Papers

Given complex separable Hilbert spaces $\mathcal{H}_i$ and bounded operators $T_i$ on $\mathcal{H}_i$, for $i=1,\ldots,n$, we consider the tensor product space $\mathfrak{H}:=\mathcal{H}_1\otimes\cdots\otimes\mathcal{H}_n$ and a tuple $(\tilde{T}_1,\ldots,\tilde{T}_n)$ on $\mathfrak{H}$ where \[\tilde{T}_i=I_{\mathcal{H}_1}\otimes\cdots\otimes I_{\mathcal{H}_{i-1}}\otimes T_i\otimes I_{\mathcal{H}_{i+1}}\otimes\cdots\otimes I_{\mathcal{H}_n}.\] A closed jointly $(\tilde{T}_1,\ldots,\tilde{T}_n)$-invariant subspace $\mathfrak{M}$ of $\mathfrak{H}$ is said to be doubly commuting if the tuple $(\tilde{T}_1|_{\mathfrak{M}},\ldots,\tilde{T}_n|_{\mathfrak{M}})$ is doubly commuting. In this paper, we show that if the hereditary polynomials in each $T_i$ are dense in $\mathcal{B}(\mathcal{H}_i)$ with respect to the weak operator topology for $i=1,\ldots,n$, then doubly commuting jointly $(\tilde{T}_1,\ldots,\tilde{T}_n)$-invariant subspaces $\mathfrak{M}$ of $\mathfrak{H}$ are characterized in the form \[\mathcal{M}_1\otimes\cdots\otimes\mathcal{M}_n,\] where $\mathcal{M}_i\subseteq\mathcal{H}_i$ is $T_i$-invariant, for each $i=1,\ldots,n$. As applications, we provide a unified framework for understanding and characterizing doubly commuting quotient modules of weighted Bergman spaces over the open unit polydisc, doubly commuting quotient modules of tensor products of complete Nevanlinna-Pick spaces, and doubly commuting invariant and co-invariant subspaces of certain operators acting on tensor products of de Branges-Rovnyak spaces $H(b)$ associated with both extreme and nonextreme points $b$. This recovers, through a different approach, the known characterizations of doubly commuting quotient modules of the Hardy space over the open unit polydisc and doubly commuting submodules of Jordan blocks of Hardy space over the open unit polydisc.

Finite convexly ordered binary branching $C$-relations have been viewed as a notable exception to the broad applicability of the partite construction in structural Ramsey theory. The absence of a proof of their Ramsey property by the partite construction was noted by Bodirsky in his 2015 survey and pointed out again by Hubička and Konečný in their 2026 survey. We overcome this limitation by giving proofs based on the partite construction of the known Ramsey properties of the class $\mathcal{CT}$ of finite convexly ordered treeable meet semilattices and of the classes of finite convexly ordered $C$-relations with arbitrary branching and with binary branching. Our proofs do not rely on Milliken's tree theorem. The key is to expand $\mathcal{CT}$ by level predicates and a predecessor function so that the locally finite subclass method applies. We then transfer the resulting Ramsey witnesses to the corresponding reduct classes and to the classes of convexly ordered $C$-relations.

We analyze fork-grating generation of electron vortex beams beyond the ideal single-mode approximation. The incident beam is described as a paraxial Gaussian ensemble with finite transverse momentum spread and a first electromagnetic Hartree phase accumulated before the grating. Within Fresnel propagation we derive an analytical expression for each diffraction order and determine the corresponding orbital-angular-momentum statistics. The mean OAM of a selected order remains fixed by the topological rule, $\langle L_z\rangle_m=mp\hbar$, while its variance is set by the residual transverse momentum spread of the beam prepared at the grating. For the Gaussian mixture, the transverse purity is $\mathcal P_{\perp,m}=[1+2(\Delta L_{z,m}/\hbar)^2]^{-1}$. The observed annular profile is governed by a separate propagation-dependent blurring scale, so a beam can retain well-defined mean OAM while having low transverse purity or a partially filled vortex minimum. Within the radial phase-screen approximation, the Hartree self-field modifies the propagated profile while preserving the full-plane OAM moments and transverse purity.

