Papers

We study a generalized contact process on \(\mathbb{Z}^d\) parameterized by an infection rate \(\lambda\) and a resetting probability \(p \in [0,1]\), modeling deterministic cure times. Once a vertex is infected, its recovery is scheduled exactly one time unit later. Incoming attempts to an already-infected vertex successfully reset its recovery clock with probability \(p\), and are ignored otherwise. This unifies spatial versions of classical Type I (\(p=0\), non-paralyzable) and Type II (\(p=1\), paralyzable) counters. Except in the fully resetting case, deterministic recovery deadlines destroy coordinatewise attractiveness and create a causal shielding effect. Using a first-moment bound on potential causal chains, we prove that the process dies out from finite configurations whenever \(\lambda<1/(2d)\), uniformly in \(p\in[0,1]\). The same causal-chain bound yields local convergence to the empty configuration from arbitrary initial states. In dimensions \(d \ge 2\), an oriented percolation exploration based on the first infective window establishes global survival for all \(p\in[0,1]\) when \(\lambda>-\log(1-p_c^{\mathrm{or}})\). Finally, in the purely non-resetting case \(p=0\), we derive a delayed identity for the one-site density and prove that this density remains strictly between zero and one at every finite time.

Hybrid manipulators combine motorized rigid joints with pressure-actuated origami segments. Published arms of this kind are controlled with decoupled per-DOF loops, and the cost of this approximation has not been quantified, because the coupled model needed to measure it has not been built. This paper derives such a model for a chain of $N$ alternating revolute joints and Kresling origami segments, including pneumatic chamber dynamics and crease hysteresis. Using the model, we measure the coupling directly and show that its strength varies joint by joint, and that decoupled control loses precisely on the strongly coupled joints while remaining competitive on the one nearly decoupled joint. Coupled model-based controllers track $2.5\times$ tighter than a decoupled PID baseline at lower torque. However, the model predictive controller (MPC) is too slow for real time, and model-free reinforcement learning stalls far below acceptable success rates on a strict settling metric. We therefore distill the MPC into a small neural policy with behavior cloning and DAgger. The distilled policy settles 93-94$\%$ of goals with zero collisions, within a few points of its teacher, and runs inside the 5 ms control step where the MPC does not. Where the teacher itself fails, we trace the failure to a limit cycle with the bellows' lightly damped mode, and we remove it by selecting goal postures holdable at low pressure.

No two robots are truly identical: calibration, battery state, sensor drift and wear give every swarm a distribution of behaviour rather than a single point, usually treated as an imperfection to be minimised. In animal collectives the reverse holds: consistent individual differences in behaviour ('temperament') are shaped by natural selection and often decisive for group performance. This perspective proposes 'temperament engineering', a bio-inspired framework that treats the swarm's distribution of temperaments, rather than the individual controller, as the design object. It borrows five evolutionarily validated axes of animal temperament (shyness-boldness, exploration-avoidance, activity, aggressiveness and sociability) as a design vocabulary, rendering each as a continuous control parameter $\tau \in [0,1]$ above the controller, realisable as a module threshold, a policy-conditioning vector in multi-agent reinforcement learning, or a constraint on a foundation-model planner. A three-phase workflow maps mission success criteria onto relevant axes, plans the shape of the $\tau$ distribution, and tunes reaction norms governing how temperament responds to environmental cues. The payoff is greatest under decentralisation: where a central planner can reassign behaviour online, a temperament distribution is a planner output, but in a swarm without global knowledge it must be an offline, anticipatory design input. Behavioural and platform heterogeneity are thereby co-design variables, and I sketch tentative robot-native axes (self-model plasticity, forcefulness, initiative and expressiveness) arising from features robots have and animals do not. Engineered heterogeneity has been shown to outperform homogeneous swarms in tasks such as aggregation and exploration; establishing when, and how much, heterogeneity repays its cost is the work the field can now take forward.

