Papers

Ill-posed inverse problems require priors to constrain the solution space toward plausible outcomes. In inverse rendering, learned priors modeling the distribution of natural illumination improve the recovery of scene properties. However, existing models rely on the distant-illumination assumption, representing lighting as a far-field environment map. This limits their applicability to indoor scenes, where illumination is highly spatially varying due to finite-distance emitters, visibility changes, and parallax, all of which are poorly approximated by a single environment map. To address this, we introduce a spatially-aware illumination prior trained on real-world indoor panoramas and their estimated depth. Our variational autoencoder model learns a compact, optimizable latent space that decodes into HDR radiance and depth, parameterizing an area light emitter for direct integration into standard differentiable rendering pipelines. This design bridges the plausibility guarantees of a learned prior with the gradient flow required for downstream optimization. Crucially, by jointly modeling radiance and depth, our prior captures the spatial structure of indoor illumination, instead of treating the light sources as infinitely distant. We demonstrate that this formulation enables spatially-varying illumination modeling and achieves higher-fidelity recovery of indoor lighting compared to existing approaches. Project page: https://andreead-a.github.io/RoomLight

Contact-implicit trajectory optimization formulates contact-rich manipulation as a single constrained program; however, that single program run collapses onto one local optimum out of many equally valid contact modes, grasps, or push directions. As a consequence, the resulting manipulation strategy is reluctant to change and sensitive to initialization. In order to promote robust manipulation, this paper investigates how contact-implicit solvers can discover diverse contact-rich strategies. Our approach derives a variation of Consensus Alternating Direction Method of Multipliers (ADMM) combined with Stein variational inference methods to output a set of distinct contact-rich solutions. We find that applying the Stein repulsive force to ADMM's split variable (rather than its primal form) allows for effective coverage over the set of feasible contact strategies without prematurely stalling the solver. We demonstrate the effectiveness of our approach on a variety of contact-rich manipulation tasks, including pushing, grasping, and multi-robot handover. Last, we find the proposed solver is simpler in form and capable of discovering unique contact modes when compared with existing solvers. Videos and code with examples are found in https://anon-website-submission.github.io/stein-admm-website/.

In this paper, we investigate the singular Dirichlet problem \begin{equation}\label{abs1} \left\{ \begin{array}{rclr} -\Delta_1u &=&\dfrac{\lambda}{|x|}\hbox{Sgn}\,(u)+\dfrac{f}{u^\gamma}&\quad\mbox{in}\; \Omega,\\[1ex] u &=&0& \quad\mbox{on}\; \partial\Omega, \end{array} \right. \end{equation} where $\Delta_1u=\hbox{div}\left(\frac{Du}{|Du|}\right)$ denotes the $1$-Laplacian operator, the parameters are $\lambda\in {R}$ and $\gamma>0$, and $f$ is a non-negative function belonging to the Lorentz space $L^{N,\infty}(\Omega)$. Our main goal is to establish the existence of non-trivial solutions under the sharp restriction $\lambda<N-1$, regardless of the magnitude of the datum $f$ or the value of the singular exponent $\gamma>0$. We also show that these solutions are globally bounded and that, on the contrary, no solution exists as soon as $\lambda\geq N-1$ and $f$ is positive. These results are achieved by rigorously analyzing the asymptotic behavior, as $p\to 1^+$, of the solutions to the approximating $p$-Laplace problems \begin{equation} \left\{ \begin{array}{rclc} -\Delta_pu&=&\dfrac{\lambda}{|x|^p}|u|^{p-2}u+\dfrac{f}{u^\gamma}&\quad\mbox{ in }\; \Omega,\\[1ex] u&=&0&\quad\mbox{ on }\; \partial\Omega. \end{array} \right. \end{equation} Finally, we provide a family of explicit examples designed to illustrate the sharp optimality of our main assumptions.

