Papers

We provide a simple derivation of the conformal dispersion relation of Carmi and Caron-Huot which reconstructs a CFT four-point function from its double discontinuity. We exhibit a hidden conformal symmetry which explains the appearance of the "magic variable" x as a simple cross-ratio, built from four physical cross-ratios. We also introduce a regulator in the double discontinuity operation and then prove that one subtraction suffices for all integrals to converge.

Recent JWST observations have revealed that the morning and evening limbs of the hot Jupiter WASP-94Ab have very different transmission spectra. An analysis of these resolved limb spectra yielded a metallicity more than an order of magnitude below that obtained from the limb-averaged spectrum, which calls into question the accuracy of traditional retrievals for heterogenous planets. Here we analyze the limb-averaged JWST NIRISS and NIRSpec transmission spectra of WASP-94Ab using both a standard one-temperature-profile (1-TP) retrieval with patchy clouds, and a new two-temperature-profile (2-TP) retrieval. The 2-TP retrieval assumes a linear combination of two atmospheric components that share the same bulk elemental composition but have independent thermal structures, chemistries, and aerosol properties. This model is implemented in PLATON 7.0, a JAX-accelerated code that is over 100 times faster than its predecessor, which is key to making the retrieval computationally tractable. The limb-averaged spectrum of WASP-94Ab favors the 2-TP model by a Bayes factor K=1.8x10^{5} and shifts the metallicity downward to Zatm/Zsun = 11^{+9}_{-4} from 170^{+30}_{-24} obtained with the 1-TP model. The 2-TP retrieval predicts two, equally weighted components that reproduce the limb-resolved spectra across both instruments without prior knowledge of them. This work demonstrates that compositional information survives limb averaging for WASP-94Ab, suggesting that 2-TP retrievals can be used to identify limb-asymmetry and extend metallicity studies beyond the small set of planets amenable to limb-resolved spectroscopy.

Inspired by recent ARPES studies on multilayer ($n\geq3$ layers) cuprate superconductors, we use the unrestricted Hartree-Fock approximation to explore the ground-state phase diagram of two coupled, inequivalently doped square-lattice Hubbard layers. In the decoupled-layer limit, the lightly hole-doped ground state is typically an incommensurate spin-stripe state. However, with sufficiently strong interlayer coupling, stripe order is destabilized relative to a commensurate Néel-ordered metal. The resulting state exhibits a reconstructed Fermi surface with hole pockets centered at $(\pm\pi/2,\pm\pi/2)$ that are similar in character to those seen in experiments. Our results illustrate the qualitatively new physics that can arise from interlayer coupling in multilayer cuprates.

Chemical enrichment shapes how galaxies form and evolve. The gas-phase metallicity is directly linked to the stellar mass, star formation rate, and cold gas of the interstellar medium. Thus, the cold gas fundamental metallicity relation (GFMR) is a powerful tool for probing galaxy evolution, bridging large-scale gas flows modulating the cold gas reservoir and small-scale metal enrichment tracing the cumulative impact of star formation. Constraining all these properties for the same representative sample of galaxies remains challenging yet essential. Using CO(3–2) band 3 observations from the Atacama Large Millimeter/submillimeter Array Chemical Evolution (ACE) survey, we investigated the GFMR in a sample of 26 main-sequence (log(M_*, med)=9.96), subsolar-metallicity (12+log(O/H)_med=8.44) star-forming galaxies (SFGs) at z~2. With 17/26 CO detections, including some of the lowest-metallicity CO detections at cosmic noon, we find that the stellar mass remains the primary driver of the chemical evolution in our sample (sigmaMZR~0.10). Whereas the molecular gas likely plays a secondary role (sigmaGFMR~0.11) similar to that of the star formation rate (sigmaFMR~0.13). This likely reflects our sensitivity to only the CO-bright component of the molecular reservoir. Our results remain consistent with gas-regulator models and suggest the existence of efficient molecular outflows, with an average mass loading factor of eta~4, regulating star formation and chemical enrichment.

