Papers

For a convex mean curvature flow in $\mathbb{R}^{n+1}$, the corresponding arrival time function solves a degenerate elliptic equation that becomes singular at extinction. We prove that it is $C^{24,\alpha}$ for any $0<\alpha<1$ in the plane, with a logarithmic modulus for its twenty-fourth derivatives. We prove that this bound is sharp combining regularity obstruction in our companion paper. We obtain asymptotic expansions of the rescaled flow to any prescribed order, including derivative estimates for the remainder. Combined with the work of Sesum for $n\ge 2$, this also gives the sharp $C^{2,2/n}$ regularity for convex arrival time functions in higher dimensions.

We derive explicit, absolutely convergent series formulas for the quantum, unassisted classical, and entanglement-assisted classical capacities of the qubit amplitude damping channel, eliminating residual optimizations and implicit roots. We also obtain analytical upper and lower bounds on two-way assisted quantum and private communication capacities by evaluating a balanced-squashing bound and optimizing the reverse coherent information. Our results characterize the optimal input populations, establish convergence and truncation properties, and provide analytical benchmarks for quantum and classical communication over dissipative channels.

Let $K/E$ be a finite unramified extension of $p$-adic local fields, and let $H$ be a one-dimensional formal $\mathcal{O}_E$-module of finite height over $\mathcal{O}_K$. We introduce the exponential period map of $H$ and use it to construct a complete regular local ring $R_{H,K}$ with imperfect residue field, an endomorphism $\varphi_E$, and a commuting action of $\Gamma=\mathrm{Gal}(K(H[p^\infty](\overline{K}))/K)$. We prove an equivalence of categories between finitely generated $\mathcal{O}_E$-modules with a continuous $\mathrm{Gal}_K$-action and étale $(\varphi_E,\Gamma)$-modules over $R_{H,K}$. This recovers the classical cyclotomic and Lubin-Tate equivalences in the corresponding cases. In general, $R_{H,K}$ can have Krull dimension greater than one, and $\varphi_E$ need not lift the $q_E$-power Frobenius modulo $\pi_E$. The proof uses $F$-dynamical systems over $\mathcal{O}_E$, which combine contraction modulo $\pi_E$ with Frobenius on the residue field. For every flat $F$-dynamical system, we establish an equivalence of categories between étale $\varphi$-modules and continuous representations of the absolute Galois group of the residue field on finitely generated $\mathcal{O}_E$-modules.

Generative AI systems are increasingly used, but aligning their outputs with user requirements poses a continuing challenge. Here, we aim to ensure that the distribution of an attribute of an AI-generated output aligns with a user-specified target. This is motivated by examples such as fairness, where we want to ensure that a protected attribute (e.g., gender, race, or age categories) follows a desired distribution, and synthetic data generation, where we want the generated data to be representative of a target distribution. We study the practically important black-box access setting, where a user can repeatedly query a generative AI model. The goal is to return $m\ge 1$ outputs whose joint attribute distribution is as close as possible to this target. For both exact and approximate alignment, we develop algorithms that minimize the expected number of queries to the generator, and we further demonstrate their optimality as the number of requested outputs $m \rightarrow \infty$. Experiments on text-to-image generation and geocoded persona generation tasks show that our post-processing algorithms improve statistical attribute alignment, complementing prompting-based interventions.

Learning robot policies for tasks with sparse success signals is challenging when completion depends on coordinated actions, precise contact outcomes, or satisfying several conditions together. Intricate physical interactions with the world further complicate these requirements. Prior work using conventional reward shaping mechanisms provides dense feedback but local progress might not translate into eventual task completion. We present Signal Temporal Logic-guided Stein Variational Policy Gradient (STL-SVPG), a population-based method that uses smooth STL robustness as a trajectory-level training objective. Differentiating this objective through the dynamics assigns credit to policy actions according to their effect on the complete task specification, rather than local progress alone. We evaluate the approach on six quadcopter and manipulator tasks that involves event-triggered responses, strictly ordered behavior, responses within specified deadlines, and physical interaction with the world. STL-SVPG achieves the highest mean success rate among the compared methods on five of six benchmarks. Simulation-trained policies trained in simulation transfer temporal and contact task behavior to the real world.