Data trading markets that span industries and regions are expanding, but the implicit trust that supports data use within an organization does not carry over to cross-domain exchange. This paper examines the Data Credit Guarantee Organization (DCGO), a proposal to institutionalize trust through third-party verification and certification, and asks what it means to trust data, what such certification can support, and under what conditions DCGO outperforms existing trading models. We decompose trust in data into four layers: authenticity of entity, authenticity and integrity of data, rights and conditions of use, and history and auditability. A third party can certify authenticity but not the correctness of content, and DCGO is positioned as a trust anchor spanning existing marketplaces and data spaces. We then extend the Law Merchant model with three data-specific properties, namely imperfect ex-post detection, cheap pseudonyms, and non-rivalry of harm, and compare bilateral trading with DCGO by agent-based simulation. DCGO keeps the buyer's payoff near its theoretical upper bound regardless of the market environment, whereas bilateral trading loses even when fraud is always detected. Identity verification proves to be a prerequisite for record sharing, and pre-verification is the only function that limits the spread of harm. On the seller side, honest sellers join voluntarily whenever the price premium exceeds the fee. Lock-in and a critical mass for diffusion, however, call for fee governance and support for entry.

Visual token pruning for multimodal large language models (MLLMs) appears highly effective, with existing methods retaining over 95% of unpruned performance on common VQA benchmarks using a quarter of the visual tokens or fewer. However, our extensive evaluation of ten methods across three MLLM families and five ability groups reveals a critical gap: strong general performance often comes at the cost of severe degradation on fine-grained tasks such as OCR and visual grounding. We trace these failures to two limitations of the prevailing paradigm of retaining the highest-ranked native patches. A single importance ranking overlooks the complementary evidence required by different tasks, while sparse patch selection disrupts both image content and spatial integrity. To address these limitations, we propose Bifocal, a training-free, two-stage pruning method built on a mixed-granularity framework. It allocates separate budgets to query-focused and image-intrinsic evidence, complemented by a pooled coarse representation of the entire image. Before the LLM, Bifocal matches question words to visual regions through a soft conjunction balanced against norm-debiased image saliency, while selecting image-intrinsic evidence to maximize representational coverage. Inside the LLM, it further prunes tokens using density-adjusted text-to-image attention. With roughly a quarter of the original visual tokens, Bifocal is the only evaluated method to retain over 90% of unpruned performance in every ability group across all three models, and ranks first on average in all nine model-budget settings. The code is available at: https://github.com/EIT-NLP/Bifocal

The continuous-time mean-variance portfolio selection problem is investigated in this paper through a rigorous integration of backward stochastic differential equation (BSDE) and Kantorovich duality theory. We propose a novel analytical framework for addressing feedback control in McKean-Vlasov stochastic systems. By solving three coupled systems of ordinary differential equations (ODEs), we derive an explicit, closed-loop optimal feedback investment strategy.

Radiative depolarization near spin resonances in electron storage rings is conventionally described by correlated-sideband and local resonance-density theories, but a quantitative description of the crossover between them has remained lacking. Here we derive a unified finite-memory response from stochastic spin dynamics near an isolated resonance. By separating the coherent resonance contribution from stochastic fluctuations, we show that the connected correlation of the accumulated resonance-relative spin phase determines the leading off-center weak-resonance depolarization rate. Both conventional theories emerge as controlled asymptotic limits of this response, which also captures the surviving synchrotron phase memory governing the crossover. Monte Carlo spin tracking validates the predicted rates throughout the crossover and reproduces the recurrence-induced generalized-sideband structure. More broadly, the connected-correlation formulation provides a basis for extending radiative depolarization theory to more general stochastic spin-orbit dynamics in storage rings.

