Papers

Pressure-sensing smart textiles convert body-surface contact into a dense, image-like signal closely tied to posture and movement, making them a promising low-cost route to wearable posture screening. Realizing that promise, however, requires more than classification accuracy: a deployable system must generalize to wearers unseen during training, expose the physical evidence behind its decisions, and tolerate the small donning offsets that occur whenever a garment is removed and re-worn. This paper addresses these three requirements jointly using a knitted piezoresistive sleeve worn on the forearm as a testbed. We regroup fine-grained everyday activities into three coarser screening categories (neutral, potentially undesirable, and functional or transitional), engineer 29 interpretable pressure-distribution features spanning global intensity, spatial center of pressure, quadrant asymmetry, distribution complexity, and short-horizon temporal change, and evaluate under a strict subject-wise split. A tuned XGBoost classifier reaches 0.818 accuracy, 0.788 balanced accuracy, and 0.801 macro F1 on unseen test subjects, with tight frame-level bootstrap 95% intervals of about plus-minus 0.01 and a subject-to-subject standard deviation near 0.06 under leave-one-subject-out cross-validation. A simple 2D-CNN baseline trained on raw frames achieves broadly similar performance, showing that hand-engineered features are not left behind by a learned spatial representation on this task. SHAP-based explanation, a feature-group ablation, per-activity error analysis inside the pooled undesirable class, class-mapping sensitivity, and a simulated donning-rotation stress test together locate what the model relies on, where it degrades, and why, directly targeting the generalization, interpretability, and robustness gaps that determine whether such a system is deployable.

Can a biological wiring diagram serve as a useful computational substrate beyond the behaviors for which it evolved? We use the publicly released MaleCNS v1.0 connectome, reconstructed from a single adult male Drosophila specimen, as the fixed recurrent topology of an artificial network. We train separate models for bounded addition and for a controlled grounded relational language task built from a fixed 100-word lexicon. In both models, one scalar is learned per anatomical edge. The anatomical graph reaches 92.77% mean accuracy on held-out addition, compared with 67.93% for directed degree-preserving rewires. On the strict paired language endpoint, which matches original and order-reversed scenes to their corresponding descriptions, it reaches 61.59% across four fixed interfaces, compared with 44.17% for matched rewires. At the canonical interface, it ranks first in a fixed 21-graph comparison. On the matched 48-group intervention subset, shuffling task-defined sensory features reduces its score from 60.94% to 19.27%. Together, these results show that higher-order MaleCNS wiring provides a reusable inductive bias for bounded addition and grounded relational language.

Self-supervised learning (SSL) at scale produces powerful visual representations. However, most scalable SSL methods rely on ad hoc combinations of multiple objectives and stabilization mechanisms. Taking a step back, we ask if we can design a high-performing, yet principled SSL algorithm. Starting from the multi-view assumption, stipulating that task-relevant content is captured by the information common to different views, we construct an information-theoretic objective decomposing into interpretable terms. This derivation yields JEM, a student-teacher method that learns by aligning corresponding patch representations across views, explicitly regularized by information and structure preservation losses. JEM trains stably from 300M to 7B parameters, and, to our knowledge, is the first latent-space patch-level method demonstrated at 7B scale. Across all scales, JEM reaches strong performance on both global and dense probing tasks, on segmentation benchmarks consistently surpassing the DINOv2 algorithm, an influential foundation for today's strongest visual SSL methods. Notably, at 7B parameters, it exceeds the performance of DINOv3 on panoptic segmentation, despite being trained on $12\times$ less data without refinement stages. These results demonstrate that we can indeed design an SSL algorithm that learns strong representations, is principled and stable.

In the framework of edge-weighted graphs, watersheds have proven to be linked to well-known optimization problems, as Minimum Spanning Tree, which allowed the design of efficient algorithms for computing (hierarchical) watershed segmentations. In the present article, after reviewing the literature related to watershed segmentation, we present a detailed end-to-end pipeline of algorithms to compute (hierarchical) watershed segmentations, starting from the computation of graph-based image representations, up to the computation of connected components of the final (hierarchical) segmentation. We consider the several variations of watersheds, including their supervised and unsupervised versions, and the various ways of computing seeds, to name a few. For the first time, we bring together all these watershed notions and algorithms in a compact and understandable way. We aim at providing a reference for those interested in employing and reimplementing the watershed segmentation framework for their task at hand.

