaptive COVID-19 Treatment Trial (ACTT) platform trial with time to recovery as the primary endpoint, we develop an estimand-first causal survival framework targeting the treatment-specific counterfactual survival curve in the concurrent population and the corresponding functionals including the concurrent restricted mean survival time (RMST). We give nonparametric identification results and formalize conditions that justify pooling using NCC. We study covariate-adjusted outcome-regression (OR) and doubly robust (DR) estimators for the concurrent RMST, comparing concurrent-only versions to pooled-control versions. Pooling improves precision for OR estimators only when the pooling assumption holds and parametric hazard models are correctly specified; otherwise, pooling can induce bias. Moreover, in certain settings, pooling NCC yields no efficiency gain for the DR estimator. Overall, the most robust route to improve precision is to target concurrent causal survival estimands and use a covariate-adjusted DR estimation that uses only concurrent controls. An ACTT application corroborates these results.

We establish the sharp rate of propagation of chaos for McKean-Vlasov equations with coefficients that are non-linear in the measure argument, i.e., not necessarily given by pairwise interactions. Results are given both on bounded time horizon and uniform in time. As applications, we deduce the sharp rate of propagation of chaos for the convergence problem in mean field games and control, and for mean field Langevin dynamics, the latter being uniform in time in the strongly displacement convex regime. Our arguments combine the BBGKY hierarchy with techniques from the literature on weak propagation of chaos.

Phototaxis of many species of green algae relies upon directional sensitivity of their membrane-bound photoreceptors, which arises from the presence of a pigmented "eyespot" behind them that blocks light passing through the cell body from reaching the photoreceptor. A decade ago it was discovered that the spherical cell body of the alga $Chlamydomonas~reinhardtii$ acts as a lens to concentrate incoming light, and that in "eyeless" mutants of $Chlamydomonas$ the consequence of that focused light reaching the photoreceptor from behind is a reversal in the sign of phototaxis relative to the wild type behavior. We present a quantitative theory of this sign reversal by completing a recent simplified analysis of lensing [Yang, et al., Phys. Rev. E 113, 022401 (2026)] and incorporating it into an adaptive model for $Chlamydomonas$ phototaxis. This model shows that phototactic dynamics in the presence of lensing is subtle because of the existence of internal light caustics when the cellular index of refraction exceeds that of water. During each period of cellular rotation about its body-fixed axis, the photoreceptor receives two competing signals: a relatively long, slowly-varying signal from the direct illumination, and a stronger, shorter, rapidly-varying lensed signal. The reversal of the sign of phototaxis is then a consequence of the dominance of the flagellar photoresponse to the signal with the higher time derivative. These features lead to a quantitative understanding of phototaxis sign reversal, including bistability in the direction choice, a prediction that can be tested in single-cell tracking studies of mutant phototaxis.

As Extended Reality (XR) systems increasingly map and understand the physical world, interacting with these blended representations remains challenging. The current push for "natural" inputs has its trade-offs: touch is limited by human reach and fatigue, while gaze often lacks the precision for fine interaction. To bridge this gap, we introduce World Mouse, a cross-reality cursor that reinterprets the familiar 2D desktop mouse for complex 3D scenes. The system is driven by two core mechanisms: within-object interaction, which uses surface normals for precise cursor placement, and between-object navigation, which leverages interpolation to traverse empty space. Unlike previous virtual-only approaches, World Mouse leverages semantic segmentation and mesh reconstruction to treat physical objects as interactive surfaces. Through a series of prototypes, including object manipulation and screen-to-world transitions, we illustrate how cross-reality cursors may enable seamless interactions across real and virtual environments.

We investigate Permutation-Invariant (PI) quantum error-correcting codes encoding a logical qudit of dimension $\mathrm{d}_\mathrm{L}$ in PI states using physical qudits of dimension $\mathrm{d}_\mathrm{P}$. We extend the Knill--Laflamme (KL) conditions for $d-1$ deletion errors from qubits to qudits and investigate numerically both qubit ($\mathrm{d}_\mathrm{L} = \mathrm{d}_\mathrm{P} = 2$) and qudit ($\mathrm{d}_\mathrm{L} > 2$ or $\mathrm{d}_\mathrm{P} > 2$) PI codes. We analyze the scaling of the block length $n$ in terms of the code distance $d$, and compare to existing families of PI codes due to Ouyang, Aydin--Alekseyev--Barg (AAB) and Pollatsek--Ruskai (PR). Our three main findings are: (i) We conjecture that qubit PI codes correcting up to $d-1$ deletion errors have block length $n(d) \geq (3d^2 + 1) / 4$, which implies an upper bound $d \leq \sqrt{12n-3}/3$ on their code distance, and that PR codes can saturate this bound. (ii) For qudit PI codes encoding a single qudit we numerically observe that increasing $\mathrm{d}_\mathrm{P}$ results in $n$ monotonically decreasing and approaching the quantum Singleton bound $n(d) \geq 2d-1$. (iii) We propose a semi-analytic extension of the qubit AAB construction to qudits that finds explicit solutions by solving a linear program. Our results therefore provide key insights into lower bounds on the block length scaling of both qubit and qudit PI codes, and demonstrate the benefit of increased physical local dimension in the context of PI codes.

