Papers

Weak measurement has proven useful for metrology, for probing quantum paradoxes, and for the direct measurement of quantum states. Weak measurements of polarization qubits with temporal pointers provide a direct route to weak-value characterization, including in regimes where the pointer is only partially coherent. We derive a closed-form expression for the post-selected temporal shift that interpolates between the incoherent and coherent (ideal) weak-measurement limits through a single parameter $\nu$, the pointer visibility. The expression is experimentally tested for a range of polarization states spanning three trajectories corresponding to rotations about the principal axes of the Poincaré sphere. Two of the trajectories provide parameter-free benchmarks, with the real part of the weak value following $\cos^2\theta$ and $1/2$. In contrast, the weak value along the third trajectory is sensitive to incoherence and is well described by the single-parameter partial-coherence model, from which a reduced pointer visibility is obtained. Time shifts are extracted from the smoothed derivative of the pulse leading edge with internal calibration, reaching few-picosecond precision on 10 ns optical pulses using commercial components. The same apparatus also gives qualitative access to the imaginary quadrature through the frequency centroid, showing that temporal weak measurements remain accessible and quantitative in partially coherent pulsed systems.

Contrastive reinforcement learning (CRL) learns goal-conditioned values by associating state–action pairs with the states subsequently reached, assuming that no unobserved variable jointly affects the recorded action and its outcome. When offline demonstrations come from a demonstrator with information hidden from the learner, this assumption fails and the critic absorbs spurious action–outcome associations. We formalize this setting with confounded Markov decision processes and introduce counterfactual transitions that separate what the data identify from what they do not; minimizing over all compatible transitions yields a worst-case occupancy that lower-bounds the true one. Causal Contrastive Reinforcement Learning (CauCRL) learns a pessimistic counterfactual transition from positive and negative offline demonstrations and trains the critic on counterfactual rollouts, substantially improving success rates over standard CRL on confounded goal-reaching tasks.

Personalized assistants accumulate long conversation histories, and passing the whole history to an LLM with every request is costly. We show that it is also unnecessary. On PersonaMem-v2 (180 questions), with GPT-5.6-terra and Claude Opus 5.5 as judges, a relevance-filtered context, built by sentence-level retrieval that ranks the history by similarity to the current request and stops at a fixed budget, matches full-history accuracy with only 5% of the text, cutting the judge's input about 20-fold. An LLM summary of the same length performs on par, but it needs an LLM to read the entire history, whereas retrieval needs only a small embedding model. While both sentence-level retrieval and LLM summary perform strongly, retrieval does so while placing the relevant evidence in the context for only 61% of the questions, and an oracle given only that evidence beats the full history by 15.6 points, making better context selection a promising path to surpassing the full history.

Feed-forward geometric foundation models (GFMs) directly predict dense geometry and camera poses from batches of images. Emerging visual SLAM methods chain together consecutive GFM batches to form dense point cloud maps. A core challenge is how to address the ambiguous geometric scale of GFM predictions: independent predictions are locally consistent up-to-scale but not constrained by any direct physical measurements. Models trained on data with known scale improve the consistency of GFM reconstructions but again do not directly measure it. Consequently, trajectories and 3D reconstructions from GFM-enabled SLAM methods inherit this issue. Motivated by parallels with classical visual-inertial odometry, we introduce FoundationVIO which integrates inertial sensing with GFM predictions to recover metric scale reconstruction using a factor-graph based approach. We demonstrate odometry estimates competitive with classical state-of-the-art VIO methods and accurate dense reconstructions that outperform GFM-enabled SLAM methods. We also add a minimal GFM-based loop-closure mechanism to create a full Visual-Inertial SLAM system capable of creating globally accurate reconstructions and pose estimates. We evaluate our method on three datasets with well known sensor systems and demonstrate its compatibility on ubiquitous camera and IMU sensors. The method runs at approximately real-time on a consumer-grade laptop GPU. Code: https://github.com/ori-drs/FoundationVIO.