Coherent uncomputation can be as costly as the computation itself, creating substantial spacetime overheads that can be prohibitive on early fault-tolerant quantum computers. We develop an algebraic framework for measurement-based uncomputation (MBU) through a quantum error-correction picture: measurements of the garbage register induce relative phases analogous to errors causing non-trivial syndromes. Accepting only zero-syndrome outcomes achieves post-selected MBU, removing the need for an uncomputation oracle at the cost of a probabilistic success rate determined by the affine rank of the populated garbage support. This rank can be much smaller than the number of garbage qubits, as illustrated through an example of the HHL algorithm. We then derive a structural condition under which the original uncomputation oracle can be reused to correct the phase for all measurement outcomes. No correction is required for the zero syndrome, while corrections for non-zero syndromes can be further adapted to individual measurement outcomes for simpler circuits, as illustrated by existing modular-arithmetic, QROM, and QRAM MBU constructions. Phase-correction circuits can be further simplified by co-optimising their implementation with the representation of the measurement-induced phases. Selecting which syndrome classes to correct interpolates between post-selected, partially corrected, and deterministic MBU, enabling trade-offs among correction cost, workspace, and repetitions.

We study Fourier-Mukai duality for a class of compactified Prym fibrations including moduli spaces of $\mathrm{SL}$ Higgs bundles over the elliptic locus. This leads to a shadow of the Hausel-Thaddeus conjecture, proof of the Corti-Hanamura motivic decomposition conjecture for these fibrations, and multiplicativity of the perverse filtration. Our approach can be described as a generalization of the Maulik-Shen-Yin package for compactified Jacobian fibrations to the case when the dual abelian fibration is a stack. This forces us to move beyond the case of full supports. Technical tools include a new pullback identity for the stacky Grothendieck-Riemann-Roch tau functor introduced by Toën, results on descent of (Arinkin-)Poincaré sheaves, and a comparison of Poincaré sheaves of the Prym varieties of families of smooth and nodal curves along the lines of Franco-Hanson-Horn-Oliveira.

Large language models (LLMs) implicitly infer attributes of their users and adapt their behavior accordingly, yet these beliefs remain difficult to inspect and causally manipulate. We introduce Belief Self-Distillation (BSD), a unified read-write framework that bridges linear and causal probing by learning a compact user representation that can be both decoded and written back into the model. The frozen LLM acts as its own teacher, distilling beliefs from natural conversations without external annotations. Unlike conventional probing, BSD isolates not only information present in activations, but a state whose causal role can be directly tested. Across multiple model families, BSD faithfully recovers user beliefs and enables substantially stronger interventions than matched hidden-state steering. Crucially, we find that refusal depends not only on the request, but on the model's inferred user intent: changing this belief alters refusal while holding the request fixed. We further uncover a striking cross-model regularity: independently trained LLMs converge on a shared geometry for representing their users. Together, these results reveal implicit user models as readable and causally writable internal states with direct implications for AI safety, shaping how models condition safety decisions on whom they believe they are interacting with.

We prove a prescribed projection theorem for any class of non-linear projections defined on open subsets of the plane which satisfies some mild geometric conditions. This generalizes Davies's classic result on prescribed projections for orthogonal projections, as well as a recent result of authors, Chang, McDonald, and Taylor, on a specific class of non-linear projection maps. We also give several geometric applications, including a proof that certain classes of plane curves can be used to cover arbitrary measurable sets with measure zero error.