This report summarizes the discussions and recommendations from the NSF Workshop on Algorithm-Hardware Co-design for Medical Applications, held on September 26-27, 2024, in Pittsburgh, PA. The workshop assembled an interdisciplinary cohort of researchers, clinicians, and industry leaders to examine foundational challenges and develop a strategic roadmap for algorithm-hardware co-design in medical computing. The workshop focuses on four thematic areas: (1) teleoperations, telehealth, and surgical operations; (2) wearable and implantable medicine, including implantable living pharmacies; (3) home ICU, hospital systems, and elderly care; and (4) medical sensing, imaging, and reconstruction. This report calls for a fundamental shift in how next-generation medical technologies are conceived, designed, validated, and translated into practice. The report recommends that NSF sustain investment in shared standardized data infrastructures and compute infrastructures, develop clinic workflow-aware systems and human-AI collaboration frameworks, promote scalable validation ecosystems grounded in objective, continuous measures, and physics-informed, and enable safe, accountable, and resilient platforms, including virtual-physical healthcare ecosystems, to de-risk translational pathways. The workshop information can be found on the website: https://sites.google.com/view/nsfworkshop.

We report high-precision heat-capacity measurements of submonolayer $^3$He adsorbed on highly crystalline graphite, revealing new aspects of the commensurate$-$incommensurate transition. Below 1K, two possible striped domain-wall phases emerge: $α_1$ with variable wall spacing and $α_2$ with fixed spacing. The $T$-linear heat capacity in $α_1$ arises from one-dimensional phonons along the walls. $α_2$ melts into $α_1$ at a critical density via a second-order transition, consistent with a quantum nematic (quantum liquid-crystal) state in $α_1$, and reconciling thermodynamic and prior nuclear-magnetic data.

We consider an elliptic operator $L$ with variable, merely bounded, and measurable coefficients on a Lipschitz domain, and study solutions to $Lu=0$ that attain given Neumann and Dirichlet-regularity data on different parts of the boundary. The boundary data lies in $L^p$ or $W^{1,p}$ respectively, and we show nontangential maximal function estimates of the gradient of the solution. This mixed boundary value problem generalizes the pure Dirichlet, regularity, and Neumann problem with rough boundary data in $L^p$, and the already established mixed boundary value problem for the Laplacian.

Remote epitaxy, where a 2D van der Waals material (usually graphene) is inserted on top of the substrate before film epitaxy, has emerged as a promising path for growing electronics with lower defect rates and less stringent lattice matching requirements. The exact mechanism behind remote epitaxy has not been definitively shown, however, and it is not obvious when examining a new substrate-film pair whether they would be compatible with the remote epitaxy process. In this paper, we use first principles calculations to test several different mechanisms for determining whether a given substrate-film pair will successfully be grown with remote epitaxy. We find that previously calculated metrics such as electrostatic potential do not hold sufficient explanatory power. We find that the sliding barrier of small islands on the surface when the atomic positions are allowed to optimize provides the most rigorous criteria for whether a given substrate-film pair is remote epitaxy active. This indicates that remote epitaxy is likely a phenomenon related to the kinetics and ease of island migration on the graphene surface.

We present a computational approach for exciton calculations in two-dimensional (2D) materials within the Bethe-Salpeter equation (BSE) framework, employing an atomistic description with point-like orbitals. Unlike widespread efficient calculations that rely on classical or effective interaction models, such as the Rytova-Keldysh model, our method incorporates quantum screened interactions. By explicitly computing the 2D dielectric function at the random-phase approximation level, we capture screening effects beyond such approximations with an accuracy akin to first-principles methods. Consequently, we can realistically estimate excitonic binding energies with a bearable computational cost. A detailed account of the various convergence parameters sheds light on a possible cause of the large dispersion of binding energies reported in the literature using first-principles GW/BSE implementations. This work thus provides an alternative pathway towards efficient and faithful dielectric screening and exciton computations in low-dimensional materials.