Discretization can change a sharp stability threshold even when the continuum threshold is recovered at infinity. We study this phenomenon for the Hardy inequality on the integer lattice in dimensions at least three: its best coefficient agrees with the continuum value through dimension eight and is smaller from dimension nine onwards. We characterize this transition by the total critical defect, the summable error obtained by testing the lattice operator against the critical continuum power. A theta-function representation proves that the defect is negative and strictly decreasing from dimension nine; explicit positive Hardy remainders establish its positivity in dimensions three through eight. An exact energy identity relates this defect to the energy saved by optimizing the profile outside the neighbours of the origin. This exterior remains stable in dimensions eight and nine, locating the first loss of positivity in its coupling to those neighbours. We give self-contained proofs of both dimensional ranges. We then describe how local attraction creates a negative eigenvalue in a general class of lattice operators with critical inverse-square tails. Its magnitude is exponentially small near the threshold, with both the rate and the multiplicative prefactor determined by zero-energy solutions. The result allows connected finite modifications of the lattice and nonradial corrections to the tail. The same analysis controls the spread of the emerging state and gives a two-dimensional return scale for the associated Markov chain in every ambient dimension.

Higher-order semi-rational solutions are constructed for the (2+1)-dimensional nonlocal multi-component Yajima-Oikawa system. This system is obtained from its local \(2M\)-component counterpart through a spatial-reflection reduction. Using Hirota's bilinear method and the Kadomtsev-Petviashvili hierarchy reduction, we derive a unified \(6\times6\) block Gram determinant. Its entries involve Schur polynomials and exponential functions. The complex-conjugation and spatial-reflection reductions are imposed through algebraic constraints on the spectral parameters and determinant blocks, with the former ensuring a real-valued denominator tau function. Separate spectral parameter sets are assigned to the rational, breather, and dark-soliton blocks. These solutions describe paired lumps or line rogue waves on breather, dark-soliton, or combined backgrounds. Pure rational, breather, and dark-soliton solutions follow by setting the appropriate block sizes to zero. Asymptotic analysis establishes the elastic interactions of the fundamental breather and dark-soliton pairs and determines their position and phase shifts.

Temporal point processes are used both to measure market mechanisms, for example how fast prices absorb news and how much of the reaction is the market responding to itself, and to predict the next event. We show that one algebraic object, the phase-type (Erlang-chain) state space, serves both purposes with exact likelihoods. For measurement, we build a multiscale phase-type Hawkes process whose parameters all enter linearly. Its log-likelihood is concave, and we compute the global maximum together with a Fenchel duality-gap certificate. A Markov embedding gives the response to an exogenous shock, echoes included, in closed form, and this response is stable if and only if the spectral radius of the branching matrix is below one. Applied to six markets around 670 scheduled macroeconomic releases (2022-2026) with a built-in placebo test, the model shows that the direct reaction to CPI, payrolls, PPI and the FOMC statement is absorbed in about a second, while the market's own echoes stretch half of the response to 16-137 s. For prediction, we introduce EPT-X, a neural point process that adds a history-dependent mixture-of-Erlang renewal channel to a linear Hawkes backbone. Its intensity and compensator remain in closed form, its states follow an affine recursion that trains with a parallel scan, and it can start from the certified fit of the measurement model. EPT-X has the best test likelihood on all five LOBSTER order-book streams and on Retweet and Taobao, and is level with the best published model on StackOverflow. We also find that the EasyTPP implementation of IntensityFree clamps short inter-event times before scoring, and that the gaps of the EasyTPP Amazon data are uniform on two fixed intervals.

In this paper we investigate the structural properties and thermal stability of metastable Ge1-xSnx epilayers (~4.5 at.% Sn) grown directly on Si(001) substrates by high-resolution X-ray diffraction (HRXRD) and Raman spectroscopy. Our results demonstrate that both 70 and 140 nm films are fully relaxed, with the thicker film exhibiting a small tensile strain (+0.09%). The thermal stability of the heterostructures was evaluated up to 813 K using temperature-dependent Raman spectroscopy and scanning electron microscopy. The surface-weighted Raman response (532 nm excitation) and surface morphology of the 70 nm film remain highly stable. In contrast, the 140 nm film undergoes severe degradation, characterized by significant attenuation and broadening of the Ge-Ge longitudinal optical phonon mode, alongside enhanced surface Sn segregation. These findings demonstrate that the thermal stability of direct GeSn/Si heterostructures is governed by the initial defect structure established during epitaxial growth, providing key design rules for understanding the fabrication of GeSn-based optoelectronic devices.