A recent experiment by Roy et al. (Nat. Commun. 17, 2853 (2026)) demonstrated a robust half-integer thermal conductance plateau, \kappa_0 T/2, at a bipolar (\nu,\nu')=(2,-1) junction in bilayer graphene, produced not by non-Abelian topology but by full equilibration of co-propagating electron and hole edge modes. We prove a theorem that fixes when the two origins can be told apart: under full thermal equilibration, the two-terminal thermal conductance of a network of chiral edge segments joined at ideal floating contacts is a rational function of the net chiral central charges of the segments alone, quantities pinned by the gravitational anomaly and invariant under arbitrary local boundary kinetics. The corollary is an impossibility statement: whenever two realizations present the same anomaly data to the same network, no thermal-conductance measurement can distinguish them. That the equilibrated (2,-1) value equals the central charge of a chiral Majorana mode is an arithmetic fact about one filling combination, but wherever such a coincidence occurs it is beyond the reach of thermometry, and the separation must come from the charge sector, which is not anomaly-pinned at a superconducting boundary. We develop the topological insulator-superconductor interface as the application: a vortex carries fractional charge e/4 from the \theta = \pi magnetoelectric coupling, the boundary hosts a chiral Majorana mode of central charge 1/2, and a laterally adjacent integer quantum Hall (IQH) region supplies the kinetic realization. The Lorenz ratio (anomalous for the isolated Majorana boundary, L_0 / (1 + 4|\nu_{IQH}|) in the composite device) and the excess shot noise (growing with B from e/4 vortex tunneling versus locked to IQH plateaus) together resolve the mechanism, provided the quantum Hall edge does not abut the superconductor.

A cryptographic secret is issued for a purpose but grants a capability, and the capability is usually larger. Deployed systems state the purpose in policy and enforce only the capability. We make the purpose a property of the secret. A mechanism sees operations, not reasons, so a scheme enforces an admissible set $A(P)$ of operations that stands in for a declared intended use $I$; whether $I$ captures the human purpose is a modeling obligation that marks where policy takes over. Against the same $I$ we define three regimes: under confinement an operation outside the intended use is infeasible, under mediation a trusted component refuses it, and under accountability use beyond a stated bound is possible but attributed to the holder. The confinement games, for unpredictability and indistinguishability, coincide with the key-query forms of functional-signature unforgeability and constrained-PRF pseudorandomness and correspond to simulation-secure functional encryption within its feasibility boundary; stated against $I$, they also register a predicate that permits too much. A payment token uses all three regimes on one secret: it pays one capped charge at one merchant, can be narrowed but not widened, is checked by the merchant, and identifies the withdrawing account if spent twice. Attenuation unforgeability reduces to unforgeable signatures and a collision-resistant hash without random oracles; traceability and non-frameability hold under discrete log and unforgeable signatures in the random-oracle model. We present this framework as a common specification against which existing primitives are stated and compared.

We consider a thermodynamically consistent diffuse-interface model for binary mixtures of incompressible viscous Newtonian fluids with a soluble surfactant. This hydrodynamic system generalizes the Abels-Garcke-Grün model for two-phase flows with unmatched densities by incorporating an additional Cahn-Hilliard equation for the surfactant concentration. We study the strong well-posedness of the initial-boundary value problem with physically relevant singular potentials, subject to a no-slip boundary condition for the fluid velocity and homogeneous Neumann boundary conditions for the phase-field variables and the corresponding chemical potentials. First, we establish the existence of local-in-time strong solutions in three dimensions and global-in-time strong solutions in two dimensions. In the two-dimensional case, we further show that, under natural growth assumptions on the singular potentials, strong solutions remain strictly separated from the pure phases, thereby guaranteeing uniqueness. In the three-dimensional case, we establish local-in-time uniqueness of strong solutions, provided that the initial data are strictly separated from the pure phases. Our results extend previous work on strong solutions to the Abels-Garcke-Grün model from the special case of constant mobility to the more general scenario with concentration-dependent mobilities and interactions with a surfactant.