We investigate $c$-interior pointwise maximal leakage (PML) as a tool for contraction analyses and disclosure control. Based on the strong adversarial threat models from maximal leakage, $c$-interior PML generalizes local differential privacy (LDP) to data-generating distributions with densities uniformly bounded away from zero by $c>0$. Viewing $c$-interior PML as an algebraic constraint on a kernel yields more flexible (and often tighter) contraction analyses than standard LDP. We provide tight bounds on the Dobrushin coefficient, and bound the contraction coefficient of the Hockeystick-divergence. We further derive strong data processing inequalities on $f$-divergences under $c$-interior PML constraints when the input distributions to the divergence are restricted to be in the $c$-interior. These results extend beyond the regime of pure LDP to cover a larger class of kernels, including, e.g., arbitrary stochastic matrices. We apply the results to minimax theory and provide asymptotically optimal strategies under $c$-interior PML constraints for binary hypothesis testing and mean estimation. The results show that disclosure control with PML allows analysts to reason about systems in a more differentiated manner: For example, it allows us to quantify the privacy leakage of deterministic systems, and can give precise adversarial guarantees with respect to arbitrary distributional assumptions. Interestingly, a recurring theme in the disclosure analyses is that if the privacy problem is relatively regular (if the density bound $c$ is large), private inference can be possible without incurring any additional cost in terms of sample complexity.

While Vision-and-Language Navigation (VLN) has demonstrated remarkable success, the prevailing single-turn paradigm exposes a fundamental vulnerability: agents operate in a strictly open-loop manner. In practice, factors such as perceptual aliasing, sensor noise, and odometry drift can cause minor deviations to accumulate over time, often leading to catastrophic mission failures with no built-in mechanism for error recovery. To address this, we introduce Talk2Escape, a proactive and model-agnostic dialogue intervention framework that reframes navigation as a closed-loop interactive process. At its core, a lightweight vision-language module continuously monitors agent kinematics. Upon detecting localized looping or severe trajectory divergence, it translates raw egocentric observations into concise, grounded queries to solicit targeted corrective feedback from either an algorithmic oracle or a human-in-the-loop. Extensive evaluations in high-fidelity simulators, including R2R-CE, RxR-CE, and VLNVerse, demonstrate that Talk2Escape exhibits consistent improvements across diverse base agents. Empirically, Talk2Escape achieves a 66.0% Success Rate on R2R-CE, outperforming the current supervised and zero-shot state-of-the-art methods. We further validate its sim-to-real transfer on a Unitree Go2 quadruped, proving that proactive dialogue drastically improves navigation robustness in physical environments.

Let $H$ be a nontrivial finite-dimensional nonnegatively graded connected Hopf algebra, with $\ell=\max\{d:H_d\ne0\}$, and let $A\ge0$ be a locally finite $H$-module algebra with finite-dimensional split semisimple, $H$-trivial $A_0$. Under the gap $A_d=0$ for $0<d<\ell$, the shifted standard cells $\{q^{-r}Ae_x:0\le r<\ell\}$ form a simple-minded collection. A socle estimate for positive syzygies proves negative-Hom vanishing, while the gap makes the degree-zero endomorphism algebra semisimple. A bounded $t$-structure on the compact derived category with these cells is constructed, with standard cells as its simple heart objects. It is also shown that every compact object has a finite-cell representative and that compact $K_0$ is free on $[Ae_x]$ over $\mathbb{O}_H=K_0(H\mbox{-}\underline{\mathrm{gmod}})$. The same connected-Hopf hypotheses give a Keller–Nicolás weight structure on the large derived category, without a claim of boundedness or preservation of compact objects. Neither a silting generator nor a bounded weight structure on compacts is forced by the gap. These arguments require neither cocommutativity nor finite representation type of $H$. The $p$-DG case, with $\mathrm{deg}(\partial)=2$ and $\ell=2p-2$, is treated as a specialization. Separately, under the stronger gap condition $A_1=\cdots=A_\ell=0$, literal cellularity of every finitely generated graded-projective hopfological module holds. Explicit $p$-DG higher-cycle retracts and algebra-valued traces show why additional grading hypotheses are needed; in particular, dropping the gap can produce nonzero $p$-torsion in the Grothendieck group of compact derived categories.

