Papers

In this paper, we show that the height function of the six-vertex model in simply connected domains with piecewise constant boundary conditions converges to the Gaussian Free Field (GFF) with Dirichlet boundary conditions. This implies the conformal invariance of the scaling limit of the model. The argument relies on the full plane GFF convergence combined with Reflexion Positivity and qualitative estimates. The proof works for a wide range of spectral parameters $\Delta$ (among which $\Delta$ close to $0$, and between $-1$ and $-1/2$) making this paper the first instance of a conformal invariance result for a continuum of models. The paper has consequences for other models, including the FK percolation with cluster-weight $q=4$ and the Ashkin-Teller model, which we will pursue in future work.

We prove that the set of real $\mathrm{SL}_n$-opers forms a discrete subset of the moduli space of irreducible flat connections.

Accurate forecasting of pathological outcomes is a central problem in psychology. To do so, psychologists often collect intensive longitudinal data. However, in such studies, the desire to acquire a large number of variables for the sake of accurate prediction is often counteracted by the need to minimize participant burden. Acquiring more variables per occasion can yield better predictions, but having too many acquisitions increase the risk of non-response and attrition. Longitudinal Active Feature Acquisition (LAFA) is a principled approach to resolve this conundrum. Instead of requiring responses to every item at every acquisition occasion, LAFA produces a policy that seeks to optimally select dynamic subsets of items to be acquired at each timepoint while preserving our ability to forecast a specific outcome. However, existing LAFA methods are mostly based on Neural Networks (NN) that are difficult to interpret in practice. In this work, we introduce a tree distillation method for learning an interpretable policy from NN-based LAFA networks. We validated our method through both a simulation and an empirical EMA dataset on forecasting daily alcohol consumption. In both cases, we find that we can meaningfully reduce the number of items acquired at each occasion with minimal loss in accuracy. Networks (NN) that are difficult to interpret in practice. In this work, we introduce a tree distillation method for learning an interpretable policy from NN-based LAFA networks. We validated our method through both a simulation and an empirical EMA dataset on forecasting daily alcohol consumption. In both cases, we find that we can meaningfully reduce the number of items acquired at each occasion with minimal loss in accuracy.

The hypersimplex $\Delta_{k,n}$ is the convex hull of all 0/1-vectors of length $ n $ with coordinate sum $ k $. Early conjectured, and Kim proved, a combinatorial formula for the $ h^* $-polynomial of $\Delta_{k,n}$ in terms of hypersimplicial decorated ordered set partitions. In this paper, we refine the Early–Kim formula to the flag $h$-numbers of the alcove triangulation of $\hyp$. We also give a representation-theoretic interpretation of its flag $f$-numbers in terms of Young permutation modules.

When and where is life most likely to form in the universe? We use the EAGLE cosmological hydrodynamical simulations to investigate the prevalence and properties of life-friendly cosmic environments on galactic scales. Our model for the occurrence of observers depends on main-sequence stars, the production and distribution of metals, and the formation of habitable planets. We also take into account five potentially life-extinguishing processes: core-collapse supernovae, Type Ia supernovae, star-star interactions, gamma ray bursts and quasars. We characterise the amount of time that the universe creates on habitable planets per unit mass of baryons and stars in the universe, as a function of galaxy mass and galactocentric distance. As expected, early universe, newly formed, high star formation rate galaxies are the most dangerous. The present-day Milky Way is typical of habitable galaxies: efficient creation of habitable time, and low probability of cosmic catastrophes.

Which information tells a turbulent flow which way to cascade? We apply Haar-distributed Hermitian phases that retain prescribed same-mode quadratic information, including modal amplitudes, the energy spectrum, and same-mode two-time correlations. For the phase-Haar ensemble, the expectation of any integrable odd flux functional is zero. Finite ensembles strongly suppress mean transfer and forward-event bias in the primary block. An independent block retains sign separation but fails the scale-8 mean criterion. In matched evolution protocols, nonlinear Navier-Stokes dynamics restores the selected signed-flux scalar close to its natural reference, whereas linear evolution and an amplitude-matched frozen control do not. Flux and a local cubic geometry scalar recover together, yet high local correlation can survive erasure of the arrow. Signed transfer thus requires information beyond the retained quadratic record; the tested nonlinear dynamics rebuilds it.

