arXiv:2606.25921v1 Announce Type: new Abstract: The Granovetter threshold model formalizes collective behavior by assuming that individual agents face a binary decision to join a movement, doing so only when the number of already active participants reaches or exceeds an intrinsic, personal threshold. In this work, we derive an exact analytical expression for the probability that a cascade halts with precisely $k$ active agents in a finite population of size $N$ triggered by a single initial instigator, and use this result to obtain the scaling corrections that govern the system near its critical boundaries. By parameterizing individual threshold heterogeneity via a Beta distribution with shape parameters $\alpha$ and $\beta$, we map how these micro-level predispositions aggregate into macro-level collective outcomes. Here, a small $\alpha$ represents a high proportion of low-threshold, highly susceptible agents, while a small $\beta$ marks a significant density of high-threshold, conservative individuals. In the infinite-population limit, a phase transition occurs at the critical parameter $\alpha = 1$, which separates an inactive phase from a regime of widespread mobilization. For a power threshold distribution ($\beta = 1$), the system exhibits a discontinuous, first-order phase transition where the active fraction jumps abruptly from 0 to 1, and the finite-size critical scaling window contracts as $N^{-1/2}$. In stark contrast, when the population features a persistent density of high-threshold agents ($\beta < 1$), the system undergoes an infinite-order phase transition characterized by an exceptionally smooth, continuous onset of collective activity, causing the finite-size critical region to contract at a drastically slower rate proportional to $(\ln N)^{-1}$. These analytical findings establish a mathematical benchmark for finite-size effects in behavioral cascades.
Science Journals
arXiv:2606.25922v1 Announce Type: new Abstract: In modern cloud architectures, multiple applications often run within the same clustered environment, sharing underlying resources. This resource sharing can cause interference among applications, leading to degraded latency and reduced system stability. As containerized microservices become increasingly central to cloud-native applications, their performance can suffer from complex interference scenarios related to resource competition. Meanwhile, most existing microservice approaches address interference either by detecting and localizing performance issues or by optimizing latency alone, without explaining why specific co-locations cause cross-application interference, and how this can inform service placement optimization. This work closes that gap by building a spatio-temporal data structure that captures the causal effects of cross-application interference. These causal effects are mathematically formalized as necessary and sufficient conditional probabilities that inform a multi-objective optimizer (Optuna). Cross-application profiling is used to simulate traces and estimate interference probabilities, while per-service latency baselines are provided by performance data, such as 95th-percentile response times (p95). Our approach supports network penalties, application isolation requirements, and adjustable weighting of necessary and sufficient causal metrics. Experimental results on real multi-application workloads show that interference-aware placements significantly reduce cross-application interference and improve response performance. Ultimately, the causality-driven multi-objective formulation gives cloud operators explicit control over interference, latency, and communication overhead when configuring service placements.
arXiv:2606.25949v1 Announce Type: new Abstract: Microservice architectures promise independent evolution through loose coupling, yet large systems often exhibit strong dependency concentration around a small set of services. In an exploratory industrial case study of a product composed of 267 microservices, we triangulated multiple dependency signals -- compile-time, run-time, and task dependencies -- and iteratively validated our interpretations with practitioners. We observed a recurring macro-structure in the dependency network that resembles a black hole: a dense core of dependency magnets, a transitional region of services increasingly entangled with the core, and an outer region of lightly connected services. Based on these observations, we propose the dependency black hole theory, mapping the network to the black hole anatomy of a singularity, an event horizon, and an accretion disk, and formulating three hypotheses about how dependency concentration emerges and evolves at scale. The theory provides an explanatory lens for reasoning about dependency growth, identifying services at risk of becoming dependency magnets, and motivating governance interventions. We outline practical implications and directions for longitudinal and multi-case validation.