The quantum Cramér-Rao bound constrains the precision of parameter estimation through the symmetric logarithmic derivative quantum Fisher information (SLD QFI). It is asymptotically achievable for regular single-parameter estimation models, but generally not in the multiparameter setting, where optimal measurements for different parameters may be incompatible. For multiparameter estimation, allowing collective measurements, the corresponding asymptotically achievable precision limit is the Holevo bound, whose standard formulation is an optimization over auxiliary Hermitian operators. We bridge this apparent difference in formulation by giving an exact characterization of the Holevo bound in terms of a family of QFIs interpolating between the SLD and right logarithmic derivative (RLD) QFIs. Specifically, for any locally identifiable finite-dimensional estimation problem, we prove that the operator-feasible region in the standard variational definition of the Holevo bound coincides with the intersection of the regions defined by the corresponding Cramér-Rao-type matrix constraints for the entire QFI family. This characterization also applies to rank-deficient states and does not require any prior choice of weight matrix. Consequently, the conventional weight-dependent Holevo bound is recovered by minimizing the corresponding weighted cost over the resulting common feasible region.

Low-rank adapters (LoRA) make it cheap to fine-tune a large language model once per task, but combining several independently trained adapters into one model remains difficult: merging the updates in weight space causes interference, retraining on all task data is expensive, and routing between separate adapters gives up the goal of a single combined model. We trace the difficulty to two choices that every composition method makes implicitly. A LoRA update admits infinitely many equivalent factorizations; the choice among them is invisible while an adapter serves alone, but it determines what a learned interaction between adapters can see. A coupling between an old skill and a new one can likewise point in either direction, and the direction decides whether the old skills keep computing what they computed before. We introduce READ (Read-only Expansion of Adapter Deltas), which fixes both choices: each adapter is rewritten into a balanced canonical form that preserves its update exactly, and the coupling grows in one direction only, so a new skill can read the input subspaces of old skills but cannot write into their output subspaces. The only trainable object at each append is the new skill's row of the coupling matrix, and the composed update folds into the base weights with no inference cost, routing, or task-specific rules. We evaluate READ across four benchmark suites and two model families, adding skills one at a time. Across several families, READ improves every suite average over the strongest published baselines built from the same adapters—by more than twenty points on SuperGLUE and more than seven points on the domain suite—and nearly all complete addition sequences end above every direct baseline. Factor coordinates and coupling direction, which a lone adapter never exposes, are what decide whether composed skills survive.

We study the regularity of the arrival time function associated with mean curvature flow, formulated as a degenerate elliptic equation encoding the singular structure of the flow. We identify a systematic mechanism obstructing higher regularity, arising from higher-order asymptotic expansions near spherical singularities. We construct uncountably many low-regularity arrival time functions in all dimensions. In particular, we settle the question of smoothness in the planar case by showing that even for convex curve shortening flow the arrival time need not be $C^{25}$. Our companion paper proves that every such arrival time is $C^{24,\alpha}$ for any $0<\alpha<1$. Hence the obstruction at order $25$ gives the optimal regularity threshold. Our approach introduces new analytic ingredients, including a precise correspondence between elliptic asymptotic expansions and parabolic long-time asymptotics of the associated rescaled mean curvature flow, a complexification of the arrival time equation, and a method for prescribing higher-order asymptotic expansions.

Scalable photonic circuits are essential for realizing practical quantum networks beyond proof-of-principle demonstrations. Although diamond-based integrated photonics has been extensively investigated over the past two decades for quantum networking applications, its integration into scalable photonic platforms remains challenging. Quantum memories based on rare-earth-ion atomic frequency combs (AFCs) offer an attractive alternative; however, most demonstrations to date have relied on bulk free-space crystals, limiting their scalability for practical implementations. In this work, we systematically investigate the potential for hybrid integration of AFC-based quantum memories with a scalable integrated photonic platform. We propose a device architecture combining thin-film lithium tantalate (TFLT) nanophotonic circuits with ytterbium-doped yttrium orthosilicate (Yb:YSO) crystals for long-distance quantum communication. Our analysis shows that the hybrid TFLT-YSO platform offers a promising and scalable pathway toward integrated quantum memories and, ultimately, large-scale quantum networks.

