arXiv:2607.06546v1 Announce Type: new Abstract: Denoising graphs is a fundamental problem in graph learning and the core operation of graph diffusion models. Attention-based architectures like graph transformers have recently shown promise in denoising graphs. However, our principled understanding of attention-based graph denoising remains limited, making it unclear whether standard attention is the right mechanism for this task. Here we show that, under a denoising objective, linear attention is suboptimal and can only learn an average spectral denoising filter over the training distribution. This creates a fundamental limitation as graphs often vary spectrally across the distribution. To overcome this limitation, we introduce Spectral Attention, which directly utilizes the input graph spectrum and provably outperforms linear attention by a margin governed by the spectral diversity of the distribution. We then derive Graph Convolutional Attention (GCA), a practical and permutation-equivariant realization of this idea that implements spectral denoising through graph-filtered queries and keys. For stochastic block models, GCA provably matches the idealized Spectral Attention mechanism. We further show that the softmax operation, that follows the attention, provides additional denoising by approximately projecting noisy eigenvectors onto the clean eigenspace. Empirically, replacing linear attention with GCA consistently improves graph denoising and diffusion on synthetic and real datasets, with gains strongly correlated with spectral diversity. In DiGress, GCA matches standard graph-transformer performance without computing expensive structural features, and when combined with the recently proposed PEARL positional encodings, avoids explicit eigendecomposition computations resulting in faster inference without degrading quality. The code can be found here: github.com/shervinkhalafi/graph_conv_att
Science Journals
arXiv:2607.06101v1 Announce Type: new Abstract: AI coding agents are rapidly reshaping how software is built, with developers increasingly delegating substantial coding tasks to autonomous agents in pursuit of higher productivity. While these gains are real, they come at the cost of incidental learning. Developers historically acquired informal knowledge through effortful problem-solving, and this has long shaped how software engineering expertise develops. However, with over-reliance on agentic coding, unpracticed skills could atrophy silently over time. As this learning pathway is short-circuited, developers risk silently accruing Knowledge Debt, a developer-level analogue of Technical Debt, where changes the agent executes that the developer cannot fully understand accrue over time. In this paper, we argue that incidental learning will not re-emerge on its own and must be consciously designed back into developer-agent interactions, and propose six design principles to guide such systems. We then present "SHIELD", a multi-agent system grounded in the notion of "agents that teach", that operationalizes these principles by leveraging the AI coding agent's own reasoning to surface contextual, out-of-band learning moments without disrupting developer flow. Through this work, we envision a path toward learning-aware development environments where productivity and learning are complementary, not competing.
arXiv:2607.06103v1 Announce Type: new Abstract: Efficient decentralized resource allocation remains a fundamental challenge in NR-V2X sidelink communications, where conventional Semi-Persistent Scheduling (SPS) and Dynamic Scheduling (DS) suffer from persistent collisions and limited adaptability under dynamic and dense conditions. This paper proposes Repeated Contention Scheduling (RCS), a novel resource allocation algorithm based on multi-round, feedback-driven contention that eliminates long-term reservations and enables fully distributed operation. Simulations demonstrate that RCS outperforms SPS and DS in terms of success probability, collision and loss reduction, and timeliness metrics such as Packet Inter-Reception Delay and Age of Information, particularly under high load. The practical feasibility of the approach is validated through an SDR-based experimental testbed, which confirms robust operation under realistic hardware impairments and closely matches theoretical and simulation results. These findings establish RCS as a viable and scalable solution for resource allocation in 5G NR sidelink and a promising candidate for future 6G vehicular communication systems.