arXiv:2606.25952v1 Announce Type: new Abstract: Dirichlet-to-Neumann (DtN) maps send boundary values of a partial differential equation (PDE) solution to its normal derivative on the boundary. Learning such maps across varying domains is important for boundary-value problems, but a black-box neural operator must model both the operator's non-smoothing principal behavior and its dependence on boundary geometry. We use the boundary integral representation of the DtN map to obtain, for smooth planar boundaries, a useful principal-part decomposition: a geometry-independent leading operator can be written as a universal Fourier multiplier, while the remaining geometry-dependent correction is smoother. We propose Principal-Part Decomposed Neural Operators (PPDNO), a hybrid analytic-neural framework that turns this decomposition into a geometry-conditioned operator learning model. PPDNO computes the principal part by FFT and trains a low-rank Deep Operator Network (DeepONet)-type architecture to approximate only the residual correction across families of boundary geometries. This design keeps the exact linear action on the boundary data, exposes the sampled boundary as an input to the model, and turns the learned target into a smoother operator family. We justify the decomposition theoretically by proving smoothing and separated-approximation properties of the residual, and we derive finite-node and training-error bounds for the reconstructed full map. Experiments on interior Laplace problems over elliptical and Fourier-parameterized domains, and on exterior Helmholtz problems over rose curves, show that PPDNO improves accuracy over direct neural operator baselines while adding little inference overhead and generalizing to unseen boundary data. These results suggest that analytic operator structure and geometry-conditioned learning can be combined effectively for boundary solution maps.
arXiv:2606.00288v3 Announce Type: replace Abstract: Large language models are undergoing a transition from model technology to system technology. Engineering challenges like cache reuse, context capacity, agent scheduling, and permission control resemble classical computer systems problems. This raises a question: if we treat the LLM as a CPU, KV cache as processor cache, context window as main memory, and agent framework as an operating system, can decades of computer architecture wisdom guide next generation model native systems? This paper pursues this analogy as a visionary survey. We map computer architecture concepts onto the emerging model native stack, survey literature across LLM as OS, memory management, agent frameworks, tool protocols, multi agent coordination, cognitive architectures, and safety governance, finding that each addresses a different layer without a unifying model. We propose the Intelligent Computing Architecture (ICA): six functional layers with interface contracts and design axioms. We resolve the tension over whether the LLM resembles a CPU or OS via a dual plane architecture a probabilistic execution plane (what can be computed) and a deterministic control plane (what should be computed), with every layer passing through as a graded crossover. We propose three Amdahl style design heuristics Semantic Locality, Context Budget, and Agent Speedup as organizing back of envelope models, illustrate their parameter ranges with published data, and identify predictive validation as the principal open task. We articulate analogy boundaries, note differences between silicon and model era architectures, and propose a research roadmap. This is a conceptual and survey contribution with no new experimental results.
arXiv:2606.25957v1 Announce Type: new Abstract: Locating survivors of building collapses within the first 72 hours is a critical challenge in disaster response, and existing sensing modalities provide only partial information about the structure beneath the rubble. This paper proposes drone-based quantum magnetometry as a complementary modality and develops a simulation pipeline spanning rubble physics, sensor-array deployment, and active spatial reconstruction. We use Unreal Engine to generate a steel-reinforced concrete parking-garage collapse and compute the induced magnetic field via a per-triangle dipole approximation, establishing that meaningful magnetic structure is recoverable in the sub-pT to sub-nT range from roughly 1 m above the roofline. Then, we feed sparse multi-sensor samples into a Gaussian Process Regression back-end driven by Bayesian active sampling and validate the pipeline across multiple independent collapse realizations; a three-sensor array optimizes the trade-off between gradient resolution and UAV payload constraints, and active sampling reaches peak structural correlation in roughly $100$ samples. Together, these results indicate that quantum-grade sensing could become a useful tool for drone-based structural analysis and potentially void detection in collapsed buildings.