Fix a degree $n$, a nonzero integer constant term, and some further coefficients of a monic integer polynomial, leaving $s$ coefficients to vary in $[-H,H]$. We first prove that, when only the leading and constant coefficients are fixed, the number of polynomials whose Galois group is not $S_n$ is of order $H^{n-2}$ for every $n\ge4$. We then prove a half-dimensional extension: for $n\ge6$ the corresponding exceptional count is of order $H^{s-1}$ whenever $s>n/2+1$, provided the coefficient slice meets the higher-multiplicity loci with a specified dimension bound. This geometric condition holds for every prescribed value if the free coefficients form an initial or final block, and for a nonempty Zariski-open set of prescribed values for arbitrary coefficient positions. It also holds for every value of one additional prescribed interior coefficient. Thus, in degrees seven and eight, any one interior coefficient can be fixed in addition to the leading and constant coefficients. The proof combines a fixed-norm version of Bhargava's primitive-group sieve with sparse Hermite interpolation. A separate imprimitive estimate, using a minimal intermediate field, gives $O(H^{\beta(n)})$ outside rational partial-product hypersurfaces, where $\beta(n)=\ell+n/\ell-2\le n/2$ for composite $n$ with smallest prime divisor $\ell$, and has no logarithmic loss. The fixed-constant quartic and quintic endpoints require separate local arguments: exceptional Fourier directions for $A_4$ quartics and a quadratic Gauss sum for quintics. We isolate further even-degree endpoint results, explain the distinct cubic obstruction, and conclude with conditional improvements under the upper-bound form of Malle's conjecture.

Learning and sensing are among the most promising applications of quantum technology, often with provable quantum advantages. In any realistic experiment, however, noise threatens to erase these advantages as the problem size grows. We introduce oracle distillation, a procedure that distills many queries to a noisy oracle into a single high-fidelity oracle. Here the oracle, an unknown unitary from a known family, models the interface through which a quantum device learns about an unknown system. We construct an explicit protocol that distills any Boolean oracle, both under adversarial noise that corrupts a constant fraction of the input qubits and under i.i.d. depolarizing noise at a constant rate on every qubit. At the heart of the protocol is the weak query, in which the device deliberately queries the oracle only weakly, trading response strength for the ability to correct errors. Our protocol is near-optimal among all protocols that distill the oracle while keeping its errors correctable, revealing a fundamental tension between these two requirements. An important implication of the protocol is a threshold theorem: every Boolean oracle problem whose quantum advantage is polynomial in the domain size, including Grover search, $k$-forrelation, and Simon's problem, retains a quantum advantage whenever the per-qubit depolarizing rate is below a constant threshold. In particular, the quadratic quantum advantage of Grover search, long believed fragile under noise, survives nearly intact at low error rates even when almost every query involves errors on one or more qubits. We further extend the protocol to fractional and continuous-time Boolean oracles. Quantum error correction can thus protect not only prescribed operations but also unknown dynamics. Our results make a large family of quantum advantages in learning robust against noise and open a path toward robust computational sensing.

3D scene graphs provide a structured representation of complex environments by encoding objects, their semantic attributes, and the spatial and functional relationships between them. Current approaches for 3D scene graph generation suffer from several fundamental limitations. They rely on complex multi-stage pipelines with explicit intermediate representations, making systems fragile and prone to error propagation. They assume access to ground-truth object annotations during inference, which deviates from real-world scenarios. They depend on proprietary models, hindering open-source deployment, or incur prohibitively slow inference. We present GraphWrit3R, a simple end-to-end method that takes a 3D point cloud, Gaussian Splats, or a combination of both as input, and directly outputs a complete scene graph as a structured JSON script. The graph lists all objects, their semantic attributes, and the relationships between them, while avoiding all of the above mentioned limitations. The choice of multiple input modalities is purely for versatility, allowing a single set of weights to handle diverse scenarios. Point cloud inputs are encoded via Sonata and Gaussian Splat inputs via Chorus, with both modalities projected onto a shared voxel grid and fused through a novel per-voxel contrastive alignment loss before being decoded by a large language model. As a natural consequence of the LLM, GraphWrit3R also supports open-vocabulary querying. On the 3DSSG benchmark, our method achieves state-of-the-art performance on object class, predicate, and triplet recall, outperforming methods that rely on ground-truth object annotations during inference. We further provide qualitative results and analyze different input modality configurations, contrastive loss formulations, and token fusion strategies.