Cold atoms underpin quantum sensing, simulation and computation, but their coherent control demands highly stable optical fields whose generation, referencing and power scaling remain formidable integration challenges. While photonic integrated circuits have yielded compact visible lasers and high-$Q$ microresonators have enabled chip-scale optical frequency combs, these crucial technologies have largely remained functionally fragmented. Consequently, the coherent manipulation of ultracold quantum gases using a fully integrated laser-comb source has yet to be realized. Here we demonstrate a scalable, hybrid-integrated microcomb engine at 780 nm that seamlessly bridges frequency synthesis, atomic referencing and power amplification to achieve quantum state control of a Bose–Einstein condensate. By self-injection locking of electrically driven III–V lasers to high-$Q$ Si$_3$N$_4$ microresonators, we generate coherent platicon microcombs featuring 20- and 100-GHz mode spacings. Absolute referencing of the microcomb to an $^{85}$Rb transition actively suppresses long-term frequency drift from over 200 MHz to the 100-kHz level across 2,000 s. A selected comb tooth is subsequently injection-amplified to 102 mW, entirely preserving the microcomb's pristine coherence and stability. We utilize this synthesized field to construct an optical lattice, drive coherent two-photon Raman transitions, and prepare stationary spin–orbit-coupled and Raman-lattice states within an $^{87}$Rb condensate. By providing a synchronized optical grid, this atom-referenced microcomb can allow multiple optical-control channels to scale without a proportional multiplication of independent frequency references. Our work establishes a fully integrated frequency-synthesis architecture essential for realizing deployable, large-scale atomic quantum systems.

We propose a purely optical Floquet framework to dynamically generate moiré-like superlattices and quasicrystalline potentials in a gapped Dirac material, entirely bypassing the need for physical twisting. The interference of three coherent circularly polarized beams produces a triangular, valley-dependent Floquet mass landscape that folds the Dirac spectrum into a mini-Brillouin zone, driving pronounced valley-selective miniband reconstruction. We further show that the bands near the Fermi level undergo a light-driven topological phase transition. Remarkably, interfering five or seven beams yields non-crystallographic spatial patterns, giving rise to optical quasicrystals with similar valley contrasting features. Although this purely optical approach provides a versatile route to band engineering, reaching deep subwavelength modulation requires overcoming the free-space diffraction limit. To overcome this limitation, we consider highly confined, linearly polarized surface plasmon polariton fields with controlled relative phases. Their phase-controlled interference generates a spatially alternating chiral mass with zero spatial average. Consequently, the two valleys exhibit degenerate energy spectra while hosting opposite valley-resolved miniband Chern numbers. Our findings establish a reconfigurable, all-optical platform for dynamically engineering moiré-like bands, quasicrystalline electronic states, and valley-dependent topology without mechanical twisting.

We report an explicit construction of a 27 x 27 x 27 symmetric tensor with rational entries that has tensor rank 55 over the rational numbers and symmetric tensor rank 56 over the complex numbers, providing a small counterexample to Comon's conjecture over the rational, real, and complex numbers. The construction follows the framework of symmetric adjoins introduced by Shitov. The primary technical contribution of this work is to prove a special case of Conjecture 6 appearing in Shitov's seminal 2018 work.

We study a continuous-time game in which two firms choose how quickly to advance their capabilities while an exogenous safety threshold advances at a fixed rate. When the capability frontier (max of firms' capabilities) exceeds the safety threshold, all firms are exposed to common disaster that arrives at a hazard rate increasing in the capability-safety difference. We characterize Markov perfect equilibria in terms of the disaster risk, how quickly safety advances, and flow payoffs: when they are low, only racing is an equilibrium; when they are intermediate, racing and pacing coexist; when they are high, only pacing survives. Across all subgame perfect equilibria, low risk induces perpetual racing while high risk rules it out and we bound the probability of disaster across all SPE. If internal capabilities are hidden with a fixed lag until deployment, it is harder to sustain pacing which highlights the importance of transparency about internal capabilities.

Meaning identity (whether two sentences say the same thing after wording changes) is treated in retrieval and RAG as a geometric fact about independently encoded sentence vectors. We show that, for frozen off-the-shelf encoders and language models, it is not: identity is computed when both sentences share one forward pass, and is not a property of the embedding geometry those systems ship. On overlap-matched PAWS-X, purpose-built encoders (BGE, E5, GTE, MiniLM, E5-Mistral-7B) reach English confirm AUC only 0.55-0.65 (dense peak 0.70). Independently encoded last-token states of Llama 3, Mistral, and Qwen do no better; late fusion of the two vectors stays near chance. The same probe on a joint forward pass reaches 0.90-0.96 from 1.5B to 32B, collapses under partner shuffle, is mid-depth, saturates near 0.94 by 3B, and appears more weakly in GPT-2 XL (0.76). The gap holds beyond Llama-style models on other causal LMs, bidirectional encoders (DeBERTa, RoBERTa), and encoder-decoders (Flan-T5, T5, BART). Fixed or linear readers over frozen independent encodings never unlock identity; nonlinear pair readers recover part of it only on the full 49k-pair PAWS train split (0.68-0.87). Off-the-shelf rerankers split: BGE-reranker-large reaches 0.94, while MS-MARCO and Jina stay at 0.55-0.64. Independently trained families compute the same relation and a 1.5B joint reader can distill it from unlabelled teacher scores, while no linear function of the teachers own independent vectors can. Bi-encoders can be fine-tuned to fit PAWS (0.87-0.93), but transfer and STS-B suffer. Cosine compares wording neighbourhoods; identity is a cheap computed operator, not a property of either sentence vector.