It is a classical fact in spectral geometry that the eigenvalues of the Dirichlet Laplacian depend continuously on the geometry of the underlying domain, under suitable geometric restrictions. We show that this theoretical property is reflected in a concrete numerical situation: the convergence rate of iterative solvers for convection-diffusion problems remains stable under deformations of the domain. The connection is a superlinear estimate for preconditioned GMRES/GCR in which the relative residual errors are bounded by an explicit expression of the eigenvalues of the Laplacian, or of a symmetric positive elliptic operator in divergence form. We prove that this bound depends continuously on the domain, uniformly in the iteration index, under either regularity hypotheses on the boundary or a topological constraint in dimension two. We also establish corresponding statements on the discrete level. Two examples delimit the theory: domains bounded by a fractal curve, where continuity still holds, and perforated domains, where it fails. The theoretical results, including both examples with rough domains, are confirmed by numerical experiments.

Visual localization enables unmanned aerial vehicles (UAVs) to maintain absolute positioning in GNSS-denied environments. A common approach matches UAV images with geo-tagged orthographic maps and estimates camera pose using Perspective-n-Point (PnP) with elevations from Digital Surface Models (DSMs). However, accurate and up-to-date DSMs are often unavailable in practice. Orthographic-perspective geometry (OPG) enables DSM-free localization in scenes with varying elevations, yet existing methods typically estimate pose indirectly through intermediate matrix estimation and decomposition. To address this limitation, we propose Latent-Depth Variable Projection (LDVP), which treats the unknown scales along perspective viewing rays as latent depths. By analytically eliminating these depths and solving for the horizontal camera center in closed form given the rotation, LDVP reduces nonlinear estimation to a rotation-only problem, enabling direct recovery of metric horizontal position without assuming a planar scene. To improve localization robustness across different scene structures, we further introduce Structure-Adaptive Coupling (SAC), which uses relative scene structure inferred from monocular depth estimation to select LDVP when the matched points are not dominated by a single plane, and Planar-PnP otherwise. Our local observability analysis reveals how scene elevation variation affects the geometric constraints of OPG, providing a basis for this adaptive strategy. Extensive experiments show that LDVP consistently outperforms existing OPG-based DSM-free methods, while SAC further improves robustness across diverse scenes and substantially narrows the gap to DSM-based localization. Code will be released at https://github.com/UAV-AVL/LDVP-SAC.

Specifying segmentation targets with natural language provides flexible semantic conditioning for medical image segmentation. However, existing methods still struggle to reliably ground high-level textual semantics into accurate pixel-level spatial prompts, especially under low-contrast lesions, ambiguous boundaries, and visually similar anatomical contexts. In this paper, we propose RADAR (Residual Aggregation and Dense Alignment Representations), a parameter-efficient framework for text-guided medical image segmentation. RADAR explicitly decouples and synergizes the medical semantic anchoring capability of BiomedCLIP with the prompt-driven mask decoding ability of MedSAM2, while enabling low-cost task adaptation via LoRA. Specifically, Guided Residual Depth Aggregation adaptively aggregates cross-layer features under semantic guidance to alleviate delayed textual injection and deep semantic dilution. Structured Dense Representation Alignment leverages a frozen BiomedCLIP to construct crop-level target, boundary, and context anchors, improving the local discriminability of dense features and the reliability of automatic prompts. Multi-modal Prompt Generation further converts cross-modal semantic responses into composite text, point, and mask prompts for MedSAM2 decoding. Experiments on three public medical image segmentation datasets show that RADAR achieves competitive performance with only 0.74M trainable parameters, demonstrating its effectiveness in parameter-efficient adaptation, semantic grounding, and dense representation enhancement. The source code is available at https://github.com/JGuiidev/RADAR.

We present a mass-weighted meshless formulation for the shifted incompressible lattice Boltzmann method (LBM) whose streaming step is exactly unitary, combining with the Carleman embedding. In traditional meshless LBM, on a scattered node set the semi-Lagrangian streaming step is an interpolation, which is not unitary; a generic block encoding of this matrix therefore requires a normalization proportional to its sparsity and logarithmically many ancillas. To overcome the non-unitarity, we instead express the interpolation as the exponential exp(a Dx + b Dy) of mimetic derivative operators. Endowing each node with its Voronoi mass and applying a mass-weighted similarity transform renders these derivative operators skew-Hermitian by enforcing moment constraints together with low-wave number trigonometric differentiation conditions, so that the interpolation becomes exactly unitary. Such unitarization of interpolation leave the local collision step unchanged up to a rescaling of its quadratic term, where the same weights define the amplitude encoding of the distribution functions. For quasi-uniform node sets, the mass-weighting diagonal remains within a unit-order normalization that degrades only mildly as the Carleman truncation order grows, thereby mitigating the cost of block encoding. Numerical experiments on the Taylor Green vortex confirm that the method reproduces the full meshless LBM, with the velocity error decreasing as the Carleman order increases.

