Papers

We develop a data-driven sensor-placement framework and apply it to aerosol monitoring in the United Kingdom (UK). A trained convolutional Gaussian neural process is embedded within the DeepSensor optimisation framework. Genetic optimisation with lazy evaluation and caching reduces mean computational time by 60% (10$\pm$3 versus 25$\pm$7 minutes) while producing sequential placement performance comparable to the greedy solver. Using the CAMS reference field to construct a retrospective oracle benchmark, Joint NLL improves by about 22% for Joint-MI-driven genetic placement after five locations for aerosol stations are identified. Seasonal and wind-regime analyses show that agreement between model-based criteria and oracle benchmarks varies with meteorological transport conditions. These results show a computationally efficient approach for data-informed expansion of environmental observing systems.

Efficient autoregressive generation is increasingly limited by the memory footprint of the key-value (KV) cache, which grows linearly with sequence length, batch size, and model depth. Existing approaches such as Multi-Query Attention (MQA), Grouped-Query Attention (GQA), Multi-Head Latent Attention (MLA), and Tensor Product Attention (TPA) reduce this cost through different trade-offs, but often sacrifice expressivity, require additional positional-encoding machinery, or impose restrictive low-rank structure. We propose Kronecker Product Attention (KPA), which represents key and value activations as sums of Kronecker products of compact, token-dependent matrix factors. KPA strictly generalizes TPA: rank-one vector-outer-product factorization arises as a degenerate Kronecker split, while non-degenerate matrix factors can represent richer block-structured patterns. We further show that a structured rotary embedding operator matched to the Kronecker representation preserves the relative-position property of RoPE while rotating only the compact factors, removing the need for a decoupled RoPE branch as in MLA. Empirically, KPA matches or exceeds TPA, MHA, MQA, GQA, and MLA across four model scales and nine downstream benchmarks under identical training conditions, while achieving up to 10x KV cache compression. The Kronecker head split is a tuneable hyperparameter that allows practitioners to navigate the compression-accuracy trade-off at design time without architectural changes.

We study multiblock convex–concave saddle-point problems of the form $\min_x\max_y\{f(x)+H(x,y)-g(y)\}$, with separately charged partial-gradient oracles for all three objective components. We impose joint smoothness and strong convexity bounds on the functions $f$ and $g$, together with blockwise Lipschitz conditions on the partial gradients of $H$, so that the resulting oracle complexities reflect the smoothness and dependency parameters specific to each oracle. Under strong convexity, we develop a randomized lifted extragradient method that achieves linear convergence while providing simultaneous complexity guarantees for all oracles. The partial-gradient complexities for $f$ and $g$ exhibit the expected square-root dependence on the corresponding block condition numbers, whereas the coupling-gradient complexities depend on the associated curvature-normalized smoothness parameters. Finite-dimensional bilinear subclasses provide lower-complexity benchmarks within a randomized blockwise linear-span model. When strong convexity of $f$ and $g$ is not assumed, a regularization argument yields expected restricted-gap guarantees with accuracy dependence $\varepsilon^{-1/2}$ for the objective-gradient oracles and $\varepsilon^{-1}$ for the coupling-gradient oracles, up to logarithmic factors. Experiments show observed oracle savings and runtime improvements in regimes of poor objective conditioning.

LLM agents can execute increasingly complex tasks, but effective assistance also requires aligning their actions with goals and constraints that users may leave unstated. We study this problem as interactive intent alignment through clarification. Yet clarification is useful only when the agent can turn the answer into better decisions. As training changes how the agent handles incomplete information and uses additional answers, the same clarification can become more or less useful. We introduce CLEAT (CLarification through valuE-guided Agent co-Training), a framework that co-trains a clarification-value controller and the task policy from shared interaction outcomes. We formulate residual query value to measure the task utility gained by asking rather than proceeding under the current policy, and estimate it through paired rollouts from the same interaction history. These paired returns train the controller to predict clarification value and the task policy to select useful questions and act on the answers. The controller guides subsequent rollout collection, while outcomes from the updated agent provide new value labels that allow clarification guidance to adapt as the agent learns. With Qwen3-4B, CLEAT achieves the highest mean score in all ten evaluation settings across four benchmarks. Gains over the strongest baseline reach 13.2 and 6.5 percentage points on UserGym Travel and IN3 underspecification judgment accuracy, respectively. Ablations show that co-training improves the task policy even when the controller is removed at inference, while adapting clarification guidance to the evolving policy yields further gains.