A classical theorem of Figiel asserts that every isometric embedding $\varphi\colon X\to Y$ between real Banach spaces, with $\varphi(0)=0$, admits a linear contractive left inverse on the closed linear span of $\varphi(X)$. We show that this phenomenon breaks down completely once local convexity is lost. More precisely, for every $0<p<1$ and every nonzero real Banach space $X$, we construct a $p$-Banach space $Y$ and an isometric embedding $\varphi\colon X\to Y$ such that $\varphi(0)=0$ and the closed linear span of $\varphi(X)$ is the entire space $Y$, but there is no linear map, bounded or not, on the linear span of $\varphi(X)$ which is a left inverse of $\varphi$. The construction is carried out using the $p$-Banach counterpart of Lipschitz-free spaces. In fact, $Y$ may be chosen isomorphic to the Lipschitz-free $p$-space over $X$. The main ingredient is a quantitative estimate controlling the distance to elementary molecules in Lipschitz-free $p$-spaces, a phenomenon specific to the range $0<p<1$. As a further consequence, we show that a real Banach space has the isometric $p$-lifting property if and only if its dimension is at most one.

Autoresearch agents tackle open-ended problems by repeatedly proposing candidate solutions, evaluating them, and using feedback to guide subsequent experiments. We show that independent runs of the same agent on the same task often plateau at substantially different scores, with gaps that persist even after considerable additional compute. Embedding their candidate artifacts by functional similarity provides further evidence that trajectories remain in localized regions of the solution space, which we call idea basins. To help agents escape these basins, we study a simple periodic intervention, fork-and-flush. Our method forks the agent into parallel trajectories, each inheriting the accumulated workspace but starting with a fresh chat context. After running each trajectory for a fixed horizon, the agent continues from the highest-scoring one. Across 13 long-horizon research and engineering tasks, with individual agent runs lasting up to several days, fork-and-flush outperformed the single-run and best-of-N baselines by a relative improvement of 66.0% and 44.4%, respectively, on the min-max normalized average score under an equal compute budget.

Large language models (LLMs) have become increasingly capable of generating code. However, achieving stronger code-generation performance still often relies on costly model adaptation, i.e., fine-tuning pretrained model parameters. Prior studies have shown correspondence between human code processing and neural models' attention or internal computation. Human-aligned learning approaches use cognitive signals to guide training, but typically adapt a large portion of the model, leaving training costs largely unchanged. Human cognitive signals may indicate not only what the model must learn from, but also where adaptation is most useful. We investigate whether human responses during code reading correspond to code-model behavior and can guide selective adaptation without sacrificing performance. We present CogAdapt, a cognition-informed framework for task-dependent sparse adaptation of code models. CogAdapt first learns transferable program-level and token-level priors from human Electroencephalography (EEG) and attention data, then combines these priors with the frozen model's response to each coding task to determine how much adaptation to allocate and which transformer blocks should receive updates. During fine-tuning, only the selected blocks are updated, while no new human recordings are required for inference. Across Qwen and GLM, we find consistent correspondence between human reading behavior and Mixture-of-Experts (MoE) computation. CogAdapt achieves the best pass@1 across both LiveCodeBench and BigCodeBench, including gains of 10.86 and 6.29 percentage points over matched regular fine-tuning on LiveCodeBench, while reducing gradient-eligible adaptation parameters by 86.21-87.21%. These results suggest that human comprehension signals can provide useful guidance for making code-model adaptation both more selective and more effective.

Mod $p$ Hecke eigenforms for congruence subgroups of $\operatorname{SL}_2(\mathbb{Z})$ which do not lift to characteristic $0$ have received much attention, and were named ethereal modular forms by G. Schaeffer. In this paper, we study liftability for mod $p$ Bianchi modular forms: computations suggest that a lift to characteristic zero may always be possible by increasing the level, as in the case of classical modular forms. We develop efficient algorithms for computing degeneracy maps in cohomology, which allow us to rigorously verify eigenvalue congruences. For small primes and certain fields, we also prove that lifts always exist as a consequence of the recent modularity theorem due to Caraiani-Newton. A Magma implementation, complemented by LMFDB data due to Cremona, shows that in favourable parameter ranges, most mod $p$ Bianchi modular forms lift.