Motivated by relevant epistemic logic, we extend Dunn's simple Kripke-style binary relational semantics for the semi-relevant logic RM to fit a modal extension of RM. It is shown that the modal axioms and rules that need to be added to RM to obtain a sound and complete axiomatisation of its modal extension give an axiomatisation of modal extensions of all logics in the family of generalised Nelson logics, also studied by Dunn.

Composition gravity ($g$) modes have been proposed as a probe of dark matter in neutron stars, on the basis of one-fluid models in which the dark matter is in chemical equilibrium with the neutrons. We computed in full general relativity the $g$- and $f$-modes of stars in which fermionic dark matter couples to the nucleons only through gravity, and inferred the dark mass fraction from NICER and GW170817 data with a prior that comprises $63$ nucleonic equations of state (EOSs) from Skyrme and relativistic mean-field functionals, among them the models of Dutra et al. and of the compilation of Sun, Bhattiprolu and Lattimer. The data do not prefer dark matter and bound its mass fraction at $0.12 - 0.26$ ($95\%$) for particle masses of $0.5$–$2$~GeV. Coupled only through gravity, the dark matter reaches the buoyancy that restores a $g$-mode only through the gravitational field: a dark core holding $10\%$ of the mass raises the fundamental $g$-mode by $10-15\%$ at fixed EOS, several times less than in the one-fluid picture. The larger effect is indirect: a star with a dark core needs a stiffer nucleonic EOS, and since the $g$-mode is set by the density dependence of the symmetry energy, its frequency reflects the EOS that the star requires rather than the dark matter it contains; at fixed radius and symmetry energy a core holding $10\%$ of the mass is equivalent to a change of the slope $L$ of $9-12$~MeV. The $f$-mode, which follows the mean density, behaves differently: a dark core breaks the relation between the $f$-mode and the tidal deformability by about one percent, far outside the posterior spread of nucleonic stars.

We present a lattice determination of the Bjorken sum rule via a Feynman-Hellmann calculation of the polarised forward Compton amplitude. We evaluate the lowest moment of the nucleon's polarised structure function, $g_1$, which we calculate over the range $0.5\lesssim Q^2 \lesssim 8$ GeV$^2$, covering both non-perturbative and perturbative regions. We compare our calculated moments with the Bjorken sum rule, and discuss implications for the calculation of higher-twist effects, as well as evaluations of $\alpha_s(Q^2)$ from hadronic quantities to complement phenomenological and other lattice methods.

In this paper, we investigate the stability threshold of the two-dimensional Boussinesq system around the Couette flow in an infinite channel $\mathbb{R}\times[-1,1]$ under Navier-slip boundary condition. To address nonlinear echo chains induced by temperature-vorticity coupling, we construct a two-level frequency-dependent temporal decomposition, with the two levels matched to the infinite and finite superposition principles for the equation, respectively. By fully exploiting the enhanced dissipation effect at each decomposition level, we prove that if the initial perturbation $(\omega^{in}, \theta^{in})$ around the Couette flow satisfies $\|\omega^{in}\|_{H^4_{x,y}\cap L^1_xH^4_y}\leq c\nu^{\frac{1}{3}}$, and $\|\theta^{in}\|_{H^5_{x,y}\cap L^1_xH^5_y}\leq c\nu^{\frac{2}{3}+}$, the Boussinesq system admits a globally asymptotically stable solution. It should be emphasized that the method in this paper provides an effective approach for the hydrodynamic equations with coupling effects.