In the paper, we prove a recursive version of the weighted Sidelnikov-Welch inequality for real and complex unit vectors. Unlike the classical form, which gives a direct lower bound for a fixed even power sum, our inequality relates two consecutive even power sums. Iteration yields the usual weighted Sidelnikov-Welch bound. We apply this estimate to maximal relative projection constants. If $\mathbb{K}^m$ admits a maximal equiangular tight frame with $M_{\mathbb K}$ vectors, then for every integer $k\geq1$, $$ \lambda_{\mathbb K}(kM_{\mathbb K}-m,kM_{\mathbb K}) = \lambda_{\mathbb K}(m)-\frac{2m}{kM_{\mathbb K}}+1. $$ Moreover, the maximal value is realized by an equiangular tight frame when $k=1$ and by a biangular tight frame when $k\geq2$.

Rufus-Air is an open and reproducible post-training recipe on GLM-4.5-Air-Base (106B-A12B), organized as a serial pipeline of eight stages: SFT, Reasoning RL, Coding RL, Instruction-Following RL, General Agent, Coding Agent, Search Agent, and RLHF. We document the data, reward design, infrastructure, stage order, and stagewise results needed to reproduce the recipe. Stages progress from basic to advanced capabilities and from hard, verifiable rewards to softer judge-based signals. Training builds on open-source components and public data, much of it used as released, without new human annotation or an in-house distillation teacher. Our main findings are that (i) diverse, high-quality SFT establishes a strong capability floor; (ii) difficulty filtering keeps RL prompts within a productive learning range; (iii) reward reliability provides a practical principle for ordering stages; and (iv) infrastructure and engineering choices are part of the recipe, not just an implementation detail. Rufus-Air improves over the official GLM-4.5-Air post-trained release and is competitive with similarly sized open models.

Integrated quantum photonic circuits are a key enabling technology for the scalability of quantum information systems. Among the available platforms, silicon photonics offers an unrivalled capability for the large-scale integration of photonic components within compact footprints. However, the strong index contrast that enables ultra-compact silicon devices also makes them highly sensitive to fabrication imperfections. As circuit complexity increases, active tuning is generally required to maintain spectral alignment among the different components, leading to significant power consumption that ultimately limit scalability. Here, we demonstrate a fully integrated silicon quantum photon-pair source operating without active tuning of any component. The circuit combines photon-pair generation in a micro-ring resonator, pump rejection using Bragg filters, and signal/idler demultiplexing through modal add-drop filters with building blocks engineered to minimize sensitivity to fabrication variations. The resulting circuit achieves excellent experimental quantum performance. Coincidence rates up to 4000 counts s^-1 with coincidence-to-accidental ratios as high as 100 are obtained across the generated spectrum, while separate two-photon interference measurements yield raw visibilities exceeding 93% for individually selected ITU wavelength-channel pairs. By eliminating the need for active spectral tuning while maintaining high quantum performance, this work addresses a major bottleneck in the scaling of complex silicon quantum photonic circuits.

Autonomous navigation in dynamic environments is hindered by two fundamental challenges: perception instability and uncertainty-optimization mismatch. The former leads to identity switches and unreliable motion estimation, while the latter prevents principled incorporation of motion uncertainty into trajectory optimization. To address these challenges, we propose UCON, an uncertainty-aware navigation algorithm in dynamic environments. For perception instability, we present a point-level historical re-association mechanism that leverages historical point cloud fragments to recover lost targets while maintaining identity continuity. Subsequently, a Kalman filter is employed to provide anisotropic motion state estimation and covariance propagation. To resolve the uncertainty-optimization mismatch, we transform predicted states and their covariances into uncertainty sectors, which are embedded as differentiable cost terms within a trajectory optimization framework. This achieves consistent uncertainty-aware dynamic obstacle avoidance while maintaining smoothness and feasibility. Extensive simulations and real-world experiments demonstrate that, while maintaining high computational efficiency, UCON achieves superior perception stability and robust navigation performance in dynamic environments compared to state-of-the-art methods. The code will be open-sourced to facilitate further research.