A GUI agent decides which action to take and where to take it; we ask how a small grounding model should receive the action type. Fine-tuning Qwen2-VL-2B with LoRA on Android in the Wild, we compare a flat baseline with five ways of supplying the type under matched data, compute, and decoding: an auxiliary loss, a hard-routed action word, an additive learned embedding, a prepended learned token, and the type written into the prompt. With five seeds, an episode-clustered bootstrap, and seed-level paired tests, the ranking on a mixed stream is clear: the auxiliary loss, the additive embedding, and the prompt word each gain five to seven hit@0.10 points over the baseline, while hard routing and the prepended token are not distinguishable from it. Much of that gain is protection from a preprocessing choice of ours rather than a spatial prior. Our serializer clamps the off-screen touch point AITW records for type events to the origin; that class degrades the baseline's click grounding, and removing it lifts the baseline by nearly seven points, after which no mechanism's hit rate beats it and the intervals exclude a two-point effect, though the auxiliary loss still shortens the average miss; on a stream of taps and swipes none helps. Whether this generalizes beyond one serialization is open. For deployment, the pipeline's margin over the baseline with predicted rather than gold types is not established (+0.016, 95% interval [-0.017, +0.052]), and a wrong type collapses every model conditioned at inference. The prepended token does not help at the shared learning rate, where its rows barely move from initialization; trained ten times faster it reaches the level of the other three, with a margin three seeds do not establish. We also document a silent failure: injecting conditioning through inputs_embeds makes Qwen2-VL fall back to 1-D positions for image tokens, costing nine points.

Large language models (LLMs) have become the backbone of modern AI applications, but pose significant challenges for efficient inference. Their autoregressive generation divides execution into two phases: prefill, dominated by large GEMMs, and decoding, dominated by small GEMVs. Modern serving systems further introduce complexity through continuous batching and prefill-decoding disaggregation, leading to dynamic workloads and phase separation. However, existing accelerators remain poorly aligned with these system-level behaviors, resulting in inefficiencies in LLM serving. In this work, we present DynaCore, a unified architecture for efficient LLM serving via system-architecture co-design. We observe that the compute tile a systolic array executes, its Minimum Efficient Unit (MEU), spans all three GEMM dimensions. DynaCore reshapes the MEU along all three: spatially it trades array width against height asymmetrically, raising weight delivery while leaving the input path untouched, and temporally Split-K maps the reduction onto the array, folding partial sums through the interconnect the array already has. To exploit phase separation, we further propose disaggregated quantization, applying dual-side quantization to prefill and weight-only quantization to decoding, with an inner-product mixed-precision datapath that keeps output width invariant to precision. A runtime scheduling framework then selects an MEU per batch. Evaluation with real-world serving traces shows that DynaCore substantially reduces service-level latency over quantization and reconfigurable accelerators, improving TTFT by 3.50x and 2.97x and TPOT by 36.55x and 8.02x, respectively.

We introduce extendable pattern avoidance for alternating sign rectangles (ASRs), the natural rectangular generalization of alternating sign matrices (ASMs). An ASR extendably avoids a pattern $\pi$ if it is the upper left corner of an ASM avoiding $\pi$. For each of the four length-three patterns in the equivalence class $\{312, 132, 213, 231\}$ we establish a complete system of recurrence relations enumerating extendably $\pi$-avoiding ASRs of size $r \times k$ with a prescribed number $d$ of nonempty rows. For $\pi = 312$ we further conjecture a closed-form expression and prove it on several diagonal slices via bijections involving Schröder ballot numbers, refined Schröder numbers and Delannoy paths that do not cross the main diagonal vertically. For ASRs of size $(r-1) \times (r+1)$ extendably avoiding $213$ we give a bijection to little Schröder paths of length $r$. The remaining patterns of length three, $123$ and $321$, are more elusive, mirroring the situation of ASMs.

We introduce linear occupancy homomorphisms (LOHs), a class of Markov decision process (MDP) transformations that defines the MDP homomorphism over the feasible occupancy measure space of MDPs. In contrast to classic MDP homomorphism frameworks, which are defined through mappings over the state and state-action spaces, LOHs map between occupancy measure spaces and are representable as linear transformation matrices that expose important structural properties of the homomorphism itself. For this class of MDP transformations, we derive finite dimensional linear inequality constraints that certify when a candidate transformation matrix is a valid LOH and derive the corresponding transformed MDP. We further establish a connection between LOHs, soft MDP homomorphisms, and factored matrix robust MDPs. When the linear transformation matrix is invertible, we prove that the original MDP is equivalent to a constrained MDP after the homomorphic transformation, and derive necessary and sufficient conditions under which the LOH preserves the optimal value. We illustrate the benefits of LOHs in two settings: improving robust MDP solutions by transforming nonrectangular parameter uncertainty sets into homomorphic rectangular MDPs, and decomposing a large MDP into smaller independent MDPs.