The Manufacturer Usage Description (MUD) standard allows IoT manufacturers to define expected network behaviors in a MUD file. This file can be translated into enforceable access-control policies, restricting compromised devices to operate solely through manufacturer-defined communication patterns. However, practical adoption of MUD depends on profiles that are accurate, complete, and maintainable. Existing approaches use traffic-based automation but require device deployment and prolonged monitoring, capturing only behavior exercised during observation. Rare, failure-triggered, or configuration-dependent communications may remain absent, producing incomplete policies that disrupt legitimate operation and offer limited insight into the software components responsible for each rule. We present AutoMUD, a source-code-driven tool that generates traceable MUD profiles for IoT devices from their firmware and software source code. AutoMUD combines static and syntactic extraction, retrieval-grounded language-model reasoning, and deterministic validation and compilation to recover the communication behavior characterizing an IoT device and translate eligible endpoints into policy rules. By analyzing code-level evidence, AutoMUD exposes rarely exercised and conditional communication paths, links every generated rule to its source-level provenance, and preserves excluded findings with explicit reasons for review. Our evaluation on a Linux-based repository demonstrates that AutoMUD recovers complete communication behavior, consolidates validated behavior into semantic endpoint groups, and generates structurally valid MUD profiles. Through a controlled semantic fault-injection campaign, we demonstrate that AutoMUD enables analysts to detect, localize, explain, and correct propagated errors, recovering policies semantically identical to their clean counterparts.

Quasi-Monte Carlo methods allow computer experiments to be run with far fewer simulations than crude Monte Carlo. A digital net in base two, such as Sobol', is however only balanced when the number of samples is a power of two, and Latin Hypercube Sampling (LHS) accepts any sample size but only controls the one-dimensional margins. This work proposes a space- filling design defined for any sample size, referred to as LAT for Latinized aperiodic tiling. The unit hypercube is cut recursively across its longest edge following the golden section into N cells of equal volume. One point is then placed in each cell, and the margins are made Latin while every point stays inside its own cell. The construction only uses integer splits and costs O(dNlog N). The recursion is shown to follow the Fibonacci word and its aperiodicity is analysed. LAT is assessed with four L2-discrepancies and with the integration error on analytical functions and engineering emulators, and compared to Monte Carlo, LHS, Halton, Sobol' and a rank-1 lattice. LAT is better than Monte Carlo and LHS as soon as the integrand has interactions. Sobol' remains more accurate at the powers of two, but its error is one to two orders of magnitude larger at other sample sizes. The accuracy of LAT does not depend on the sample size. Finally, the cells form a partition of the hypercube for any N. This allows one to refine the design locally, to search for an optimum by splitting cells and to sample non-rectangular regions.

Scott and Sokal asked whether every homogeneous polynomial with the half-plane property has a completely monotone negative power. We answer this question affirmatively and prove the Riesz-positivity conjecture of Michałek, Sturmfels, Uhler and Zwiernik, restated by Kozhasov, Michałek and Sturmfels: in $n$ variables, every exponent $\alpha\ge4096n^2$ is admissible, independently of the degree and coefficients. For complete hyperbolic polynomials the Riesz density is strictly log-concave, with relative Gaussian error at most $512n^2/\alpha$ and explicit curvature bounds. We characterize admissible exponents by a common spectral Dirichlet law, prove $n\le m+\alpha m(m-1)$ with its equality case, and obtain the sharp degree-dependent gap $0<\alpha<1/(2(m-1))$ whenever the degree-$m$ polynomial has a nonlinear irreducible factor. A nonnegative fourth-order defect of $-\log p$ vanishes at one point precisely for products of positive integer powers of Euclidean Jordan determinants. We classify the corresponding logarithmic Monge-Ampère equation and answer the question of Etingof, Kazhdan and Polishchuk about polynomial multiplicative Legendre transforms within irreducible complete hyperbolic polynomials; the general question has counterexamples, the Clifford quartics of Kogiso and Sato. The classification extends to reducible polynomials under a boundary-visibility hypothesis, and asymptotic common-power formulas for the Riesz densities force exact Jordan formulas.