Backchannels, brief acknowledgements like "uh-huh" produced while the other party may still be talking, are central to natural conversation, but full-duplex spoken dialogue models rarely model them explicitly. We introduce a lightweight backchannel head that predicts, from a full-duplex model's own hidden states, when a backchannel should begin. Once this probability crosses a tunable threshold, a backchannel is force-decoded. Attached to both a 7B (PersonaPlex) and a 1B (F-Actor) model, it generalizes across scale. Probing confirms the hidden states anticipate real human timing, and generation evaluation shows more frequent, better-timed backchannels. Human raters judge the resulting backchannels on par with real ones.

This paper deals with image-based visual servoing and pose estimation by observing four and five lines. Our main interest is to determine the relative configurations of the camera and the observed lines that lead to problems in control and stability. Since it is equivalent to finding the singularities of the corresponding Jacobian matrix, we use tools from computational algebraic geometry to seek configurations such that all of its minors vanish simultaneously. By choosing a suitable basis for this matrix, we revisit the problem in the case of three lines to show that one type of the singularities is when the camera lies on the hyperboloid of one sheet uniquely defined by the lines. This result is further exploited to prove that the one-dimensional singularities, if any, in the case of $n$ lines appear when the camera lies on the transversals to the observed lines. Thus, by forcing the transversals to be complex, we can avoid the aforementioned type of singularities in the case of four lines although the algebra shows that there can always be up to 10 inevitable singular locations of the camera for the other type of singularity. For five lines, we find out that there are no singularities in the generic case. The singularities are also characterized for four and five lines with orthogonality and parallelism constraints. Furthermore, a visual servoing library is used to conduct some simulated experiments to substantiate the theoretical results. As expected, we observe problems in control in the vicinity of a singularity as well as increased errors in pose estimation.

Diffusivity of passive tracers in complex mixtures is widely relevant for industrial applications and for probing biological systems. Interactions with the surrounding medium typically generate a drag force that suppresses tracer diffusion, although self-propulsion can accelerate tracers via active fluctuations. Similar effects are not understood in mixtures with particle conversion and exchange, although these are particularly relevant in biological contexts, where actively driven reactions prevail. By studying a thermodynamically consistent model of chemical reactions in mixtures, we show that reactions provide an additional relaxation pathway that suppresses interaction-induced memory, reducing the drag on tracers and restoring their diffusivity toward the value expected in the absence of solutes. Moreover, active reactions generate nonequilibrium fluctuations that can push tracer diffusivity beyond this limit, an effect we confirm with particle-based simulations. Our results identify chemical activity as a distinct route to controlling mass transport and offer a framework for interpreting microrheology experiments in chemically active mixtures.

Optical Kerr nonlinearity is central to optical bistability in high-Q microcavities. Here, we show that optical Kerr nonlinearities in Fabry Perot resonators can also result in self-focusing effects, that can substantially modify the Q-factors of the resonators. For the studied cavities, up to five-fold increase in Q-factors is predicted, attributed to reduction of sidewall leakage, confirmed via simulations performed on curved cavities. We also show that for high Q-factor cavities, the higher-order Kerr effect can become relevant already at modest input intensities scaling inversely with Q-factor for a particular n2/n4 ratio. We investigate numerically the role of higher-order Kerr effect on optical bistability responses and find that its inclusion can shift the bistability threshold to higher input intensities than predicted by the standard n2-only model.

We prove the coarse Erdős-Pósa conjecture of Georgakopoulos and Papasoglu. Informally, any graph either contains many fat cycles that are pairwise far apart, or there is a small number of bounded radius balls that together hit all of them. To be more precise, if $G$ is a graph with no $q$-fat model of $k \cdot K_3$ for some $q, k \in \mathbb{N}$, then there is a set $X\subseteq V(G)$ of $\mathcal{O}(k\log k)$ vertices such that every $q$-fat model of $K_3$ in $G$ has distance $\mathcal{O}(q)$ from $X$. In another form more closely resembling Manning's theorem that characterises quasi-trees: if $G$ is a graph with no $q$-fat model of $k \cdot K_3$ for some $q, k \in \mathbb{N}$, then $G$ is $\mathcal{O}(q)$-quasi-isometric to a graph $H$ that contains a set $X\subseteq V(H)$ of $\mathcal{O}(k\log k)$ vertices such that $H-X$ is a forest. Bootstrapping this result, we further prove that every graph with no $q$-fat model of $k \cdot K_3$ is quasi-isometric to a graph with no $k \cdot K_3$ minor, where the quasi-isometry can be chosen to only have additive distortion. This result also holds for $k = \infty$. We also obtain an Erdős-Pósa theorem for long induced cycles that are far apart.