Little red dots (LRDs) may be powered by supermassive black holes (SMBHs) accreting above the Eddington limit. Spectroscopy of LRDs often shows absorption troughs blueshifted by $\sim100-300\,{\rm km\,s^{-1}}$, implying a slow wind. This is puzzling: super-Eddington disks drive much faster winds, $\gtrsim10^3-10^4\,{\rm km\,s^{-1}}$. We argue that LRDs are super-Eddington SMBHs viewed off-axis and engulfed in a slow wind that covers most sight-lines; the fast wind escapes near the poles. Trapped light puffs the inner disk into a quasi-spherical envelope that launches the slow wind. The wind may be “photon-tired”, meaning the light only barely unbinds it. Such marginally unbound winds lead to fountain flows, where some gas escapes and the rest falls back. We model the envelope with idealized, spherically symmetric “marginally unbound” ($v\sim v_{\rm esc}$) and “photon-tired” winds. We feed these profiles into the radiative transfer code Sirocco to study how the wind reprocesses the light from an accreting $10^6\,M_\odot$ SMBH. We describe most of the wind as a “Balmer cocoon” – a Compton-thick region in which depletion of Balmer continuum photons ($h\nu >3.4\,{\rm eV}$) rather than Lyman continuum photons ($h\nu > 13.6\,{\rm eV}$) keeps the gas ionized. The spectra span the range of LRD-like sources: “little blue dots” at lower outflow rates ($\sim2.5\,M_\odot\,{\rm yr}^{-1}$); V-shaped LRDs with a Balmer break ($\sim5-10\,M_\odot\,{\rm yr}^{-1}$); and red LRDs with full breaks ($\sim15\,M_\odot\,{\rm yr}^{-1}$). Our Balmer line profiles show P~Cygni features atop broad, exponential wings, as is observed. The break is possible at lower wind densities than in LTE models because Lyman~$\alpha$ trapping sustains our $n=2$ hydrogen population and electron scattering enhances the optical depth. Our arguments are also applicable to winds from supermassive stars or quasi-stars.

We propose an M-theory origin for the two massive deformations of type 0A string theory by extending Hull's realization of massive type IIA in the context of a recent proposal for massless type 0A from M-theory. We introduce an M-theory setup that we call quantum fibration, in which two independent integral monodromies yield the Romans masses, T-dual to the two Chern numbers of the quantum fibration. A key ingredient is a formulation of the type 0B duality group in terms of a marked elliptic curve. We discuss further implications of this description and some puzzles concerning the M-theory origin of branes and Chern–Simons terms.

We explore dark matter isocurvature perturbations in cosmological scenarios with entropy dilution resulting from a late decaying massive state that temporarily dominates the universe before big-bang nucleosynthesis. The dilution mechanism features a non-standard scaling window of the radiation energy density, which allows for a new way to derive the entropy dilution factor. On super-horizon scales, the same scaling window also governs the evolution of isocurvature, and we present an analytic approach to solving the perturbation equations. We characterize various regimes where dark matter isocurvature survives and is subject to constraints from the cosmic microwave background observations. For cosmologically viable scenarios, we find that dark matter is dominantly produced from its dilutor decay, and the isocurvature is suppressed by the entropy dilution factor to the $4/3$ power. Our work demonstrates the complementarity between isocurvature and collisionless damping of dark matter as powerful probes of the entropy dilution mechanism.

We study the gauging of discrete symmetries of the 5d rank-one $E_n$ SCFTs that fix the Coulomb branch coordinate but act nontrivially on the Higgs branch chiral ring. Using generalized toric polygons and $(p,q)$-brane webs, we identify symmetries of the moduli space that extend to symmetries of the full SCFT. In many cases they are non-anomalous, and we analyze the moduli space of the gauged theories. We realize the resulting Higgs branch quotients as Coulomb branches of wreathed magnetic quivers and compute their Hilbert series; the flavor algebras extracted from moment maps agree with the fixed-point subalgebras of $\mathfrak{e}_n$. We also lift the discrete actions to the Seiberg–Witten geometry and recover the expected restriction on the mass deformations. For $\mathbb{Z}_2$-wreathings that exchange adjacent gauge nodes, we find that the monopole formula requires a flux-dependent sign and propose a corrected prescription. Finally, we conjecture a higher-rank extension and verify it for the rank-two $E_6/\mathbb{Z}_2$ Higgs branch.