arXiv:2606.25960v1 Announce Type: new Abstract: Large language models are turning from isolated predictors into agentic systems: they call tools, retrieve evidence, obey environment constraints, use verifiers, and complete tasks through search and multi-turn interaction. We adopts an analytical viewpoint based on "compression is intelligence": under a fixed task distribution, interface, and compute budget, a stronger agentic system lets a target object be reconstructed with fewer bits. We operationalize the measure with arithmetic coding, seed coding, and a fallback, and evaluate it in five settings: reversed text, chess moves, protein sequences, retrieval-augmented question answering, and semantic story compression; in all of them agentic components reduce codelength. These small, controlled experiments cover component types typical of real agentic systems, show that codelength can analyze how components, observers, and budgets change residual uncertainty, and offer guidance for evaluating real agent systems.
arXiv:2606.25973v1 Announce Type: new Abstract: Software vulnerability remediation is a cognitively demanding task that requires specialized security expertise often lacking in general developers. In the meantime, Large Language Models (LLMs) assisted tools show potential in vulnerability detection, location, and repair tasks. [Hypothesis:] While LLM-assistance is hypothesized to accelerate patching, it also risks introducing hallucinations or insecure code, leading to a higher likelihood of generating superficial repairs that bypass the standard functionality checks but fail the security validation. [Objective:] We aim to present an empirical experiment, unveiling the capability of LLM-assisted vulnerability patching compared to manual debugging on human participants in real-world scenarios. [Method:] We plan to conduct a controlled experiment using a Balanced Crossover design. For that, we have developed a WebApp for code execution and integrated hidden Ghost Tests to verify patch integrity beyond visible functional requirements. The experiment involves training and evaluation scenarios. The remediation speed, remediation efficacy for both standard functionality tests and security tests, and participant perception will be evaluated. [Pilot Study:] A pilot experiment with a small sample of participants has been conducted, providing insights for the following study.
arXiv:2606.25992v1 Announce Type: new Abstract: Ammonia is a high-density hydrogen energy carrier and can be decomposed to produce hydrogen for use in fuel cells. However, a significant challenge in ammonia-decomposition-based fuel cell applications is the unavoidable presence of trace ammonia impurity, which can poison the fuel cell, but the poisoning mechanism remains unclear. To address this, a three-dimensional numerical model of proton exchange membrane (PEM) fuel cells with ammonia impurities is established to explore the transport process and underlying poisoning mechanism. The influences of key factors, including ammonia concentration, operating temperature, operating humidity, and membrane thickness, are studied. The poisoning mechanism is analyzed from the perspectives of the distributions of proton conductivity, current density, and dissolved water content. The results show that ammonia diminishes the cell performance by substantially reducing the proton conductivity of both the PEM and the anode catalyst layer. Higher operating temperatures and higher operating humidity can alleviate ammonia poisoning. Decreasing the membrane thickness can also help to mitigate ammonia poisoning, but may lead to less uniform current distribution.
arXiv:2606.26013v1 Announce Type: new Abstract: We introduce a Gaussian-based spatially weighted loss framework (G-PINNs) for physics-informed neural networks (PINNs) to improve the resolution of sharp discontinuities and shock waves. The proposed method dynamically prioritizes collocation points in high-gradient regions during optimization. Without requiring prior knowledge of the shock location or trajectory, the framework can autonomously detect and track moving discontinuities directly from the PDE residual landscape, making it broadly applicable to problems in which the position of shocks or discontinuities is unknown \textit{a priori}. The approach is validated using one-dimensional quasi-inviscid Burgers' problems exhibiting both stationary and moving shock waves. For the low-viscosity regime $(\nu = 0.0005)$, the proposed method achieves $L_2$ relative errors of approximately $13\%$ and $14\%$ for the stationary and moving shock cases, respectively, compared with $45\%$ and $33\%$ obtained when using standard PINNs.