The joint expectation values of quantum observables measured by two parties typically depend on the causal structure of the measurement protocol. The two causal structures we investigate here are the direct-cause scenario, in which a single quantum state is measured twice in series with a general quantum channel between measurements, and the common-cause scenario, in which a shared bipartite quantum state is measured in parallel. Through a variety of examples of qubit channels with tunable parameters, we identify the full set of input states where the direct-cause joint expectation values of Pauli observables coincide with those obtained from a common cause, a situation that we call causal confusion. More generally, for arbitrary finite-dimensional quantum systems and light-touch observables, we prove that a channel exhibits causal confusion for some input state if and only if it is a positive-partial-transpose (PPT) channel, thereby endowing PPT channels with a new operational meaning in terms of causal confusion. Using this result, we characterize the set of qubit channels for which there exists an input state leading to causal confusion as the set of entanglement-breaking channels.

Style transfer lacks a reliable evaluation standard: ground truth is inherently ill-defined, and existing automatic metrics often fail to reflect human preference. This paper introduces ASTRA (Assessment of Style TRansfer Algorithms), an approach for automatic evaluation of style transfer algorithms; it contains two components, ASTRA-Data and ASTRA-Score. ASTRA-Data consists of a benchmark image set of content and style references, a collection of style transfer results generated on the benchmark set, and user study data capturing human judgements through a two-stage pairwise comparison protocol. From these annotations, we derive ranking-based ground truth for content preservation, style fidelity, and overall preference. Based on ASTRA-Data, we construct ASTRA-Score, a learnt evaluator that predicts preference-aligned scores from content-style-stylization image triplets, enabling automatic and scalable evaluation of new models applied to the benchmark set. Experimental results demonstrate that ASTRA-Score achieves substantially higher correlation with human rankings compared to prior metrics. Overall, ASTRA establishes a robust mechanism for standardised evaluation of style transfer methods.

We study the randomness required to share possibly correlated secret bits among parties connected by a graph. A dealer places shares on the edges so that each party can recover its own secret from its incident shares and learn nothing about the others beyond what its own secret reveals. Anilkumar et al. completely determined the minimum randomness required for three binary secrets. We extend this study to four secrets and obtain results for arbitrary numbers of secrets on general graphs. For four parties on a complete graph, we determine the minimum number of random states for every set of permitted secret combinations: the possible values are one, two, three and four. We also characterize when one random bit suffices on an arbitrary graph.

We investigate how cotunneling affects passive-state ordering in a Photosystem II reaction center modelled as a nonequilibrium molecular junction. We use a full pigment excitation manifold, with excitonic and charge-transfer rates computed within a Nakajima-Zwanzig formalism using realistic spectral densities. Cotunneling is introduced through a microscopically constructed doubly reduced acceptor state obtained from relevant quinone-side two-electron configurations, while photoexcitation is allowed into the full excitonic manifold. Passive-state permutations are quantified through ergotropy and energetic capacitance. We find that thermodynamic smoothness in ergotropy and energetic capacitance can conceal microscopic state rearrangements. Cotunneling redistributes the extractable nonequilibrium energy among the quinone acceptor, the donor-pheophytin radical pair, and excitonic states with strong contributions from pigments on the inactive branch. At high Coulomb interaction, cotunneling produces no passive-state reordering. Piecewise-linear relations among ergotropy, energetic capacitance, and mean energy further reveal the population reorderings generated by cotunneling.

Adversarial attacks on bandits aim to mislead a learner toward a target arm while keeping the attack cost small. Existing attacks typically achieve this by suppressing non-target arms. In practice, however, manipulation such as fake reviews often directly promotes the target item. We study this gap through bounded offline attacks on warm-start bandits, where an attacker can inject only valid action-reward pairs into the warm-start history before deployment. We show that target promotion is not merely a heuristic: when the target arm lies near the lower reward boundary, any order-optimal-cost attack against UCB that makes it selected in nearly all online rounds must allocate a nonvanishing fraction of its cost to the target arm. We then design an attack that achieves the optimal sublinear cost and characterize its allocation between target promotion and non-target suppression. We further extend the attack to Thompson Sampling, $\epsilon$-greedy, and a broader class of bandit algorithms. Experiments on real-world and synthetic data validate the effectiveness of our attacks.