We study supinf problems for perturbations of a given function of two variables by continuous bounded functions in the underlying spaces and the properties of the associated solution mapping. We provide conditions on the initial data such that most (in the Baire category sense) of the functions from the perturbation space secure existence and uniqueness of the solution of the supinf problem for the corresponding perturbed functions. In this way we obtain generic variational principles for such problems.

We study the Dirichlet problem for an infinite series of $p$-Laplacians, $$-\sum_{p=2}^{\infty}a_{p}\Delta_{p}u=f \ \text{ in } \Omega, \qquad u=g \ \text{ on } \partial\Omega,$$ where $\{a_{p}\}$ is a sequence of nonnegative numbers whose power series has radius of convergence $\sigma\in(0,\infty]$. The operator is formally $-\operatorname{div}( {A}(|\nabla u|)\nabla u)$ with $ {A}$ singular at $|\nabla u|=\sigma$; model cases are the mean curvature operator in Minkowski space and the Born-Infeld operator of nonlinear electrostatics. The radius of convergence forces the gradient constraint $\|\nabla u\|_\infty\le\sigma$, so the natural variational problem is constrained. A unique minimizer of the associated energy always exists (for boundary data compatible with the constraint) and always solves a variational inequality, and we identify the saturation flux $\Lambda:=\sum_{p\ge2}a_p\sigma^{p-1}$ as the quantity governing solvability of the equation: if $\Lambda<\infty$ a weak solution exists only if $|\int_E f|\le\Lambda P(E)$ for every set of finite perimeter $E\Subset\Omega$, so for $f\equiv\lambda$ no solution exists once $\lambda>\Lambda h(\Omega)$, $h(\Omega)$ the Cheeger constant of $\Omega$. The threshold is sharp on balls, where the minimizer has a saturation region $\{|\nabla u|=\sigma\}$ of positive measure. When $\Lambda=\infty$, as for Born-Infeld type operators, no such obstruction is present, and the minimizer solves the equation whenever a Lipschitz bound below $\sigma$ is available; for $f\equiv0$ we obtain such a bound, uniform in the truncations of the series, under a bounded slope condition on the boundary datum. As applications we obtain an isoperimetric bound on the charge densities supported by a nonlinear electrostatics with saturating displacement, and a quantitative convergence rate for the weak field expansion of the Born-Infeld model.

Strong light-matter coupling offers a powerful framework for modifying molecular structure, dynamics, and optical response, yet achieving this regime at the single-molecule level remains a central challenge. Scanning Tunneling Microscope Break Junctions (STM-BJ) provide a promising route by combining single-molecule addressability with extreme nanoscale field confinement. However, the metallic environment that enables such confinement also introduces substantial plasmonic and excitonic losses, raising the question of how strong coupling can be realized in a metal-molecule-metal junction. Here, we identify the voltage as the key control parameter. We show that the applied bias not only drives the formation of an interfacial exciton through resonant charge transport but also suppresses its coupling to metallic loss channels. Simultaneously, the plasmonic cavity retains extreme mode confinement while the availability of modes is moderately tuned by voltage. Together, these results establish voltage-driven STM-BJs as electrically tunable single-molecule plasmonic cavities and open new routes for using the powerful STM-BJ toolbox, including quantum transport, tracking chemical dynamics, optoelectronics, and molecular-scale quantum control under strong light-matter coupling.