arXiv:2607.06565v1 Announce Type: new Abstract: Unified 3D foundation models aspire to generate 3D assets and reason about them in language within a single backbone, but their text-3D interaction remains largely implicit. Existing methods concatenate text and 3D tokens into a flat sequence and rely on self-attention, collapsing coarse structural cues and fine geometric details into one undifferentiated representation. We introduce ELSA3D, a unified 3D model that addresses this with elastic semantic anchoring, structuring language and geometric reasoning jointly along matched abstraction scales. ELSA3D represents geometry with a scale-aware octree tokenizer and introduces Anchor Tokens, sparse cross-modal units that select semantic cues, route them to the most relevant 3D scale, retrieve scale-specific geometric evidence, and write the fused signal back into the unified representation, keeping interaction sparse yet precise. A lightweight per-block router makes both computation and reasoning elastic, choosing which text tokens instantiate anchors at which geometric scale so that cross-modal capacity concentrates where alignment is most needed. ELSA3D achieves state-of-the-art performance across image-to-3D generation, text-to-3D generation, and 3D captioning, outperforming the strongest unified baseline while roughly halving FLOPs and inference latency relative to the non-elastic version of the same model.
arXiv:2606.08048v1 Announce Type: cross Abstract: Diffusion language models (DLMs) offer substantial speed advantages through parallel decoding, but the lack of token dependencies limits generation quality compared to autoregressive (AR) models. Recent progress attempts to bridge the gap via importance sampling, with DLM being the proposal and AR being the target. However, due to the huge gap between their distributions, the sampling requires a large number of particles and is thus expensive to compute. In this paper, we introduce PoE-Bridge, a novel decoding framework that drastically improves generation speed and accuracy by introducing an intermediate distribution to bridge the gap. The distribution is constructed as a Product-of-Experts (PoE) of the DLM proposal and the AR target. With the intermediate distribution, we first use the DLM to draft multiple continuations in parallel, then apply rejection sampling to verify the drafted tokens and move the resulting candidates toward the PoE. We then use importance sampling to further correct the PoE-aligned candidates toward the AR target. We further propose several improved techniques, including mixed-temperature sampling for enhanced diversity and elastic rejection windows for reducing wasted verification. Empirically, PoE-Bridge achieves significantly improved accuracy with $5\times$ speedup over the standard DLM decoding approach, and recovers at least 95% of the target AR model's performance, efficiently advancing most of the quality gap on challenging mathematical reasoning and coding tasks. Our code is available at https://github.com/juntongshi48/poe-bridge.
arXiv:2607.05705v1 Announce Type: new Abstract: Multi-agent motion prediction is essential for automated vehicles to understand the intentions of surrounding vehicles. However, previous prediction-based and anchor-based methods have limitations in mode diversity and prediction accuracy, respectively. These limitations may cause inadequate safety assessments and behavioral deviations in automated vehicles. To address this issue, a mode-world weighted regression loss is proposed to bridge the gap between these features. Specifically, this approach mitigates mode collapse while simultaneously improving world ranking and top-1 confidence. Furthermore, the proposed iterative decoder improves prediction accuracy by recurrently and segmentally generating trajectories. Experimental results show the proposed method ranks first in the Argoverse 2 multi-agent motion forecasting benchmark against other methods.
arXiv:2607.05709v1 Announce Type: new Abstract: Cognitive therapies have been shown to enhance the quality of life and well-being of people living with dementia (PwDs). However, their use remains limited due to a shortage of trained professionals and the significant time and training required of informal caregivers. To address this gap, we developed and deployed a social robot capable of autonomously delivering cognitive stimulation therapy (CST) in the home. Nine PwDs participated in a one-week ($7$ days) study that involved daily robot-led sessions. Participants engaged positively with the system, completing nearly half of the scheduled sessions, an adherence rate higher than typically observed in caregiver-led CST. Our findings also highlight the crucial role of family members, who often supported session initiation and occasionally joined the activities, enriching the interactions. This work demonstrates the feasibility and potential of socially assistive robots to deliver in-home cognitive therapy, offering a scalable approach to extend access to dementia care.
