Papers

The Meir–Moser rectangle-packing problem asks whether all rectangles with side lengths \(1/n\) and \(1/(n+1)\), for \(n\ge1\), can be packed into the unit square with pairwise disjoint interiors. We establish a tail version of this problem. Let \(R_n\) denote the rectangle with these side lengths. We prove that there exists an integer \(m_0\) such that, for every \(m\ge m_0\), the family \(\{R_n:n\ge m\}\) admits a packing, by translations and right-angle rotations, into a square of side length \(m^{-1/2}\), with pairwise disjoint interiors. The area of the square equals the sum of the areas of all the rectangles. The geometric construction recursively decomposes rectangular gaps, while local randomized quotas and random permutations assign subsequent integer indices. We separately control the total area of waiting gaps and the assignment load at each index. The proof is organized in six steps: a finite-prefix reduction, geometric row decompositions, an area bootstrap, a sharp source-load estimate, control of the actual adaptive construction, and a compactness limit. For every finite time horizon, the probability of failure has a bound that is independent of the horizon and can be made arbitrarily small. The adaptive step uses a permanent load ledger, actual fresh height queries, and a one-sided comparison with a frozen source experiment. Compactness then yields an infinite packing. The final packing statements have been checked in Lean 4. A sufficient threshold is \(m_0=10^{1000}\). This result applies only to sufficiently late tails and does not resolve the original Meir–Moser rectangle-packing problem for the full sequence starting at \(n=1\), which remains open.

Origami structures typically have a multiplicity of folded states that are connected to a flat sheet, making the folding protocol for specific end shapes challenging to design and deploy. Here, we introduce reprogrammable origami hinges that use bistable buckled shims to reversibly control their preferred folding direction. A shim embedded across a hinge produces an asymmetric torque-angle response that favors either mountain or valley folding. Switching the shim between its two stable states reverses this response, allowing the folding direction of each hinge to be reprogrammed after fabrication. By independently controlling the states and geometries of the shims, we enable a single origami sheet to access multiple folding branches and transform into prescribed three-dimensional shapes. We further introduce self-switching hinges in which folding causes the shims to snap between their stable states. These elements allow the sheet to reprogram its folding pathway under global mechanical inputs applied to the boundaries. Our approach embeds both shape selection and transition rules directly within the mechanics of the hinges, providing a versatile framework for creating multifunctional, deployable, and reconfigurable structures.

Particle accelerators have carried fundamental physics to remarkable precision, but the Planck scale remains fifteen orders of magnitude beyond any foreseeable collider. We argue that this impasse is not a temporary shortfall but an insurmountable one. The way out runs through condensed matter physics: laboratory tests of generalized uncertainty relations, analog systems, and — most provocatively — frameworks in which spacetime itself is a condensate. We review the string-loop picture, in which quantization turns the world sheet into a three-dimensional fractal, the corpuscular description of black holes as self-sustained graviton condensates, and the phase-transition structure connecting the Riemannian phase to a pre-geometric one. The conclusion is deliberately provocative: the question of quantum gravity is no longer a question of energy, but of crossing the bridge.

Artificially generated muon beams, with tunable parameters, are highly valuable in imaging objects that are opaque to any other scanning technique. Lower-energy muon beams are currently produced at accelerator facilities, while higher energies have only recently been observed as a result of the interaction of laser-wakefield-accelerated electrons and solid targets. This work focuses on using muography imaging detectors to measure the profile of a muon beam generated via the Bethe-Heitler process and to perform muon imaging in an experimental setup extending up to 42 meters from the muon source. By comparing the data with Monte Carlo simulations, we confirm that the measured beam profile and object imaging are consistent with artificially produced muons of energy of a few GeV. To our knowledge, this represents the first demonstration of imaging dominated by an artificial, laser-driven muon beam.

Machine learning tools have significantly aided automatic piano music transcription; however, this domain has focused primarily on accurately predicting the pitches and timings of played notes. To produce sheet music for the piano, notes must be separated into two staves, one for each hand, and good sheet music often contains fingering annotations to guide the player when sight-reading or learning fast or complex pieces. We propose 8 statistical approaches for combined hand and fingering annotation of transcribed piano notes, including baseline hidden Markov models, rule-based methods, a synthesis of existing approaches, and N-gram language models. Furthermore, we develop a pipeline for complete transcription from piano audio to fingering-annotated sheet music. Evaluations with the PIG dataset demonstrate that our Synthesis model achieves a hand separation accuracy of 90.8% and a joint hand and finger annotation accuracy of 56.6%. These approaches serve as a new baseline for further research into this problem, while our pipeline demonstrates the feasibility of a combined system for automated note transcription, hand separation, and fingering annotation.