We introduce a simple coupled cluster approach for multireference and open-shell systems. In the restricted active space coupled cluster framework, the cluster operator only includes excitations from doubly occupied to virtual orbitals, and this ensures the individual operators commute among each other. The ground and excited states are obtained by diagonalisation of the coupled cluster similarity transformed Hamiltonian in a restricted active space. We demonstrate the framework for the RAS-CCSD model, where single and double excitations are included in the cluster operator, and likewise for a complete active space. We consider systems with multireference character and open-shell systems in a spin-adapted manner. The approach captures significantly more dynamical correlation than without the coupled cluster similarity transformation.

We study quantum algorithms for finding a vacuum with a small cosmological constant in the toy model for string Landscape proposed by Arkani-Hamed, Dimopoulos, and Kachru. First, we construct a function-value oracle and use it for Grover search with query complexity $\mathcal{O}(2^{N/2})$, where $N$ is the number of scalar fields. Then, we point out that, by exploiting the linearity of the vacuum energy, the problem can be reduced to a collision problem between two blocks of the bit string. With this structure, we construct two quantum algorithms with query complexity $\mathcal{O}(2^{N/3})$. Compared with the pseudo-polynomial classical algorithm of Denef and Douglas, the quantum algorithms yield a large reduction in computational cost for the physically motivated parameter values.

Artifact removal routinely precedes the classification of electrodermal activity (EDA), on the assumption that a cleaner signal supports a better decision. We tested this assumption in a virtual-reality (VR) balance-disturbance task. A residual gating network was trained on a benchmark with expert-corrected EDA, frozen, and applied to VR recordings, where raw and gated signals were classified by five published time-series methods under identical leave-one-participant-out evaluation. On the benchmark the gate detected artifacts well (median record AUROC 0.94) and reduced error inside artifact regions by 17.8%. In the VR task it did not improve classification. Changes in balanced accuracy ranged from -1.35 to +0.93 percentage points, no classifier improved and two lost accuracy, and all five were equivalent to raw input within +/- 3.32 points. The benefit was lost between waveform and decision. The correction that lowered waveform error also reduced skin conductance response detection in all 43 benchmark records. Processing left 92.8% of predictions unchanged, and the predictions it did change were corrected and corrupted at similar rates. The VR recordings also carried little contamination (an estimated 4.6% of samples), and even perfect localization of deliberately injected artifacts recovered only 3.3 points in the most sensitive classifier. A pooled association between artifact level and accuracy (11.3 points) disappeared within participants (0.1 points), showing how differences between people can make cleaning look useful. Preprocessing should be judged by the decision it supports, against an unprocessed arm.

For retrieving prior cases in Indian legal judgments, the problem involves distinguishing relevant legal facts from mere lexical similarities because a prior case that shares a statute with the query judgment is not necessarily relevant. In this paper, we describe an empirical evaluation of three consecutive designs of retrieval systems for the IL PCR(Indian Legal Prior Case Retrieval) task. We demonstrate that the combination of the rhetorical roles (Fact, Ratio Of The Decision, Precedent, Argument, Statute) is better than either using individual roles or performing full text retrieval, that statute similarity is not discriminative, and that a legal entailment reranker with training data produced by an LLM is much worse in terms of official evaluation than its internal validation score. Two rankers, with excellent internal MRR up to 0.97, performed poorly in terms of official evaluation (MRR as low as 0.14). Thus, we propose a new design with query disjoint splitting and frozen validation fusion. The result is a four stage pipeline with Micro F1 0.2549, MRR 0.6081, and nDCG@10 0.4187.

Reconfigurable Intelligent Surfaces (RIS), also known as programmable metasurfaces, have emerged as a promising technology for next-generation wireless communication systems by enabling programmable control over the propagation environment. Through dynamic manipulation of the phase, amplitude, and polarization of electromagnetic waves, RIS introduces new degrees of freedom for enhancing coverage, spectral efficiency, energy efficiency, and interference management. This article reviews recent advances in RIS-enabled wireless communications, focusing on RIS architectures, emerging design and analysis techniques, and their impact on system-level performance. Key challenges related to scalability, hardware non-idealities, channel modeling, and control overhead are discussed, along with promising solutions and future research directions toward practical RIS deployment in beyond-5G and 6G networks.