arXiv:2607.06334v1 Announce Type: new Abstract: We give a concise description and an improved analysis of the Random-Action-Removal algorithm for solving 2-player, 0-sum, turn-based, possibly infinite duration, stochastic or non-stochastic games played on graphs, or on finite sets of states. More generally, the algorithm can be used to find the sink of an Acyclic Unique Sink Orientation (AUSO) of a non-binary hypercube. The families of games that can be solved by the algorithm include discounted and non-discounted stochastic games (SGs) and Mean Payoff Games (MPGs). The obtained algorithm is the fastest known randomized algorithm for solving such games, slightly improving on a much more complicated algorithm of Hansen and Zwick (STOC 2015). The Random-Action-Removal algorithm is an adaptation of the Random-Facet algorithm used to solve linear programming (LP) problems, or, more generally, LP-type problems. Two dual variants of the Random-Facet algorithm were developed independently by Kalai (STOC 1992) and by Matou{\v{s}}ek, Sharir and Welzl (SoCG 1992). For LP problems, the algorithm of Kalai is a primal \emph{simplex} algorithm, while the algorithm of Matou{\v{s}}ek, Sharir and Welzl is a dual \emph{simplex} algorithm. The Random-Action-Removal algorithm for games or AUSOs is an adaptation of the dual algorithm of Matou{\v{s}}ek, Sharir and Welzl, and is a randomized \emph{strategy iteration} algorithm. Our improved analysis shows that the Random-Action-Removal algorithm solves games with~$n$ states and $m\ge 2n$ actions in $e^{O(\sqrt{n\ln(m/n)})}$ time. This improves on a previous $e^{O(\sqrt{n\ln(m/\sqrt n)})}$ bound for the algorithm that follows from the analysis of Matou{\v{s}}ek, Sharir and Welzl (SoCG 1992). An $e^{O(\sqrt{n\ln(m/n)})}$ bound, with worse constant factors, was previously obtained using a much more complicated algorithm for solving LP and LP-type problems of Hansen and Zwick (STOC 2015).
arXiv:2607.05410v1 Announce Type: new Abstract: We present CANONIC: governed intelligence that compiles digital artifacts into an evidence ledger at scale. Large language models generate prose faster than anyone can check it, the failure Oxford Languages named 'slop', its 2025 Word of the Year. CANONIC governs whether content may enter a corpus the way a compiler decides whether a program is well-formed: mechanically, by a grammar, at the boundary of admission. Governance reduces to three axioms (Triad, Inheritance, Introspection) that map one-to-one onto compiler theory's syntax, scope-resolution, and type-system layers, and admission is a decidable, linear-time check. We then ask, with a pre-registered cross-provider benchmark across four regimes, whether structural admission keeps slop out. It does not: no prose-reading gate reliably separates reliable from unreliable content. Slop is not a property an algorithm computes. It is a verdict of domain expertise. So a governance layer does not decide slop; it keeps the record auditable -- every claim anchored to a definition, a commit, and an evidence window, reproducible and checkable end to end.
arXiv:2607.05492v1 Announce Type: cross Abstract: Quantum information theory is built on entropic quantities; among them, the sandwiched R\'enyi relative entropy is a fundamental divergence with various applications, and its data processing inequality (DPI) under quantum channels is a cornerstone result. In this work, we present a Lean 4 library for quantum information, designed as a reusable formal infrastructure for theoretical analysis. As a central demonstration of the library, we formalize the DPI for the sandwiched R\'enyi relative entropy for positive semidefinite operators on finite-dimensional quantum systems. The library provides a basis-independent operator-theoretic framework for finite-dimensional quantum mechanics compatible with the standard mathematical library Mathlib, including reusable interfaces for finite-dimensional systems, states, channels, tensor products, partial traces, Choi operators, Kraus representations, and Stinespring representations. It also builds infrastructure for noncommutative trace inequalities, including operator monotonicity and convexity via the real continuous functional calculus, block-operator positivity, Hilbert-Schmidt operator spaces, Jensen's operator inequality, generalized perspectives, operator power means, and Lieb-Ando trace inequalities. On top of this framework, we formalize entropy-specific ingredients for the DPI: variational formulas for the sandwiched quasi-entropy via Young and reverse-Young inequalities, tensor-product compatibility of real powers, and Haar measures on unitary groups. Together, these components yield a Lean formalization of the DPI, give strong subadditivity as a corollary, and provide the last missing component needed to complete the Lean formalization of the generalized quantum Stein's lemma. More broadly, the development provides machine-checkable foundations for future formalized and AI-assisted research in quantum information theory.