Stacked intelligent metasurfaces process the transmitted field layer by layer, and fluid antennas make the position of every radiator a design variable. Combined, they pack radiators at sub-wavelength spacings within and across layers, where mutual coupling governs the physics that current models omit. This paper develops a coupling-consistent model of a fluid transmit layer illuminating a stack of passive fluid beyond-diagonal layers. The multiport impedance matrix of any port constellation is shown to be the impedance kernel sampled at the three-dimensional separations, in one closed spherical-Hankel form whose in-plane restriction is intra-layer coupling and whose axial restriction replaces the scalar Rayleigh–Sommerfeld propagator. Only the transmitter is driven: the layer currents are induced, and the familiar cascade is the single-pass limit of one matrix inversion. In the wavenumber domain the light circle still separates radiation from reaction, now with a plane-wave propagator attached, every Fourier mode sees a transmission line loaded by the layers, and an efficiency identity shows that what the stack costs in efficiency is set by its total induced-current norm, not by its layer count. Because the load is never assumed layer-diagonal, interconnections may join atoms on different sheets, and vertical networks repeated at every site are spectrally local. Alternating optimization designs precoders, positions, and loads with closed-form gradients. Numerically, fluid ports on a $\lambda/8$ grid perform within a few per cent of continuously movable ones, while a design based on the conventional cascade model can do worse than open-circuiting the stack.

Existing multi-agent benchmarks primarily test in competitive settings, short-horizon interactions under 20 steps, or simply aggregate individual performance, failing to isolate and highlight genuine collaboration capabilities of LLM-based agents. We introduce AgentWorld, a benchmark of 100 human-annotated tasks (with 100 augmented variants) for evaluating long-horizon, multi-agent collaboration. Tasks span 50+ interaction rounds across a rich MMORPG sandbox and require 3-20 agents with asymmetric roles and abilities to coordinate through communication, joint planning, and resource sharing under a blackbox setting where each agent acts independently without access to others' internal states. To quantify collaboration effectiveness in addition to conventional binary task success, we propose Causal Collaboration Effectiveness (CCE), a graph-based metric that traces causal dependencies between agent actions and measures what fraction of a team's effort actually contributed to the outcome. Experiments with Gemini 3 Flash, Claude Haiku 4.5, GPT-5 Mini, and DeepSeek R1-70B show that even the best model achieves only 52.0% task success, with systematic failure modes including communication breakdowns, role confusion, and inability to maintain shared plans across rounds. AgentWorld is fully open-source.

Direct feedback alignment (DFA) trains hidden layers through fixed random projections of output error. With tanh hidden units and independent sigmoid outputs, plain stochastic gradient descent can stall near the loss of a constant predictor of class frequencies. We trace this stall to the error's common mode, the component shared across inputs. An exact mean-covariance decomposition separates a rank-one update formed by the mean teaching signal and mean presynaptic activity. Its leading component drives tanh units toward saturation. At initialization, random feedback provides no systematic correction of the shared error on average; readout learning limits its duration. A reduced model initialized from the network, without fitted parameters, predicts the concentration of activation sensitivity across 48 settings. On MNIST, class decodability largely survives collapse, but readout learning remains slow at a fixed learning rate. Adam learns faster despite deeper collapse. Calibrating the baseline readout to the class prior suppresses collapse and speeds learning; weaker feedback trades less collapse for slower learning. Replacing errors by their signs sustains collapse; subtracting the signal's batch mean prevents sustained collapse and improves learning in the tested setting. Related effects occur in deeper and convolutional networks and on CIFAR-10, with severity and cost depending on the readout, optimizer and input statistics.