arXiv:2606.26069v1 Announce Type: new Abstract: We develop a robust algorithm for locating bound states in coupled-channel calculations. Bound states exist at energies where an individual eigenvalue of a log-derivative or ratio matching matrix passes through zero. We describe an algorithm to identify the required eigenvalue of the matching matrix over the full range of energy where it exists. This allows much simpler programming than previous methods. We also consider the choice of the matching distance $R_\textrm{match}$, where the matching matrix is defined; coupled-channel methods are most efficient if $R_\textrm{match}$ is chosen to be in the classically allowed region for all channels that support bound states of interest, but not very close to a node in the wavefunction.
arXiv:2602.06566v3 Announce Type: replace Abstract: Despite recent successes, test-time scaling -- i.e., dynamically expanding the token budget during inference as needed -- remains brittle for vision-language models (VLMs). Unstructured visual reasoning chains entangle perception and reasoning, leading to long, disorganized contexts where small perceptual mistakes may cascade into completely wrong answers. Reasoning also requires expensive reinforcement learning with hand-crafted rewards. Here, we introduce SPARC (Separating Perception And Reasoning Circuits), a modular framework that explicitly decouples visual perception from reasoning. Inspired by sequential sensory-to-cognitive processing in the brain, SPARC implements a two-stage pipeline where the model first performs explicit visual search to localize question-relevant regions, then conditions its reasoning on those regions to produce the final answer. This separation enables independent test-time scaling with asymmetric compute allocation (e.g., prioritizing perceptual processing under distribution shift), and supports selective optimization (e.g., improving the perceptual stage alone when it is the bottleneck for end-to-end performance). It also accommodates compressed contexts by running global search at lower image resolutions and allocating high-resolution processing only to selected regions, thereby reducing visual token count and compute. SPARC outperforms monolithic baselines and strong visual-grounding approaches across challenging visual reasoning tasks, such as improving Qwen3VL 4B on the $V^*$ VQA benchmark by 6.7 points and surpassing "thinking with images" by 4.6 points in an OOD setting with a $200\times$ lower token budget.
arXiv:2605.17863v2 Announce Type: replace Abstract: Watch-time prediction is a central regression task in short-video recommender systems, where labels are highly long-tailed and residual errors vary systematically across observed watch-time regions. In practice, a model may appear globally calibrated while still overestimating short views and underestimating long views, because opposite errors cancel out in aggregate. Existing methods mainly improve the first-stage watch-time predictor, but often leave such residual distributional bias insufficiently corrected. We propose DADF, a distribution-aware debiasing framework for watch-time regression. Instead of replacing a deployed predictor, DADF performs second-stage multiplicative residual correction on top of it. DADF combines three complementary designs: a dynamic distribution-aware transformation for stabilizing long-tailed correction targets, a debias-factor-aware module for modeling heterogeneous residual patterns using inference-time observable factors, especially video duration, and a multi-label-aware module that exploits auxiliary prediction signals from engagement heads. We evaluate DADF on public short-video benchmarks and a large-scale industrial ranking system. DADF consistently improves both pointwise accuracy and ranking quality across datasets and backbones. In the industrial setting, it achieves an aggregated 2.07 percentage-point ranking-quality gain over the production baseline, consistently reduces MAE, and yields statistically significant online lifts of 0.649% in average time spent per device and 0.656% in total app time. These results demonstrate that DADF effectively mitigates local calibration bias and provides a practical plug-in solution for debiasing long-tailed continuous targets. The source code is available at https://github.com/liuzhao09/DADF.
arXiv:2606.25118v1 Announce Type: cross Abstract: In this paper, we analyze the bit complexity of deciding whether a given polynomial can be represented as a sum of squares of polynomials. We show that the weak membership problem for the sum-of-squares cone lies in $\mathrm{P}$. Furthermore, we give a polynomial-time algorithm which computes, for a given polynomial and positive parameter $\epsilon$, an $\epsilon$-relaxed closest sum-of-squares polynomial.