We present a bootstrap framework that yields rigorous two-sided bounds on ground-state observables of quantum systems with quenched disorder. The key idea is to extend the operator algebra to include classical disorder variables and to encode the disorder distribution through a set of moments. The method directly bounds disorder-averaged expectation values for finite or infinite lattice systems and for arbitrary disorder distributions. In contrast to conventional approaches, we do not need to sample disorder realizations, which enables us to make thorough use of symmetries that hold only on average rather than for each disorder realization. Additionally, we show that multi-replica operators can be used to access disorder fluctuations such as the variance of an observable. We apply the method to the one-dimensional random transverse-field Ising model (RTFIM) with discrete, uniform, and Gaussian disorder, obtaining tight bounds on the disorder-averaged ground-state energy density and short-range spin-spin correlators, as well as bounds on the disorder variance of the energy density. Additionally, we show that the difference between the upper and lower bounds on the disorder-averaged ground-state energy density, which we term the bootstrap gap, can be used to map out the phase diagram of the RTFIM. The bootstrap gap is small and flat within the paramagnetic and ferromagnetic phases at weak disorder, grows upon entering the Griffiths regions, and peaks along the critical line.

We present evidence that ten-dimensional type IIB string theory orbifolded by the $\mathbb{Z}_3$ duality symmetry at the strong-coupling fixed point $\tau=\exp(2\pi i/3)$ defines a consistent theory. Motivated by its F-theory dual description and its duality with M-theory in nine dimensions and type IIA string theory in eight dimensions, we argue that the resulting theory is a ten-dimensional chiral non-supersymmetric theory with a discrete gauge symmetry whose bosonic part is the automorphism group of the Narain lattice $\Gamma^{2,2}(A_2)$ ($S_3 \times S_3 \times \mathbb{Z}_2$). We further identify the ten-dimensional tachyon fields with the corresponding Narain moduli. Gauge anomalies cancel nontrivially through a topological Green-Schwarz mechanism involving a $\mathbb{Z}_3$-valued two-form gauge symmetry: the ten-dimensional lift of the familiar zero-form orbifold quantum symmetry in the eight-dimensional type IIA description.

Using on-shell methods, we derive an all-order non-renormalization theorem for general four-dimensional effective field theories, relying on Poincaré invariance and unitarity. Each operator $\mathcal O$ is assigned the weights $(w,\bar w)=(\ell-h,\ell+h)$, where $\ell$ and $h$ are the number of particles and total helicity of its minimal configuration. At $L$ loops, the mixing $\mathcal O_j\to\mathcal O_i$ vanishes when $\ell_j-\ell_i=L-1$ and either $w_i<w_j-2(L-1)$ or $\bar w_i<\bar w_j-2(L-1)$, in the absence of non-holomorphic Yukawa couplings. These zeros follow entirely from tree-level data and are scheme independent under finite renormalizations that preserve the operator-length selection rule. For operators of dimensions five through eight, we identify broad classes of previously unknown zeros at higher loop orders, with particular emphasis on two loops, where the theorem provides direct checks on current calculations, as in the Standard Model Effective Field Theory.

Recent studies have hypothesized that little red dots (LRDs) are rapidly accreting black holes surrounded by dense gaseous environments. Both neutral and ionized gas play a key role in explaining many of the puzzling spectral features of LRDs, including the emission line profiles in the optical-infrared bands, although the physical conditions required for these gas components remain poorly constrained. We propose that free-free emission provides a robust, independent probe of ionized gas in LRDs. Free-free self-absorption produces a characteristic spectral turnover whose critical frequency and luminosity depend on the electron column density and the characteristic size of the ionized region, such that radio observations simultaneously constrain both quantities. The spectral slope at frequencies below the turnover further probes the radial density distribution on spatial scales far below those achievable by current and future optical-infrared observatories. We also present predicted free-free spectral energy distributions for two representative LRDs in the local and high-redshift universe and show that future radio-to-millimeter observations with ALMA and ngVLA can probe the range of ionized-gas parameters inferred from current observations. Free-free emission therefore offers a unique way to probe the geometry and physical conditions of the ionized gas surrounding LRDs.