Analog ReRAM-based process-in-memory (PIM) accelerators provide high parallelism and energy efficiency for deep convolutional neural networks (CNNs) inference. However, their susceptibility to permanent faults, such as stuck-at high (SaH) and stuck-at low (SaL) resistance states, poses a major challenge by permanently corrupting the CNN weights mapped to conductance values of ReRAM cells and degrading inference accuracy, which leads to system unreliability in safety-critical applications. In this paper, we propose a fault-tolerant scheme for analog ReRAM-based PIM accelerators to tackle stuck-at faults (SAFs) with minimal redundancy overhead to recover classification accuracy degradation. The proposed scheme contains a redundancy-based hardware solution alongside fault-aware mapping method for ensuring reliable analog computation in ReRAM crossbar. We analyze the impact of varying number of redundant rows and columns on accuracy and design metrics. Subsequently, a multi-objective optimization (MOO) problem is formulated and solved to efficiently determine the number of redundant rows and columns, considering trade-offs among various design metrics. Furthermore, a fault-aware weight mapping is proposed for dual-crossbar structures to further compensate for the accuracy degradation caused by SAFs. Simulation results show that, for the SimpleNet model using the MNIST dataset, the inference accuracy is recovered by approximately 22.39%, on average, across four configurations of optimal solutions, each offering a trade-off between reliability and area, energy consumption, and latency overheads. The mean-time-tofailure (MTTF) improves by about 61x on average compared to the baseline. These selected configurations also reduce energy and area overheads by 32%, on average, in comparison to row-only and column-only configurations.

This paper addresses the challenge of encoding biochemical GC-content constraints in composite DNA-based data storage. Previous deterministic models impose high rate penalties by avoiding any possibility for a strand to fall outside the allowed range. To account for the stochastic nature of composite DNA, we introduce an $\epsilon$-probabilistic constraint framework, and derive capacity bounds for global constraints using composition types and for local sliding-window constraints via finite-state Markov chains. Furthermore, we propose a capacity-achieving multi-type enumerative encoder.

The ionization conjecture for the Thomas-Fermi-Dirac-von Weizsäcker model asks how many electrons a given nuclear configuration can bind. So far, only the single-center case has been settled by Frank, Nam, and Van Den Bosch, while the original molecular case has still remained open. We advance this conjecture in the two-center case. We prove that for two distinct nuclei of total charge $Z$, the number $N$ of bound electrons satisfies $N\le Z+C Z^{153/154}(1+\log Z)^{3/8}$, with constants independent of the nuclear positions and the nuclear charges. The proof relies on a comparison with the neutral Thomas-Fermi density and on localization and exterior $L^1$-estimates coupled through the screened potential. Our results could be extended to molecules with any fixed number $K$ of nuclei.

The proposed approach relies on high-frequency multivariate time series collected at the Seine aval (SIAAP 1 ) treatment plant, including pH, temperature, conductivity, and total suspended solids, as well as exogenous variables related to precipitation and measurements from an upstream plant. The objective is to forecast wastewater quality over a 24-hour horizon. A multivariate Long Short-Term Memory (LSTM) recurrent neural network is implemented to capture complex temporal dependencies and nonlinear patterns in the data. The model is trained on one year of data and validated on four months of data (one per season), and is compared with a persistence model and SARIMA models. The evaluation shows an overall superiority of the LSTM model, particularly for variables exhibiting high levels of noise and nonlinearity.

Agentic artificial intelligence systems can carry out a broad range of tasks in software engineering and scientific research, from writing and translating code to running workflows for data analysis and visualization. In scientific computing, the difficulty is verifying that agent-generated code is both correct and understandable to teams whose members bring different areas of expertise. We therefore argue that these systems are best used within collaborative team structures rather than as full automation. In the workflows we propose, domain experts write the specification and plan, and agents operate under a deterministic orchestration pattern to write the target code. Each stage ends with a numerical comparison against the reference code and requires human review and approval before the next begins. We evaluate these workflows on the translation of a large high-energy physics application from Fortran to C++, running the same task under different orchestrators, design patterns, and models. Across fourteen experiments, a simple author–reviewer loop with enforced limits completed a comparable number of files to a multi-agent workflow at about one-third of the cost per file.