Sampling from Boltzmann distributions of molecular systems is an inference problem that has seen significant recent developments fuelled by advances in neural density estimation. We develop a novel sampling algorithm, Neural Transport Nested Sampling (NTNS), which combines the classical strengths of nested sampling with modern neural flow-based methods. NTNS uses a flow matching velocity as the drift in a Metropolis–Hastings corrected Langevin kernel inside a nested sampling outer loop, requiring only evaluations of the target energy function and providing scalable estimation of the full partition function of high-dimensional particle systems. We benchmark NTNS on challenging molecular sampling benchmarks, scaling up to Lennard–Jones clusters of 55 interacting particles, where it reduces both interatomic distance and energy Wasserstein errors to reference MCMC by over an order of magnitude relative to the strongest neural baselines at lower wall-clock cost. To our knowledge, NTNS is also the first neural sampler to return a calibrated, temperature resolved partition function estimate at this scale, recovering the phase structure across temperature from a single run.

Inverter-based resources (IBRs) are increasingly dominating modern power systems, posing significant challenges to cost-effectively maintain system strength for stability. At the same time, the operating behaviors of IBRs are software-defined, including both their steady-state power outputs and control modes, e.g. grid-forming (GFM) and grid-following (GFL). Such flexibility has not been fully explored to efficiently operate future power systems. This paper develops a novel framework that simultaneously optimizes IBR operating behaviors and ensures adequate system strength. A comprehensive solution is provided to integrate system strength constraints into scheduling models, despite their inherent strong non-convexities. We derive a rigorous linear-matrix-inequality (LMI) reformulation of the system strength constraint, effectively addressing non-explicit formulations and dimension variation issues caused by GFM/GFL mode switching of IBRs. Then, we equivalently convert the original non-convex implicit system strength-constrained scheduling problem into an explicit mixed-integer semi-definite programming (MISDP) problem by incorporating the reformulated system strength constraint along with other operational constraints. We further provide a Rayleigh Cut method, which is compatible with standard mixed-integer linear programming (MILP) solvers, to solve this system strength-constrained scheduling problem. Case studies on a modified IEEE 118-bus system and a practical Jiangsu power system demonstrate the performance of the proposed methods.

We establish intrinsic continuation criteria and finite-energy global solvability for the stochastic tamed Navier–Stokes equations on $\mathbb R^3$ driven simultaneously by multiplicative cylindrical Wiener and compensated Poisson noise. Under local coefficient hypotheses, the maximal local $L^p$ solution, $p>3$, satisfies a blow-up alternative independent of auxiliary cutoffs and a Serrin criterion with time exponent $2p/(p-3)$. Additional coercivity of the taming term and compatible $L^2$ and gradient noise bounds yield the global well-posedness theory for divergence-free initial data $u_0\in L^p(\Omega;L^p)\cap L^2(\Omega;L^2)$. No smallness or initial $H^1$ regularity is required. The solution has càdlàg $L^p\cap L^2$ paths and gains $H^1$ regularity at positive times, with time-weighted $H^1$ and $H^2$ estimates. The proof combines finite-energy persistence with endpoint completion that retains terminal Poisson jumps and permits restart in the original uniqueness class.