In this work, we study the neural scaling laws of RydbergGPT, an autoregressive transformer model trained on qubit projective measurement data gathered from interacting Rydberg atom arrays. The quantum system is known to exhibit a finite-size remnant of a critical point as the laser detuning parameter is varied. We find that near the critical point the transformer loss as a function of training dataset size is well described by a power-law with a loss floor correction. However, away from criticality the quality of the power-law description is substantially reduced. We then compare the statistical structure of both Rydberg measurements and natural-language corpora using an entropy-normalised, finite sample corrected mutual information "two-point" function. We find that near-critical statistics of the two point functions are closest to those observed in natural-language, whilst other qubit configurations far from the critical point have two-point functions that decay more rapidly. This supports the hypothesis that multi-scale dependence contributes to stable neural scaling, and that scaling behaviour should be viewed as a property of the model-data pair.

In this work we calculate, for the first time, the dominant perturbative contributions to axion–matter couplings explicitly in string theory. Concretely, we compute these couplings in Calabi–Yau compactifications of heterotic string theory where the vector bundle is a sum of line bundles. They are expressed as overlap integrals requiring the Ricci-flat metric, the Hermitian Yang-Mills bundle metric, and the matter field harmonic forms. We compute these by solving the corresponding coupled differential equations with neural networks. Our results establish a characteristic hierarchy of four-dimensional couplings: axions couple to fermions as $\mathcal{L} \supset c_\psi\,\frac{\partial_\mu a}{f_a}\, \psi^\dagger \bar{\sigma}^\mu \psi$ with $c_\psi$ an $\mathcal{O}(1)$ function of Kähler moduli for the model-dependent axions, while the corresponding coupling for the model-independent axion is suppressed by $\alpha_{\rm YM}$ at the ultraviolet matching scale. The model-dependent axions thus couple to fermions similarly as DFSZ-like four-dimensional axions, whereas the model-independent axion's couplings are loop-suppressed as in KSVZ-like constructions. The methods developed here apply directly to the large class of heterotic line bundle models with realistic spectra, and can be adapted to type II constructions.

Matrix-valued time series, arising in diverse fields such as economics, neuroscience, and recommender systems, have become increasingly prominent in modern data analysis. Among various modeling frameworks, the matrix-variate CP-factor model represents an important and widely applicable class for capturing low-rank structures in matrix time series. In this paper, we provide a unified treatment for the identification problem of CP factor models using both analytic and algebraic tools. In particular, we characterize the parameter space as the union of two subspaces, one identifiable and the other non-identifiable. We show that existing estimation methods only apply to an open proper subset of the identifiable subspace. In contrast, we propose a quasi-maximum likelihood estimation (QMLE) procedure for CP factor models, which allows consistent estimation on the whole identifiable subspace. Moreover, we show that the estimated loading matrices by QMLE achieve a faster convergence rate compared to existing approaches. A simulation study and a real application are conducted to demonstrate the finite-sample performance of the proposed method.

Multiplayer PC gaming on Linux faces a structural problem: the anti-cheat systems that publishers require operate as proprietary Ring 0 kernel modules that are architecturally incompatible with Linux's security model, GPL licensing, and stable ABI guarantees. We argue the right response is not to port these invasive modules to Linux, but to replace them entirely. This paper presents TPM-Attest, a hardware-rooted remote attestation framework that uses the Trusted Platform Module (TPM) 2.0 and the Linux Integrity Measurement Architecture (IMA) to prove, cryptographically, that a client booted cleanly and ran only authorised software – without any kernel driver, without proprietary code, and without scanning player memory. The system intercepts Epic Online Services (EOS) SDK calls via a userspace LD_PRELOAD hook, gates session access on a live TPM quote bound to a server-issued nonce, and constructs an index-prefixed Merkle tree over the IMA log that is immune to duplicate-leaf collision attacks. Across 500 constructed tamper sessions we achieve a 100% detection rate; incremental leaf caching reduces repeat-attestation latency to under 3 seconds on real TPM 2.0 hardware. A controlled red-team evaluation against a live demo game confirms all four file-backed attack vectors are blocked while precisely characterising the two confirmed bypass conditions. The full implementation is released as open-source software.