Models with near-identical predictive performance can yield substantially different predictions, a phenomenon known as predictive multiplicity. Prior work has mostly studied this at the level of individual scalar outputs. In time-series forecasting, however, predictions across horizons jointly define a trajectory, and horizon-wise comparisons can hide important differences in predictive behavior. To address this problem, we introduce temporal predictive multiplicity, a framework that characterizes disagreement over complete forecast trajectories among models with near-identical predictive performance. We show that constraining predictive performance alone can still admit a broad range of different trajectories. We further show that constraining multiplicity at individual horizons partially reduces, but does not eliminate, trajectory-level multiplicity. Experiments with 19 neural forecasting architectures on 11 datasets confirm that near-optimal models can exhibit substantial variability in the forecast trajectories they produce, and trajectory-level disagreement is largely unrelated to horizon-wise disagreement. Our framework, therefore, exposes a gap in existing multiplicity studies: models with indistinguishable predictive performance imply fundamentally different temporal trajectories, with consequential downstream effects.

Spatial defect signatures on wafer bin maps (WBMs) trace yield loss to specific process faults, yet supervised classifiers recognize only the defect types seen during training, and one-class detectors built on a single mechanism tend to capture either local structural deviations or global distributional violations, but rarely both. This work proposes a hybrid one-class framework that couples a patch-based student-teacher detector (EfficientAD) with a denoising diffusion probabilistic model (DDPM) used for partial-diffusion reconstruction, and fuses their percentile-calibrated scores through a fixed convex combination. Trained on only 700 normal wafers from the WM-38K mixed-type dataset and evaluated on 18,658 held-out wafers, the fused detector reached an AUROC of 0.9985 and reduced misclassifications from 852 (DDPM) and 1,412 (EfficientAD) to 618, with all pairwise differences significant at p < 0.001. Beyond aggregate accuracy, the analysis shows that the gain arises from weakly overlapping errors between the two modules, yet fixed-weight fusion recovers only 40-70% of the correction available to an oracle selector. Under the benchmark's inverted class balance, average precision and F1 saturate, while the Matthews correlation coefficient and negative predictive value expose unreliable normal predictions. Pixel-level maps further show that strong image-level separability does not imply spatial localization, and the diffusion module succeeds as a local density prior rather than through global geometric reasoning. These findings motivate sample-adaptive fusion and imbalance-aware evaluation of hybrid wafer anomaly detectors.

We define coarse variants of the notions of connectivity, hamiltonicity, toughness, and spanning trees. Our notions are invariant under quasi-isometries, and they obey the same relationships between them as their classical analogs. We pose several open problems that are coarse versions of classical results and conjectures about hamiltonicity.

Mathematical programming formulations are routinely modified through algebraic reformulations, perturbations of constraint functions, and the addition or removal of constraints. Some of these modifications preserve the feasible set, whereas others reflect newly imposed modeling requirements and therefore change the optimization problem itself. This paper develops a metric framework for quantifying the robustness of formulation-dependent properties. Formulations are modeled as typed collections of constraint functions. Within each fixed typed-cardinality class, their distance is defined by optimally matching constraints of the same type and measuring the resulting discrepancies in a norm on the underlying function space. As a concrete demonstration of the framework, we study the Linear Independence Constraint Qualification (LICQ). We introduce the pointwise LICQ radius, defined as the distance from a feasible formulation to the set of formulations that remain feasible at a prescribed point but fail LICQ there. Under suitable assumptions, we derive an explicit formula for this radius and characterize the effect of adding a single equality or inequality constraint.