We develop an explicit plane-wave (PW) $\times$ photon-Fock approach to the quantized, velocity-gauge Pauli–Fierz Hamiltonian for periodic, first-principles calculations: because the quantized vector potential is spatially uniform, the light–matter coupling reduces to an operator-valued shift of the crystal momentum, $K\to K+\hat{\mathbf A}/c$, and the existing plane-wave machinery of ordinary solid-state DFT is reused essentially unchanged. This PW$\times$Fock construction puts first-principles cavity QED of periodic solids on the same footing as the Fock-space coupled-cluster and configuration-interaction methods already developed for molecules, opening hitherto inaccessible systems—materials in a linear or chiral cavity, in particular—to first-principles plane-wave calculations. We illustrate the method with monolayer graphene in linear and chiral cavities, obtaining a polarization-selective Haldane gap together with the corresponding density-of-states, real-space, and circular-dichroism optical signatures. A full Brillouin-zone Berry-curvature calculation confirms the topological character of the chiral-cavity gap directly: the occupied manifold carries a quantized Chern number that steps through a non-monotonic sequence, $C=1\to3\to{-1}\to1\to2\to{-1}\to1$, with two narrow, sign-reversed windows—a property of extended, vacuum-dressed matter with no counterpart in a finite molecular system.

Maintaining consumer-end voltages within mandated limits is a central task in operating power distribution systems. Rising penetration of distributed generation, electric vehicles, and flexible loads complicates this task, while a scarcity of real-time measurements leaves distribution networks largely unobservable. Operators commonly monitor a few bellwether meters, which indicate operational health but certify nothing about the unmeasured buses. This work asks how to select measurements that are reported in real time and can certify network-wide voltage-limit compliance. We first illustrate the geometry of the measurement values that certify voltage safety at unmeasured nodes. Building on this geometry, we formulate a bilevel optimization that selects measurements to maximize certification capability, introducing a novel safety-violation metric with favorable monotonicity properties. We derive a strong-duality-based single-level reformulation and two scenario-reduction schemes with quantifiable suboptimality. Numerical tests on the SCE 56-bus system corroborate the superior certification capability and computational efficiency of the proposed approach.

In this paper, we investigate how script knowledge is distributed across the layers of LLMs using two complementary interpretability methods: logistic regression probing and logit-lens analysis. Our probing experiments reveal a clear asymmetry: both the input script and the instructed output script are encoded in the earliest layers of the network, while, in contrast, commitment to the actual output script emerges only in the final layers, with the model's intermediate representations defaulting to Latin throughout most of the layers. This two-stage process is confirmed by logit-lens analyses, which show that script commitment consistently occurs at the very last layers of the LLMs. Together with the weaker script-following performance observed in smaller models, these results form a converging body of evidence linking script commitment to model depth, with broader implications for the design of sufficiently deep, inclusive multilingual architectures.

This article describes the Residential Electricity Consumption Dataset for Sri Lanka (RECON-SL), a multi-source resource that integrates utility records, high-frequency smart meter data, and household surveys from the service area of Lanka Electricity Company (LECO) in Sri Lanka. The dataset captures electricity use for 4,063 households, collected over the period October 2022 to January 2025, with coverage at monthly, 6-hour, and 15-minute intervals. Monthly billing-cycle data provide complete coverage across all households, while smart meter data are available for a subsample of 1,438 households, offering both fine-grained 15-minute readings and coarser 6-hour records. Three survey waves complement these consumption measures, collecting information on demographics, housing, appliance ownership, and perceptions of energy security. Across its components, the dataset includes more than 50 million meter readings and detailed survey responses from over 11,000 household interviews. As the first dataset of its kind in Sri Lanka, and among the few worldwide to link smart meter records with longitudinal survey data at this scale, it provides a unique resource for energy, machine learning and policy research, with known gaps in smart meter coverage documented for users. The dataset can support diverse applications, including electricity load forecasting, socio-economic and behavioral energy research, distribution planning, and policy analysis in energy affordability and equity. Access is provided through an open repository, with accompanying documentation and scripts to facilitate reuse.