Grain boundary engineering is a major avenue for tailoring the mechanical behavior of polycrystalline materials. Grain boundary complexions, including amorphous intergranular films, are classically accessed through thermal driving forces and solute segregation. Here, we discover that plastic deformation can drive amorphous complexion transitions at room temperature in a chemically primed nanocrystalline binary CuZr alloy. High-resolution and four-dimensional scanning transmission electron microscopy reveal that the amorphous complexions preferentially emerge at incoherent twin boundaries. Spatially-resolved electron pair distribution function analysis at the atomic scale, the local-order characterization of amorphous complexions, demonstrates short-range and medium-range order gradients from crystal-templated interfaces to a metallic-glass-like core. We thus uncover a novel amorphous complexion transformation-induced plasticity mechanism that concurrently increases the yield strength, fracture strain, and tensile toughness about a factor of two relative to a designed reference material. Our findings establish mechanical deformation as a non-thermal pathway to trigger amorphous interfacial states for enhancing damage tolerance in nanostructured metals.

For many decades, the National Institute of Standards and Technology (NIST) Atomic Spectroscopy Group housed a growing collection of thousands of photographic glass plate negatives. With the closure of the NIST Atomic Spectroscopy Group in March 2025, the irreplaceable collection needed a new home. Staff from NIST were contacted by staff from the Harvard Plate Stacks at the Center for Astrophysics | Harvard & Smithsonian (CfA). The Harvard Plate Stacks is the largest collection of astronomical glass plates in the world, with over 500,000 glass plate negatives from the 1880s to the 1990s. Given the long-standing history of the Harvard Plate Stacks and the expertise of the staff, it was decided that the NIST archive would move to the CfA. We summarize the contents of this collection regarding the instruments used and the spectra measured, and we present the tools and procedures we use for digitizing the collection. This includes the use of calibrated flatbed scanners for digitizing the plates themselves, as well as the digitization of correlated lab notebooks with important metadata associated with the plates.

Quasars are luminous objects in the universe that exhibit stochastic brightness variations encoding information about the supermassive black holes powering them, and modeling these variations from ground-based survey data time series, known as light curves, is a statistical challenge. This paper reviews how stochastic differential equations (SDEs) have been adapted with neural network parameterizations to overcome this challenge in history. We create the Continuous-Delayed-Memory Stochastic Gradient Descent which depend on the past state of the discrete iteration process. We performed the simulation on some 2-dimensional landscape and observed some wider-exploration and more precise convergent behavior compared to Vanilla SGD by adjusting hyperparameters. Besides, we proposed a reinforcement learning structure with continuous time policy gradients for exploratory policies without solving HJB PDE, and we show that its optimality conditions recover the Gibbs policy of previous works.

In this work, we present an uncertainty-driven training framework for three-dimensional computed tomography (CT) lung nodule classification, where validation-based uncertainty estimates guide loss reweighting to enhance predictive performance and probability calibration. Two Uncertainty Quantification (UQ) methods are considered: Monte Carlo Dropout (MCD) and Evidential Deep Learning (EDL). Both provide per-class uncertainty estimates that modulate the loss and encourage focus on hard or unreliable classes. The framework is evaluated with ResNet, DenseNet, EfficientNet, Vision Transformer (ViT), and Swin Transformer backbones on two datasets: the clinical LIDC-IDRI cohort and the NoduleMNIST3D benchmark. Uncertainty-driven training achieves classification performance similar to conventional training while substantially improving calibration, with an expected calibration error (ECE) reduced by up to 65% on LIDC-IDRI. EDL attains competitive performance on shallower architectures with single-pass inference, whereas MCD is more robust on deeper networks. Analysis across architectural families reveals that uncertainty-driven training benefits convolutional backbones more consistently than transformer-based architectures: EDL in particular degrades on ViT, suggesting that the Dirichlet evidence parameterisation may interact unfavourably with attention-based architectures at lower input resolutions. A posteriori temperature scaling proves highly effective across all configurations, indicating that a simple scalar calibration can be competitive even without explicit uncertainty-aware training. Our results indicate that integrating UQ into the training loop can significantly improve probabilistic calibration and support more trustworthy deployment of three-dimensional medical imaging models.