Recent studies have shown that Large Language Models can effectively solve problems and fix bugs in diverse programming environments, including competitive programming. Existing approaches primarily evaluate LLM performance in problem solving or bug fixing independently, but do not explore the relationship between these two capabilities. This work focuses on determining how much the LLM deviates from a buggy solution to fix the bug compared to a human-written patch, and if there is a bias towards generating entirely new solutions. We construct a dataset with all the submissions ($\sim$ 3000) from a couple of users from Codeforces, and we match each buggy submission with its corresponding human fix. By using the similarity between the buggy solution and the human fix as a baseline, we evaluate the quality of LLM-generated bug fixes on 3 OpenAI GPT models (gpt-5-nano, gpt-5-mini, gpt-5.1). We check if the generated solutions solve the problem by using the Codeforces-R1 dataset, an openly available dataset that has tests generated with the DeepSeek-R1 model. Our findings suggest that LLMs tend to modify more lines than necessary compared to human fixes and, in some cases, generate entirely new solutions. We also observe that LLMs solve more problems correctly when allowed to generate solutions from scratch rather than patch buggy submissions, even when those submissions are close to the human patch. This has important implications for the design of AI-assisted programming tools, particularly in supporting user debugging processes and promoting incremental problem-solving strategies rather than solution replacement.

In this paper, a method for achieving exact unlearning for Gibbs supervised learning algorithms is proposed using a variational formulation inspired by empirical risk minimization subject to relative entropy regularization (ERM-RER). Such a method consists of maximizing the expected empirical risk over the dataset to be unlearned subject to a regularization by relative entropy with respect to the original algorithm. The optimization variable is a probability measure on the models; and the solution is another Gibbs probability measure that represents a new Gibbs supervised learning algorithm. The method guarantees exact unlearning in the sense that the new Gibbs algorithm coincides in distribution with the algorithm that would have been obtained by retraining from scratch on the dataset to be retained. As a byproduct, a framework for reweighting data points in ERM-RER by strategically choosing both the reference measure and the regularization factor is obtained. In this framework, exact unlearning is the special case in which zero-weight is assigned to the contribution of the data points to be unlearned. More generally, depending on the choice of certain parameters, data points can be up-weighted or down-weighted in ERM-RER problems for particular purposes, e.g., controlling the generalization error of Gibbs algorithms. This paves the way for new constructive or adversarial views on classical reweighting data points in ERM-RER.

We obtain a nontrivial bound on the number of triples of positive integers $(a,b,c) \in [1,H]^3$, which are multiplicatively dependent but each pair of its elements is not, and so is the triple $ (a+1,b+1,c+1)$. The method is based on studying factorisations of some resultants and a recent improvement by G. Binyamini, R. Cluckers and F. Kato (2025) of the classical Bombieri–Pila bound.

Assembly using robots often requires specially designed fixtures, or relies on top-down only assembly strategies. Using multiple robots, we can avoid using fixtures and make robotic assembly more flexible. Planning assembly sequences for multiple robots is challenging due to the high number of possible task assignments and orders. In addition, we need to reason over forces that occur during the assembly process, e.g., to decide if multiple robots are required for support, or if external support such as a table should be used. We present Wrap, a multi-robot assembly planner for multi-part assemblies, given the inter-part ordering-dependencies, the part meshes, and their initial state. We formulate a linear program to reason about valid grasps for supporting the forces that occur during assembly. The search leverages the assembly sequence, and greedily finds a feasible solution per assembly step by computing a heuristic via a cheap backwards search, and using the heuristic in the more expensive forward search. We then solve the multi-robot, multi-goal motion planning problem, and for execution, we split the plan into contact-rich assembly skills, and free space motion. We benchmark the planner on a variety of multi-part assemblies, and apply the planner to groups of robots differing in size and kinematics. We validate the work both in a physics simulation, and in real. Videos and code are available at https://www.vhartmann.com/wrap.