Bilevel data selection is a fundamental task with numerous applications in machine learning and statistics. A common strategy for tackling this problem is to relax the original bilevel combinatorial optimization into a continuous one. However, existing methods, including 0-1 relaxation and probabilistic relaxation, still suffer from several limitations, such as unstable gradient estimation and infeasible rounding. To address these issues, this paper proposes a new probabilistic relaxation for the multi-source bilevel data selection problem. Our key idea is to introduce multiple learnable categorical priors to parameterize a probability distribution supported only on feasible data subsets, thus naturally yielding a lossless rounding scheme. We further show that our proposed relaxation admits an effective two-point gradient estimator, which can simultaneously avoid the inverse-Hessian computation required by existing 0-1 relaxation and the unbounded score term appearing in prior probabilistic relaxation. Furthermore, we develop a reducible representation of this estimator, which substantially reduces the number of lower-level retrainings required for gradient computation. Built upon this reducible two-point estimator, we then design a novel stochastic gradient algorithm, termed ReSGD, for multi-source bilevel data selection problem, and establish a rigorous approximation guarantee for the subset returned by ReSGD under weak submodularity. Finally, extensive experiments are conducted to validate the effectiveness of our proposed ReSGD.

Diffusion-based policies have recently emerged as a powerful paradigm for offline reinforcement learning, but their reliance on multi-step denoising introduces substantial computational overhead and requires backpropagation through time during training, limiting scalability and practical deployment. In this work, we propose Instant Flow Q-Learning (InsQL), a single-step generative policy learning framework that retains the expressive capacity of diffusion models while eliminating iterative sampling and BPTT. InsQL builds on the flow-matching perspective of diffusion policies, but replaces marginal velocity parameterization with average-velocity modeling and introduces a principled compositional mechanism, yielding a theoretically grounded objective that learns average velocity consistently across scales. This formulation provides a direct noise-to-action mapping and enables single-step action generation. InsQL further unifies compositional average-velocity modeling with behavior-regularized actor–critic optimization in a single framework, requiring only a single policy network and avoiding distillation, multi-stage procedures, and Jacobian computations during training. At inference time, actions are generated in a single forward pass and can be refined via value-guided candidate selection to improve performance. Extensive experiments on standard offline RL benchmarks and real-world robotic manipulation tasks show that InsQL matches or surpasses state-of-the-art diffusion-based methods while substantially reducing both training and inference time. Overall, these results establish compositional average-velocity modeling as an efficient and scalable alternative to multi-step generative policies for offline RL.

Lifelong learning enables artificial systems to adapt to changing environments. To achieve this, an effective artificial learner should dynamically reorganize past and new experiences, maintaining stability while enabling flexible knowledge integration. However, existing efforts primarily mitigate catastrophic forgetting, lacking the ability to adaptively update memory akin to biological systems. Here, by integrating the full memory life cycle of engram neurons into artificial learners, we propose a framework that constructs a structured memory from gradient representations, which regulates parameter updates and guides memory management. Through comprehensive evaluations on four benchmarks, our approach shows promising lifelong learning capability, maintaining stability over long task sequences and supporting flexible adaptation. Beyond the performance gains, our approach offers a computational perspective on robust and flexible lifelong learning, echoing mechanisms observed in biological memory systems.