arXiv:2606.24897v1 Announce Type: new Abstract: Biomedical text mining, scientometrics, and the construction of training corpora for biomedical large language models (LLMs) all assume that the abstract text returned by a bibliographic API faithfully reproduces the published abstract. This pre-registered audit (OSF osf.io/269b5) tests that assumption for four widely used public APIs (PubMed E-utilities, Crossref, OpenAlex, Semantic Scholar) against PubMed Central (PMC) JATS XML as a common ground truth. From a complete enumeration of the PMC Open Access subset for 2024 (about 700,000 records), a simple random sample of 4,000 English-language research articles was drawn; for each, we recorded whether Unicode characters from four pre-specified classes present in the JATS abstract (typographic punctuation, mathematical/scientific symbols, Greek letters, special whitespace) were preserved by each API. Two systematic, deterministic losses met the pre-registered criterion (upper 95% CI bound below 5%): the PubMed AbstractText field preserved typographic punctuation in only 0.6% of eligible abstracts (95% CI 0.3-1.0%), and OpenAlex preserved special whitespace in 0% (0.0-0.4%). A blinded mechanism audit attributed the first loss to character substitution and the second to inverted-index serialization. Mathematical symbols and Greek letters were preserved faithfully (over 95%) by all four APIs. Separately, Crossref returned no abstract for 24.6% of papers (coverage 75.4%, 95% CI 74.1-76.7%), concentrated in specific publishers (Elsevier and ACS: 0%). Character-level fidelity is therefore API-dependent and undocumented: the same publisher-deposited JATS text carries different surface signatures depending on the serving API, with direct consequences for tokenization-sensitive bibliometrics, corpus construction, and character-level indicators of LLM-assisted writing.
arXiv:2606.24986v1 Announce Type: new Abstract: Automated cattle posture-classification systems frequently report near-perfect accuracy, yet their robustness under realistic deployment conditions remains largely unknown. In particular, it is unclear whether multimodal sensor fusion improves generalisation or leads models to rely on context-specific signals that fail under distribution shift. Here, we evaluate the robustness of automated posture classification (lying versus standing) using collar accelerometers, rumen-bolus sensors, and environmental measurements collected from a pasture-based beef cattle herd across two consecutive years (2024-2025). XGBoost served as the primary model, with Logistic Regression, Random Forest, and Long Short-Term Memory networks evaluated as comparative baselines. Model robustness was assessed under progressively more stringent evaluation protocols, ranging from conventional random train-test splits to leave-one-animal-out validation and cross-year evaluation on an independent cohort of previously unseen animals recorded one year later. While multimodal models achieved strong within-year performance (macro-F1 0.94), the performance declined substantially under cross-year evaluation (macro-F1 0.49). Explainability analysis revealed persistent reliance on rumen-bolus activity and environmental variables even when predictive performance deteriorated. Distribution-shift diagnostics further confirmed substantial differences in feature distributions between recording years. Our findings demonstrate that commonly used evaluation protocols can substantially overestimate real-world performance and that multimodal sensor fusion may reduce, rather than improve, robustness under temporal distribution shift. More broadly, the results highlight that benchmark accuracy alone is insufficient to assess deployment readiness and underscore the need for robustness-centred evaluation in livestock-monitoring research.
arXiv:2603.29813v3 Announce Type: replace Abstract: The demand for better prediction accuracy and higher execution performance in neural networks continues to grow. The emergence and success of Large Language Models (LLMs) have produced many cloud-based tools for software engineering tasks such as code suggestion. Although effective, cloud deployment raises concerns over privacy, latency, and reliance on network connectivity. Running LLMs locally on personal devices such as laptops would address these issues, because it enables offline use and reduces response time. However, local deployment is challenging, since commodity devices lack high-performance accelerators such as GPUs and are constrained by limited memory and compute capacity, which makes it hard to execute large models efficiently. We present Ditto, a framework that optimizes both the model size of Code LLMs and the inference programs that execute them. Our approach integrates two components. The first is a quantization technique inspired by product quantization, which groups model parameters into per-block codebooks via K-Means clustering and stores each weight as a bit-packed low-bitwidth index. The second component is a compilation pass integrated into LLVM that automatically detects and replaces unoptimized General Matrix-Vector Multiplication (GEMV) operations, with calls into Basic Linear Algebra Subprograms (BLAS) libraries that are highly optimized for the target hardware. The output of Ditto is a compiled executable that runs the selected Code LLM on commodity hardware. We evaluate Ditto on three popular Code LLMs, namely Code Llama, MagicCoder, and OpenCodeInterpreter, achieving up to 10.5$\times$ faster inference, 6.4$\times$ lower memory usage, and 10.5$\times$ lower energy consumption compared with their original inference pipelines, while preserving accuracy close to the full-precision models, with an average loss of only 0.27% in pass@1.