The repeated assembly of the sparse Jacobian matrix constitutes a primary computational bottleneck in the Newton-Raphson power-flow analysis. Through an algebraic equivariance analysis of the Jacobian matrix, this paper proposes a direct sparse Jacobian assembly method based on symbolic permutation. By pre-applying the permutation to the admittance matrix during a one-time symbolic phase, the runtime bus-type projection overhead is entirely eliminated. Consequently, complex Jacobian differentiation and global matrix assembly fuse into a single operation, yielding a single-pass, branchless algorithm that streams values directly into contiguous memory. The framework is realized in the open-source RustPower solver. Benchmarks on IEEE test systems and PEGASE 9241 demonstrate that the proposed assembly is 24.4-30.1x faster than the MATPOWER- style baseline and 6.0-7.8x faster than the Schafer-Braun optimized assembly. End-to-end, the grid-level solve time is 11.7x-154.3x faster than pandapower 3.5.4 with Numba, while leaving numerical results and convergence behavior unchanged. Compared with the native C++ LightSim2Grid 1.0.0, grid-level performance is comparable on IEEE 39 and 1.3x-1.8x faster on IEEE 118 and the PEGASE systems. The method extends directly to general problems where a sparse Jacobian inherits its structure from a static network operator, including transient stability analysis, EMT simulation, and OPF Hessian assembly.

A tropical quantum field theory is an exactly solvable deformation limit of an ordinary QFT, governed by a non-linear partial differential equation. We use the integrable two-dimensional sine-Gordon theory as a testbench to compare the exact features of an undeformed model with its tropical counterpart. We classify scale-invariant tropical QFTs in $D=2$ and leverage functional renormalization group methods to demonstrate that all scale-invariant theories with periodic effective actions are infrared fixed points of flows originating from sine-Gordon Lagrangians. For the tropical sine-Gordon model, we compute the $\beta$-functions exactly, solve the renormalized theory both via a convergent expansion and numerically for all admissible couplings, and illustrate the complete renormalization group flow from the Gaussian to the IR fixed point. Finally, we study the large-order behaviour of the loop expansion and relate it to the Hamilton-Jacobi equation, whose solutions we interpret as tropical instantons.

We investigate the full statistics of entropy production in coherent mesoscopic conductors beyond the weak-coupling regime. Using the inside-outside perspective and the Landauer-Büttiker scattering framework, we relate entropy production to the full counting statistics of particle transport and show that the corresponding cumulant-generating function satisfies the fluctuation symmetry independently of the coupling strength. We obtain closed analytical expressions for the cumulant-generating function in the weak- and strong-coupling limits, enabling a detailed characterization of entropy production distributions and higher-order cumulants. These cumulants reveal distinct signatures of resonant transport and coherent fermionic partitioning. While coupling-induced broadening substantially modifies the transport statistics, the fluctuation symmetry imposed by microscopic reversibility remains preserved in the long-time limit.