Magnetic multilayers with structural inversion asymmetry, perpendicular magnetic anisotropy (PMA), and large Dzyaloshinskii-Moriya interaction (DMI) are widely studied for magnetic domain wall- and skyrmion-based data processing applications. In this work, we report a controlled, nonvolatile, but reversible local modification of such a system by electrically driven oxygen migration through the metallic film structure by using ionic liquid gating. Our findings provide direct evidence for the modification of the oxidation state at the heavy metal (HM)/ferromagnet (FM) interface. As a result, we observed changes in fundamental magnetic properties, such as an increase in the effective anisotropy constant (Keff) and coercive field (Hc) with oxidation, and a decrease with the reduction of oxygen ions. Positive gate voltages relative to the thin film extract oxygen ions from the magnetic layer, significantly reducing the domain nucleation field. In contrast, negative voltages drive oxygen ions into the magnetic layer, leading to a reversible increase in the extent of domain wall pinning near saturation. We observe a corresponding decrease in the magnetic moment and DMI, with negative voltage reducing both. This magneto-ionic modulation in fully metallic structures is beneficial for spintronic device applications, particularly in field-programmable domain wall and skyrmion devices.

We compute the local and global Denef–Loeser topological zeta functions of the determinant on the space of symmetric matrices. It verifies the strong monodromy conjecture of the symmetric determinant function. The computation relates to the geometry of complete quadrics and wonderful embeddings.

In this paper, we improve the upper bound for the tensor rank of the $n \times n$ determinant tensor to $\mathcal{B}_n-2^{n-1}+n+1$ by finding a new tensor decomposition of the tensor, where $\mathcal{B}_n$ denotes the $n$-th Bell number. The main idea is to replace a part of the tensor decomposition suggested by Houston–Goucher–Johnston with a tensor that is essentially the same as the $n \times n$ permanent tensor, and to use Glynn's formula. This upper bound gives an improved upper bound for the Waring rank of the $n \times n$ determinant polynomial for $n \geq 17$ as well.

Equivariant machine learning interatomic potentials (MLIPs) promise atomistic simulations with accuracy approaching that of quantum-mechanical calculations. However, the high computational cost of their core Clebsch–Gordan tensor product (CGTP) convolutions severely limits model scalability and efficiency. In this paper, we rethink the parallel execution of CGTP convolutions and introduce LunaTP. Built on node-centric execution, LunaTP exploits path-group parallelism and multi-level reuse to accelerate CGTP convolutions and higher-order derivative computation while preserving the underlying mathematical formulation. On an NVIDIA H100 GPU, LunaTP achieves kernel speedups of up to 250.0$\times$ over e3nn and 17.1$\times$ over OpenEquivariance. It also delivers end-to-end training throughput gains of up to 28.7$\times$ over e3nn and 3.11$\times$ over OpenEquivariance. Finally, LunaTP demonstrates scalability and robust performance across models, workload scales, and GPUs, delivering substantial acceleration for training and atomistic simulation with high-accuracy equivariant MLIPs.

We study coding multiplicity for self-similar sets on the real line. When the similarity dimension exceeds one, almost every point with respect to the natural self-similar measure has infinitely many codings. We focus on the case when the similarity dimension is at most one. Our analysis proceeds through the recurrence properties and the size of the critical set, defined as the union of the pairwise intersections of the first-level pieces. Our main structural result shows that when the critical set is finite, unboundedness of coding multiplicity is equivalent to periodic recurrence to the critical set. Moreover, every commensurable system with a finite critical set has uniformly bounded coding multiplicity. This conclusion is sharp in the incommensurable setting. We construct a one-parameter family of four-map systems such that for Lebesgue almost every parameter, the critical set is a singleton and the open set condition fails, while the attractor contains a point with infinitely many codings. More generally, for transversal families, the set of parameters admitting an infinite coding fibre is dense among those for which the strong separation condition fails. We also obtain a quantitative lower bound for the Hausdorff dimension of this parameter set. Such parameters can form a meagre set. We continue the study of the geometric size of branching, obtaining dimension formulae for typical coding fibres and almost-sure upper bounds on the dimension of the critical set in transversal families. In contrast, we construct an exponentially separated system with no dimension drop whose critical set has the same Hausdorff dimension as the attractor and whose coding map has a fibre of continuum cardinality. Although we work in the one-dimensional setting, several results and arguments extend to higher dimensions.