In scientific machine learning, $\Delta$-learning trains models on residual errors relative to physical baselines, assuming that more accurate baselines with smaller residual scales inherently improve downstream performance. Here, we demonstrate that residual scale alone is an insufficient heuristic for learnability. Evaluating molecular graph neural networks on total energy targets, we show that complex local descriptor baselines can yield small residual targets that are disproportionately rough within architecture-informed proxy spaces and harder to learn relative to their scale. Conversely, semi-empirical baseline reduces both scale and normalized roughness, improving in-domain and out-of-domain prediction. We introduce scale-normalized graph Dirichlet roughness ($D_{\text{IQR}}$) as a pre-training diagnostic for residual learnability and establish baseline complementarity as a core target-design principle, elevating target space formulation alongside model architecture as a key axis for scientific machine learning.

We initiate the study of approximating the top eigenvalue and eigenvector of a random symmetric matrix $ A \in \mathbb{R}^{n\times n} $ using $ q(A)b $ where $q$ is a degree-$d$ polynomial and $b$ is a standard Gaussian vector independent of $A$. For spiked GOE $ Y = \lambda vv^\top + X $, we identify $ d_\star = \frac{\log(n)}{2\log(\lambda)} $ to be the critical degree threshold above which accurate approximation of the top eigenvalue and eigenvector is possible. This sharpens the common belief that spectral methods can be implemented by $ O(\log(n)) $-step power iterations and offers a precise connection between spectral methods and low-degree polynomial algorithms, a popular proxy for all polynomial-time algorithms. For GOE $X$, we identify $ d_\star = n^{1/3+o(1)} $ to be the critical degree threshold for top eigenvector approximation, whereas constant degree suffices for top eigenvalue approximation. Moreover, in the limit where $ d/n^{1/3} $ converges to a positive finite constant, we compute the exact asymptotic eigenvector approximation accuracy in terms of the expected squared overlap. These results significantly improve upon predictions made in randomized numerical linear algebra for deterministic data matrices that the iteration count of power methods with random initialization is governed by the inverse spectral gap. Technically, our analyses leverage extremal properties of Chebyshev polynomials and draw upon the rich literature of random matrix theory.

We continue the study of the Menger and Rothberger games on lattices carried out in "Pointless proofs of the Menger and Rothberger games" (Topology Appl. 300 (2021), 107774). This time, we extend the earlier results by dropping some hypotheses that turned out to be unnecessary, and use Stone duality to recover known game characterizations for dense open families. We also give a formulation of $\mathsf U_{\mathrm{fin}}$ for partially ordered sets and prove its game characterization without any lattice assumption. Finally, almost disjoint families give complete distributive lattices on which the selection principles and the corresponding games differ. Dias's results give the lower bounds $\operatorname{cov}(\mathcal M)$ and $\mathfrak d$ for the least sizes of such counterexamples.

This paper presents a controlled comparison of exactly-once Kafka pipelines implemented with Apache Flink and Kafka Streams, two engines with different state-management architectures. The state management in Flink occurs through checkpoints in external storage, whereas Kafka Streams restores local state by replaying broker changelogs. The experiments evaluate the effects of the two designs on latency, resource consumption, configuration sensitivity, and recover from injected failures. The engines produced expected outputs across 50 correctness trials, five for each engine-workload combination (exact 95% CI 0.929-1.000). The latencies, however, showed differences when tested in 30 minute trials at a fixed rate of 100 events/sec. The measured ingestion to output interval was 4-6 ms for stateless workloads and 4.3-6.2 s for windowed workloads. The median p99 was 1.97-1.97s for stateless workloads and 5.68-9.92s for windowed respectively. Further, a sensitivity study showed that increasing the durability interval from 1,000 to 10,000 ms shifted the latency distributions in Kafka Streams and Flink between stages. Kafka Streams' W3 median p99 T2-T1 increased from 6,085 to 23,155 ms; Flink's T3-T2 increased from 732 to 8,702 ms. Failure injection experiments demonstrate that latency can interfere with incomplete processing behavior. The results show that exactly-once correctness is a necessary but insufficient measure of stream processing performance. Kafka Streams completed 0/5 stateful JVM-kill and 1/5 in each stateful local-volume-loss trials, while corresponding Flink cells completed 5/5. The cost, placement and magnitude depend on state management, architecture, configuration, and measurement location. Accordingly, evaluations of fault-tolerant streaming systems should holistically measure latency, completion, recovery behavior, and correctness.