arXiv:2607.05484v1 Announce Type: cross Abstract: The adoption of non-parametric machine learning models for regulatory capital estimation introduces a fundamental governance challenge: the inability to explain model outputs in a manner auditable by supervisory bodies. This 'black box' problem remains a major barrier to the adoption of Gaussian Process Regression (GPR) and related ML architectures in ICAAP and CCAR workflows despite their predictive advantages over traditional parametric approaches. This paper addresses this barrier through SHARC (SHAP for Regulatory Capital), an explainability framework for the Hybrid GPR-HS architecture and its stress-testing extension. SHapley Additive exPlanations (SHAP), derived from cooperative game theory and satisfying the properties of Local Accuracy, Missingness, Consistency, and Efficiency, are applied to Stressed Value-at-Risk (SVaR) outputs under three macro scenarios: West Asia War, Climate Risk, and AI Bubble/Regulatory Burden. SHARC decomposes SVaR into baseline, mean-driven, and volatility-driven components, enabling transparent linkage between scenario design and capital outcomes. Two findings emerge. First, SHARC consistently links non-linear SVaR outputs to underlying scenario inputs, confirming framework fidelity and providing auditable traceability of capital drivers. Second, under stress conditions, the mean return component (directional loss magnitude) dominates the variance component (volatility baseline) in determining capital levels, with implications for capital limit-setting, position management, and hedging strategy. The results establish SHARC as a regulator-aligned explainability layer that makes the Hybrid GPR-HS framework fully auditable and consistent with FRTB, ICAAP Pillar 2, and CCAR transparency requirements.
arXiv:2607.05501v1 Announce Type: cross Abstract: Pipe diagrams have emerged as a powerful framework for flexible lattice surgery compilation and spacetime optimization for the surface code. In contrast, analogous compilation techniques for color code architectures remain largely unexplored, despite the color code's favorable properties, including reduced qubit overhead and transversal single-qubit Clifford gates. In this work, we develop a pipe diagram representation for the triangular color code on the 6.6.6 lattice and establish its correspondence to ZX-diagrammatic descriptions of computation. We present distance-independent constructions of color code pipe diagrams together with explicit realizations of correlation surfaces, stabilizers, and syndrome extraction circuits. This framework enables both macroscopic optimization of logical computations in spacetime and microscopic compilation to executable syndrome extraction circuits. We demonstrate the potential for compact spacetime embeddings with the color code's geometry. These results provide a foundation for automated lattice surgery compilation and diagrammatic optimization in color code architectures.
arXiv:2607.05539v1 Announce Type: cross Abstract: Bregman Proximal Gradient methods (BPGM) exploit the underlying geometry of the objective function through a carefully chosen mirror map. In this work, we introduce a novel notion of strong convexity, termed Restricted Relative Strong Convexity, and establish linear convergence rates for BPGM under this condition. We then exploit the proposed theoretical framework to provide an in-depth analysis of the convergence of BPGM for (regularized) Kullback--Leibler regression problems, covering scenarios with both unique and non-unique minimizers, as well as regularized and unregularized formulations. Specifically, we demonstrate that using the popular Burg's entropy as a distance-generating function may only yield linear convergence for certain KL regression problems. In contrast, we show that employing a smoothed version of the Burg's entropy induces the suitable geometry required to guarantee linear convergence. We conclude with numerical experiments that nicely align with our theoretical findings.
arXiv:2607.05546v1 Announce Type: cross Abstract: We develop a unified function space theory of deep fully connected neural networks. Functions in our spaces are defined recursively as $\ell^1$-bounded linear combinations of activated functions from preceding layers, with a dictionary of affine functions at the first layer. Unlike existing theories that are largely specialized to homogeneous activations such as the ReLU, our framework provides a meaningful notion of functional complexity for deep networks with a broad range of homogeneous and non-homogeneous activation functions commonly used in practice. This simple construction unites several seemingly disparate ideas from the literature, including norm-based complexity bounds and variational characterizations of depth, and facilitates novel analyses of what kinds of functions deep norm-constrained networks can represent. To this end, we prove a novel representer theorem for our spaces and establish novel function-space complexity bounds showing that the associated function classes remain qualitatively small at arbitrary depth. In the univariate ReLU case, we prove a "depth saturation" result: depth in this setting yields only a small constant rescaling of the function class, with no added functional diversity. As a consequence, we show that deep norm-controlled ReLU functions in any dimension cannot exhibit high frequencies along any direction. This finding reveals that some commonly cited expressivity benefits of depth disappear once network complexity is controlled by an appropriate function space norm, rather than parameter count or other representational costs that permit compounded rescaling across layers. Overall, our results illustrate how a function space perspective yields new structural insights into the relationship between depth and complexity.
