Accretion-disc corona sources are high-inclination low-mass X-ray binaries in which the innermost regions are hidden and the observed X-ray emission is dominated by radiation scattered above the disc. 4U 1822-37 is a key binary system of this class, but its geometry is still debated. X-ray polarimetry offers a direct probe of the scattering structure. We present the first X-ray spectro-polarimetric study of 4U 1822-37 and test whether its spectrum and polarisation can be explained within the accretion-disc-corona scenario. We analysed a coordinated campaign with IXPE, XMM-Newton, NuSTAR, and Swift. We performed broadband spectral modelling and model-independent, energy-resolved, and orbital-phase-resolved polarimetric analyses. The broadband spectrum requires a soft thermal component, a Comptonised continuum, a hard power-law tail, and relativistically blurred reflection. The observed 0.1-100 keV luminosity, $L_{\rm obs}\simeq6.1\times10^{36}\ {\rm erg\,s^{-1}}$, is far below the intrinsic luminosity expected from the orbital evolution, supporting a geometry in which only a small fraction of the intrinsic emission is scattered into the line of sight by an extended, optically thin corona. In the 2-8 keV band, IXPE measures ${\rm PD}=7.9\pm0.6\%$ and ${\rm PA}=-24^\circ\pm2^\circ$. The PD increases with energy, while the PA remains approximately constant. During eclipse, the PD decreases to ${\rm PD}=5.5\pm1.7\%$, with no significant PA variation. This behaviour is consistent with the companion occulting the most polarimetrically efficient part of the extended corona. The high PD, stable PA, energy-dependent polarisation, and eclipse behaviour support a picture in which 4U 1822-37 is observed in an extreme high-inclination, scattering-dominated regime. The extended corona is the main structure shaping both the observed X-ray emission and its polarisation.

We prove a strengthened form of a conjecture of Sun on a determinant attached to a binary quadratic form. Let $n>3$ and let $c,d\in\Z$. If $n$ is composite, then \[ \det\big[(i^2+cij+dj^2)^{n-2}\big]_{0\leq i,j\leq n-1}\equiv 0\pmod {n^2} \] with no condition on $c$ and $d$. If $n=p$ is prime, the same congruence holds whenever the Legendre symbol $\leg{d}{p}$ is $-1$. For composite $n$, a polynomial determinant is divisible by two Vandermonde factors; after specialisation, their product already yields the required square divisor. For prime $n=p$, we estimate the rank of the matrix modulo $p$. The required rank defect follows from a coefficient cancellation obtained from the involution $t\mapsto d/t$ on $\Fp^\times$ and the condition $\leg{d}{p}=-1$.

Let $\mathcal{L}$ be the infinitesimal generator of an analytic semigroup $\big\{e^{-t\mathcal L}:t>0\big\}$ on $L^2(\mathbb R^n)$ with Gaussian upper bounds, and suppose that $\mathcal{L}$ has a bounded holomorphic functional calculus on $L^2(\mathbb R^n)$. For given $0<α<n$, let $\mathcal L^{-α/2}$ be the generalized fractional integral associated with $\mathcal{L}$, which is given by \begin{equation*} \mathcal L^{-α/2}(f)(x):=\frac{1}{Γ(α/2)}\int_0^{+\infty}e^{-t\mathcal L}(f)(x)t^{α/2-1}dt, \end{equation*} where $Γ(\cdot)$ is the usual gamma function. In the limiting Sobolev case $λ=n-αp$ and $1\leq p<n/α$, the author proves that the operator $\mathcal{L}^{-α/2}$ is bounded from the Morrey space $M^{p,λ}(\mathbb R^n)$ into $\mathrm{BMO}_{\mathcal{L}}(\mathbb R^n)$, and is bounded from the vanishing Morrey space $VM^{p,λ}(\mathbb R^n)$ into $\mathrm{VMO}_{\mathcal{L}}(\mathbb R^n)$, where $\mathrm{BMO}_{\mathcal{L}}(\mathbb R^n)$ and $\mathrm{VMO}_{\mathcal{L}}(\mathbb R^n)$ are the spaces of bounded mean oscillation and vanishing mean oscillation associated with the operator $\mathcal{L}$, respectively. As a consequence, the author obtains that the operator $\mathcal{L}^{-α/2}$ is bounded from $L^{p,\infty}(\mathbb R^n)$ into $\mathrm{BMO}_{\mathcal{L}}(\mathbb R^n)$ when $p=n/α$ and $0<α<n$. The proofs are based on pointwise kernel estimates of the operators $\mathcal L^{-α/2}$ and $(I-e^{-t\mathcal L})\mathcal{L}^{-α/2}$ for $0<α<n$.