Audio-language models (ALMs) can exploit textual shortcuts to answer questions while overlooking acoustic evidence, weakening audio understanding. On-policy distillation (OPD) trains compact ALMs by supervising student-generated responses with teacher predictions, but does not explicitly distinguish acoustic support from linguistic predictability. We propose Reward-Tilted On-Policy Distillation (RT-OPD) to strengthen acoustic grounding. Given the same question and student-generated text, a frozen teacher predicts the next token with and without audio inputs. Their log-probability contrast defines a reward that reshapes the teacher distribution for reverse-KL distillation, emphasizing the additional evidence provided by audio. Across two compact students and three benchmarks, RT-OPD consistently outperforms Vanilla OPD. Experiments with silenced and replacement audio further suggest that RT-OPD strengthens the student's reliance on acoustic evidence. Our 3B model achieves 72.72% accuracy on MMAU, the highest among the compared 3B models and competitive with several 7B and 8B models. Code and model checkpoints are available at https://github.com/KaiyangLi1992/RT-OPD.

To provide data-driven quality services to their citizens, every institution determines the acceptability of the citizen data and datafied mechanisms through institutional protocols, including preset standards and policies. However, data meeting standards at one institution might fail to meet a different institution's standards in subsequent phases of the intended citizen services due to mismatched protocols, leading to data devaluation in the citizen service ecosystem. Terming this phenomenon cross-institutional data devaluation, we investigate its causes and workarounds through interviews with 41 Bangladeshi participants. We found that traditional data auditing mechanisms cannot solely address data devaluation; hence, we draw on our findings and theory of cross-institutional AI audits to propose the Citizen-centered Cross-institutional Data Audit (CCDA). We also discuss design and policy implications of CCDA in HCI and datafied citizen services.

We propose a framework that learns cross-task relationships in multi-task models by approximating the joint distribution of task labels through targeted pairwise relationships. This approach improves performance via transfer learning and enhances information extraction without the intractable complexity of modeling the full joint space. Although our framework applies to any multi-task system, we demonstrate its efficacy within YouTube's production recommendation systems. Experiments across the Notifications, Homepage, and Watch Next surfaces show improvements in both accuracy and user satisfaction metrics. Finally, we propose a workflow template to facilitate broader future implementation.

Ultrasound imaging increasingly targets portable, point-of-care, and wearable settings where constraints on power, bandwidth, and hardware complexity often necessitate sparse data acquisition in spatiotemporal scanning. However, image reconstruction using the sparse data can introduce insufficient phase information in coherent beamforming process, resulting in grating-lobe artifacts that degrade imaging contrast resolution. We present a physics-guided, data-driven framework for sparse-to-dense radio-frequency (RF) reconstruction that aligns training with downstream image formation. Our approach trains an end-to-end interpolation network using a hybrid supervision scheme that combines an RF-domain and a beamforming-domain loss with exponential moving average (EMA) to stabilize the multi-objective training. To improve generalization under variable acquisition layouts, we also introduce a random-skip masking strategy that varies sparsity patterns during training so a single model can handle diverse decimation factors and irregular channel configurations. We evaluate the framework on a held-out test set using the mean structural similarity index measure (SSIM) between reconstructed and ground-truth beamformed images. Across decimation factors $\times 2$ to $\times 13$, the best-performing configuration maintains mean SSIM around 0.95. Overall, the results show consistent gains in RF reconstruction and post-beamforming image quality across diverse acquisition conditions. This approach enables robust, high-quality ultrasound imaging at resource-constrained settings by allowing more sparse scanning in spatiotemporal domain.