LLM agents executing multi-step workflows fail in two fundamentally different ways: recoverable slips, which further attempts can repair, and knowledge gaps, which retrying cannot resolve. Expert feedback can address the latter, but expert attention is scarce. The key challenge is therefore not whether to ask for feedback, but where feedback can change the outcome. Existing approaches either avoid expert feedback, allowing agents to reinforce their own errors, or allocate feedback at the task level without identifying consequential decisions. We present SynAct, an active learning framework that treats expert attention as the binding constraint and allocates feedback at the level of individual decisions. SynAct ranks decisions by the mutual information between the selected action and the terminal outcome across repeated rollouts, queries an expert at the highest-value decisions, and distills the resulting corrections into transferable rules that the agent can reuse without expert access at deployment. We theoretically characterize what this signal identifies under finite repeated sampling: with k rollouts and at least m observations per action, outcome-constant decisions have zero mutual information, while outcome-separating decisions have mutual information at least H2(m/k) bits, yielding exact separation for any threshold t in (0,H2(m/k)). This also explains why success-based acquisition can be blind when all rollouts fail: success is constant even when failed runs reach different outcomes. Across four agent benchmarks and four models spanning three families, SynAct improves held-out accuracy in all 16 evaluated settings, by +11.7pp on average. The same signal transfers to inference-time routing, where SynAct outperforms budget-matched cascade, uncertainty, and expert-judge routers in 15 of 16 settings, while a single targeted correction outperforms seven additional unaimed retries.

When you ask a vision-language model (VLM) a question with an image, it answers your question based on the image. But to act means to choose: saying one thing means choosing to respond not say another. This becomes an issue when the image contains multiple features that equally relate to the question at hand: how would VLMs choose to respond? This problem is precisely studied by the classical Stroop task in psychology: among a set of deliberately designed images whose text and color conflicts (e.g., \textcolor{blue}{RED}), participants are instructed to report the color. We adapt this psychological paradigm to a benchmark and prompted a range of contrastive and generative VLMs on their behavior. Across models, we observe a persistent bias toward the feature of text in Stroop images: when text and color disagree, models preferentially generate responses centered to the text rather than color. We then opened the black box and examined the source of this bias and why certain features influences the model's behavior more than others. In the embedding space, we found that textual cues are represented more strongly and separably than color cues. This representational asymmetry predicts intervention success: steering models toward text-related directions is substantially easier than steering them toward color-related directions. Using a classical psychological paradigm, we demonstrate, at both behavioral and representational levels, that distinct features within the same image can exert unequal influence on VLM behavior. Our findings suggest that VLMs assign different degrees of saliency to different features within the same image, highlighting the need to understand how cue-specific saliency shapes their performance in widely used downstream applications.

Program verification has become commonplace in software development projects, and much of its feasibility can be attributed to the potential of SMT solvers to automate model checking and other verification techniques. However, SMT instability, a phenomenon where semantically equivalent permutations of source code take much longer to solve or timeout, has been found to interrupt workflows and make software engineers more likely to avoid verification. Previous efforts to measure SMT instability have had difficulty quantifying it due to the abnormal runtime distributions it produces. In this paper, we use the coefficient of variation to model instability across an extensive dataset of SMT queries from three software domains. Our results show that SMT instability is significant in each area, and that it increases for queries that take longer on average. However, using a novel method to quantify instability, we show that a different approach is possible: if a solution were to optimize the structure of queries for runtime, rather than variance, instability could be mitigated while also improving overall solver performance.

The classical vertical shear instability (VSI) is a baroclinic instability that arises from height-dependent azimuthal velocities and is a leading candidate for driving anisotropic turbulence in discs with extended vertical modes. The classical VSI requires fast cooling times and radial temperature gradients, which are absent in an isothermal stratified (barotropic) setup. We investigate the dust-driven vertical shear instability in an isothermal, stratified shearing box, where the VSI is generated by drag forces acting on the gas due to dust rather than radial thermal stratification. We construct two-fluid (gas+dust) vertically stratified equilibria including dust diffusion and use these profiles to initialise 2D (radial-vertical) hydrodynamical simulations with FARGO3D. To separate dust-driven vertical shear instability (DVSI) from drag instabilities, we employ a dust-analogue model in which dust-induced drag on the gas is prescribed as a time-invariant and height-dependent acceleration, such that the underlying spatial distribution of the dust is assumed to be constant. The DVSI grows from regions of strongest vertical shear away from the midplane, exciting predominantly radially short, vertically extended disturbances (large k_x/k_z) and producing banded structures in the perturbed azimuthal and vertical velocities during the linear phase. In the nonlinear regime, the instability saturates via a Kelvin-Helmholtz-like parasitic instability that breaks the coherent vertical-shear modes into smaller-scale eddies, which balance the growth of the vertically extended modes, driving sustained vertical stirring. Dust-driven vertical shear can drive anisotropic turbulence and vertical mixing in an isothermal model without invoking global thermal gradients and could play an important role in the stratified streaming instability.