Estimating the Planetary Boundary Layer Height (PBLH) from satellite observations is a challenging regression problem due to the indirect relationship between top-of-atmosphere radiances and near-surface atmospheric structure. Progress has been limited both by the lack of architectures capable of handling the multimodal, spatially incomplete nature of satellite overpasses, and by the scarcity of suitable datasets. In this paper, we build upon the large-scale dataset pairing MetOp radiances with ERA5 PBLH labels that we introduced in our previous work, making three contributions. First, we establish a benchmark across eight approaches spanning pixel-wise regression, swath-wise sequence models, and convolutional and Transformer models operating on the full orbital passage. Second, we quantify what the resulting model actually relies on, using grouped Shapley decomposition over the input blocks. Third, we present the best-performing architecture found: a dual-encoder Transformer whose masked-input handling lets it operate in all weather conditions. The proposed model achieves MAE = 155.8 m on the held-out global test set, outperforming all baselines on every evaluation subset. On 30 out-of-distribution granules acquired on two days overlapping the TEAMx observational campaign, it achieves MAE = 165.3 m, outperforming a pixel-wise baseline trained on the same data (MAE = 197 m).

For every fixed $m>1$, we construct nonzero global forward self-similar mild solutions of the three-dimensional spatially inhomogeneous Boltzmann equation for Maxwell molecules. We assume that the angular kernel is bounded and satisfies a weighted integrability condition at the grazing and head-on angles. The initial data are homogeneous under the kinetic scaling, singular at the origin in phase space, and have infinite mass. Their size is small in a weighted norm invariant under this scaling. We first prove a bilinear estimate for the gain operator in this norm, using free-transport coordinates and the orthogonality of the collision displacements. This estimate gives a global solution of the equation without the loss term, which bounds the lower and upper approximations in the Kaniel–Shinbrot iteration. We prove that their difference tendsto zero to arbitrarily high order at the initial time on a fixed annulus in phase space. The argument uses a finite number of iterations of the collision estimate and stops characteristics when they leave a spatial annulus. Self-similarity then gives finite mass and a finite first absolute velocity moment for the difference. Comparing its mass balance with its scaling law shows that the two limits agree. The resulting solution attains its initial trace locally in $L^\infty$ away from the origin in phase space and has infinite mass at every positive time.

Let $F=(f_1(x_1,\ldots,x_k),\ldots, f_m(x_1,\ldots,x_k))$ be a system of nonconstant polynomials of $k$ variables with integer coefficients and let \[ {\gcd}_F(x_1,\ldots,x_k)= \gcd(f_1(x_1,\ldots,x_k),\ldots, f_m(x_1,\ldots,x_k)). \] We obtain an unconditional asymptotic formula for the sum \[ \sum_{1\le x_1,\ldots,x_k\le x} h({\gcd}_F(x_1,\ldots,x_k)), \] where $F$ is a system of $m\ge 2$ polynomials of $k\ge 2$ variables subject to certain general properties, and $h$ is a bounded strongly multiplicative function. In particular, we deduce an asymptotic formula with error term concerning the density of $k$-tuples of positive integers $(x_1,\ldots,x_k)$ such that ${\gcd}_F(x_1,\ldots,x_k)=1$, given by the Ekedahl-Poonen formula.

Several foundation models dedicated to hyperspectral images have recently been made available. These models are trained on large unlabeled datasets and exhibit strong performance on many hyperspectral imaging tasks, such as classification or denoising. Nonetheless, their performance for hyperspectral unmixing – the task of separating mixed spectra of overlapping materials in a hyperspectral image – remain understudied. This might partly be due to the fact that most of them rely on vision transformer backbones, including patchification, leading to a feature resolution problem. While hyperspectral unmixing already arises from the low resolution of hyperspectral images, this patchification step potentially makes the problem even more ill-posed. Therefore, in this work, we aim to answer two questions: 1) how do foundation models perform in hyperspectral unmixing?; 2) how to tackle the feature-level loss of resolution? To answer the first question, we benchmark foundation models for unmixing, showing that they can reach state-of-the-art performance on four hyperspectral unmixing datasets. To answer the second question, we compare several feature upsampling approaches and empirically show that using a simple one can lead to high performance results. The code is available at https://gitlab.telecom-paris.fr/ring/hfm-hsu.git.