We obtain explicit formulas for heat kernels of the normalized Laplacians for two infinite families of Cayley graphs. The first family corresponds to free products of finite groups $G=G_1*\dots*G_r$, with $r\ge2$, and where all factors $G_i$ have the same order $L\ge2$. The second family corresponds to free products of two arbitrary nontrivial finite groups $G*H$ of unequal order. In both families, the generating set consists of all non-identity elements in each factor. Extending the approach of Chung–Yau, we show that the Cayley graph in each family strongly and regularly covers a weighted half-line and a weighted line, respectively. We solve the spectral problems on the half-line and the line, and then apply spectral transfer principles for strong and regular coverings to derive formulas for the heat kernels on the Cayley graphs. For the first family, the spectrum of the Laplacian consists of a single interval together with, when $L>r$, one additional isolated eigenvalue. When $L=2$, we recover the well-known results for regular trees. For the second family, the spectrum of the Laplacian consists of two intervals and two eigenvalues.

This article concerns Garding Dirichlet operators, and also the theory of Garding polynomials. Garding Dirichlet operators are those which arise from homogeneous polynomials on the space S(n) of symmetric $n \times n$ polynomials, which are hyperbolic with respect to any positive definite matrix. (In particular, any polynomial on ${\mathbb R}^n$, which is hyperbolic with respect to elements in $({\mathbb R_+})^n$, gives rise to a Garding operator on S(n), in many ways.) Here a new duality theorem is developed with many special cases and examples. The dual $g^*$ of a Garding operator $g$ is used to prove a new basic inequality for $g$. An important Lemma of Guo-Phong-Tong is improved upon as a final application.

In this work, we study a family of transmutation operators for the Sturm–Liouville operator in impedance form with an integrable potential satisfying a smallness condition. Specifically, we consider transmutations associated with the pair \[\textbf{L}_r=\frac{1}{r^2 (x)}\frac{d}{dx}r^2 (x)\frac{d}{dx} \quad \text{and} \quad \textbf{M}=\frac{d^2}{dx^2}. \] We extend existing results by showing that a particular transmutation operator on $W^{3,1} (-a,a)$ can be represented in integral form, where the kernel function satisfies a corresponding Goursat problem. We establish the existence of this kernel using two distinct approaches: the classical method of successive approximations and an application of Picard's theorem.

Large language models (LLMs) have demonstrated strong capabilities in financial analysis and reasoning, inspiring recent advances in agent-based trading frameworks. While these systems show promise, prior approaches either emphasize long-horizon forecasting or operate as stateless analyzers, limiting their applicability to the demands of trading in complicated settings. To address these gaps, we introduce META (Memory Enhanced Trading Agent), the first RAG-like episodic-memory-augmented multi-agent framework for financial decision making. META integrates a family of specialized indicator agents (e.g., Trend, MACD, Stochastic, RSI, SMA, AVWAP, Heikin-Ashi) with a Decision Agent that fuses their reports, and a Memory module that retrieves and updates past trading episodes encoded as market state embeddings with outcomes and reflections. By recalling relevant experiences and adaptively reweighting signals under similar market regimes, META achieves improved directional accuracy and robustness under short-horizon evaluation. Our results demonstrate that episodic memory provides a powerful mechanism for regime-aware, interpretable, and low-latency decision-making in trading and decision making. The code of this project is released on GitHub.

In genuinely rotating holographic backgrounds, Wilson-loop observables are usually constructed for a quark–antiquark pair static with respect to the rotating plasma. We investigate how this choice affects the heavy-quark sector by comparing two descriptions of the same rotating geometry: a corotating frame, in which the pair is static with respect to the plasma, and a static frame, in which it is static with respect to the static observer. We consider an equal-rotation Myers–Perry black hole in asymptotically global AdS and study Wilson loops oriented longitudinally and transversely to the rotation. We analyze the effective string tension, physical quark–antiquark separation, and heavy-quark potential at fixed thermodynamic temperature measured in the corresponding frame. We find a strong frame dependence of the rotational response. In the corotating frame, the longitudinal and transverse configurations respond qualitatively differently: rotation can either decrease or increase the separation and effective string tension, depending on orientation and, for the latter, on the bulk position and parameter range. The heavy-quark potential increases with angular velocity in both orientations. In the static frame, by contrast, the effective tension, physical separation, and maximal separation decrease with angular velocity in both orientations, while the heavy-quark potential increases. Thus, the anisotropic response is substantially stronger in the corotating frame, both qualitatively and quantitatively. In both frames, rotational modifications generally become less pronounced at higher temperature. These results show that the frame in which the quark pair is static is an essential part of the physical specification of Wilson-loop observables in rotating holographic systems.