A wide range of important cloud applications, e.g., database analytics, graph analytics, and genome analysis, spend a considerable amount of time performing bulk bitwise operations (e.g., AND, OR, XOR). These applications often operate on highly sensitive data, making data privacy a critical concern. Homomorphic encryption (HE) enables secure computation on encrypted data without requiring decryption, ensuring privacy in untrusted and shared environments. We analyze 13 end-to-end applications across three domains (healthcare, graph, and database analytics) and observe that bulk bitwise operations take 62-100% of the execution time of the healthcare and graph workloads. The key problem is that existing HE approaches perform them with high-latency homomorphic operations (e.g., multiplication or lookup tables) and significantly increase the data size. Our goal is to enable fast bulk bitwise operations on homomorphically encrypted data by designing an efficient HE algorithm that reduces the use of these costly operations. To this end, we propose HULK, which performs two key steps: (1) it constructs bulk bitwise operations using low-cost homomorphic additions, which compute the Hamming weight of the encrypted operand bits in every slot of a packed ciphertext without any homomorphic multiplication, and (2) it decodes the result of an AND, OR, or XOR from the Hamming weight with a single indicator polynomial, keeping the result in the standard encoding. Across 13 end-to-end applications in healthcare, graph, and database analytics, HULK improves performance over the arithmetic approach used by prior works by up to 7.26x (CPU) and 6.65x (GPU), and on average by 2.32x/1.78x/1.45x (CPU) and 2.08x/1.70x/1.51x (GPU) for healthcare/graph/database analytics. When we increase the reduction depth in a representative application, HULK's speedup grows to 10.10x over the state-of-the-art GPU baseline.

We investigate whether the past of an auxiliary time series provides predictive information about a target beyond that contained in the target's own history. We compare matched out-of-sample target-only and target-plus-source forecasts and introduce the forecast-error distribution entropy (FEDE) predictive-causality framework, where predictive causality is understood in the Granger sense: auxiliary history is informative when it improves prediction beyond the target's own past. FEDE quantifies how the full signed forecast-error distribution changes across prediction horizons. Controlled nonlinear benchmarks hide source-target dependence behind nonlinear transformations not supplied to the predictors. LightGBM recovers these hidden channels, whereas Ridge does not. Across four equal-power nonlinearities and four noise levels, the mean response-sensitivity statistic for FEDE remains 29.00, 27.47, 23.22, and 28.67, compared with 14.09, 10.68, 12.67, and 12.71 for mean log-RMSE gain. Directional and source controls separate the true source-to-target channel from the reverse direction and from independent periodic, quasiperiodic, chaotic, and autoregressive auxiliaries. Chronological Granger-style comparisons show strong model-form dependence: a degree-2 polynomial model is exceptionally sensitive to the matched quadratic channel but becomes weak or oppositely aligned for other nonlinearities, while basic convergent cross mapping is weak or directionally inconsistent in this stochastic, partly non-invertible setting. FEDE remains positively aligned across all 108 tested combinations of window length, history length, and maximum forecast horizon. Together, these results establish FEDE as a sensitive and robust horizon-resolved tool that extracts predictive information beyond conventional error-magnitude measures when the nonlinear interaction form is unknown. Code available in Zenodo.

Large language models are increasingly used as judges to reduce reliance on costly human evaluation, yet their scores can systematically disagree with human judgments. We ask whether responses to an explicitly imposed evaluative bias can help correct a judge's implicit scoring biases. We introduce PRISM (Probe-based Residual Inference of Scoring Misalignment), which holds the evaluated content fixed and measures score changes when attributes are emphasized or de-emphasized. A local sensitivity model motivates representing these responses as a surrogate Jacobian. Ridge regression on human labels learns a correction to the baseline score. The resulting scoring protocol is rubric-free: it uses overall scores without requesting criterion-level ratings. In the main Jev and Sol comparisons on SummEval summarization and HANNA story evaluation, PRISM and its learned-baseline variant significantly improve agreement with human rankings over uncalibrated scores while remaining competitive with rubric-based methods. A controlled SummEval comparison yields similar agreement for rubric-derived quality probes and style probes, supporting calibration without reproducing rubric criteria. The learned coefficients reveal shared and opposing correction directions across judges.