Given a convex polytope $P\subset\Bbb R^d$ with $\mathcal F(P)$ many flags, we prove $$\operatorname{vol}(P) \operatorname{vol}(P-P)^\circ \le \frac{\mathcal F(P)}{(d!)^2}.$$ This implies the following relation between Mahler volume and the number of flag conjectured by Freij, Schmitt, Schymura and Ziegler: for a centrally symmetric polytope $P\subset\Bbb R^d$ holds $$\operatorname{vol}(P)\operatorname{vol}(P^\circ) \le \frac{2^d}{(d!)^2} \mathcal F(P).$$ This shows that the Mahler conjecture implies Kalai's flag conjecture.

We prove the finiteness of the integral of the top power of the Ricci form on a complete, noncompact Kähler manifold with positive bisectional curvature. This settles a special case of a conjecture of Yau and Yang. An immediate corollary is the finiteness of the fundamental group of such manifolds. As in our previous work, the main idea involves the construction and use of plurisubharmonic weight functions with finite Monge-Ampère masses.

We study adaptive stabilization of known control-affine systems by treating the current parameterized critic itself as a Lyapunov candidate. Its total derivative contains a parameter-velocity term that can compensate unfavorable state evolution. A projection onto the intersection of a bounded admissible velocity set and one decay halfspace enforces parameter invariance and Lyapunov decrease simultaneously. We give an exact pointwise feasibility test, a conditional state-stability theorem, and a counterexample showing why a positive critic family containing a stabilizing member does not imply persistent feasibility. A convex endpoint constraint provides a distinct sampled implementation. A generic periodic polynomial-factor critic with a local Riccati anchor is evaluated on a force-limited cart-pole without mechanical-energy features, replay training, waypoints, or controller switching. The frozen controller passes stabilization and numerical decay checks on 600 sampled initial states across two draw sets; 400 matched continuous trajectories also pass. Independent reintegration audits and a conservative local feasibility certificate are distinguished from a global or machine-arithmetic guarantee. Compared with nonlinear model-predictive control, the measured implementation uses less CPU but has higher cost, settling time, and cart travel. The results support a conditional adaptive stabilization mechanism.

The physical origin of Modified Newtonian Dynamics (MOND), which predicts galaxy rotation curves via a single empirical acceleration constant $a_0$ without the need for dark matter, remains unknown. I propose a modified-inertia origin for both MOND's interpolating function and $a_0$ within a framework closely related to Gravitoelectromagnetism, the linearized limit of General Relativity. Following Sciama's model unifying gravity and inertia, which implements Mach's principle and the relativity of acceleration through gravitoelectric induction, I consider an idealized homogeneous universe undergoing constant Hubble expansion. I identify $a_0 \sim H_0^2R_u \sim c^2/R_u$ with the relative recession acceleration of cosmic matter near the horizon, which dominates the cosmological contribution. I show that this scale enters local inertial dynamics only when the relative acceleration of the universe becomes anisotropic and the Rindler horizon is comparable to or larger than the cosmic Hubble horizon, at accelerations of order $a_0$ and below. By the simplest Ansatz for the observer's acceleration-dependent causal volume, accounting for the interplay between the cosmic and Rindler horizons, I derive MOND's simple interpolating function as a modified inertia law without the need to insert it by hand or make any further ad hoc adjustments. Physically, the region brought into causal connection ahead of the accelerating observer by the deformation of the cosmic horizon contributes less inertial drag than is lost from the region removed behind him by the Rindler horizon. This proof of concept motivates the possibility that MOND arises from large-scale linear inertial frame-dragging induced by the expanding universe within General Relativity.

We construct area-preserving irrational pseudo-rotations of the closed disk that fail to be $C^0$-rigid. For every Brjuno rotation number we obtain $C^1$ examples, and they may be chosen arbitrarily $C^1$-close to the rigid rotation with the same rotation number. For $0<\beta<1$, a weighted Brjuno condition gives $C^{1,\beta}$ examples that are arbitrarily close in the $C^{1,\beta}$ topology; this weighted range contains every rotation number with denominator-growth exponent strictly smaller than $1/\beta$ and also some numbers at the critical exponent. For a suitable Brjuno–Liouville rotation number, we also obtain an example whose derivative growth is not bounded by any polynomial.