Modern GPU kernels fuse increasingly more work into a single kernel, and intra-kernel tracing has become the mainstream method to profile them. Tracing inserts probes into the kernel to record its runtime states, and the fidelity of the trace determines the efficiency of performance optimization. Unfortunately, existing tools insert probes before compilation. These tools interfere with the compiler's optimizations, so they trace a different binary from the one the GPU executes. They also add significant runtime overhead. Xtrace is the first GPU kernel tracing system with near-zero compile-time interference and minimized runtime overhead. Xtrace inserts probes directly into the compiled kernel binary. It reuses only the registers that hold dead values at the insertion address and resolves all hazards with the compiler's hazard tables. It further schedules the instruction order, register allocation, and control bits to minimize the runtime overhead the probe introduces. Xtrace supports 19 NVIDIA and AMD GPU architectures, and is publicly available for use at https://g-watch.github.io. We evaluate Xtrace on major production large language model (LLM) kernels against the state-of-the-art tracers Neutrino and IKET from NVIDIA. On H100, B300, and MI300X GPUs, Xtrace preserves 94-98% of the instructions of the kernel, while existing tools preserve only 8-48%. Xtrace adds only 0.9-2.8% overhead, while existing tools add 3.8-75.6%. Xtrace guides a coding agent to reach the same FlashAttention-3 performance with 3.9x fewer iterations than existing traces do. Thanks to our binary-level instrumentation, Xtrace also traces the faster closed-source cuDNN kernel, which guides the agent to lift the open-source FlashAttention-4 by 5.2-13.3% in throughput.

A new simulation approach (J. Chem. Phys. 163, 164113), based on the seamless combination of the electron transfer at the electrode/electrolyte interface with the charge and mass transport in electrolyte solutions, holds the promise to advance the comprehensive modeling of basic electrochemical devices such as electrolytic cells and batteries. The underlying model also includes a fully consistent treatment of structural, thermodynamic and statistical properties of the electrical double-layer at non-ideal electron-conducting interfaces. As a result, subtle aspects such as Tafel and Butler-Volmer equations, the overpotential concept, as well as (stationary) non-equilibrium features such as the entropy production, arise naturally from the model, with a minimum of ad-hoc assumptions and elaborations of the simulation results. We illustrate these aspects for a simple model of electrochemical interface, and discuss further improvements of the method meant to enhance its ability to model systems and phenomena of interest for electrochemistry. One such improvement, concerning the effect of fluctuating electric fields on the electron transfer rate, is explicitly developed.

Real-world perception systems must adapt to changing environments, but manual image annotation cannot scale to field data volumes. We present BirdsEye, which shifts expert annotation from images to the field: an operator records target locations in world coordinates using RTK positioning and calibrated projective geometry propagates each observation to all frames where the target is visible. To quantify how well physical annotations align with image observations, we derive a first-order mapping from camera-pose uncertainty to pixel uncertainty and validate it against Monte Carlo simulation. This mapping is linear in the six per-axis pose variances, so it inverts into a sensor design tool: we give a sufficient condition converting an annotation tolerance into a convex set of admissible pose-noise budgets, a closed-form largest admissible scaling of a deployed sensor suite, and a unique per-axis pose specification under an equal-budget-share allocation. We also analyze the planar-surface approximation underlying the projection, which holds up to 10 degrees of terrain slope. By direct measurement, we show that system projection accuracy is sub-decimeter (sub-30 pixel) at AGL altitudes of 10-20m under conditions excluding sustained yawing. During an in-field case study across three agricultural sites, two field workers produced 12,524 annotated frames carrying 55,600 labels in roughly 12 hours (25.5x per-worker rate increase over manual labeling). Detectors trained on imagery collected by this workflow recovered 56-89% of in-view surveyed targets at a geographically distinct farm, at pre-registered operating points; human review of the leading configuration estimates detection precision at 83-87%, spanning three tie-break conventions for clusters carrying contradictory human verdicts.