arXiv:2607.05561v1 Announce Type: cross Abstract: This paper introduces the topology-independent distributed multichannel Wiener filter (TI-dMWF), a novel algorithm for distributed node-specific signal estimation in wireless acoustic sensor networks (WASNs) with unconstrained topologies. The TI-dMWF enables each node in the network to compute its centralized multichannel Wiener filter solution by exchanging only low-dimensional fused signals, without requiring iterative estimation, unlike state-of-the-art approaches such as the topology-independent distributed adaptive node-specific signal estimation (TI-DANSE) algorithm. The TI-dMWF is proven optimal when each source is observed by either all nodes or only one node. Theoretical analysis and numerical simulations confirm that it achieves centralized estimation performance in a single run. Its latency as a function of the pruned-tree depth and its computational complexity are also analyzed. Its robustness is assessed in reverberant-room simulations under estimated second-order statistics, various network topologies, and deviations from the assumed observability model.
arXiv:2607.05672v1 Announce Type: cross Abstract: More than 80 years ago Kramers published a paper calculating how fast a Brownian particle escapes from a potential well over an activation barrier. Since then Kramers' model has been widely adopted by nuclear physics, biophysics and chemical physics communities as a description of activated barrier crossing. From a chemical kinetics perspective, Kramers' theory provides a mapping from continuous dynamics to discrete-state chemical kinetics. Motivated by recent developments, this Perspective provides a rigorous way of performing such a mapping, explaining why and how Kramers' theory works from several points of view. Specifically, we consider transitions of a Brownian particle between two potential wells corresponding to the ``reactant'' and the ``product'' of a chemical reaction. A central unifying idea is to divide the equilibrium ensemble of possible states of the system into two sub-ensembles corresponding to the reactant and product states and then to consider fluxes between these sub-ensembles. Importantly, naive separation based on the location measured relative to the barrier top does not result in a mapping that is physically tenable, and instead the past of the trajectory should be considered. Thus constructed reactant and product ensembles provide an internally consistent description of the problem when also viewed from two different perspectives: one based on the definition of the rate as a conditional transition probability per unit time and the other based on the relaxation modes of the time-evolution operator governing the dynamics.
arXiv:2607.05832v1 Announce Type: new Abstract: Counting queries are ubiquitous in database systems, particularly for driving internal system optimization. Learned models for cardinality estimation rely heavily on large-scale training data, yet generating such data by executing massive batches of counting queries is expensive. We propose BaCon, an efficient algorithm for batch evaluation of counting queries on top of a database system, without modifying its internals. BaCon integrates the idea of factorized databases with a workload-aware domain quantization strategy, allowing it to evaluate batches of counting queries using compact data structures rather than materializing massive join results. BaCon's design is compatible with most database management system, and we have implemented it as a client-side application on PostgreSQL with a lightweight C-language UDF (user-defined function). This implementation delivers speedups between 2$\times$ and 178$\times$ over baselines and good performance across various workloads, making training and maintenance of learned cardinality estimation models significantly more practical.
arXiv:2507.01577v3 Announce Type: replace Abstract: We consider interpolation from the viewpoint of fully automated theorem proving in first-order logic as a general core technique for mechanized knowledge processing. For Craig interpolation, our focus is on the two-stage approach, where first an essentially propositional ground interpolant is calculated that is then lifted to a quantified first-order formula. We discuss two possibilities to obtain a ground interpolant from a proof: with clausal tableaux, and with resolution. Established preprocessing techniques for first-order proving can also be applied for Craig interpolation if they are restricted in specific ways. Equality encodings from automated reasoning justify strengthened variations of Craig interpolation. Contributions to Craig interpolation that emerged from automated reasoning include variations for logics used in databases and logic programming. As an approach to uniform interpolation we introduce second-order quantifier elimination with examples and describe the basic algorithms DLS and SCAN.