GRPO-style reinforcement learning has advanced vision-language reasoning, but its sequence-level rewards provide limited credit assignment for individual reasoning tokens. On-policy distillation (OPD) addresses this issue by providing dense supervision on student-generated trajectories, yet standard OPD assigns similar importance to all teacher-preferred tokens, including template phrases and visually irrelevant continuations. We introduce Visual Counterfactual On-Policy Distillation (VC-OPD), a grounding-aware distillation method that prioritizes tokens whose correctness depends on image-specific evidence. After a teacher-supervised warm start that stabilizes response formats and reduces noisy rollouts, VC-OPD performs on-policy distillation with two teacher evaluations for each student trajectory: one under the original image and one under a counterfactual image with corrupted instance-specific evidence. The original-image teacher distribution determines the distillation target, while the original–counterfactual teacher gap estimates token-level visual dependence and softly reweights the loss. To avoid unstable response-level update scales, VC-OPD further applies mass-preserving normalization to the token weights. This design preserves the dense supervision of OPD while shifting learning capacity toward visually grounded reasoning tokens. Experiments on multimodal reasoning benchmarks show that VC-OPD improves visual reasoning performance and produces more effective token-level distillation.

In this work, we study operator controllability of finite-dimensional closed quantum systems driven by a single coherent control. Two general Lie-algebraic results on controllability of such systems are proved. The first gives sufficient conditions under which controllability of the system is preserved when controlled energy-level shifts are added. The second gives a sufficient basis-element condition under which the dynamical Lie algebra contains $\mathfrak{su}(N)$ and the system is therefore operator controllable. These results, together with known controllability conditions, are applied to obtain a complete classification of operator controllability of all three-level quantum systems in terms of their free and interaction Hamiltonian matrix elements. This classification covers all combinations of energy-level and level-spacing degeneracies, two or three allowed transitions, as well as the presence or absence of controlled energy-level shifts, and gives necessary and sufficient conditions for operator controllability in each case.

How do language models generalize from their training data? This is a central challenge for alignment: models reliably learn their training distribution given enough samples, but we want models that behave well when deployed in new contexts. We study out-of-distribution (OOD) generalization of propensities. Our central experiment uses a range of elicitation techniques – system prompting, few-shot learning, SFT on reference answers, and GRPO – to increase a target propensity in a model, then measures how it spills over onto others across the resulting cross-elicitation matrices. We find that spillover is highly correlated between models when the same elicitation technique is used, but our SFT and GRPO runs induce different spillover profiles. Elicitation of benign traits can sometimes generalize towards undesired traits, for example a model trained to claim that it is sentient often becomes more power-seeking. We further find that spillover partially resembles trait correlations found in humans and identify three clusters of traits that account for about half of the variance using exploratory factor analysis (EFA). Across many elicitation runs, we observe that models change in characteristic ways that don't depend on the targeted trait, a phenomenon we refer to as drift. Drift moves Qwen3.5-9B towards its base model. When investigating if LLMs are able to predict spillover, we find that Claude Opus 5.5 predicts spillover slightly better than the models themselves, but worse than data-driven approaches using alternative elicitation methods or models. Overall, no single dominant predictor emerges, and generalization remains hard to predict. Code and data are available at https://github.com/nielsrolf/propensity-spillover.

Diffusion policies are increasingly used in robotic control and manipulation, vision-language-action models, and world-model-based agents. Their ability to represent multimodal action distributions offers rich opportunities for exploration in reinforcement learning (RL). However, optimizing diffusion policies with RL can reduce the behavioral diversity and further limit their exploration capability. In RL post-training, directly fine-tuning a pretrained policy may also disrupt its acquired capabilities, while action-space residuals may lack the expressive power for multimodal exploration. Together, these issues reveal a common challenge across online and offline-to-online diffusion RL: improving task performance while retaining the behavioral diversity and capabilities needed for continued adaptation. We introduce CFG-Policy, a unified, plug-and-play framework that separates exploration and exploitation into two generative policies and combines their score or velocity fields during sampling through classifier-free guidance. For online RL, a frozen exploration branch sustains behavioral diversity while an exploitation branch learns from task rewards; for offline-to-online RL, a pretrained exploitation branch remains frozen while a trainable branch steers the composed behavior. CFG-Policy preserves the underlying RL objectives and improves performance with QSM and QVPO on 5 MuJoCo tasks and with Flow-SDE+PPO on 4 RoboTwin manipulation tasks. Project page is at https://zhy-liu.github.io/cfg-policy-page.