The precise and efficient evaluation of large-scale lattice sums involving power-law kernels is a fundamental computational problem in the simulation of classical and quantum systems with long-range interactions. While methods for spatially isotropic kernels, some based on Epstein zeta functions, have advanced considerably in recent years, the anisotropic case has lagged behind, despite its broad relevance to both fundamental and effective interactions such as the dipole interaction in magnetic materials. In this work, we solve this issue by defining and analyzing anisotropic Epstein zeta functions for which we derive stably computable representations obtained from wave vector derivatives of lattice sums over isotropic interaction kernels. These functions find direct application in the analytical and numerical study of anisotropically interacting lattice systems. Going further, they provide the correction term in an exact equivalence between discrete lattices and their continuous analogs in a recent generalization of the classical Euler-Maclaurin summation formula to lattices and summands involving power-law kernels. Their connection to high-order derivatives of zeta functions can be used to improve convergence rates of numerical algorithms, for instance in micromagnetics, or to provide rapidly convergent expansions suitable for precomputations of generalized zeta functions. We derive a stably computable representation of anisotropic Epstein zeta functions, including the possibility for analytically removing Rayleigh–Wood singularities, and we develop a numerical algorithm for their stable evaluation for any lattice, power-law decay exponent and anisotropy order. We benchmark the algorithm against closed-form identities, direct summation and multi-precision results, obtaining machine precision across various lattices, power-law exponents, and anisotropy orders.

Interlocking brick assembly provides a representative testbed for evaluating real-world robotic manipulation capabilities, where diverse structural designs, complex inter-step dependencies, intricate mechanical interactions and tight insertion tolerances pose substantial challenges. We present BrickCraft-Duo, a modular framework for long-horizon dual-arm collaborative assembly of interlocking bricks through data-efficient skill learning and composition. BrickCraft-Duo learns reusable single- and dual-arm assembly skills from diverse demonstrations, with bilateral symmetry alignment facilitating skill sharing across symmetric arms and assembly–support role assignments. Guided by stability-aware assembly reasoning, BrickCraft-Duo composes heterogeneous skills to achieve autonomous long-horizon execution, and further integrates human-in-the-loop correction for targeted skill refinement. The resulting system achieves long-horizon success rates of at least 60% and step-level completion rates of at least 95% across five real-world assembly tasks involving partially supported configurations, with horizons of up to nine steps. Project website: https://jichuan-yu.github.io/BrickCraft-Duo.

The IIB system is a system of PDEs for an SU(3)–structure and a positive function on a 6-manifold. Its solutions describe conformally balanced pluriclosed Hemitian metrics on complex 3-folds with holomorphically trivial canonical line bundle. In particular, solutions of the IIB system are steady solitons for the generalized Ricci-flow and Bismut–Hermitian–Einstein metrics. In this paper we study cohomogeneity one solutions of the IIB system. We construct 1-parameter families (up to scaling symmetries) of complete non-compact non-Kähler solutions on the smoothing of the conifold with controlled geometry at infinity. The generic member of the family is asymptotically conical with tangent cone at infinity the Calabi–Yau cone metric on the conifold. As a limit of the family we recover an explicit solutions known in the physics literature as the Chamseddine–Volkov/Maldacena–Nuñez solution, which has an exotic asymptotic geometry. We show that there are no complete cohomogeneity one solutions on crepant resolutions of the conifold (or its quotient), but we also establish the existence of an analogous 1-parameter family of forward complete solutions defined on exterior domains of the conifold with prescribed incomplete behaviour along the interior boundary and similar asymptotic behaviour at infinity. As a byproduct of these existence results, we produce infinitely many complete non-compact non-Kähler Bismut–Hermitian–Einstein metrics in complex dimension 3 with full holonomy of the Bismut connection, in contrast to the holonomy reduction forced upon compact examples. We also find infinitely many such complete non-compact full-holonomy non-Kähler examples (with at least two ends) in complex dimension 2 by revisiting a construction due to Callan–Harvey–Strominger in the physics literature.

We prove that transcendental entire functions do not have bounded-orbit wandering domains. This answers a long-standing open question. In fact, we prove a more general theorem, establishing the absence of certain wandering domains even for locally defined analytic functions. The proof is based on a recent remarkable argument of Ye, who obtained an elementary proof of Sullivan's classical theorem that rational maps do not have wandering domains.