arXiv:2607.05596v1 Announce Type: new Abstract: AI/ML workloads increasingly run as containers, where a container image must be downloaded to the host before the workload can start. This cold image pull lands on the critical path whenever a training or inference job scales up or a host is updated, and for GPU workloads it has become the dominant component of startup time as AI/ML images reach 31--48~GiB compressed. We present Disk-Backed Parallel Pull (DBPP), an alternative to the in-memory ordered reassembly used by containerd~2.2, the upstream container runtime. containerd splits layers into chunks fetched concurrently over HTTP range requests, but chunks that arrive out of order accumulate in the runtime heap until a sequential consumer drains them in order. This backlog grows with image size, and on GPU nodes where host memory is shared with frameworks and model weights, it leads to out of memory (OOM) termination of the runtime itself. DBPP writes each chunk directly to its target byte offset on disk, eliminating the ordering dependency and bounding memory regardless of image size. Because each layer lands on disk as a complete, seekable file, DBPP runs SHA-256 digest verification and decompression simultaneously, two passes containerd must run one after the other. In controlled experiments across five production-scale images (up to 48.5~GiB), DBPP reduces peak daemon memory by 8.7--25.3$\times$ while maintaining comparable pull throughput. On a memory-constrained node, containerd~2.2 is OOM-killed pulling a 31.4~GiB image while DBPP completes the same pull. The underlying idea reaches past container images: any pipeline that buffers data in memory only to enforce ordering can move that buffer to disk once the backing store is fast enough, trading a scarce, contended resource for an abundant one.
arXiv:2607.05758v1 Announce Type: cross Abstract: Automated experimentation is moving from closed-loop optimization toward open decision-making, where human or AI planners must forecast the consequences of candidate actions before executing them. Such forecasts require a model of both sides of the experiment: how the sample is likely to respond and what the instrument is likely to detect. We therefore introduce a coupled digital-twin framework that separates these roles and then links them. In this framework, the sample twin encodes material state inferred from prior knowledge and measurements till the moment. The instrument twin captures signal formation, feedback dynamics, and operating constraints based on prior knowledge. When coupled, the two twins estimate expected outcomes, uncertainty, and risk for candidate microscope operations. For amplitude-modulation scanning probe microscopy, we realize this framework with a physics-informed encoder of force-distance curves, a deterministic scanner model of cantilever and feedback dynamics, and sparse learned residual corrections. The encoder first recovers scanner-driving descriptors with sub-nanometer accuracy. The calibrated scanner then reproduces typical traces within a few nanometers and identifies operating-point noise amplification as the main source of mismatch. Supplementary phase analysis localizes residual error to the phase channel, which clarifies where added physics is needed. Together, these results establish coupled sample and instrument twins as a practical foundation for predictive microscope operation and autonomous experimental planning.
arXiv:2607.05778v1 Announce Type: cross Abstract: Using unprecedentedly long 2D particle-in-cell simulations, we study electron and ion acceleration in weakly magnetized quasi-parallel shocks, propagating at velocities ranging from transrelativistic to subrelativistic. At a fixed upstream magnetic field strength, low-velocity quasi-parallel shocks are dominated by the Bell instability, whereas high-velocity shocks are dominated by the Weibel instability. Both regimes accelerate ions with similar efficiency, with the Bell-dominated regime exhibiting faster growth in the maximum particle energy. The electron acceleration efficiency is strongly dependent on shock velocity. Weibel-dominated shocks have $\sim15\,\%$ of shock energy in nonthermal electrons, whereas in the Bell-dominated regime we attribute less than $\sim2\,\%$ of shock energy to nonthermal electrons. We discuss applications of our results to the bright X-ray emission from the late-stage afterglows of gamma-ray bursts, the radio emission from fast blue optical transients, and the X-ray variability in microquasars.