Pipeline parallelism has become a critical technique for training large language models. To address the throughput limitation of existing sequence-level methods that schedule subsequences unidirectionally, we propose bidirectional sequence-level interleaved pipeline parallelism (BSIPipe), which co-schedules two opposing V-shaped interleaved pipelines at the subsequence level. To bound the activation accumulation from subsequence scaling, BSIPipe introduces a basic-unit concatenation mechanism that keeps activation memory invariant to the subsequence count. To eliminate communication deadlock risk from bidirectional scheduling, BSIPipe employs a communication optimization strategy that combines topology-aware device mapping with communication-computation overlap. In addition, BSIPipe composes with tensor parallelism to overcome the memory limitation of single-dimensional parallelism, neutralizing its bidirectional memory overhead while maintaining throughput. Experiments on GPT and LLaMA3 demonstrate that BSIPipe achieves average speedups of 1.11$\times$ to 1.13$\times$ in long-sequence training over SOTA sequence-level baselines.

Ultra-low-bit scalar quantization offers a regular arithmetic structure for efficient deployment of large language models, but preserving predictive behavior at extreme precision remains challenging: with only a few reconstruction levels, accurate weight representation must translate into consistent predictions from a small calibration set. We propose FidelityQ, a scalar quantization framework that preserves predictive fidelity at weight precisions down to 2 bits. For accurate quantization, we introduce Information-Aligned Analytic Coding (IAC), which shapes each weight row toward a centered symmetric source via randomized Hadamard mixing and fits a mirrored four-level minimum-distortion quantizer to its empirical weights. Every level set in this family decomposes exactly into two sign-valued bases with associated scales, combining source-adaptive reconstruction with lookup-free decoding compatible with scaled integer arithmetic. Our analysis further shows that residual predictive discrepancies are heavy-tailed and concentrate on tokens the teacher predicts confidently, motivating Knowledge-Intensive Calibration (KIC) for consistent quantization. KIC ranks sequences by the tail of token-wise teacher-student divergence, allocates a limited calibration budget to the highest-scoring samples, and restores predictive agreement by updating only quantization levels and scales under teacher supervision, keeping pretrained weights frozen. Experiments on the LLaMA and Qwen families demonstrate the effectiveness of FidelityQ in weight-only and joint quantization settings. On LLaMA-2-7B, FidelityQ achieves a WikiText2 perplexity of 6.62 at W2A16 and improves the prior state-of-the-art W2A4KV4 result from 8.31 to 6.96, while reducing linear-layer weight memory by 8.0x relative to FP16.

Generative AI gives audiences new ways to portray real sporting figures through familiar fictional worlds. Expanded opportunities to create, however, need not broaden cultural representation or distribute attention evenly. We examine this tension through the supply, demand, and circulation of anime style football videos on Instagram. Using 2,021 posts and associated video and account data, we combine caption entity extraction, human-reviewed visual identity clustering, engagement analysis, and content-reuse networks. Representation is uneven across athletes, while Blue Lock, Naruto, and One Piece account for 60.1% of explicit franchise mentions. Among posts referencing generative tools, rankings by total engagement differ from rankings by average engagement per video, distinguishing aggregate visibility from response to individual posts. Reuse is extensive: 772 of 1,548 evaluated videos belong to 124 detected groups, including 71 spanning multiple known accounts. Shared material connects a large account component alongside smaller groups, and later observed uploads receive lower median normalized engagement than first observed appearances. These findings characterize generative cultural crossover as a practice organized around concentrated cultural resources, uneven attention, and extensive recirculation. More broadly, they distinguish opportunities for visual authorship from the processes through which particular representations become widely visible.

Clustering is typically performed using only object features, although additional information about relationships between objects may be available and can be incorporated through constraints. Among these, pairwise constraints require two objects to belong to the same cluster or to different clusters. Several extensions of the k-means algorithm accommodate such constraints, but they sometimes fail to find a feasible assignment or incur high computational cost. Motivated by these limitations, we propose an algebraic approach to k-means clustering with pairwise constraints. The algorithm simplifies the constraints using Gröbner bases before optimization, improving the efficiency of cluster assignment. It can also detect whether the constraint set has a feasible assignment before optimization. Comparative experiments with existing algorithms showed that the proposed algorithm achieved comparable or better clustering quality at a lower computational cost, particularly when the numbers of constraints and clusters were small.