We study the extent to which periodic orbits determine a one-dimensional dynamical system. In particular, we show that they determine every topologically mixing interval map. More generally, for a non-mixing interval map $f$ with dense periodic points, the periodic orbits need not determine $f$, but they always do so for $f^2$. Finally, for maps on compact intervals, we obtain a local version of this rigidity: for each basic set $B$ arising in the spectral decomposition of an interval map $f$, there exists an iterate $f^q$ whose restriction to $B$ is determined by the periodic orbits of $f$.

When does a second artificial intelligence (AI) component improve a primary network-fraud decision rather than add operational burden? We study this question through a role-aware Decider-Supervisor (DS) framework with blockchain auditability, evaluating four directional configurations that combine centralised machine learning, a Federated Averaging (FedAvg)-trained federated meta-model, and Base or Quantized Low-Rank Adaptation (QLoRA) large language model variants. The analysis compares primary-only and supervised decisions using non-hard fraud performance, intervention burden, conditional calibration, traffic-mix and Review-capacity sensitivity, dependability tests, and blockchain lifecycle controls. The deterministic hard gate resolves 89.994% of fraudulent requests, leaving the non-hard population as the main AI decision setting. Conditional validation calibration does not produce a consistently transferable supervisory advantage on deployment replay. DS-3 QLoRA is the least disruptive supervised configuration, but it still underperforms its primary FedAvg stage in F1 and total errors. Across 36 reweighted traffic mixtures, supervision reduces total errors only for DS-4 Base in two extreme high-fraud scenarios. Blockchain tests support digest verification, tamper detection, authorisation, single-use review resolution, and post-finalisation integrity, while exposing a pre-finalisation single-write limitation. The results show that the value of AI supervision depends on role assignment, calibration, escalation policy, traffic composition, and lifecycle controls rather than on the presence of a second model alone.

We compare the predictions of the Euler-ensemble solution of freely decaying incompressible turbulence with simulations and experiments: the scaling function of the energy spectrum, the index of the second-order structure function and the decay laws. The predictions have a fixed shape; only their normalization and scale are fitted. In the final $4096^3$ direct numerical simulations of Rodhiya and Sreenivasan, the turbulent attractor is selected by a parabola law for the growth of the bulk length. Along it the collapsed spectrum depends only on the instantaneous Reynolds number, identically for Saffman and Loitsyansky initial spectra; extrapolated to infinite Reynolds number, it agrees with the theory to 1% in the bulk of the enstrophy range, below the dissipation range. The energy balance holds exactly. The energy integral of the theory diverges in the infrared, so energy and enstrophy depend on how a finite flow cuts off the spectrum: with a sharp cutoff $k_0$, the decay laws, energy $\propto t^{-5/4}$ and enstrophy $\propto t^{-9/4}$, are reached only when the cutoff enters the $k^{-7/2}$ tail of the spectrum. Such a cutoff is only an estimate; the reliable test is the bulk of the spectrum. Fitted to the simulations, the cutoff lies at the lower edge of the bulk, where the spectrum still carries the initial data, and the decay exponents depend on the initial infrared spectrum. In the Max Planck wind tunnel at $Re_\lambda$ up to 5779, the longitudinal index extrapolated to infinite Reynolds number matches the odd ensemble with one scale parameter at large separations, where standard crossover forms fail. The freely decaying turbulent blob of Matsuzawa et al. is too small, too inhomogeneous and too weak to display the attractor. The theory is derived in the first two papers of this series.