arXiv:2606.25101v1 Announce Type: new Abstract: We consider wideband channel estimation for extremely large-scale multiple-input multiple-output (XL-MIMO) arrays under hybrid analog-digital compression, in which a uniform linear array (ULA) is observed through far fewer radio-frequency (RF) chains than antennas. At a carrier frequency of 28 GHz with bandwidths reaching several hundred MHz, the standard narrowband polar-domain channel model fails: the near-field Fresnel curvature becomes subcarrier-dependent, and the compressed observation destroys the per-subcarrier spatial covariance structure that narrowband methods exploit. We propose the Wideband Cross-subcarrier Kullback--Leibler (WB-CL-KL) estimator, which jointly estimates angle and range directly from the compressed sample covariance, without full-array reconstruction, by fitting a structured Fresnel covariance model across orthogonal frequency-division multiplexing (OFDM) subcarriers via a cross-subcarrier Kullback--Leibler (KL) divergence criterion. We also derive the wideband compressed-domain Cram\'er--Rao bound (CRB) -- the performance lower bound for this hybrid architecture -- from the Slepian--Bangs formula, and decompose its gain over the narrowband bound into a data-diversity component of +27.093 dB and a geometric-diversity component of +0.701 dB, totalling +27.793 dB at B = 400 MHz (Propositions 1 and 2). In the single-path line-of-sight regime, WB-CL-KL attains a range root-mean-square error of 19.8 mm against a 19.9 mm bound at signal-to-noise ratio (SNR) = 10 dB, a ratio of 0.996. Under the 3GPP Urban Micro (UMi) path-loss and shadow-fading SNR distribution, it achieves a bound ratio of 0.959 at the median deployment SNR of 9.6 dB, indicating near-CRB operation at the representative deployment point, where the compressed-domain bound is evaluated at the scene-median geometry.
arXiv:2606.25313v1 Announce Type: new Abstract: Probabilistic computers built from p-bits have been proposed as hardware accelerators for sampling and optimizing Ising models, but existing systems have been confined to a single chip, capped by its capacity and memory bandwidth. Here we break this limit by networking FPGAs into a single Ising machine far larger than any one device could hold, realizing a programmable probabilistic computer with one million p-bits. The machine performs Gibbs sampling at over a trillion flips per second while keeping every coupling weight in local on-chip memory. During execution, devices exchange nothing but 1-bit boundary states. This architecture exposes a question fundamental to any distributed sampler: how frequently boundary information must be refreshed for a partitioned machine to behave as an unpartitioned one. Using three-dimensional Edwards-Anderson spin glasses, we show that the answer is set by a single timing ratio, eta = f_comm/f_p-bit, of the boundary-exchange frequency to the local p-bit update frequency. Above a topology-dependent threshold, the distributed machine matches a monolithic GPU reference. Below it, residual energy still decays as a power law but with a reduced exponent, turning parallelism into a quantifiable throughput-accuracy tradeoff. A theoretical cluster mean-field model reproduces the same behavior, showing that this tradeoff is a universal property of partitioned stochastic dynamics. These results provide a programmable million-p-bit platform, demonstrated across spin glasses, Max-Cut, and Boolean satisfiability, together with a quantitative design rule for scaling probabilistic computers beyond the single-chip limit.