We study how local coherenAAce of abelian categories behaves under gluing. For AB5 locally finitely presentable abelian categories, we give conditions on the gluing functors under which local coherence is transferred along a gluing $(\mathcal{A}, \mathcal{B}, \mathcal{C})$: from $\mathcal{A}$ and $\mathcal{C}$ to $\mathcal{B}$, and conversely from $\mathcal{B}$ to $\mathcal{A}$ or $\mathcal{C}$. The coherence theorem for augmented homotopes of Bondal and Zhdanovskiy is recovered as a special case, the coherence theorem for trivial extensions of Fossum, Griffith, and Reiten is a companion result in the same direction. We also introduce quasiprojective pairs of adjoint functors and prove a coherence criterion that generalises the criterion of Gomez Pardo and Martinez Hernandez to arbitrary Grothendieck categories. Finally, we extend Stenström's characterisation of coherence via FP-injective modules to compactly assembled Grothendieck categories: such a category is coherently assembled if and only if the class of CM-injective objects, defined through compact morphisms, is closed under filtered colimits. Along the way we revisit the various equivalent conditions for the coherence of a ring, collecting them in a single place. The proofs make use of the compactly assembled categories of Efimov.

The notion of tipping points and related terminology have so far had inconsistent and sometimes confusing definitions in both scientific and popular literature. While it is difficult for the scientific community to align popular usage of the term tipping point with a precise definition, technical usage of related terms would benefit from greater consistency and rigor. Toward this end, we offer a systematic set of terms to clarify formal communication around potential tipping dynamics, with focus on examples from Earth system dynamics.

We study electrically charged black branes in four-dimensional Einstein-Maxwell-scalar theory with Maxwell coupling $Z(\phi)=e^{3\phi/\sqrt7}$, whose potential has an AdS$_4$ fixed point only in the infrared. For nonzero hair parameter $\alpha$ the scalar grows logarithmically at large radius and the geometry is not asymptotically AdS, so the holographic dictionary is a working assumption. With the scale-invariant multi-trace boundary condition of the neutral branes, giving conformal thermodynamics, we work to second order in the charge, obtaining the Maxwell field and susceptibility in closed form, plus the thermodynamics, condensate, incoherent conductivity and cumulant ratio $T^2\chi_4/\chi_2=6c(\alpha)<0$ for all $\alpha$ considered. Independent perturbative computations and first-law closed forms agree within $4\times10^{-6}$; nonlinear solutions reproduce second-order results to $1.2\times10^{-5}$ and $c$ to $6\times10^{-4}$. They are locally thermodynamically stable where constructed, and the pressure is analytic in $(\mu_Q/T)^2$ near zero density. No regular extremal horizon exists at finite scalar value, and $\rho/s<\sqrt{21}/(2\pi)$ exactly. The extremal limit is an AdS$_2\times\mathbb R^2$ throat where the scalar grows as $\ln\ln(1/u)$ in the AdS$_2$ radial coordinate $u$; the bound is saturated there, and extremal values are approached as powers of $1/\ln(\mu_Q/T)$. With a Dirichlet condition on the scalar source, the same solutions describe a non-conformal theory with scale $\Lambda$, whose charged branes exist only below $T_{\max}(\mu_Q)$, which falls from $0.194\Lambda$ at zero density to zero at $\mu_Q=0.506\Lambda$. This boundary is a diffusive instability where the charge susceptibility diverges at nonzero density, and the bulk viscosity violates Buchel's bound at all densities. Quasinormal modes with the normalizable large-radius condition reproduce its hydrodynamics.

Persistent viral infections arise from complex interactions between viral replication, host cell responses, and ongoing viral evolution. A general framework linking viral fitness to persistence dynamics is lacking. Here, we develop for the first time a mathematical model of viral persistence that takes into consideration viral fitness variations. Essential to the model is the partition of the classical fitness parameter into three components: replicative, infective, and dispersal fitness. The model was initially inspired by a new experiment on hepatitis C virus (HCV) persistence, established in human hepatoma cells, also reported in this work. This experiment documents two strikingly different viral trajectories depending on the initial replicative fitness of the viral population used to establish persistence. The dynamical model describes the interactions among uninfected cells, infected cells, and infectious virions, and it incorporates, through a continuum, two alternative mechanisms of viral release from cells: budding and lysis. Analysis of the model reveals that viral fitness parameters organise infection outcomes into distinct dynamical regimes. Low replicative and dispersal fitness values lead to viral extinction, whereas high values enable persistence through either stable coexistence or recurrent infection waves. The space of fitness discloses a hierarchy among these parameters, with replicative and dispersal fitness being able to trigger important shifts in the outcome of the infection as opposed to infective fitness. The model identifies trade-offs between replication and dispersal that shape viral production and predicts slow dynamical regimes in which infection may persist despite low detectable viral loads. It provide candidates mechanisms capable of generating the persistence patterns observed experimentally.