We formulate an extended holographic dark energy scenario based on a recently proposed two-parameter generalized entropic functional. Unlike constructions that phenomenologically impose modified entropy-area relations at the horizon level, the present framework is rooted in a microscopic entropy functional and the corresponding microstate counting. For bounded systems, the entropy acquires a generalized holographic scaling with two independent area contributions, recovering the Bekenstein-Hawking entropy in the appropriate limits. Implementing this entropy within the holographic principle, we derive a generalized dark energy density containing two distinct holographic sectors, naturally embedding standard holographic dark energy and $Λ$CDM as limiting cases. We analyze the cosmological evolution for both Hubble and future event horizon cutoffs and show that the model successfully reproduces the matter-to-dark-energy transition. The two entropic exponents enrich the dynamics, allowing for quintessence-like behavior or phantom regimes, while remaining compatible with the standard thermal history of the Universe.

According to the literature, mobile devices as experimental tools (MDET) can offer educational benefits by creating authentic, real-life contexts for physics learning, enhancing student motivation through the use of familiar technology, and supporting cognitive processes by providing multiple representations of phenomena. However, concerns have been raised about potential distractions and cognitive overload. Regarding these conflicting perspectives, few empirical studies on the impact of MDET in real classroom settings of regular, full-length physics courses are available, focusing on a non-specialized high-school target group. We present a study of a mechanics course in such a new setting, addressing the tight curricular, material, and practical constraints inherent to it. A quasi experimental pre post design comparing a treatment group using MDET and a control group without (same content, lesson plan, and teachers) was used. The 19-week teaching sequence focused on conceptual learning and motivational outcomes, controlled by several predictor variables. Findings reveal substantial pre post learning gains for both groups (Cohen d = 0.9) and small gains for perceived relation to reality (d = 0.29). But no significant differences between treatments were found, indicating that MDET do not outperform conventional teaching under the given constraints. Moreover, no evidence of negative effects such as distraction or cognitive overload was observed, and little to no interactions with predictors such as gender or prior knowledge were found. In conclusion, MDET show considerable potential as an effective option for integrating technology into teaching, offering learning outcomes comparable to those of successful conventional teaching, but not better.

Monostatic ISAC sensing differs from communication because the transmitter can monitor its distorted transmit waveform. Thus, the aggregate $κ$ distortion model, which treats impairments as unknown noise, is appropriate for communication but pessimistic for monostatic sensing. We derive PA-aware sensing Cramér--Rao bounds (CRBs) and a PN-aware CRB that reveals an irreducible velocity-error floor, and quantify when $κ$-based bounds overestimate sensing degradation. Simulations validate the analysis and show robustness to practical DPD template errors (less than 1~dB overhead at a typical $-25$~dB NMSE).

Stone duality is an indispensable tool for the study of compact, zero-dimensional, Hausdorff spaces. In the case of general compact Hausdorff spaces one can get quite a bit of mileage by considering the `Wallman duality' between compact spaces and lattices of closed sets. I will argue that the Gelfand--Naimark duality between compact Hausdorff spaces and unital, commutative \cstar-algebras provides great insight into compact Hausdorff spaces, and \v Cech--Stone remainders and their autohomeomorphisms in particular.

Brains and artificial neural networks compute with continuous variables such as object position or stimulus orientation. However, the complex variability in neural responses makes it difficult to link internal representational structure to task performance. We develop a statistical-mechanical theory of regression capacity that relates linear decoding efficiency of continuous variables to geometric properties of neural manifolds. Our theory handles complex neural variability and applies to real data, revealing increasing capacity for decoding object position and size along the monkey visual stream.

Machine learning and high-throughput screening approaches to superconductor discovery require physically meaningful descriptors that capture essential physics while remaining computationally tractable. The superfluid weight is an ideal descriptor as it is a prerequisite for superconductivity, determines the magnetic penetration depth and the Berezinskii-Kosterlitz-Thouless transition temperature in two-dimensional materials, may limit the critical temperature in unconventional superconductors through phase coherence, and reveals quantum geometric contributions to supercurrent transport. We develop a computationally efficient framework for calculating the zero-temperature, mean-field superfluid weight for uniform pairing from density functional theory band structures and Bloch wavefunctions. We separately evaluate the conventional contribution from band curvature and the geometric contribution from quantum geometry. To validate the method, we calculate London penetration depths for a few conventional superconductors (Al, Pb, Nb, MgB$_2$, LuRu$_3$B$_2$ and YRu$_3$B$_2$) and find good agreement with experiment after accounting for nonlocal corrections, strong-coupling effects, and sample quality. The conventional contribution dominates by orders of magnitude in these wide-band materials, as expected. This framework provides a foundation for large-scale screening of superconducting candidates and exploring quantum geometric effects in unconventional superconductors.