Quantum Zeno dynamics constrains a continuously monitored system to measurement-selected subspaces. Here we show that the structure of such Zeno subspaces can be governed by a latent symmetry, namely a symmetry that is absent from the geometry of the underlying physical network. We consider a minimal circuit-QED network of coupled microwave resonators subject to quantum-nondemolition (QND) monitoring of local photon occupations. Two distinguished resonators are geometrically inequivalent, yet are exactly exchanged by a latent symmetry of the network. Strong monitoring partitions the single-excitation Hilbert space into three quantum-Zeno subspaces, two of which correspond to localization on the distinguished resonators. Latent symmetry exactly exchanges these two Zeno subspaces and enforces identical escape and residence statistics despite their different microscopic environments. In the strong-measurement regime their residence times grow linearly with the measurement strength and diverge in the ideal Zeno limit, where the measurement subspaces become dynamically disconnected. Our results show that latent symmetry can act as a hidden organizing principle of quantum Zeno dynamics, imposing exact relations between measurement-selected subspaces that are geometrically inequivalent in the physical system.

We investigate the construction of unitary $t$-designs in a multi-photon Fock space on programmable linear-optical interferometers. Using the frame potential as the optimization objective, we identify architectures that realize approximate unitary 1- and 2-designs with considerably fewer controllable parameters than required for universal linear optics. For example, we find numerical evidence suggesting that for unitary 1-designs, the required number of programmable parameters scales empirically as $2d$ with the number of modes $d$, instead of $O(d^2)$. We benchmark the resulting ensembles using single-photon transition probabilities and average channel fidelities. Furthermore, as a practical result, we develop a photon-number estimation protocol for multi-photon Fock states that leverages these optimized 1- and 2-designs. Our findings demonstrate that shallow interferometers can accurately reproduce Haar-averaged first moments, while second-moment-sensitive observables provide a considerably stricter test for approximate unitary 2-designs.

The even-denominator fractional quantum Hall (FQH) states, understood as topological superconductors of composite fermions, are predicted to support elementary quasiparticles (QPs) or quasiholes (QHs) obeying non-Abelian braid statistics. Using the microscopic framework of parton theory, we investigate many experimentally observed paired composite-fermion states and find that their elementary QPs and QHs in general bind to form Abelian molecules, thus obscuring non-Abelian braid statistics. An exception is the $\nu=1/2$ state in wide quantum wells, where our calculations show free QPs or QHs; we thus identify this state as an especially promising candidate for realizing and studying non-Abelian braid statistics. We also indicate how the study of such bound states can help reveal the topological structure of the state.

Backdoor Attacks on Large Language Models (LLMs) typically follow a trigger-response pattern, where satisfying a trigger condition activates a single terminal behavior. However, this single-point backdoor activation does not explore attacks in which malicious behavior develops gradually through multiple intermediate stages before reaching the terminal activation stage. We present Cancerous Backdoor Attack, that gradually corrupts an LLM's reasoning over a sequence of interactions by leveraging invisible tokens and a stage controller. Specifically, invisible tokens provide hidden stages to the model without appearing in the user's visible request and the stage controller tracks the attack's progression during inference to realize gradual activation. We evaluate Cancerous Backdoor Attack across several reasoning datasets. The attack consistently produces gradual reasoning corruption across models and tasks. We compare Cancerous Backdoor Attack with prior backdoor attack baselines to demonstrate our proposed attack outperforms the baselines. Our results indicate that reasoning corruption can develop gradually before it becomes visible, making answer accuracy alone insufficient for detecting backdoor attacks.