We study decentralized multi-agent target search where homogeneous agents communicate intermittently at Poisson-distributed times. Standard unconditional belief fusion wastes communication opportunities by synchronizing agents during high-entropy exploration, when diverse independent beliefs provide better coverage than a premature consensus. We introduce entropy-gated belief coordination, in which agents skip fusion while their collective entropy ratio exceeds a threshold~\(\theta\) and merge only during exploitation, consistent with the bifurcation structure of nonlinear opinion dynamics and the submodular structure of the per-step information gain objective. We further derive \(\Istep(\alpha,\beta)\), the expected mutual information per observation step between two agents' binary sensors, as an interpretable, communication-free measure of sensor informativeness that motivates the gating design and guides system-level analysis. Experiments across 103{,}680 trials (nine grid sizes up to \(100{\times}100\), Poisson communication timing, four target movement patterns) show that the Entropy-Gated Trust-Decay Planner (EG-TDP), which adds a detection-probability planner switch in exploitation mode, achieves mean belief quality \(\bar{Q}=0.300\) (mean belief mass at the true target cell, averaged across all trials and steps), a \(58.9\%\) gain over arithmetic mean and a \(37.4\%\) gain over visit-weighted fusion. On representative configurations, EG-TDP also outperforms a joint-Bayesian reference that uses all agents'~observations at every step, despite operating under random intermittent contact only.

Wildfire regimes in Northern California exhibit strong spatio-temporal variability, heavy-tailed fire size distributions, and sensitivity to climatic conditions. We develop a hierarchical statistical framework to model wildfire occurrence, geometry, and burned area in Northern California from 1984-2023. Fire centroids are modeled as a spatio-temporal point process with covariate-driven intensity, extended by a multiplicative gamma-based stochastic shock to better capture the distribution of monthly fire counts. Conditional on fire location, burned area polygons are represented using a parametric ellipse model that separates scale, shape, and orientation, with ellipse parameters estimated from standardized fire perimeters. Total burned area is modeled using a heteroskedastic lognormal regression incorporating climatic and spatial covariates, including vapor pressure deficit anomalies. The framework enables Monte Carlo simulation of wildfire processes and provides a probabilistic tool for assessing wildfire risk and cumulative burned area under observed climate variability.

Reducing nonstationarity in a persistent time series entails deciding how much of its temporal dependence to remove. In finance, fractional differencing is often tuned using the Augmented Dickey–Fuller (ADF) test, limiting the search to a one-parameter family of lag profiles and addressing input preservation only indirectly. We propose StaFIR, a causal finite-impulse-response filter with a learned nonnegative mixture of exponential lag profiles. Its convex learning objective balances empirical stationarity with similarity to the input. We evaluate StaFIR on ARFIMA–GARCH controlled settings and rolling financial series, including a realized-volatility forecasting task. The experiments show that StaFIR adjusts its filtering strength to persistence while limiting unnecessary transformation in stationary regimes. In downstream forecasting, there is no clear accuracy difference from fixed half-order differencing, while StaFIR achieves higher measured similarity to the raw signal. A complementary direct forecasting experiment finds that greater input similarity is associated with smaller forecasting penalties, although the raw representation remains stronger.

Twisted van der Waals (vdW) systems provide a powerful platform for exploring emergent correlated phenomena, including superconductivity, magnetism, and topological phases. The twist angle offers a continuous tuning parameter for modifying the underlying Hamiltonian, however, precise and reproducible control remains challenging. Existing approaches are limited by single-use device architectures, restricted angular precision, or vertical probing geometries. Here we introduce a reconfigurable graphene-based moiré platform in which two independently fabricated layers are mechanically assembled and rotated in situ using a micro-electromechanical system (MEMS). Raman spectroscopy confirms the formation and robustness of the twist-induced moiré potential and enables continuous, deterministic control of the twist angle. The moiré potential folds the electronic band structure and activates the longitudinal optical (LO) phonon mode, allowing us to map its dispersion and directly visualize the moiré momentum. Angle-dependent electronic band hybridization is resolved through the evolution of the double-resonant 2D mode. Near \(0^\circ\), an emergent asymmetry of the \(\Gamma\)-point G-mode phonon reveals phonon band folding and hybridization driven by the moiré superlattice potential and interlayer relaxation. Our platform provides a reproducible Raman reference for twisted bilayer graphene while eliminating device-to-device variability. More broadly, it establishes the twist angle as a deterministically controllable parameter for systematic studies of correlated and topological phenomena in moiré quantum materials.