Multimodal large language models (MLLMs) have shown strong potential for remote sensing understanding, yet reliable reasoning remains challenging when tasks require fine-grained visual grounding and multi-step inference. Existing approaches typically rely on either costly pre-constructed reasoning trajectories or self-generated signals such as response consistency, which can reinforce shared errors and provide unreliable supervision. We introduce Reasoning–Diagnosis Self-Evolution (ReDiS), a framework that separates reasoning exploration from candidate evaluation while allowing the two processes to evolve jointly. ReDiS instantiates two role-specific experts from a shared multimodal backbone: a Reasoner that explores diverse visual evidence–answer candidates and a Diagnoser that jointly evaluates the complete candidate set and provides credibility-aware feedback. As the Reasoner evolves, it exposes new candidate distributions and failure modes; the Diagnoser adapts to these changes and, in turn, reshapes the learning signal for subsequent exploration. To handle groups in which all sampled answers are incorrect and group-relative advantages vanish, we further introduce Failure-Triggered Recovery (FTR), which provides minimal outcome-level correction without prescribing intermediate reasoning trajectories. Experiments on LHRS-Bench, MME-RS, and CHOICE show consistent improvements over Qwen3.5 backbones at 0.8B, 2B, and 4B scales. ReDiS improves category-averaged accuracy by 6.47 percentage points at 0.8B, while ReDiS-4B achieves the highest average performance among the compared remote sensing MLLMs.

The most widely used investment risk measures - variance, standard deviation, and tracking error - treat upside deviations as equally undesirable as downside losses. In stable markets with assumed symmetric return distributions, this simplification is potentially harmless. In the climate transition age, it is not. Climate risk is two-dimensionally asymmetric, across assets and over time. Both dimensions are negatively skewed against investors. Hence, climate transition investment strategies deliberately deviate from benchmarks that reflect an insufficiently decarbonising global economy. When fiduciaries enforce tracking error budgets that penalise outperformance just as heavily as underperformance, they inadvertently constrain exactly the portfolio return opportunities that climate-aware investing seeks. We argue that replacing symmetric deviation-based risk measures with their downside-only counterparts - semi-variance, standard risk and trailing error - resolves this conflict without sacrificing any fiduciary discipline. The distinction is not merely semantic: as the gap between climate transition trajectories and market benchmarks widens over the coming decades, symmetric risk budgets will become binding constraints on transition strategies well before actual investment risk warrants it. We propose specific changes to mandate design that would allow institutional investors to pursue climate transition opportunities within genuinely risk-aware (rather than deviation-averse) frameworks.

Manipulation tasks such as unscrewing a cap or sliding a part in contact with a surface require imposing force along a high-friction direction: the robot must overcome a resistance rather than yield to it. Generative visuomotor policies predict the motion for such tasks but not the authority needed to realize it, and that authority is bounded by the impedance controller beneath them: when the resistance exceeds what a compliant controller can exert under a bounded tracking error, the task is unattainable however accurate the prediction is. The required amount cannot be anticipated either, since it depends on a contact state the observation does not reveal. In this paper, we propose a residual stiffening layer placed underneath an unmodified policy. Resistance is recognized, without force sensing, from the mismatch between the motion the policy commands and the motion the robot realizes, and a four-mode supervisor raises the stiffness along a single direction read off the policy's own action chunk, retains it while the task progresses and releases it afterwards. The layer needs no compliance labels, no retraining and no re-collected demonstrations. On two real tasks, unscrewing a bottle cap and pushing a T-nut along a T-slot groove against non-homogeneous friction, evaluated at six resistance levels of which two were withheld from the demonstrations, the layer raises the success rate from 52% to 90% while producing 61% less peak off-axis force than a uniformly stiff controller at the same resistance.