Nested integrals $\int f\left(\int g(\boldsymbol{y},\boldsymbol{x})\mathrm{d}{}\boldsymbol{x}\right)\mathrm{d}{}\boldsymbol{y}$ where $\boldsymbol{y}\in[0,1]^{d_1}$ and $\boldsymbol{x}\in[0,1]^{d_2}$ frequently arise in Bayesian experimental design, medical decision making, and computational finance. Statistical estimators for nested integrals are more computationally demanding than for standard integrals. Recent studies demonstrate that the median randomized quasi-Monte Carlo (mRQMC) method achieves super-polynomial convergence rates for analytic integrands. We extend mRQMC methods to nested integrations and propose a novel double-loop mRQMC estimator with super-polynomial convergence rate if both the inner and outer integrands are analytic. Established estimators for nested integrals, such as double-loop or multilevel Monte Carlo, are by contrast limited to algebraic convergence rates. However, expected information gain (EIG) applications from experimental design typically do not fulfill this condition due to a lack of regularity in the outer integrand. We address this through a theoretically-grounded importance sampling regularization scheme. Although super-polynomial convergence rates remain achievable for the inner integral, only the algebraic rate $\alpha+3/2-\epsilon$ for any $\epsilon>0$ can be theoretically guaranteed for the outer integral in the EIG, where $\alpha\in\mathbb{N}\cup\{0\}$ denotes the order of the mixed derivatives of the regularized outer integrand. Our approach shows substantial improvements over double-loop randomized quasi-Monte Carlo methods based on the sample mean in moderately high-dimensional settings for a simple polynomial example. Moreover, we demonstrate improved convergence behavior of the median-based estimator for the more challenging setting of EIG estimation.

Motion retargeting is a critical preprocessing step for transferring human motion data to humanoid robots. While existing methods are effective for single-character motions, interactions involving multiple characters and objects introduce additional contacts and spatial relationships that must be preserved. Retargeting is commonly formulated as a weighted multi-objective optimization problem, where conflicting objectives can require careful tuning of relative weights and can still compromise important motion characteristics. We introduce PriMoRetarget, a prioritized motion-retargeting framework that replaces relative objective weighting with an explicit priority hierarchy. Lower-priority updates are constrained to preserve higher-priority objectives, allowing critical characteristics such as foot placement and interaction contacts to take precedence over lower-priority pose objectives. The method is evaluated on four datasets spanning single-character motion, character-object manipulation, and character-character interactions. The resulting motions better preserve task-relevant interactions and provide reference trajectories that can be tracked more reliably than those produced by widely used retargeting methods.

We study how interpolation affects local steps and parallel sampling in monotone variational inequalities (VIs), with $m$ workers, $K$ oracle calls per worker per round, and $N$ rounds. Under the strong growth condition (SGC), we determine the minimax rate for affine VIs, attained by local extragradient with worker averaging. For nonlinear monotone VIs and convex-concave saddle problems with Lipschitz operators satisfying SGC, we improve the stochastic terms of bounded-variance expected-gap guarantees from $(KN)^{-1/2}$ to $(KN)^{-1}$ with local steps and from $(mKN)^{-1/2}$ to $(mKN)^{-1}$ with minibatches. Under strong monotonicity, we improve the noise-dependent condition-number scaling of existing extragradient bounds from quadratic to linear. The resulting monotone-gap and strongly monotone accuracy bounds match lower bounds up to logarithmic factors in $m$. Under generalized smoothness and SGC, adaptive steps give polynomial dependence on the initial radius. For affine VIs with globally bounded oracle variance, we also attain the minimax rate: the deterministic rate over $KN$ sequential calls plus the statistical rate over all $mKN$ samples. For composite VIs with smooth convex sample interpolation and an exactly evaluated monotone Lipschitz component, accelerated mirror-prox sliding achieves an $N^{-2}$ gradient term, a $(KN)^{-1}$ monotone term, and a $(mKN)^{-1}$ sampling term, without assuming SGC.