Quantum circuit optimization is critical for mitigating the noise inherent in current quantum hardware. Quantum compilers typically sequentially apply multiple optimizations (also called “optimization passes”) to improve the circuit. The impact of the order in which these passes are executed has yet been largely unexplored. This paper investigates the significance of the order of optimization passes within quantum circuit compilation, specifically analyzing interactions between different optimization methods and quantifying their mutual influences. Using Qiskit's compiler, we systematically evaluate pairwise combinations of 16 selected optimization passes, measuring circuit depth and gate count across various benchmark circuits. Our findings indicate dependencies between certain optimization passes, demonstrating that the order of the passes affects the optimization quality. In some cases, the worse performing sequence can be corrected through repeated pass application. %such that they are as good as the best performing one by extending the sequence. Experiments on multi-pass sequences show that more than two optimization passes may have an impact on each other but that this always links to the previously found pairwise effects. We observe that it is important to initially choose the best order of optimization passes to get the best possible optimization for the given circuit. The experiments reveal some factors which are important to choose the best, or at least a good, order; among those, the resulting optimization sequence depends the most on the native gate set.

We adapt Reinforce Adjoint Matching (RAM), a reward-based post-training method, to generative speech enhancement (SE). Starting from a pretrained SE model, RAM tilts the model's conditional distribution toward outputs with higher reward. During training, the current model generates enhanced speech on-policy, evaluates each generated endpoint with a potentially non-differentiable reward, and analytically re-noises the endpoint to construct inputs for a reward-guided regression objective. This enables post-training directly on real recordings using weak supervision, such as text transcripts, without requiring paired clean speech targets or reward gradients. We investigate word error rate (WER)-based post-training and whether recognition performance can be improved without compromising perceptual speech quality. Experiments on real CHiME-4 recordings reduce WER by 5.08 percentage points relative to pretrained FlowSE without reducing any of the reported non-intrusive speech quality metrics. A subjective listening test at the default reward scale finds no statistically significant preference between the post-trained and pretrained models.

Equilibrium modeling for power markets usually assumes convexity of each players' optimization problem. Although the importance of accounting for fixed generation costs and start-up costs, minimum generation levels and/or minimum up-time and down-time restrictions in production scheduling is widely acknowledged, such modeling does not allow for discrete decisions. This paper considers unit commitment constrained Nash equilibria. First, we derive novel optimality conditions tailored for the mixed-integer convex programming problem of joint unit commitment and economic dispatch of a self-scheduling profit-maximizing producer. Next, we use these to formulate a Nash equilibrium as a mixed-integer complementarity problem, which facilitates the development of a procedure to obtain multiple equilibria. The approach can be adapted to both perfectly and imperfectly competitive market settings. While an equilibrium may not always exist, we give sufficient conditions under which a Cournot-Nash equilibrium can be obtained by mixed-integer convex programming under the standard assumption of an affine inverse demand curve and convex generating costs, and use this to establish existence. A case study demonstrates the feasibility of using optimisation to obtain a Cournot-Nash equilibrium for unit commitment constrained market clearing. Our results confirm that ignoring unit commitment creates significant welfare losses, although these vary substantially across equilibria.

Learning surrogates for time-dependent partial differential equations often requires a new simulation corpus when the governing operator changes. We introduce RD-JEPA, a joint-embedding predictive architecture for self-supervised pretraining on reaction-diffusion trajectories. A single model is pretrained on five parameterized systems and then adapted to three held-out systems whose reaction operators and trajectories are excluded from pretraining. Using one, five, or ten complete trajectories from a held-out system, RD-JEPA achieves lower mean relative discrete $\ell^2$ field error and mean absolute spatial first-difference error than five supervised surrogate baselines, an independently trained control that removes the trajectory-dependent predictive latent pathway, and an architecture-matched model trained from scratch. Within the evaluated equations, output resolution, forecast horizons, and choices of adaptation trajectories, the results indicate that prediction of future-state representations can support data-efficient adaptation across related reaction-diffusion systems.