Many voice interaction applications require exact control over both the content and delivery of responses, typically using pre-recorded lines. Recent full-duplex models respond with low latency but cannot guarantee exact content or reproduce a specific recorded performance, while cascaded systems can be constrained to predefined responses at the cost of additional latency. We propose RePlay, a spoken dialogue system adapted from PersonaPlex that handles multi-turn conversations by retrieving and playing pre-recorded lines. Using probing, we identify the layer and frame at which the upcoming response becomes recoverable, and use this hidden state as the retrieval query. RePlay retains only the layers up to that point and replaces text and speech generation with lightweight turn-taking and retrieval heads. In simulated multi-turn interviews, RePlay reaches a median latency of 383 ms, 3 to 7 times lower than ASR-LLM cascades of comparable dialogue quality, at the cost of lower exact-line accuracy. In a user study, participants preferred RePlay in 63% of ratings versus 12% for a fast cascade with a small LLM (p = 0.008), and showed a non-significant preference (46% vs. 21%) over a slower cascade with a stronger LLM.

We investigate whether natural-language documentation helps coding agents resolve software issues, and we build the tools to construct and evaluate it. We introduce a roundtrip benchmark that scores code descriptions by whether code regenerated from them passes the original tests, and show that completeness, not length, drives a description's fidelity. Using the benchmark as an optimization signal, we discover a description-writing prompt that reaches full fidelity and generalizes to unseen files. We then test the hypothesis that motivated the work: that better documentation helps an agent resolve real repository issues. Across two model families and ten repositories, and against a positive control confirming that our evaluation can detect a genuine improvement, we find that it does not. When the source is present, neither static compact documentation nor retrieved context beats the issue alone. We report this negative result together with the benchmark and the optimizer, and we characterize the boundary at which documentation helps.

Decision Transformer performance degrades on long rollouts because the conditioning context drifts out of the training distribution. We show that this drift is visible through the model's own next state prediction error, which rises during rollout and stays elevated, giving a direct signal of when context has become unreliable. We introduce Trust Guided Decision Transformer (TGDT), which selects context before applying value guidance. At each step, TGDT evaluates several recent context suffixes using rolling next state prediction error, calibrated against held out offline data via split conformal prediction. It keeps only suffixes whose error stays within the calibrated threshold, then uses a frozen critic to choose the highest value action among the trusted suffixes. This reverses the order used by value only elastic selection, where the critic may choose an action generated from a context the model itself has flagged as unreliable. Experiments on D4RL navigation and locomotion tasks show that state prediction, critic guidance, and hard context reset each solve only part of the problem. TGDT reduces persistent high error runs and improves return over vanilla Decision Transformer, reset based context control, and value only context selection.

The GlueX-III experiment at Jefferson Lab, planned to run in 2027-2029, will enhance the laboratory's capability to explore charmonium production near threshold and related aspects of QCD in the non-perturbative regime. A central upgrade for GlueX-III is a large-scale triple-GEM Transition Radiation Detector (TRD) optimized for electron identification and pion suppression in the hadron-rich environment of fixed-target photoproduction. This document describes the motivation for and efforts related to such an upgrade, including the design, construction, and performance of a 720x528mm$^{2}$ triple-GEM-TRD prototype that was tested in the existing GlueX-II experimental acceptance during the 2025 run. Results validate the prototype's integration, timing performance, and electron identification capability. Its projected impact in the GlueX-III setting is discussed, with background reduction in a $J/\psi$ candidate sample demonstrated. The development and use of a modern TRD technology in a high-background environment at Jefferson Lab may inform detector design choices as a future upgrade path for the EIC.