arXiv:2606.23870v2 Announce Type: replace Abstract: PLCverif is the most mature open-source platform for PLC formal verification, developed at CERN and in production use since 2019. Yet it has two fundamental limitations: no support for Ladder Diagram (LD) programs, the dominant PLC notation, and reliance on CBMC as its primary backend, which restricts verification to bounded proofs. The PLCverif authors themselves identified ESBMC as the appropriate backend improvement. Prior work established ESBMC-PLC (a textual LD frontend with k-induction) and ESBMC-GraphPLC (graphical PLCopen XML support); together, they cover LD with unbounded proofs but not Structured Text (ST), and graphical LD with timer/counter function blocks remains unverifiable. This paper presents ESBMC-PLC+, a unified framework that closes both gaps: (1) an ST/SCL frontend via the MATIEC IEC 61131-3 compiler, routing C-compiled ST to ESBMC with nondeterministic input modeling and YAML property injection; (2) function block state semantics for graphical LD, extending the DFS resolver to model TON/TOF/TP timers, CTU/CTD counters, and R_TRIG/F_TRIG edge triggers as persistent scan-cycle state variables in the GOTO IR. ESBMC-PLC+ is the first open-source PLC verification framework to support all three major IEC 61131-3 input formats via a single ESBMC backend, enabling k-induction-unbounded safety proofs. A feature comparison with PLCverif and experimental evaluation on 8 benchmark programs, including programs with up to 8 integer timers, shows that ESBMC-PLC+ matches PLCverif's input coverage while providing stronger guarantees. Against nuXmv's BDD backend, ESBMC-PLC+ is 400-2,000x faster on timer programs and completes proofs where nuXmv BDD times out at 120s.
arXiv:2606.25988v1 Announce Type: cross Abstract: We efficiently conflict-free color every planar graph with 4 colors. An (open-neighborhood) conflict-free coloring assigns colors to vertices in a way that every vertex v has a neighbor w such that the color of w is distinct from the colors of the other neighbors of v (i.e., the color of w is unique in the open neighborhood of v). A previous best upper bound on the conflict-free chromatic number of planar graphs was 5, and it is known that 4 colors are sometimes necessary. Deciding whether, e.g., a planar graph admits a conflict-free coloring with 3 colors is NP-complete. Our approach uses a refined variant of the classical Gallai-Edmonds decomposition and the Four Color Theorem. In fact, our result is equivalent to the Four Color Theorem.
arXiv:2606.24900v1 Announce Type: new Abstract: This paper proposes a new approach to near-sensor computing, in which a lightweight Neural Architecture Search (NAS) is performed directly on the deployment device to find the best tiny neural architecture for analyzing the real-time data acquired through sensors. This new adaptation capability can be particularly useful in the case of human-machine interfaces for which the neural network analyzing the biometrical data can be re-designed each time the user changes, after a guided data collection procedure, fighting the typical data variations between individuals on a new level. To implement the proposed approach a new NAS has been designed and then validated on the Italian Sign Language dataset (ISL), a collection of surface electromyography (sEMG) signals of the signs of the Italian alphabet, using several embedded systems. Moreover, further validation on the Case Western Reserve University dataset (CWRU), a benchmark for intelligent fault diagnosis, is presented to suggest another possible application of the proposed approach. When run on a Raspberry Pi 4, the proposed NAS performs beyond the state of the art proposing a tiny neural architecture having 0.63 times less RAM occupancy and 5.96 percentage points of more accuracy in the case of the ISL dataset; and 0.44 times less RAM occupancy and 0.2 percentage points of more accuracy in the case of the CWRU dataset.