A proper coloring of vertices of a graph $G$ is called $t$-frugal if no color appears more than $t$ times in the neighborhood of any vertex of $G$. While $1$-frugal coloring coincides with $2$-distance coloring, we study $2$-frugal colorings of planar graphs with maximum degree $4$ and $5$, respectively. We prove that every planar graph with maximum degree $4$ admits a $2$-frugal coloring with $7$ colors, while a planar graph with maximum degree $5$ admits a $2$-frugal coloring with $10$ colors. The results present variations of parts of the famous Wegner's conjecture, which for planar graphs with maximum degree $\Delta\in\{4,\ldots,7\}$ states that their $2$-distance chromatic number is at most $\Delta+5$.

We study the reheating epoch and total bounce-to-present expansion in modified loop quantum cosmology using current observational determinations of the scalar amplitude and spectral index. We consider the power-law plateau potential, whose normalization is determined independently from the observed values of the scalar amplitude and spectral index. We find that, for the kinetic-energy-dominated initial conditions, the quantum-bounce regime is remarkably insensitive to this normalization, while the subsequent inflationary and reheating evolution shows a more appreciable dependence. We then investigate the sensitivity of the results to the inflationary potential by considering the Starobinsky and polynomial chaotic potentials. The reheating e-fold number and reheating temperature are found to depend strongly on both the form of the potential and, in the polynomial case, the branch selected. In contrast, the total bounce-to-present expansion satisfies the conservative bound N > 129 over the ranges considered here and remains close to the characteristic scale found in LQC. Moreover, the difference between mLQC-I and LQC is remarkably stable for all three potentials. These results suggest that reheating is strongly model dependent, whereas the small systematic shift in the total expansion is primarily associated with the different background quantum geometries of LQC and mLQC-I.

Day-ahead electricity forecasts can help building operators schedule heating, ventilation, and other services around anticipated demand. Choosing a forecasting model also requires balancing accuracy with its forecast-time inputs, local training, and computational requirements. We benchmark statistical, machine-learning, recurrent neural-network, and pretrained TimesFM models for a university building. We use chronological validation and evaluate all configurations on the same 57 test days, comparing accuracy across workdays, weekends, and holidays alongside local fitting and forecasting time. Weather covariates use retrospective observations. TimesFM 3.0 with covariates achieves the lowest overall errors, reducing mean absolute error by approximately 43% relative to weekly seasonal-naive forecasting. XGBoost remains competitive, although paired daily comparisons do not establish a clear mean-absolute-error advantage for TimesFM. TimesFM also performs strongly using only past electricity consumption. Adding covariates improves its holiday forecasts but slightly worsens workday and weekend forecasts, leaving overall mean absolute error almost unchanged. TimesFM requires no building-specific weight training, while XGBoost offers rapid local fitting and inference. The evaluated LSTM takes longer to fit without outperforming either approach. An exploratory historical evaluation reveals seasonal variation, while a separate weather-source comparison produces only small changes in the selected TimesFM configuration's accuracy. These results support pretrained TimesFM as a strong initial forecasting baseline for this building, with XGBoost as a competitive locally fitted alternative. Covariates are particularly useful when improved holiday forecasts justify the additional input preparation.

We consider hole closure in a planar multi-agent system whose sensing disks form a time-varying Čech complex. We propose a harmonic-covariance feedback that uses harmonic edge signals to locate holes and converts those signals into agent forces. For distributed evaluation, we use a fixed-degree polynomial of the regularized Hodge Laplacian. This polynomial is evaluated through local operator applications. The closed loop has a unique global trajectory from every safe initial state. The model data and initial state are supplied with procedures for approximation to any requested accuracy with explicit error bounds. We assume that hole area is measurable and bounded, holes evolve continuously without splitting or merging, and only finitely many temporary new holes appear. Under these conditions, offline finite calculations produce rational lower bounds for the cumulative hole area on the time horizon without querying trajectory data. These bounds converge to that cumulative area, whether finite or infinite. If it is finite, holes close in the time-averaged sense: the average normalized hole area over every fixed-length time window tends to zero as time tends to infinity. In a 15-second numerical demo, all holes close by 9.9s and remain closed through the end.