Hybrid motor-imagery brain-computer interfaces (MI-BCIs) combining EEG and fNIRS can outperform EEG-only systems by exploiting complementary electrophysiological and hemodynamic information. To obtain such hybrid information when paired EEG-fNIRS acquisition is unavailable or inconvenient, recent studies have focused on EEG-to-fNIRS cross-modal generation. However, existing methods still suffer from slow generation and often require pretraining, limiting their use in real-time MI-BCI scenarios. Although one-step generative models offer an attractive route to low-latency synthesis, removing the iterative refinement process can reduce generation fidelity and introduce non-physiological artifacts. To address these problems, this paper proposes Bio-MF, a latent-free one-step MeanFlow framework for EEG-conditioned fNIRS generation. Bio-MF performs direct signal-space x-prediction, converts this signal-space output into MeanFlow velocity supervision, and completes inference with one network evaluation. To preserve task-relevant hemodynamic structure under heterogeneous sensor layouts, Bio-MF integrates Spatial-Temporal Interactive 4D Encoding, cross-modal classifier-free guidance, and noise-level-gated FFT regularization. On Dataset 1, EEG + synthetic fNIRS improves ACC over EEG-only by 3.37 and 4.15 percentage points for HbR and HbO, respectively. On Dataset 2, the corresponding gains remain 2.98 and 2.50 percentage points under the unseen 64-channel EEG montage. On an RTX PRO 6000 GPU, Bio-MF generates one fNIRS trial in 7.0 ms, corresponding to an 857x speedup over the 1000-step SCDM latency. These results show that Bio-MF enables fast EEG-to-fNIRS synthesis while preserving task-relevant generation quality for downstream hybrid MI decoding. Our code is available at https://github.com/psychosiwa/Bio-MF.

Condensed configurations are compact incidence data obtained by grouping the cyclic flats of a matroid. We show that their inverse incidence matrices give explicit Schubert expansions and hence determine every valuative or covaluative matroid invariant. For the extended binary Golay matroid, this unexpectedly produces non-real-rooted Kazhdan-Lusztig and Z-polynomials. To our knowledge, the latter is the first counterexample in the literature.

Motivational interviewing (MI) is a collaborative approach to elicit autonomous motivation for health behavior change. Generative AI (GenAI) offers new ways to deliver MI via conversational systems, but evidence on their design, assessment, and translation into interventions remains fragmented. This scoping review characterized evidence on GenAI-MI chatbots across system design, safety, MI quality, user perceptions, and intervention outcomes. We conducted a PRISMA-ScR scoping review. Nine datasets were searched for studies published or publicly available from January 1, 2015 to June 2, 2026 that used GenAI to generate MI chatbot responses or counselor utterances. Data were extracted using a predefined framework and synthesized descriptively. Forty-seven reports (48 studies) were included. Twenty (41.7%) focused on system design without direct participant use; 28 (58.3%) involved direct interaction. Most systems were text based and disembodied; 23 (47.9%) incorporated dynamic adaptation. Safety measures were unevenly reported. Among studies with direct use, 21/28 (75.0%) reported informed consent or user education. Thirty (62.5%) assessed MI quality, generally suggesting MI-consistent interactions. User perceptions were favorable, especially empathy, usability, helpfulness, and intention to use, though measures were heterogeneous. Eighteen (37.5%) reported intervention outcomes, mostly after a single session. Positive findings were more consistent for short-term motivation than sustained behavioral or functional change. GenAI-MI chatbots can deliver MI-consistent interactions perceived favorably, but evidence for sustained behavioral or functional change is limited. Future research should strengthen runtime safety monitoring, standardize MI quality assessment, and use longer-term comparative designs with behavioral and functional outcomes.