The interaction between the electrons and the lattice vibrations in a solid is responsible for various important effects, such as formation of polarons, temperature dependent bandgaps, phonon-limited carrier transport, and conventional superconductivity. Most works assume a linear electron-phonon interaction, where the electron only interacts with one phonon at a time. However, the validity of this assumption has not been verified in polar anharmonic materials, where large ionic displacements may invalidate the assumption of linear interaction. Here, we show that nonlinear electron-phonon interactions contribute significantly to the finite-temperature electron mobility of the inorganic lead halide perovskite CsPbI$_3$. We calculate the electron mobility from first principles using the self-energy relaxation time approximation and the long-range approximation. The effect of nonlinear interaction is taken into account using the recently derived expression for the long-range part of the one-electron-two-phonon matrix element. We show that due to the low phonon frequencies of CsPbI$_3$, the one-electron-two-phonon interaction changes the temperature scaling of the mobility and contributes about 10\% to the mobility at room temperature. The results underscore the importance of including nonlinear electron-phonon interaction in anharmonic halide perovskites.

The Laplacian energy of a digraph $G$ is defined as $\sum_{i=1}^n λ_i^2$, where $λ_i$ are the eigenvalues of the Laplacian matrix of $G$. A (di)graph $G$ is said to be $H$-free if it does not contain a copy of the fixed (di)graph $H$ as a sub(di)graph. In this paper, we extend the Turán problems to spectral Turán problems in digraphs: what is the maximal Laplacian energy of an $H$-free digraph of given order? In particular, we determine the maximum Laplacian energy and characterize the extremal digraphs of $\overrightarrow{C_{k+1}}$-free digraphs.

We report the discovery of the optical dipper and low-luminosity infrared stellar transient Gaia20ehk (hereafter, Gaia-GIC-1), which is currently undergoing high-amplitude variability due to transiting dusty material. In this work, we identify Gaia-GIC-1 as a likely young F-type star based on the spectral energy distribution before the onset of the high-amplitude optical variability. We detect a significant periodic modulation of 380.5 days in Gaia-G band before the onset of the infrared brightening, consistent with a $\sim$1.1 AU orbit assuming circular orbits and a 1.3 M$_{\odot}$ star. The system has remained in an infrared bright state for $>$4 years since the last near-infrared detection, confirmed by recent SPHEREx observations, while continuing to undergo large amplitude irregular optical dimming. We measure the dust temperature from the freshly generated debris to be $\sim$900 Kelvin based on available WISE photometry, and the dust clump size to have a minimum cross-sectional area of 0.13 AU$^{2}$, and the dust mass $4\times 10^{20}$ kg. Currently, optical follow-up spectroscopy has not revealed any prominent features in the system, likely due to its highly variable nature. We hypothesize that Gaia-GIC-1 represents debris recently formed in a planetary collision, which produced a clumpy dust cloud on a bound orbit, producing the observed dimming events. The ongoing collisional activity in this system presents a unique opportunity for understanding terrestrial planet formation.

We show that for all $γ> 0$ and $Δ\in \mathbb{N}$, there is some $n_0$ such that, if $n \geq n_0$, then every oriented graph on $n$ vertices with minimum semidegree at least $(3/8 + γ)n$ contains a copy of each oriented tree on $n$ vertices with maximum degree at most $Δ$. This is asymptotically best possible.

In this paper we investigate a class of variational reaction-diffusion systems with strong competition driven by beyond-pairwise interactions. The model involves $d$ nonnegative components interacting through $k$-wise terms, with $3 \leq k \leq d$, and includes symmetric interaction coefficients accounting for multi-component effects as well as suitable nonlinear terms. We focus on minimal energy solutions, proving uniform-in-$β$ Hölder bounds up to an explicit threshold exponent depending only on the dimension of the space and on the order $k$ of the interaction. As $β\to +\infty$, we show that minimizers converge strongly in $H^1$ and in Hölder spaces to a partially segregated configuration, characterized as minimizer of a natural variational problem under a $k$-segregation constraint. Finally, we prove that every minimizer of the limit problem enjoys the Hölder regularity and we derive some basic extremality conditions.

Recently, generative diffusion priors have made huge strides as inverse problem solvers, including the ability to be adapted for inference on out-of-distribution data. Concurrently, implicit neural representations (INRs) have emerged as fast and lightweight inverse imaging solvers that are amenable to hybrid approaches that combine learned priors with traditional inverse problem formulations. In this paper, we present a diffusive computed tomography (CT) inversion framework for regularizing INRs called Diffusive INR (DINR), designed to enable high-quality reconstruction from sparse-view neutron CT. Pretrained purely on synthetic data, DINR is evaluated on simulated and experimentally obtained observations of concrete microstructures, where traditional reconstruction methods suffer substantial degradation when the number of views is reduced. Our approach delivers superior performance, reduces reconstruction artifacts, and achieves gains in PSNR and SSIM, enabling accurate micro-structural characterization even under extreme data limitations compared to state-of-the-art sparse-view reconstruction techniques.