arXiv:2606.24902v1 Announce Type: new Abstract: The "First Proof" benchmark [1] posed ten research-level mathematics questions to the strongest publicly available LLMs and found them consistently wrong-not silent, but confidently, fluently wrong. This paper asks why. Working from the per-question post-mortems in First Proof's Appendix A, I identify four failure modes: citation fabrication (F1), premise smuggling (F2), silent problem reformulation (F3), and local-to-global compatibility gaps (F4). I then audit eight one-shot proofs generated by Gemini 2.5 Flash on Questions 1, 2, and 5 of the benchmark, using two instruments built specifically to surface F1 and F2. The central finding is uncomfortable for anyone who sees retrieval-augmented generation (RAG) as the obvious fix: not one of the eight proofs contained a confirmed fabricated citation, yet every single one contained at least one load-bearing claim asserted as a "fundamental result" or "standard argument" with no justification attached. That failure mode-F2, premise smuggling-is invisible to citation verification by design. A premise-audit instrument I introduce flags it at 100% precision (5/5 judge-confirmed flags are true positives) and 50% proof-level recall in this corpus. The taxonomy and the audit together suggest that the right long-term objective is building inference-time pipelines that prevent these failure modes from occurring, not just detecting them after the fact. Index Terms--Large language models, mathematical reasoning, hallucination, premise smuggling, failure-mode taxonomy.
arXiv:2606.24905v1 Announce Type: new Abstract: This study investigates pulse waveform adjustment in a portable inductive energy storage (IES) pulsed power system and its effect on nitric oxide (NO) generation in atmospheric spark discharges. While previous studies have focused on pulse energy, pulse width, and repetition rate, the role of rise time remains insufficiently explored. Existing pulse generators with adjustable rise time are also bulky and unsuitable for portable applications. To address these limitations, this study examines rise time control strategies within a compact IES architecture and employs a parallel high-voltage capacitor to generate adjustable waveforms. Optical emission spectroscopy was used to measure excited N2 and NO gamma emissions, and a NO analyzer was used to monitor NO concentration. In addition, electron excitation temperature, plasma-absorbed power, and rotational temperature were estimated to clarify the influence of waveform characteristics on plasma chemistry. The results show that although rise time can be adjusted, it is coupled with pulse width and input energy in the system. Comparative analysis of spectral intensities, NO concentration, electron excitation temperature, and absorbed energy indicates that NO production depends primarily on energy input rather than rise time. Electrode temperature varies only minimally under different waveform conditions, suggesting that NO formation is mainly influenced by electron impact and ionization processes. This work proposes a portable and simplified IES-based high-voltage pulsed power generator, identifies the constraints associated with rise time control, and demonstrates the feasibility of waveform adjustment. The findings clarify the dominant mechanisms governing NO generation and provide a reference for the design of future portable plasma-based NO production systems.
arXiv:2606.24911v1 Announce Type: new Abstract: Variable-order Markov models preserve local symbolic syntax by adapting context length, but long continuations can enter recurring high-order "tunnels": repeated suffixes, locally periodic passages, or copied fragments longer than the formal Markov order. This paper introduces signed pattern control for variable-order Markov generation with BP-Regular sampling. A weighted recurrence automaton computes an activation R for a chosen family of target patterns, and belief propagation samples exactly from P_beta(x) proportional to P_0(x) exp(beta R(x)). Negative coupling makes the target patterns costly during sampling; positive coupling rewards the same patterns and turns them into controlled attractors. The target family may be mined online from overactive generated material, supplied by a score or style vocabulary, or designed as an experimental probe. The main experiments use the online homeostatic case, choosing patterns that become overactive in the sampling history. On six duration-bearing monophonic sources, including Bach and Telemann material, the negative branch reduces generated 8-gram self-reuse, increases the effective number of generated 8-grams, and increases coverage of training-supported 4-gram contexts while preserving substantial lower-order support. A pitch-sequence replication on five Weimar Jazz Database solos gives the same anti-reuse signature outside Baroque material. The same signed mechanism also provides a positive branch for probing attractor basins, phase transitions, and hysteresis in the underlying variable-order model.