The rapid growth of hyperscale data centers challenges grid expansion planning, yet existing studies focus largely on operational flexibility rather than long-term investment decisions. This paper examines how large data center loads sited at multiple buses affect co-optimized Transmission Expansion Planning (TEP) and Generation Expansion Planning (GEP). The problem is formulated as a multi-year, Unit Commitment (UC)-embedded mixed-integer linear program on the modified IEEE 24-bus Reliability Test System (RTS-24) with Electric Reliability Council of Texas (ERCOT)-calibrated renewable energy profiles. A 500 MW data center load, about 17.5% of the base-year peak, is allocated across four buses by voltage level, generation headroom, renewable co-location, and network connectivity. Integrating this load raises the 15-year net present value of total system cost by 1,794 million USD (+61.6%) and the system-average locational marginal price (LMP) by 45.2%, with operating cost dominating capital investment (84.2% versus 15.8%). Renewable curtailment remains negligible: existing renewables are already near full utilization, so the added demand is served almost entirely by incremental thermal generation. Most notably, the load shifts the optimal plan from transmission-only to generation-only, replacing the base-case 230 kV reinforcement with a new 400 MW combined-cycle gas turbine and showing that strategically sited generation can substitute for network reinforcement.

Ground-based experiments such as the IceCube Neutrino Observatory and the High-Altitude Water Cherenkov Gamma-Ray Observatory detect cosmic-ray anisotropy on Earth, but magnetic deflections within the heliosphere complicate interpretation. Understanding the original spatial distribution of cosmic rays in the interstellar medium requires modeling particle propagation across the heliospheric boundary. We constructed a simulated transport model that backtracks antiprotons from Earth to the interstellar medium and maps spatial transfer probabilities across energies using HEALPix representations. Because our transfer matrices are singular, inversion relies on singular value decom- position regularization. Ground-based observations lose the equatorial North-South anisotropy component, severely degrading interstellar map recovery. We developed a geometric circle-fitting algorithm to estimate and reintroduce the missing component into the observed signals. Our results show that restoring the North-South anisotropy en- ables more accurate recovery of the interstellar dipole structure. Furthermore, Poisson statistical fluctuations on the detected event counts dominate matrix-transformation errors when spread over multiple energies.

This paper proposes a method for distribution system operators (DSOs) to design spatially fair dynamic price signals for flexible prosumers, accounting for both distribution grid constraints and the stochastic behavior of prosumers. Since locational pricing can introduce price unfairness when grid constraints are active, the proposed approach includes mechanisms to enforce price fairness across the network. The method involves the DSO solving a scenario-based optimal power flow (OPF) problem to derive, similarly to locational marginal prices in transmission systems, the Lagrange multipliers associated with grid constraints and to compute individualized price signals for each prosumer under various PV generation and demand scenarios. Subsequently, two methods are introduced to aggregate these individualized prices into a single fair price across prosumers. Their performance is evaluated through simulations on a model distribution grid, comparing prosumer revenues, grid constraint violations, and analyzing the impact of fairness on reducing cost variance among prosumers.

Stencil computations are a fundamental class of workloads in scientific and engineering applications. Although Tensor Cores offer new opportunities for stencil acceleration, existing tensorization methods suffer from substantial redundant computation and insufficient data reuse. We propose PrismStencil, a stencil tensorization algorithm that introduces a novel mapping scheme between matrices and stencil grid points. PrismStencil employs multidimensional vector mapping to accommodate the multidimensional data dependencies of stencil computations and a unified gather–scatter tensorization scheme to exploit the relative sizes of the matrix dimensions in Tensor Core operations, thereby reducing the redundant computation introduced by tensorization. Moreover, it introduces a cross-product data-reuse mechanism that exploits the overlap among neighboring stencil updates to further enhance data reuse. Across representative stencil kernels on an NVIDIA A100 GPU, PrismStencil achieves average speedups of 2.13x and 2.17x over state-of-the-art Tensor Core stencil methods with FP64 and TF32 precision, respectively.

Aerial mobile manipulation requires unmanned aerial vehicles (UAVs) to traverse heterogeneous environments such as indoor and outdoor domains, and connect navigation with subsequent physical interaction within the same trajectories. Existing aerial benchmarks are typically confined to single-environment settings, limiting evaluation of agents across continuous environmental transitions. When interaction is evaluated, agents are often initialized near the target, leaving the transition from navigation to interaction largely unassessed. This work introduces CrossFly, a benchmark for long-horizon interaction-oriented aerial mobility across heterogeneous environments. CrossFly contains 15K trajectories across more than 20 reconstructed scenes under a unified simulation and evaluation framework, covering Indoor, Outdoor, and Indoor$\leftrightarrow$Outdoor trajectories. It further introduces Interaction Readiness Rate (IRR) to assess whether terminal navigation states provide suitable conditions for downstream interaction without assuming a specific manipulation policy. Experiments with five representative aerial vision-language-action (VLA) agents and the proposed CrossFly-Agent show that Indoor$\leftrightarrow$Outdoor settings are more challenging than single-environment settings, with the highest success rate reaching 9.7% on unseen scenes. A downstream manipulation case study further validates the relevance of interaction-oriented arrival to subsequent physical interaction. We hope CrossFly helps advance aerial embodied intelligence toward unified mobility and physical interaction in heterogeneous environments.