Long, slender instruments are essential for minimally invasive surgery (MIS), but achieving precise distal manipulation becomes increasingly difficult when actuation extends along the entire instrument. Here, we present an electrothermally actuated fiber-based robot designed for MIS procedures, in which Joule heating is concentrated in the distal active segment. The fiber is fabricated using a thermal drawing process and uses embedded metallic wires for thermal actuation. This robotic fiber, 1.9 mm in diameter and 1.2 m in length, can precisely manipulate surgical laser fibers with positional precision below 100 $\mu$m. The compact size of the fiber robot allows it to pass through the working channel of a flexible endoscope, while keeping both devices mechanically uncoupled to allow independent motion. A phantom demonstration combining the robotic fiber with a da Vinci instrument conceptually demonstrated its compatibility with existing endoscopic systems for clinical applications. Our robotic fiber enables precise distal motion and holds the potential to improve clinical outcomes by enhancing precision in MIS procedures.

We present a minimal classical lattice model of superfluidity at arbitrarily high temperatures, using a modified three-dimensional XY model with “soft" rotors. The global U(1) symmetry is spontaneously broken above a positive critical temperature due to entropic order. We study hydrodynamics in this high-temperature regime and verify consistency with the fluctuation-dissipation theorem, explaining how the large noise variance at very high temperatures is not sufficient to destroy superfluidity or the long lifetime of Goldstone modes.

The Richtmyer-Meshkov instability (RMI) is initiated when a shock wave interacts with a perturbed interface between two materials, imparting an initial velocity to the interfacial perturbation. When the materials are viscoelastic, the subsequent evolution is influenced by the coupled effects of inertia, viscous dissipation, and elastic resistance. The interplay of these effects remains poorly understood and is important for predicting the dynamic response of shock-loaded soft materials, e.g., in blast-induced injury. Using the incompressible Cauchy momentum equation with a Kelvin-Voigt constitutive model, we conduct a linear stability analysis for the early-time post-shock evolution of a single-mode interface perturbation of two viscoelastic materials. We derive an implicit dispersion relation for the temporal growth rates of the perturbation. This relation depends on density, viscosity, and elasticity contrasts between the two materials and an viscoelastic parameter which is a bounded ratio of the viscous dissipation and elastic resistance response rates. Four material cases, spanning symmetric to highly contrasted interfaces, are examined to show how the viscoelastic number affects the growth rate structure as complex-dominated (oscillatory) or real-dominated (monotonic relaxation). The critical viscoelastic number separates these two regimes and is primarily governed by the density and viscosity contrasts. These results provide a theoretical criterion for predicting the early-time response of shock-driven interfaces involving fluids and viscoelastic solids.

We compute the first homology of the unordered configuration space of $n$ open unit-squares in the $w$ by $h$ rectangle for all positive integers $n$, $w$, and $h$. Letting $w$ and $h$ vary, these square configuration spaces form a bi-filtration of the unordered configuration space of $n$ points in the plane, so their fundamental groups approximate the $n$-strand braid group. Using a pair of spectral sequences, we prove that these square and point configuration spaces have naturally isomorphic first homology groups if $w,h\ge 3$ and $n\le wh-3$. In the $h=2$ case, we show that the first homology groups of these square configuration spaces are free of rank $n-1$ for $n\le 2w-2$, whereas they are free of rank $w-1$ for $n=2w-1$.