The energy densities of the quantised scalar and electromagnetic fields need not be positive, but their averages along timelike worldlines are constrained by Quantum Energy Inequalities (QEIs) that hold in flat and curved spacetimes for arbitrary Hadamard quantum field states. However the general QEI bound is not easy to compute in closed form. Here, we compute closed form expressions for the massless scalar and electromagnetic fields along stationary worldlines in Minkowski spacetime. These worldlines are solutions to the four-dimensional Frenet-Serret equations with constant curvature invariants and include inertial, uniformly linearly accelerated, and uniformly rotating worldlines as special cases. The QEI bound depends on a choice of tetrad along the worldline, and we compute it for any tetrad with constant angular velocity relative to the Frenet-Serret tetrad. Optimising over the angular velocity, we show that the tightest electromagnetic QEI bound occurs when the tetrad is invariant under Fermi-Walker tetrads. Surprisingly, the Fermi-Walker tetrad does not produce the tightest QEI bound for massless scalar fields, and we investigate the optimal bound both analytically and numerically. Our results and methodology significantly improve on those in [CJ Fewster & J Thompson, Class. Quantum Grav. 40 (2023) 175008], in which only Frenet-Serret tetrads were considered for massless scalar fields.

Multi-finger hands contact objects at different times, so a global close command can overload early-contact fingers while others are still moving. Dense tactile arrays address this problem but add hardware, calibration, bandwidth, and computation. We present an edge-native pipeline that uses only built-in joint-angle and pre-use-calibrated actuator-load feedback to recognize the grasped object and predict an independent Stop event for each finger. Four samples and their first differences form a 4-by-20 contact-evolution window. At its core is a heterogeneous dual-expert architecture, termed DualExpert, that assigns complementary tasks to a Temporal Convolutional Network (TCN) and a Finger Graph Filter Network (FGFN). The TCN models short-term contact evolution and supplies all five Stop probabilities, while the FGFN encodes finger topology and contributes only to object classification. Fixed 0.7/0.3 class-probability fusion reaches 93.78% trajectory-level classification accuracy on 225 held-out trials, improving the standalone TCN and FGFN by 4.00 and 2.22 percentage points, respectively. The TCN Stop path attains 95.25% F1. The dataset contains 1,500 automatically collected trajectories from five object instances. In Flash deployment, mixed accelerator execution retains 93.78% classification accuracy and 94.84% Stop F1 with 2.890~ms mean inference time and 9.172~ms mean sample-to-stop latency. Across 50 physical trials, the system achieves 96.00% recognition and 98.00% grasp success while the complete embedded board draws approximately 0.80~W.

In a type theory with a cumulative universe hierarchy, subtyping is often incorporated to lift lower universe levels to higher ones. In practice, kernels of proof assistants typically implement universe subtyping conservatively: subtyping only propagates covariantly into the output types of $\Pi$ types, while input types must be equivalent. A full-blown subtyping relation also compares the input types contravariantly. However, contravariant subtyping is not justified by the existing set-theoretic model, and poses challenges in the development of a complete subtyping algorithm. We present \mclttsub, a complete mechanized study of contravariant universe subtyping for a core Martin-Löf type theory (MLTT), built as an extension of the verified McTT kernel in Rocq. We re-establish the syntactic meta-theory and the soundness and completeness properties of the normalization-by-evaluation (NbE) algorithm. To complete the verified pipeline for a type-checker, we give two complete and sound subtyping algorithms. The first one renormalizes output types in every $\Pi$ iteration. Despite a simple completeness proof, this algorithm incurs additional computational cost. The second algorithm hence circumvents this cost by avoiding the renormalization at all. It simply recursively compares two already normalized types structurally. Nevertheless, a completeness proof of this algorithm in a semantic approach requires to reason about normalization in sub-contexts, a capability beyond what the current semantic gadget offers. Instead, we conduct a program equivalence proof through bisimulation relations. Using this technique, we prove that the NbE algorithm returns equal normal forms in sub-contexts up to universe levels, and successfully conclude the completeness of the subtyping algorithm.