Large-scale indoor localization is increasingly needed in campuses, smart buildings, factories, and digital-twin infrastructures, where wireless conditions, access-point deployments, and spatial layouts evolve over time. Such systems must be accurate, extendable, and maintainable, allowing new buildings, floors, rooms, and service areas to be added without retraining a monolithic model. Modular learning-based localization supports this goal by assigning independent models to buildings, floors, and fine-grained spatial regions. However, this extendability introduces a high-performance inference challenge: each query may require selecting and executing among hundreds or thousands of local models, making exhaustive inference costly in computation, accelerator memory residency, model loading, and scheduling. This paper presents a resource-aware modular inference framework for WiFi fingerprint-based indoor localization on high-performance and distributed computing platforms. The framework organizes local autoencoder models into a building-floor-spot hierarchy and formulates localization as model selection over a large pretrained model ensemble. To reduce inference cost under resource constraints, we introduce two lightweight execution-pruning strategies: Hierarchical Candidate Pruning, which performs coarse-to-fine model selection, and Trajectory-Aware Pruning, which uses temporal locality in user movement to restrict inference to spatially plausible neighboring models. Experiments on a real-world dataset demonstrate that the proposed framework delivers scalable inference without sacrificing localization quality. Compared with exhaustive evaluation over 735 spot models, Hierarchical Candidate Pruning requires only 67 model evaluations, while Trajectory-Aware Pruning reduces this number to just 10, cutting model executions by 98.6%.

We study the tangent bundle $T_\mu$ to a Radon measure $\mu$ in Euclidean space, introduced by Bouchitté, Champion and Jimenez (2005). Its construction, inspired by Monge-Kantorovich optimal transport theory, involves the duality between Lipschitz functions and the so-called Arens-Eells space, a Banach subspace of distributions obtained by completing the set of balanced signed measures. Precisely, a velocity field $\sigma$ is $\mu$-tangent when the divergence of $\sigma \mu$ lies in the Arens-Eells space. The tangent bundle $T_\mu$ defined $\mu$-almost everywhere provides a local projection that allows to construct a $\mu$-tangential gradient operator on Lipschitz functions that is weakly continuous and enjoys integration by parts. In this paper, we introduce a new quantitative estimate involving the tangential and normal components of a given velocity vector field $\sigma \in L^1_\mu(\mathbb{R}^d)$. Specifically, we show that the tangential condition $\sigma \in T_\mu$ holding $\mu$ a.e. is equivalent to each of the following two conditions: the convergence in the Arens-Eells space of $h^{-1} \left((id+h \sigma)_{\#} \mu - \mu\right)$ as $h \to 0$, and the differentiability of Lipschitz functions along $\sigma$. Moreover, given a field of non-tangent directions, we construct a Lipschitz function that is not differentiable on a large set, confirming that $T_{\mu}$ agrees with the decomposability bundle of Alberti and Marchese. We finally relate $T_\mu$ to the tangent measures of Preiss and survey further properties of the tangential differential calculus.

A Devil's staircase is a sequence of transitions between topological sectors as a control parameter is varied. Such staircases are predicted in frustrated magnets and lattice gauge theories, but observing them is hard: the winding number that labels each sector is topologically protected, so local quantum dynamics alone cannot move the system from one step to the next. Here we propose and analyze an experimentally feasible way to realize a thermal quasi-Devil's staircase in a finite Rydberg-atom array. We study the anisotropic triangular-lattice Ising antiferromagnet using a dimer mapping, a directed-string description, exact thermodynamics, and Monte Carlo simulations. In the defect-free string manifold, the commensurate–incommensurate onset follows from a simple energy–entropy balance, and the exact Ising critical relation reduces to the same condition when triangle-rule defects are rare. On a finite lattice, this onset appears as a quasi-Devil's staircase of winding-sector crossovers, which we resolve through winding distributions, structure factors, and directional correlations. The key point is that thermal fluctuations overcome the topological barriers that block sector changes under purely quantum dynamics, and the staircase exists precisely at the finite sizes and tunable effective temperatures of current Rydberg platforms. This makes the effect directly observable in existing experiments. Our comparison also shows that the finite-size steps are not phase transitions: in the thermodynamic limit only a single phase transition survives, and the system crosses over to a defect-dominated paramagnet.