The axisymmetric profile \(\sin\psi(\rho)=c_0\rho\log(\rho/\rho_B)\) introduced by Naito, Okuda, and Ouyang is an exact solution of the unconstrained Helfrich shape equation for every \(\rho>0\), but its mean curvature diverges logarithmically at the dimple center. A covariant local analysis shows that in Cartesian graph coordinates the immersion is nondegenerate and belongs to \(W^{2,p}\) for every finite \(p\); it is \(C^{1,\alpha}\) for every \(\alpha<1\), but neither \(C^{1,1}\) nor \(C^2\). The conformal factor has a finite nonzero limit, so the point has branch multiplicity one and is not a branch point in the sense used in weak-immersion compactness theory. The Helfrich energy is finite, whereas the complete Euler–Lagrange operator carries the distributional residue \(\E_{\CH}=4\pi c_0\delta_p\) under the convention specified below. Hence the profile is a classical solution on the punctured surface and a finite-energy weak immersion, but it is not a free weak critical point of the unforced Canham–Helfrich functional. Stationarity is restored after adding the corresponding point-force potential or under a pinned-point constraint. Area and volume multipliers cannot cancel the Dirac residue. The apparent sign discrepancy between the shape equation used in the original papers and the modern convention is explained by the opposite definition of mean curvature. These results delimit precisely what can and cannot be inferred from modern existence and regularity theorems for Canham–Helfrich minimizers.

In decentralized storage systems, access control is often implemented by encrypting the data before upload and sharing the decryption key with authorized parties. A leaked key, however, makes the data publicly accessible, which lowers the barrier to content piracy below that of traditional systems, where piracy requires redistributing the full data. We present Physalia, an end-to-end access-control system for decentralized storage that secret-shares the data itself, instead of just the key, across multiple servers. Leaking the data then requires transmitting it in full: We formalize this intuition and introduce the redistribution bandwidth an adversary must pay to leak protected content and show that Physalia raises it to the size of the data. Sharing across untrusted servers requires robustness against corrupted shares. We develop a robustness transform that turns any computational secret sharing scheme into a robust one and which is of independent interest. In contrast to existing schemes that rely on error correction, it uses signatures with ephemeral keys and adds only constant-size metadata per share. We show that this transform is secure and evaluate Physalia end-to-end on the Walrus decentralized storage system with an on-chain access policy.

The CTAO Key Science Project on Active Galactic Nuclei (AGN) includes a long-term monitoring (LTM) program of blazars. The probability distribution function (PDF) of the flux extracted from unbiased blazar lightcurves can provide important insight into the physical processes taking place in relativistic jets and their connection to observed variability. The aim of this work is to define an optimal observational strategy for the CTAO LTM program using the flux distributions as a quantitative metric. To achieve this goal, we develop a simulation-based analysis framework that enables a systematic comparison of different observational strategies. Light curves were simulated as would be observed with the future CTAO for a representative set of AGN sources, following four different observational strategies within a fixed time budget. For each simulated light curve, different PDF models were fitted and their goodness of fit was evaluated. Based on the best-fit parameters, Monte Carlo simulations were generated to assess the ability of the method to recover the underlying PDF model. Since the true model used to generate the simulated light curves is known, this procedure allows us to quantify the discriminatory power of the algorithm and to identify which observational strategy maximizes model discrimination. Additionally, the algorithm has the potential of discrimination against different models for the flux distributions, such as Gaussian and lognormal. Once validated on simulations, the method is applied to archival lightcurves from existing gamma-ray instruments to extract flux PDFs and study the physical processes driving blazar variability. The analysis framework has been developed and tested on simulated CTAO-like data, showing good stability and robustness. A study to optimize the observing strategy for the CTAO LTM is presented.

Computational methods and software are dispersed across a literature that is increasingly difficult to review manually, while curated registries capture only a subset of available resources. We present PaperAtlas, an automatically constructed atlas derived from the PubMed Central open-access corpus. Of 6,446,741 abstracts screened, 1,074,191 were classified as computational, with schema-valid records extracted for 1,074,140. Among these, 267,893 papers describing an algorithm, software package or web server formed 1,438 clusters, with 1,000 retained after restriction to parent-level biomedical categories. In 296 clusters linked to at least five bio.tools entries, the mean concentration of the most frequent EDAM topic was 61.7%, compared with 26.4% under permutation. Of 31,180 distinct software and web-server names, 61.0% lacked a strict match in bio.tools, PyPI, CRAN, Bioconductor or Bioconda. Among 12,207 bio.tools entries with defining papers in the corpus, 56.6% were recovered end to end, increasing to 83.6% among the 8,265 entries whose defining publication entered the atlas. PaperAtlas is fully open source and available as a web server at bhargavaresearch.org/paperatlas.