We introduce a new class of backward logarithmic orthogonal functions and generalized backward logarithmic orthogonal functions, constructed by applying a terminal-endpoint logarithmic mapping to generalized Laguerre polynomials. These functions are designed for backward spectral approximations of problems whose solutions exhibit weak singularities at the terminal endpoint. The proposed basis functions generate non-polynomial weighted approximation spaces with nodes naturally clustered near the singular endpoint, and therefore provide an effective framework for resolving algebraic and logarithmic endpoint singularities. We develop the basic approximation theory for these backward logarithmic orthogonal functions, including recurrence relations, derivative formulas, orthogonality, Sturm–Liouville characterization, mapped Laguerre–Gauss quadrature rules, weighted projection estimates, backward Lagrange interpolation estimates, inverse inequalities, and stability properties in weighted Sobolev-type spaces defined through a terminal logarithmic pseudo-derivative. A generalized version of the basis is also introduced by incorporating an algebraic scaling parameter, which improves the flexibility of the approximation space and allows singular factors to be represented more effectively. The error analysis and numerical results show that the proposed backward logarithmic basis is particularly suitable for weakly regular functions with terminal-endpoint singularities and can recover exponential or high-order convergence rates that are typically lost when usual polynomial approximations are applied directly.

By considering arc presentations and grid diagrams of satellite knots, we prove that if K is a satellite knot with companion C and wrapping number w, then its crossing number satisfies $c(K) \geq \frac{2}{5}(w^2c(C))^{1/11}$. We also prove other similar bounds regarding the crossing number and arc index of satellite knots and links. This is partial progress on Problem 1.2 of the K3 Problem List.

Satellite communications are an essential component of sixth-generation (6G) mobile networks, which provide ubiquitous connectivity for global services. However, the satellite uplink remains a critical bottleneck for ground devices: their limited transmit power and antenna apertures result in low data rates and high packet errors. To overcome this bottleneck, this paper advocates a novel relaying paradigm termed generate-and-forward (GF) communications, where satellites exploit on-orbit generative artificial intelligence (AI) to robustly reconstruct corrupted data prior to forwarding. Specifically, we propose SpaceDiffusion, an over-the-orbit diffusion framework for satellite-assisted image transmission. The core of this framework is a channel-distortion-aware diffusion theory developed using the following approach. By formulating the recovery of compressed and lost image tokens as an inverse problem, this theory incorporates a channel-distortion correction term directly into the conventional denoising diffusion implicit model (DDIM) update. As a result, this design enables a single pretrained diffusion model to adapt dynamically to varying packet-loss patterns and compression distortions without retraining. Furthermore, we analytically characterize the progressive token-reconstruction error and derive a diffusion-step activation threshold that predicts when SpaceDiffusion is expected to outperform conventional decode-and-forward (DF) relaying. Building on these theoretical insights, we further develop an energy-aware early-exit policy to efficiently deploy SpaceDiffusion in orbit. Experimental results demonstrate that SpaceDiffusion achieves lower end-to-end latency compared to DF scheme with retransmission protocol and saves approximately 15 dB of uplink transmit power at a target perceptual quality.

Thermodynamic topology provides a topological classification of black hole states and their branch structures in thermodynamic parameter space. We investigate the thermodynamic topology of the charged nonextremal magnetic Gibbons–Maeda family in four-dimensional asymptotically flat Einstein–Maxwell–dilaton gravity, with particular emphasis on its string-theory member at the dilaton coupling $a=1$, the Gibbons–Maeda–Garfinkle–Horowitz–Strominger (GMGHS) black hole. An analytic classification over the complete domain of regular outer horizons shows that the dilaton coupling separates the family into three limiting structures of the inverse Hawking temperature. At $a=1$, the GMGHS defect curve approaches a nonzero lower inverse temperature endpoint and contains a single unstable branch. In particular, the magnetic GMGHS black hole provides an explicit realization of the previously proposed $\overline W^{1-}$ thermodynamic topological subclass within an asymptotically flat Einstein–Maxwell–dilaton solution. This result demonstrates that the global topological number $W$ alone does not completely characterize black hole thermodynamic topology. The asymptotic behavior of the inverse Hawking temperature near the boundaries of the physical horizon domain provides an additional criterion for distinguishing thermodynamic topological subclasses with the same $W$.