We prove that $\mathrm{C}^*$-simple groups which admit a faithful extreme boundary are $\mathrm{C}^*$-selfless. More precisely, we establish complete selflessness of the canonical inclusion of the reduced group $\mathrm{C}^*$-algebra into the reduced crossed product. In particular, the Higman–Thompson groups and the Brin–Thompson groups are $\mathrm{C}^*$-selfless.

Multimodal attributed graphs connect entities, visual content, language, and observed relations. Learning one foundation across such graphs requires more than compressing each node into a fused Euclidean vector. The representation must preserve entity semantics, construct interaction state from graph neighborhoods, and expose that state to prediction units with different geometry. Our empirical study shows why these requirements are inseparable. Higher-grade channels recover pair relations across the foundation graphs, specialized queries reveal information hidden by a generic readout, and rigid blade isolation removes cross-grade capacity. We therefore introduce ICE (Interaction-aware Clifford Encoder), a multimodal graph foundation model built on a node-indexed Clifford latent field. Topology, text, and images enter explicit Cl(3) addresses. Edge-aware geometric products transform these directions into scalar, bivector, and trivector relations over observed neighborhoods. A protected Grade-1 route preserves entity semantics, while the full grade and depth bank remains available to fresh node and link heads. We establish exact cross-grade reachability, node-permutation equivariance, and a bound on the task residual around the semantic score. Experiments span one shared foundation over eleven graphs, six node-classification datasets, three link-prediction datasets, and matched few-shot tasks. ICE ranks first in all 30 reported supervised and few-shot comparisons. Core removals reduce every task summary, and mechanism controls connect the gains to higher-order transport, retained multidepth structure, semantic protection, and direct field access.

Ternary (1.58-bit) weights are attractive for microcontroller-class language models, but the sub-1M-parameter regime rests mainly on isolated, single-seed comparisons. One prominent example reports that a routed ternary block (convolution, diagonal SSM and sparse attention mixed by a per-token router) beats a parameter-matched full-precision transformer by 22% at 60K parameters, attributing this to inductive bias. We re-run it under one fixed recipe, three seeds per cell, 98 byte-level runs on one laptop. (i) Baseline shape dominates: at a 16M-byte budget, param-matched transformers span 22.6% in validation loss purely by depth/width choice - far more than any architecture effect we measure there - and the best-shaped transformer ties the routed model, so the published margin is at least partly a baseline-shape effect; the ordering of shapes reverses with budget, so no single fixed shape can be trusted. (ii) At 130M bytes the routed model does win, by 22.2-24.0% over the three transformer shapes we evaluate there - but a plain gated diagonal-SSM block beats it by a further 9.1%, and the routed model's own router puts most of its weight on its recurrent pathway, so the gain does not require routing. (iii) The ternary penalty differs by architecture at the larger budget (+5.3% best transformer vs. +19.5% routed, +28.1% gated SSM), but we cannot attribute that to architecture alone: our transformers keep learned positional embeddings in full precision, 11-22% of their parameters, so they are less quantized than the models they are compared with. (iv) A 90/10 full-precision-then-ternary schedule beats all-ternary training, but only at a stage-2 learning rate about 10x the pretraining peak; at a conventional fine-tuning rate it looks 15.3% worse, reversing the conclusion. The from-scratch baseline was not itself learning-rate tuned, which bounds (iii) and (iv). Code and run logs released.

This paper presents and evaluates a Deep Learning-based (DL-based) Signal Quality Assessment (SQA) model to distinguish between clean and noisy ambulatory Electrocardiograms (ECG). The model is trained on Copenhagen Center for Health Technology-Contextualized Arrhythmia Database (CACHET-CADB), which, to the best of our knowledge, is the first ambulatory ECG database with both physical and patient-reported contextual data. The model shows stable performance on different databases such as MIT-databases and the latest PyhsioNet/Cinc Challenge 2021 databases. Subsequently, the paper demonstrates how complicated ECG noise can be investigated by the SQA model and the physical contextual data.