The electrical properties of biological tissues depend on their composition and microstructure and determine their response to applied electric fields. In bone tissue, these properties are closely related to its composition, porosity, and microstructural organization. However, simplified models that link bone microstructure (trabecular and cortical) to its effective electrical properties while accounting for the electrical anisotropy of cortical bone remain scarce. In this work, a multiscale approach was developed, combining finite element simulations with Bruggeman-based homogenization models. Trabecular bone was modeled using microCT derived geometries, and its effective conductivity was analyzed as a function of BV/TV and free water content. Cortical bone was represented by a simplified three-dimensional network of Haversian canals (axial = z) and Volkmann canals (transverse), incorporating their directional organization through an anisotropic Bruggeman formulation. The models captured the conductivity range reported experimentally for trabecular bone (approximately 25-200 mS/m) and reproduced the anisotropic behavior observed in the cortical FEM simulations, with higher conductivity in the axial direction. In the generated cortical geometries, 65.5% of the total porosity was associated with axial Haversian canals. At the macroscale, the tibia model with lower trabecular and cortical BV/TV and reduced cortical thickness showed an approximately 38-39% reduction in impedance relative to the reference model. These results indicate that microstructural variations in bone tissue are reflected in its effective electrical properties and in the macroscopic impedance of the model, providing a physical and computational basis for future investigations into the sensitivity of electrical measurements to changes in bone microstructure.

Imaging an inhomogeneous medium with waves rests on the response of a boundary measurement to a change of the medium inside, formally the sensitivity kernel of the inverse problem. Here we show that the kernels of radar, seismology, medical ultrasound, and diffuse optics all reduce to just two classes. Every kernel is the product of a forward and an adjoint field, and a real measurement retains one quadrature of that product. These quadratures are the two classes, selected either by a component of the material parameter or by the misfit, the structure that persists for the coherent-wave kernel in both the ballistic and the diffusive regime. We place these areas on one diagram of scattering strength and transport depth, exposing a shared computational limit set by wavefield storage, and propose a broadband on-shell compression that can relax that limit.

Given power series $f_1,\dots,f_r\in z^2K[[z]]$ over a field $K$, we show that the semigroup $\langle f_1,\dots,f_r\rangle$ generated by the $f$'s under composition is free of rank $r$ whenever the multiplicative semigroup $\langle\mathrm{lc}(f_1),\dots,\mathrm{lc}(f_r)\rangle$ in $K^\times$ is free commutative of rank $r$; here $\mathrm{lc}(f)$ denotes the first nonzero coefficient of $f$. To do this, we associate an affine linear transformation to every $F\in\langle f_1,\dots,f_r\rangle$ and then apply a ping-pong lemma. In particular, combining this with work of Pappalardi, Sha, Shparlinski, and Stewart, it follows that most semigroups of polynomials over a number field $K$ are free, and we make this statement precise through a counting argument.

Geometrically frustrated magnetism conventionally arises from pre-existing magnetic moments on lattices whose geometry prevents their interactions from being simultaneously satisfied, giving rise to highly degenerate states and rich collective behavior. Creating such frustration in an intrinsically non-magnetic material presents a fundamentally different challenge, requiring both the magnetism and the competing interactions to emerge from correlated electrons. Here we show that this can be realized in graphene through lithographically programmable strain engineering. Patterning strain and the associated pseudo-magnetic field (PMF) into superlattices creates a correlated electronic system with flat bands and strong interactions. Transport measurements reveal interaction-driven insulating behavior, anisotropic magnetic hysteresis, and slow relaxation dynamics reminiscent of spin freezing, qualitatively captured by Monte Carlo simulations of competing magnetic moments on the PMF-defined ruby superlattice. Cryogenic magnetic force microscopy further reveals magnetic textures associated with the PMF landscape. These observations demonstrate frustrated magnetism emerging from correlated electrons in otherwise non-magnetic graphene. Our results establish lithographic strain engineering as a general and scalable route to flat bands and correlated states in van der Waals materials, providing a versatile platform for programmable quantum matter.