We study the algebraic and geometric structures of gravitational decoupling within a fixed class of globally static, spherically symmetric spacetimes with non-vanishing areal-radius differential. We show that (minimal and extended) geometric deformations of the seed metric define a groupoid of partial transformations. We also draw a connection between the geometric deformation procedures and disformal transformations. It is shown that every admissible minimal geometric deformation admits a disformal representation using the areal radius as an auxiliary scalar. For extended deformations, we derive a necessary condition and exhibit a global obstruction that persists under diffeomorphisms preserving the areal radius and the static Killing direction up to constant normalization. Finally, we verify that the disformal construction reproduces the standard minimal geometric deformation source equations and separate conservation law, including anisotropic seeds.

With the rapid development of deep learning, supervised convolutional neural network methods have greatly improved the performance of low-dose computed tomography (CT) denoising. However, they require paired noisy-clean training data, which is difficult to obtain in practice. Some classic self-supervised denoising methods rely on the assumption of pixel-wise independent noise, making them ineffective for correlated noise in low-dose CT (LDCT) images. Considering the high similarity and weaker noise correlation between adjacent CT slices, several recently proposed self-supervised methods use adjacent LDCT slices for training. Nevertheless, these approaches fail to effectively account for the non-rigid misalignment between slices caused by anatomical variation, hindering them from satisfying the equal-mean condition required by the classic Noise2Noise framework. In this paper, we propose Noise2Match, a self-supervised LDCT denoising method based on adaptive inter-slice matching. Noise2Match introduces an inter-slice matching network to model the label transition process between adjacent slices, and then applies correction to the denoiser's outputs to better satisfy the equal-mean condition. We theoretically prove that, under idealized conditions, training Noise2Match using adjacent LDCT slices is equivalent to supervised training with paired noisy-clean images. We further find that Noise2Match can also effectively perform low-dose conebeam CT (CBCT) denoising, which could be attributed to its correction operation that reduces inter-slice noise correlation. To the best of our knowledge, Noise2Match is the first effective image-domain self-supervised method for low-dose CBCT. Extensive experiments demonstrate that Noise2Match outperforms existing image-domain selfsupervised methods, offering broader applicability and higher practical value.

Applying process-based Earth science models to new sites and questions often requires expert calibration decisions. Reliable delegation to language-model agents must preserve scientific competence and reproducibility. Here we develop a general calibration harness (GCH) for end-to-end delegation from a calibration request to assessed results. Constrained by a knowledge infrastructure (KI) and a validation convention, agents define parameter domains, observation mappings and objectives, and generate model-specific code. GCH checks the formulations against the same declarations and freezes them before numerical search and assessment, which require no further agent judgement. Agent-authored workflows executed across six model families, with assessment identifying unmet criteria. In snow-model tests, five of five knowledge-guided specifications executed on the first attempt, compared with none of five given only the model name, achieving validation Nash-Sutcliffe efficiency (NSE) of 0.81-0.94 against 0.57 for defaults. Under a common objective, independent GR4J formulations yielded scores within 0.001 NSE; re-evaluating eleven saved parameter vectors reproduced their metrics. In ten paired VIC tests with matched budgets, fixed search was non-inferior to continuing agent proposals (margin, -0.02 NSE; median difference, -0.003). This separation enables end-to-end calibration delegation with inspectable scientific choices and reproducible numerical evaluation.