arXiv:2607.05829v1 Announce Type: cross Abstract: Averaged models are widely used to analyze periodically switched linear systems, yet the stability of the averaged flow does not automatically guarantee the stability of the true switched dynamics. The discrepancy arises from noncommutativity among the subsystem generators, so stability certificates benefit from bounds that expose this dependence in a form compatible with Lyapunov contraction metrics. We derive an explicit operator-norm bound for the one-period mismatch between the switched and averaged propagators, in which the leading-order error depends explicitly on the pairwise commutator norms of the scaled mode generators, with a closed-form prefactor depending only on the generator norms. This bound yields a computable threshold for the switching period below which the switched system inherits exponential stability from its averaged model, uniformly certified over admissible duty fractions. The analysis extends to an arbitrary number of switching modes via telescoping induction, and a semidefinite program provides sampled duty-dependent Lyapunov metrics for implementing the certificate.
arXiv:2607.05870v1 Announce Type: cross Abstract: Spatially heterogeneous environments continually challenge the ability of active matter to sustain coherent collective motion. Understanding how collective motion remains robust under changing environments is central to both the functioning of biological systems and the design of smart active matter. Here, we extend the Vicsek model to include a circular non-noisy region surrounded by a noisy environment - a configuration in which the noise difference sets up a contrast in local directional order between the two regions. We find that, as the surrounding noise is increased, the system passes through three distinct dynamical regimes: (i) conventional global flocking at low noise; (ii) geometry-locked motion, aligned with simulation boundaries, at intermediate noise; and (iii) vortical motion within the non-noisy region at high noise. Extending the environment to multiple non-noisy regions, we find that the geometry-locked regime can develop a directional coupling, while the vortex mode leads to antiferromagnetic order between the regions. Taken together, our results demonstrate that the spatial modulation of order and disorder offers a powerful and generic strategy for steering active matter, aligning with recent experimental observations of active particles in patterned landscapes.
arXiv:2607.05967v1 Announce Type: cross Abstract: This paper introduces, analyzes, and applies variants of the enumeration framework symmetric lexicographic symmetric-subset reverse search for the enumeration of symmetric feasible subsets of a finite set up to symmetry. The framework is implemented in detail for three applications: cocircuits, circuits, and triangulations of int configurations. There are two new methods presented and analyzed to check the lexicographic minimality of a subset in its orbit: the critical-element method and the modified switch-table method. Moreover, new application-dependent methods to reduce the number of necessary enumeration nodes are introduced: rank-pruning for cocircuits and lex-pruning for triangulations. With a C++-implementation of the ideas in the software package TOPCOM, in all three applications known benchmarks can be computed faster by a large margin. The following new numbers could be computed for the first time (among others): the number of cocircuits of the 9-cube, the number of circuits of the 8-cube, and the number of all triangulations of the product of a 5- and a 3-simplex, as well as the number of all triangulations of a point configuration in dimension six with 17~points with disconnected flip-graph (constructed by Santos). Moreover, for Santos's triangulation it has computationally been checked that its flip-graph component is indeed purely non-regular. Furthermore, in another instance in dimension five with 26 points (also constructed by Santos), a flaw has been detected: Santos's triangulation can be heuristically flipped to a regular triangulation in the original point configuration. In a mildly modified version of the point configuration, the heuristics cannot flip Santos's triangulation to a regular triangulation anymore.
arXiv:2607.06082v1 Announce Type: cross Abstract: We study a generalization of the star coloring problem on hypergraphs. For a family of connected subhypergraphs $\mathcal{F}$, we define an $\mathcal{F}$-coloring of a hypergraph as a coloring avoiding monochromatic hyperedges and any 2-colored member of $\mathcal{F}$. We let $\chi^r_{\mathcal{F}}(d)$ be the maximum of the minimum number of colors needed for an $\mathcal{F}$-coloring of an $r$-uniform hypergraph with maximum degree $d.$ We show bounds for $\chi^r_{\mathcal{F}}(d)$, that also yield results on star and acyclic coloring problem on hypergraphs.