Applying adhesive tape to secure wire harnesses or seal packages requires robots to coordinate a flexible strip, a moving roll, and surfaces that attach and detach. Simulation could make these interactions repeatable for robot development and evaluation, but resolving every adhesive layer is expensive and can suppress roll motion at practical solver tolerances, while a permanently rigid roll cannot release material. We present TapeSim, a tape simulator that concentrates deformation near the unwinding region and along the released strip. We will release the source code. A rigid cluster represents most wound material, while an advancing deformable collar enables payout and leaves released tape flexible and reattachable. Optional releasable bonds simplify adhesive interfaces and reduce mean step times for smaller rolls. Controlled swing tests show improved roll rotation. At 32 turns, clustering gives 3.2-3.4x mean physics-step speedups at a fixed Newton tolerance and 4.5-8.4x for comparable roll motion. Across five real-motion Stick replays, the clustered variants reduce mean image-plane core-landmark error by 23-29% relative to the full-shell cohesive baseline. On 100 paired Peel cases, they improve balanced accuracy from 50% to 72.9-76.3%, with interface rankings varying across tasks. A teleoperated box-sealing sequence demonstrates attachment, dispensing, cutting, and sealing in a continuous workflow.

Reinforcement Learning with Verifiable Rewards (RLVR) performs well on problems with clear rewards, such as mathematics and coding, but whether it also works where the reward is less clear remains open. The reason-over-search recipe applies RLVR to open-domain question answering, where retrieval grounds the answer and a match against the reference supplies the reward. So far it has been demonstrated on large models, and below one billion parameters only with distillation from a larger teacher. We test the recipe on a small model. We train Qwen3.5-0.8B with Group Relative Policy Optimization (GRPO) and an interleaved Wikipedia-search tool on MuSiQue, varying only the reward across three shapes over three seeds each, and we evaluate every checkpoint held-out on a seven-benchmark question-answering suite. The recipe works: the best run reaches 0.352 average exact match against a 0.092 untrained floor, a 3.8-fold gain, with no distillation step in the training loop. The reward shape also matters. The Search-R1-faithful exact-match-only reward is the worst of the three at every seed at the matched training horizon, and it is worst even on exact match, the metric it directly optimises. We conclude that the sparse exact-match reward, RLVR's default in mathematics and code, is the wrong starting point for models of this size. The reason-over-search setting can supply a suitable reward for RLVR on small models, but small-model RLVR needs its own reward-design study rather than a scaled-down copy of a large-model recipe.

This paper considers the existence of a unique global-in-time strong solution to the heat equations in two unbounded domains $\Omega_A$, $\Omega_B$ and the interface $\Gamma (= \partial \Omega_A \cap \partial \Omega_B)$. We introduce and study some function spaces in the two unbounded domains and the interface. We apply our function spaces and maximal $L^p$-regularity for Hilbert space-valued functions to show the existence of a local-in-time strong solution to our heat equations. By using an energy equality of our heat system, we prove the existence of a unique global-in-time strong solution to the system with large initial data when the slope of the interface is gentle and our parameters are limited. The key ideas for showing the existence of our strong solutions are to transform our system into a system of equations in two half spaces $\mathbb{R}^3_+, \mathbb{R}^3_-$ and the whole space $\mathbb{R}^2$, and to make use of nice properties of the heat semigroups and kernels for $\mathbb{R}^3_+$, $\mathbb{R}^3_-$, and $\mathbb{R}^2$. In Appendix (I), we derive our heat equations in the two unbounded domains and the interface from an energetic point of view. In Appendix (II), we study representation formulas for differential operators on unbounded domains and surfaces.

Employing methods based on symmetries for the theoretical description of rare-earth nuclei offers many advantages. Among these, the pseudo-SU(3) shell model has proved to be a very useful method to describe characteristics of these systems and to understand various properties. A theoretical description of the low-lying energy spectrum and electromagnetic properties of isotopes $^{168-178}$Yb is carried out for the first time with this model, comparing theoretical results with the experimental values, where possible. The Hamiltonian includes the $Q \cdot Q$ term which preserves the symmetry, as well as the breaking symmetry of Nilsson and pairing terms. Additionally, three rotor type terms are included that allow us to make a subtle adjustment of the spectrum. The results show that the energy spectrum, the B(E2) transitions, the g-factors and the electric quadrupole moments can be described adequately with the model. Although the model is a powerful tool in the description of low-lying properties of normal parity in heavy deformed nuclei, it finds its strongest limitation in the abnormal parity sector, which has been left out of the description.

This note presents a general form for a proper scoring rule that can be used for possibly right-censored survival data without requiring any knowledge or assumptions about the censoring process, so long as it is independent of survival time.