In 1994, Friedman, Joichi and Stanton conjectured that coefficients of the power-series $q+(1-q)\prod_{i=n}^{2n-1}\frac{1}{1-q^{i}}$ are nonnegative for $n\geq3$ and $n$ being odd. Let $\qbinom nm$ denote the Gaussian polynomial. In 2003, Prellberg and Stanton conjectured that coefficients of the power-series $(1-q)\qbinom nm\prod_{i=0}^{m-1}\frac{1}{1-q^{i+m}}$ are nonnegative for $0<m<n$, except when $n$ is even and $m\in\{2,n-2\}$. The latter conjecture implies the former. In this paper, we prove a stronger result concerning coefficientwise nonnegativity of another power series, which implies the conjecture of Prellberg and Stanton. The proof uses a Möbius correction from Gaussian polynomials, weight-preserving injections on partitions, explicit linearly independent vectors in the kernel of a derivation operator and the KOH identity.

Time-inconsistent stochastic control admits a natural game-theoretic interpretation in which successive decision dates are represented by different selves. In the Markovian framework of Björk-Khapko-Murgoci, the corresponding continuous-time equilibrium HJB system can be motivated by discrete subgame-perfect games, but the general discrete-to-continuous passage is not automatic. We establish a quantitative convergence theorem for a smooth uniformly elliptic class in which the control may enter both drift and diffusion. Using the exact sample-and-hold transition law on each time step, we construct, near a verified continuous equilibrium branch, a unique regular discrete Markov subgame-perfect equilibrium and prove first-order convergence of the continuation objects in an anisotropic $C^{2+\beta}$ topology and of the equilibrium policies in $C^0$. The key stability mechanism is structural: the discrete first-order condition forces the differential feedback correction in the frozen linearization to be nilpotent, which yields mesh-uniform block estimates through a two-norm dyadic Schauder argument despite the second-order coupling caused by controlled volatility. We also formulate a conditional transfer principle for structured polynomial-growth classes, with error-space stability stated as a separate hypothesis.

A learned representation is useful beyond its source task only if later tasks can make use of what the encoder has already learned. Source-task performance, however, gives no guarantee that the representation itself will remain useful once the original head is removed. We study representation reuse with respect to a specified family of future tasks. For such a family, we define the task-relevant state as the coarsest deterministic state sufficient for all of its tasks. A larger task family can require a finer state, and losing a required distinction makes at least one future task unrecoverable on a target support containing that conflict. Exact reuse also depends on how the retained information is presented to the downstream rule. We separate this into structural accessibility, which concerns whether the required distinctions remain recoverable, and coordinate consistency, which concerns whether those distinctions can be interpreted by the same downstream rule across samples. Both failure modes appear separately in the experiments. Reuse improves as task-relevant distinctions become more accessible. Reversible sample-dependent coordinate changes can sharply reduce reuse even when the representation remains recoverable, and inverting the applicable coordinate change restores performance. The same accessibility-reuse ordering appears in prospectively specified CIFAR-100 experiments with both ResNet-18 and DenseNet-121. Finally, preserving a candidate state that contains the distinctions needed by the anticipated task family improves reuse on compatible held-out tasks, with the clearest benefit when target supervision is limited. Representation reuse is therefore relative to the tasks that follow source learning: a useful representation must retain the distinctions those tasks need and make them available in a form that a shared downstream rule can use.

RGB-based category-level 9D pose estimation remains highly challenging because a monocular system must generalize across unseen object instances while jointly inferring 3D translation, 3D rotation, and 3D size. Unlike instance-level pose estimation, the category-level setting requires the network to learn both what is shared across objects within a category and how individual instances vary in structure. This challenge is amplified in the RGB-only setting, where pose cues, category-level commonality, and instance-specific variation are entangled in appearance without direct geometric constraints, making it difficult for existing frameworks to learn a representation that is truly aligned with the category-level estimation objective. To address this problem, we propose SchemaPose, a schema-guided framework for RGB-based category-level pose estimation. SchemaPose equips the estimation pipeline with an explicit parametric schema for modeling category-level regularities together with structured instance variation, and uses the inferred schema variables to guide pose-related prediction in an end-to-end query-based framework. The same formulation also supports template instantiation, synthetic annotation, and pose learning within a unified framework. Experiments on synthetic and real data show that SchemaPose achieves state-of-the-art performance among RGB-based methods for category-level 9D pose estimation.