Squared Wasserstein distance is a frequently used tool to measure discrepancy between probability distributions. This distance is typically computed between empirical measures of size $n$ from two underlying random samples. Unfortunately, even in lower dimensional Euclidean space problems $\left( d \in \{2,3\} \right)$, algorithms for Wasserstein distance computation with approximate or exact precision guarantees scale poorly in the runtime as a function of $n$ and the desired precision. In response, we consider the computational-statistical runtime, where the goal is to estimate from samples the Wasserstein distance between potentially smooth measures up to $ε$-additive error in expectation with respect to the sampling; we allow $O(1)$ computational cost for collecting a sample. Towards this, we develop a Sample-Sketch-Solve paradigm where we introduce a regular cartesian grid sketch of the samples. We show that (especially under $α$-Hölder smooth distributions) this can compress the data without increasing asymptotic error, and also regularizes the structure which enables faster exact algorithms. Ultimately, we approximate $W_2^2(P,Q)$ within $ε$ error in $ε^{-\max(2,\frac{d+1+o(1)}{1+α})}$ time for $0 1/2$ when $d=2$ and nearly optimal as $α\to 1$ when $d = 3$.

Current neural architecture search (NAS) methods are often limited by their predefined, restrictive search spaces. While recent large language model (LLM)-assisted NAS methods enable open-ended search spaces, they often suffer from inefficient exploration due to biased or low-quality design ideas. To address these issues, we propose to semi-automatically structure model design knowledge to guide the search process. Our approach first defines a high-level structural template of architectural attributes. An LLM then populates this template by analyzing papers, creating a rich and diverse search space that embodies this structured design knowledge. To efficiently explore this vast space, we introduce FairNAD, using a multi-type mutation that enables broad exploration through mutation with fair idea sampling, Pareto-aware mutation, LLM-driven iterative mutation, and a fine-grained feedback loop. We demonstrate the effectiveness of FairNAD in discovering high-performing architectures that yield 0.84, 2.17, and 2.35 points improvement on CIFAR-10, CIFAR-100, and ImageNet16-120, respectively, compared to current state-of-the-art methods.

To support operations and passenger-facing services, transit agencies need reliable passenger load trajectories. Currently, load estimates are typically inferred from imperfect sensing systems rather than fully observed, and the accuracy of modern automatic passenger counting (APC) systems still varies with station layout, flow intensity, and operating conditions. To address the challenges of robust passenger load estimation from heterogeneous data streams, including incremental count errors, evidence conflicts, and context-dependent sensor reliability, we propose a closed-loop, state-centric, multi-agent framework. This method enforces physical feasibility at every step, allocates trust dynamically among evidence sources, and feeds physics-derived violation residuals back into training for robustness improvement. The architecture consists of a unified stop-event backbone, a coupled Perception--Physical--Fusion loop for stop-by-stop inference, and optional trip-level macro-correction and closed-loop calibration modules.

A sub-class among Young Stellar Objects (YSOs), known as FU Ori type stars, undergo sudden rises in luminosity by several orders of magnitude on timescales of a few months to a few years, and decay back to quiescence on timescales of a few decades. Modelling the light curves of these objects is crucial to understanding how different components of these accretion disk systems evolve during outburst. For this purpose, we use a parametric model that couples the stellar photospheric emission, magnetospheric accretion shocks, an irradiated dust disk, and a viscously heated gas disk. We adopt time-dependent accretion rate profiles that mimic the observed morphologies of FU Ori outburst light curves, and we use the accretion model infrastructure to simulate multi-band light curves, as well as color curves. The model enables us to study how different components dominate the flux in each band over the course of an outburst, providing insight into star-magnetosphere-disk interactions throughout the outburst cycle. We find that throughout an accretion outburst, red optical and near-infrared lightcurves generally follow the same or very similar form as the input accretion profile, being sensitive to heating in the accretion shocks and inner gas disk, while mid-infrared lightcurves are more responsive to the location and heating of the innermost dust disk.