Edge-on protoplanetary disks provide a spatially resolved view of the vertical distribution of icy planetary building blocks, but inferring their relative abundances requires radiative-transfer (RT) modeling with multiple anisotropic scattering. Each model costs $10^{1}$-$10^{3}$ CPU hours, which precludes principled Bayesian inference and homogeneous, population-scale analyses. We develop and validate a fast and reusable surrogate for Bayesian inference with ice-bearing edge-on disk models. We train a Fourier Neural Operator on a grid of RADMC-3D spectra. The network maps disk parameters and analytic physical input fields to the spectrum, using mixed-resolution spectra. We use the surrogate in an explicit-likelihood nested sampler and validate it on held-out simulations and synthetic recovery tests with TARP coverage. Finally, we use it to retrieve the disk structure and ice abundances of ESO-H$\alpha$ 569 from its spectral energy distribution. The surrogate reproduces the RADMC-3D spectra with a median error of 4.84%. We recover synthetic parameters without detectable bias and with nominal coverage. For ESO-H$\alpha$ 569, the posterior favors a massive ($M_{\rm gas}=0.028^{+0.015}_{-0.011}\,M_\odot$), nearly edge-on ($i=79.8^{+5.2}_{-2.4}$ deg) disk consistent with the image-plus-SED model of Wolff et al. (2017). Its ice abundances and cavity size remain weakly constrained by broadband data alone. The marginal spectrum-evaluation speed-up is $\sim10^{9}$-$10^{10}$. Neural-operator emulation makes full posterior inference feasible within the adopted model and training prior. Key posterior points should still be checked with high-fidelity RT models. By drastically cutting evaluation time, this approach enables for the first time homogeneous population studies of ices in disks, which new JWST surveys can capitalize on to map the range of compositions within planetary nurseries.

Recently, soft robotic procedures are being developed aiming at achieving targeted minimally invasive operations or drug administration in specific locations in the human body. Accordingly, specialized path-planning algorithms need to be investigated for the estimation of efficient paths that would protect the delicate tissue structures and simultaneously satisfy a set of requirements for the efficient navigation of the robot. In this context, we propose an image-based 3D pathplanning algorithm, which is an extension of the A* algorithm, for the navigation of a soft-growing robot inside the spinal subarachnoid space (SSS). The proposed algorithm is capable of estimating a safe pathway towards the goal location, while ensuring the establishment of anchor points that facilitate the efficient steering of the soft robot. The algorithm is evaluated using a highly detailed model of the SSS with respect to its capacity to satisfy the robot movement requirements and path efficiency.

The Tu-Deng Conjecture, made in 2011, asserts that for $k\geq2$ and $1\leq t<2^k-1$, the set \[ S_{t,k}=\left\{(a,b)\in\{0,1,\ldots,2^k-2\}^2: a+b\equiv t\pmod{2^k-1},\quad \wt(a)+\wt(b)<k\right\} \] satisfies \[ |S_{t,k}|\leq 2^{k-1}. \] Proofs of the conjecture were given independently by the author and by Liu, Luo and Xie in arXiv in 2026. Let $r=\wt(t)$, and let $z=k-r$ be the number of zeros in the $k$-bit expansion of $t$. We prove that equality holds in the Tu-Deng Conjecture if and only if every cyclic distance between consecutive zeros is at least $z$. We give several other simple necessary and sufficient conditions, including a forbidden-pattern condition, a packing condition for the zero positions, a composition condition for the gaps, and equivalent conditions involving the coefficients of the polynomial $H_W(u,v)$ in the proof of the Tu-Deng conjecture. We also count the equality words having a prescribed number of zeros.

Community accounts of ADHD can complement clinical understandings by foregrounding members' own definitions of time-management difficulties and support. We used human-led, LLM-assisted thematic analysis to examine 5,379 relevant r/ADHD posts from 2020 to 2025. Across five challenge and nine strategy themes, members described difficulties beginning intended tasks, disengaging from digital media, and sustaining support. Tools often demanded the self-regulation they were meant to support, while lost time and tool breakdown carried guilt and self-blame. Members drew on people, routines, and environments alongside digital tools, often seeking advice and recognition from peers. These accounts broaden the design problem to include the practical and emotional work of sustaining support. They motivate tools that reduce this burden and evaluations that consider recovery after distraction and emotional costs alongside task outcomes.