We study a minimal classification problem: Given independent labeled observations $X\sim P$ and $Z\sim Q$ from two unknown distributions $P,Q$, and given an independent target $Y$ drawn with equal probability from $P$ or $Q$, can one classify $Y$ strictly better than chance whenever $P\neq Q$? The one-nearest-neighbor rule succeeds for every pair of multivariate Gaussian distributions with distinct means and a common positive-definite covariance matrix but can perform strictly worse than chance even for smooth densities on the real line. We construct a fixed randomized kernel rule whose expected accuracy is exactly $1/2+\operatorname{MMD}_k^2(P,Q)/4$, and obtain characteristic kernels on countably generated measurable spaces from countable families of measurable binary questions. We also prove that a deterministic order rule on $\mathbb R$ beats chance for every pair of distinct Borel probability measures. A measurable encoding then gives a deterministic distribution-free rule which beats chance on every countably generated measurable space, in particular every separable metric space. Finally, we show that no rule works for every distinct pair of distributions and every unknown unbalanced class prior; under adaptive target-class selection, every rule other than a fair coin is strictly worse than chance for some finitely supported pair.

Among all gravitational solutions, traversable wormholes stand out as truly fascinating, yet within general relativity, they almost always demand exotic matter that necessarily violate null energy requirement. The inclusion of matter-geometry coupling in modified gravity theories provides a viable platform where wormholes remain open which are supported by effective gravitational field. We therefore examine the structure and properties of slowly rotating traversable wormholes using the $f(R,T)$ framework. We formulate stationary wormhole models coupled with the anisotropic fluid and show that they are regular, horizon-free, approach a flat spacetime geometry at large distances, and satisfy the flare-out requirement at the throat. Our results indicate that the required matter meets both the null and strong energy conditions, demonstrating that rotating wormholes do not necessarily require unconventional sources. We further study particle trajectories, frame dragging phenomena, and non-geodesic behavior resulting from matter-geometry coupling, alongside the weak-field and lensing effects caused by the rotation. Our results establish the potential astrophysical viability of rotating wormholes in $f(R,T)$ gravity.

Compact summaries are a key tool for approximate query processing over large datasets. For range-query workloads, an $\varepsilon$-net provides a small summary that hits every sufficiently large range. However, classical $\varepsilon$-nets only guarantee range validity and do not control the group composition of the selected tuples. As a result, the summary may be range-valid but poorly representative, which can propagate imbalance to downstream query results. Motivated by recent work on fair $\varepsilon$-nets and fair geometric hitting sets \cite{dehghankar2025fair}, we study fairness-aware range summaries under prescribed target group ratios. Different from previous sample-and-repair approach, we propose a target-stratified sampling method. For demographic parity (in which the ratio of fairness is determined by group proportion), our sample size is $O(A_{\varepsilon})$, coinciding with the standard $\varepsilon$-net bound, improving previous bound of $O\!\left(A_\varepsilon\log\frac{k}{\varphi}\right)$. For custom-ratio targets (in which the ratio of fairness is determined by manually defined proportion), our sample size is $O(A_{\Gamma})$, where $\Gamma$ is a parameter measuring the gap between the customized ratio and the demographic parity; we prove that this dependence on $\Gamma$ is unavoidable, with a worst-case lower bound of $\Omega(\Gamma/\varepsilon)$. Using our target-stratified sampling method, we could improve the previous approximation ratio for the fair geometric hitting set problem by a logarithmic factor, and making use of this result, we could in turn improve the size of custom-ratio fair $\varepsilon$-net. Experiments on real and synthetic datasets demonstrate that our method constructs smaller fair summaries than existing approaches, scales to large datasets and fine-grained group constraints, and improves downstream range query processing.