Toroidal modes enable high-Q resonances, but electric toroidal excitations remain unexplored compared to magnetic ones. This work establishes electric-magnetic toroidal duality in a hexagonal metasurface. Using finite element simulations, we analyze electric and magnetic toroidal modes in a hexagonal silicon nanorod supercell under mirror-symmetry breaking via height modulation. Eigenfrequencies, Q-factors, power flow, and polarization responses are computed. We identify electric TO and ATO modes with complementary near-field topologies to magnetic analogues. Direct frequency intersections (magnetic and electric TO/ATO) yield high-Q quasi-BICs. Polarization selectivity reverses between families: 0° excites magnetic TO/electric ATO; 90° excites magnetic ATO/electric TO. A loss hierarchy (magnetic TO > magnetic ATO > electric ATO > electric TO) and protective layers compatibility are demonstrated. Electric and magnetic toroidal responses are dual manifestations of the same symmetry, providing a unified design framework for high Q metasurfaces in sensing, nonlinear optics, and loss-tolerant devices.

The terms responsive, adaptive and intelligent are widely used in soft matter but inconsistently defined. This paper formulates them as information channels of increasing architectural complexity: a memoryless map p(y|x) (responsive), a state-conditioned map p(y|x,s) (adaptive), and a feedback-modified channel p(y_t|x_t, X_past, Y_past) (intelligent). Existing complexity metrics for cross-class comparison fail at least one of: dimensional consistency, common reference, thermodynamic coupling, scale-bridging. Three information-theoretic metrics are proposed: configurational diversity I1, Hazen functional selectivity I2, and stimulus-response information transfer I3. Treating the material as the channel yields a complexity-function relationship: internal complexity raises potential information capacity but also raises attenuation and dissipation. This implies a thermodynamic scaling ceiling and an optimal internal complexity N* set by transmission efficiency, stimulus energy and thermal noise (a Carnot-analogue limit). A benchmarking framework compares synthetic soft matter, biological systems and hard-matter architectures in common information coordinates. Ten representative systems are mapped on the volumetric rate (I3 per unit volume) versus power density plane. They form four bands above the Landauer floor: 10^18 to 10^20 for soft matter and shape-memory alloys; 10^10 to 10^16 for silicon digital and electromechanical; 10^9 to 10^10 for memristor neuromorphic; 10^5 to 10^8 for evolved biology (all uncertain to at least one order of magnitude). The mechanistic origin of the gap between synthetic soft matter and biology is the per-element substrate energy scale (1 to 10 kBT versus 10^4 to 10^5 kBT). Three architectural routes - feedback, multi-channel orthogonality, and molecular memory - are proposed to let soft matter populate this gap.

Existing 3D foundation models typically align point clouds to frozen vision-language spaces like CLIP, which achieve strong cross-modal retrieval by compressing 3D shape into a global vector. However, this global-only alignment cannot establish fine-grained pixel-to-point correspondence. To solve this, we present Tango3D, a foundation model that unifies dense correspondence and global retrieval. We use a geometry-aware 2D visual backbone and a pretrained 3D VAE to encode images into 2D patches and point clouds into 3D tokens. These are mapped into a single shared space to achieve both local pixel-to-point alignment and global semantic alignment. To stabilize the joint learning of dense and global objectives, we introduce a three-stage progressive training strategy. Experiments show our model successfully achieves object-level pixel-to-point alignment while maintaining competitive global retrieval, a joint capability not offered by existing 3D foundation models. By establishing a fine-grained alignment feature space, Tango3D injects rich semantics into purely geometric 3D tokens, paving the way for a wide range of dense 3D downstream tasks.