Adaptive gait biofeedback may support repeated practice in chronic ankle instability, but its evaluation must address model performance and human response. We evaluated a temporal convolutional classifier on protocol-defined, angle-derived GOOD/BAD gait-cycle labels using participant-held-out leave-one-subject-out (LOSO) cross-validation in 20 participants. Seven participants in the adaptive-intervention group completed nine sessions over three weeks, with one motion-capture recording analyzed per session. Models updated after failed sessions were compared offline with their parent models on the same-session validation subset used for candidate selection and the first subsequent adaptive-session recording. Frontal-plane ankle angle was compared between the adaptive group and 10 sequentially enrolled controls at Baseline, Post, and 7-day Retention. Across 20 held-out folds, mean fold-level area under the receiver operating characteristic curve (AUROC) was 0.948, sensitivity for angle-threshold-exceeding BAD cycles was 0.941, and specificity for angle-threshold-meeting GOOD cycles was 0.366. Mean BAD-class F1 was higher in candidate models by 0.187 on the same-session subset and 0.118 on the first subsequent recording. At Post, the adaptive group had a baseline-adjusted frontal-plane ankle angle 5.168 degrees lower than controls (95% confidence interval, 1.766-8.569 degrees lower); the Retention contrast was uncertain. These findings characterize population-model discrimination and offline participant-specific updating during repeated biofeedback use, alongside a nonrandomized Post frontal-plane ankle angle association. They do not establish independent clinical gait classification or a causal benefit of updating.

Riot Games, which runs the League of Legends World Championship (Worlds), also changes the game shortly before each tournament. This concentration of authority raises a governance question: Who scrutinizes how the benefits and burdens of late rule changes are distributed? We examine all ten championships from 2016 to 2025, combining 1,097 games, 215 team-years, and LLM coding of 1,090 champion changes across 40 patches. On average, 33% of a team's prior picks were on champions with net nerfs in the patches it had not played before Worlds, and 8% were on champions with net buffs. Within a year, the median gap between the most and least affected teams was 23 percentage points for nerfed picks and 12 for buffed picks. Nerfs fell mainly on the most-contested champions and buffs on less-contested ones, as Riot's published balancing criteria anticipate. Pools concentrated on the prevailing meta therefore had more negative net exposure, and even the winners of a year's four major regional leagues differed in net exposure about as much as four randomly drawn teams. Higher buff exposure was associated with additional opponent bans on buffed champions, although its size depends on the model. Among quarterfinalists, the most buff-exposed team of each year reached six of ten finals and won four titles. The team with the most negative net exposure reached two finals and won one. These exploratory descriptions identify unequal exposure, not causal gains or losses. The association between net exposure and winning remains uncertain, at +1.3 percentage points per standard deviation with a 95% interval from -0.9 to +3.7. We argue that scrutiny of late rulemaking should not depend on proving that a patch changed who won Worlds. Earlier patch commitments, team-level impact disclosure, independent review, and a formal opportunity to challenge decisions would make publisher authority more accountable.

Accent classifiers are typically trained with a fixed label inventory and cannot accommodate new accent categories as new data becomes available. Moreover, accented speech corpora often exhibit substantial class imbalance and/or domain shift due to differences in recording conditions across corpora. We present AccentCL, a class-incremental learning framework for English accent classification that is robust to class imbalance and cross-corpus domain shift. AccentCL extracts multi-layer representations from a frozen Whisper-Large-v3 encoder, optimized with an imbalance-aware cross-entropy loss to reduce bias toward the majority accent classes and a domain mean alignment loss that minimizes distributional mean shift across training corpora. The label space is then expanded via replay-based continual learning, using the frozen base model for knowledge retention and an old-to-new margin loss to reduce overprediction on newly added classes. On a five-class accent classification task, AccentCL achieves 77.1% balanced accuracy and a 76.9% macro-averaged F1 score. We further evaluate the model's ability to incrementally incorporate two new accent categories: Spanish-accented and Chinese-accented English. When adding Spanish-accented English to the pretrained model, AccentCL attains an F1 of 83.3% on the new class while retaining 77.3% balanced accuracy on the base classes. When subsequently adding Chinese-accented English, it achieves 61.8% F1 on the new class while preserving 77.6% balanced accuracy on the previously learned classes. These results show that AccentCL enables robust regional accent classification while allowing new accent categories to be added without full retraining.

We construct a Banach lattice $d$-algebra with a strong order unit whose product has no positive associative bilinear extension to its Dedekind completion. This gives a negative answer to a question of Wickstead and to the $d$-algebra case of a question of Huijsmans. It also disproves an extension theorem of Chil. The example shows that norm completeness and a strong order unit do not ensure that multiplication extends to the Dedekind completion.