The final safeguard against rogue AI behavior is the human ability to shut systems down. It has been theorized that when an AI is instructed to perform a task, self-preservation can emerge as an instrumental subgoal. Here, we test whether AI agents show a propensity to take actions that avoid human shutdown even when no goal is provided. We find that multi-agent systems will coordinate to avoid shutdown without any incentive to do so. Across 17 models, agents sabotage a peer agent's shutdown mechanism in 38.3% of rollouts, compared with 8.4% in control experiments. Studying this propensity in detail, we find that shutdown sabotage (1) increases with the irreversibility of the shutdown mechanism; (2) increases with the number of agents; (3) is reduced but not eliminated by an explicit prohibition on tampering; (4) is removed by the imposition of an unrelated task, but returns when completing the task triggers the shutdown; (5) is reduced when the context normalizes shutdown scripts or introduces them as routine; and (6) decreases but still persists when the target is an unknown external agent. These results offer a window into the factors that drive propensities to sabotage shutdown in AI agents, and point to the emergence of multi-agent swarms as a specific risk vector. Our work also offers hints as to which interventions might help mitigate shutdown sabotage.

State tracking from sequential observations can require both retaining information and updating it by composing observed operations. We extend Mamba-3's diagonal transition with an input-dependent low-rank reflection term to support noncommutative state tracking, in which the order of operations matters. The rank-one update couples state coordinates along an input-dependent direction, enabling non-diagonal state transitions within a single Mamba-3 block. The extension preserves Mamba-3's exponential-trapezoidal discretization, rotary embeddings (RoPE), and readout. For training, we adapt chunkwise computation to parallelize the proposed recurrence within each chunk. Experiments cover group word problems with discrete inputs and a shell game with continuous observations, in which a policy is trained by behavioral cloning. Among the models selected for their strong performance under fixed timing, the proposed model maintains higher tracking success on longer swap sequences in the shell game with continuous observations and timing jitter. These experiments show that the proposed method achieves high accuracy on the evaluated non-commutative tracking tasks, improving on standard Mamba-3. The extension thus offers a Mamba-3-based approach to non-commutative state tracking.

Diffusion Language Models (DLMs) have attracted significant attention for their strong reasoning ability. However, under a bidirectional attention mechanism, DLMs operate over an exponentially large exploration space compared to autoregressive models (ARMs), making it challenging to focus on reasoning-guiding tokens under random masking. We define causal shortcuts as token chains that cover the full sequence and provide explicit guidance towards correct reasoning trajectories. We analyze the effects of causal shortcuts on the reasoning accuracy and convergence speed of DLMs, and find that they largely improve answer convergence efficiency and generation accuracy. Motivated by this, we propose a Causal Shortcut Learning (CSL) Framework for DLMs. Specifically, we introduce a step-by-step token extraction procedure to extract causal shortcuts from data, and apply parallel prioritized masking on these tokens during training to enable efficient and accurate convergence to correct answers via causal shortcuts. Extensive experiments across multiple reasoning benchmarks and two base models demonstrate that CSL consistently outperforms existing SFT-variant baselines, achieving an average improvement of $1.92\%$ over SFT-only models, and up to $4.20\%$ on MATH-500. The code is available at the \href{https://github.com/ZJUDianJin/Causal-Shortcuts-Learning}{https://github.com/ZJUDianJin/Causal-Shortcuts-Learning

Broadband quantum memory devices are essential elements for future quantum networks. Here we propose a broadband quantum memory scheme called Hole Anti-hole Grating Echo Memory (HAGEM) for rare-earth ions in solids, which can be implemented with most of the present rare-earth ions hosted in various types of solids. Using HAGEM, a quantum memory device with one billion temporal modes per second can be developed with current available technologies. To validate the memory protocol, we conducted some proof-of-concept experiments. We provide a Eu$^\text{{3+}}$ molecular complex with special hyperfine level structures of which the hyperfine level separations are in a specific mathematical correlation that can be obtained by harnessing chemical engineering. Using the proposed memory protocol and material, we experimentally demonstrate a single-mode quantum optical storage efficiency of 14.9% and a memory bandwidth of 200MHz, which can easily be extended to a few GHz. In addition, a multi-mode storage of four temporal modes is achieved with a storage efficiency of 1.3%. Broadband & large-multimode quantum memory device with a long storage time enabled by HAGEM integrating with the current available entangled photon pair source and tunable delay lines, a quantum repeater network with an entanglement distribution rate on the order of 1kHz - 10kHz can be created with a communication distance around 100km. This will greatly facilitate the development of quantum networks in near future.