arXiv:2607.14947v1 Announce Type: cross
Abstract: Modern generative models are increasingly trained using model-generated signals, creating both opportunities for self-improvement and risks of collapse. We study optimal self-distillation (SD) for rectified flow (RF): given a suboptimal teacher velocity field, can a student trained on a mixture of true RF velocities and teacher velocities provably improve the teacher? For linear RF with ridge regularization on fixed interpolation pairs, we prove an exact affine path identity, derive the optimal mixing coefficient in closed form, and show strict improvement in integrated velocity risk whenever the teacher risk is nonstationary along the regularization path. The optimal coefficient obeys a sign rule: positive mixing corrects under-regularized teachers, while negative mixing corrects over-regularized teachers. We also give one-shot generalized cross-validation (GCV) and validation tuning procedure that avoids grid search over mixing weights and repeated refitting. Combining this theorem with RF Wasserstein convergence bounds, we show that optimal self-distillation improves the velocity estimation terms controlling continuous-time and finite-step generation error. Experiments with Gaussian models, Gaussian mixtures, and image data show that optimal self-distillation improves velocity risk, mode recovery, and finite-step generation relative to both the teacher and pure distillation.
Science Journals
arXiv:2607.14985v1 Announce Type: cross
Abstract: An accurate estimation of the molecular abundances of isomers in the interstellar medium (ISM) is necessary to unravel the underlying chemistry and physics. After the recent detections of both isomers of formic acid ($cis-$ and $trans-$HCOOH) in dense dark cold clouds, their accurate molecular line modeling became of interest. The conditions of these environments do not necessarily follow the local thermodynamic equilibrium, thus taking into account the competition between the radiative and collisional processes is required. This involves the knowledge of the rotational excitation data for collisions with the most abundant interstellar species \textemdash He and H$_2$. In this paper, the first potential energy surfaces (PES) for the interaction of the two rotamers of formic acid with He atoms are computed using the explicitly correlated coupled-cluster theory [CCSD(T)-F12]. The obtained PESs demonstrate qualitative similarities and high anisotropy. The global minima are found with $V=-53.0$ cm$^{-1}$ and $V=-46.0$ cm$^{-1}$ for $cis-$HCOOH and $trans-$HCOOH respectively. Collisional excitation cross sections calculated for total energies up to 100 cm$^{-1}$ demonstrate similar propensity rules for both isomers. Quantitative differences of the cross sections associated with the two rotamers are also discussed.
arXiv:2607.15116v1 Announce Type: cross
Abstract: Let $T_k$ be the minimum positive integer $t$ such that, for every positive integer $n$, every equinumerous $t$-coloring of $[tn]$ contains a rainbow $k$-term arithmetic progression. Jungi\'{c}, Licht, Mahdian, Ne\v{s}et\v{r}il and Radoi\v{c}i\'{c} conjectured that $T_k=\Theta(k^2)$, while Conlon, Fox and Sudakov proved that $T_k=O(k^2\log k)$. We prove the matching lower bound $T_k=\Omega(k^2\log k)$, and hence $T_k=\Theta(k^2\log k)$.
arXiv:2607.15119v1 Announce Type: cross
Abstract: We introduce a thermodynamic theory of voting and show that it provides a good description of distribution of party votes in EU elections. The theory traces parallels between system energies of coupled nonlinear oscillators and party vote fractions. Such a classical system evolution is characterized by the conservation of total energy and probability norm that leads to the Rayleigh-Jeans (RJ) thermalization and condensation at low energy states. A similar thermalization also describes the wealth inequality in society. This feature belongs to the phenomena of constraint driven condensation known in statistical mechanics. We show that the RJ theory well depicts the Lorenz and Pareto curves obtained from the EU vote results. The theory also recovers the dispersion of votes between candidates of first round presidential elections in France.
arXiv:2607.15122v1 Announce Type: cross
Abstract: Hysterons provide a minimal description of memory in driven matter: bistable elements with distinct switching thresholds whose interactions generate hysteresis, avalanches, and return point memory or its violation. Experimental realizations have so far been dominated by solid state mechanical systems, where bistability is usually encoded structurally through buckling, snap through, or geometric incompatibility. Here we realize hysteron physics through a hydrodynamic route. A single elastic fiber anchored in a microfluidic channel becomes bistable through nonlinear elastohydrodynamic feedback: viscous loading deforms the fiber, deformation reshapes hydraulic resistance, and flow redistribution modifies the loading. This feedback produces a fluidic hysteron whose onset is organized by a cusp catastrophe in geometric control parameters. A parallel bypass channel acts as a geometric load line that reshapes, and can even eliminate, bistability while simultaneously mediating long ranged hydraulic interactions between fibers. In arrays, varying a single geometric parameter drives a transition from a non interacting Preisach regime with return point memory to an interacting regime with avalanche like switching and return point memory violation. These results establish a passive hydrodynamic route to hysteron networks, in which memory emerges from flow structure feedback and global hydraulic constraints rather than solid state multistability or external control.
arXiv:2607.15159v1 Announce Type: cross
Abstract: We construct a new family of Calderbank-Shor-Steane (CSS) codes using the generator and parity-check matrices of Low-Density Generator Matrix (LDGM) codes, with row operations applied to both matrices in order to achieve the desired quantum rate. Decoding is performed in an iterative manner, by applying message passing over the associated graph, and discrete Density Evolution (DDE) is used to optimize performance in the depolarizing channel. The proposed construction offers high flexibility and easiness in the design, producing quantum codes that possess excellent error correction capabilities. By properly designing the structure of the code, we are able to control and bound the weight of the stabilizer generators to a small value, which results in codes particularly well suited for fault-tolerant quantum computation. At the same time, these codes achieve very good performance in terms of error correction capability.
arXiv:2607.15198v1 Announce Type: cross
Abstract: We introduce the REAL-TSE Challenge, an IEEE SLT 2026 satellite challenge on target speaker extraction~(TSE) from real conversational recordings. Given a multi-speaker mixture and one or more enrollment utterances from a target speaker, participating systems must recover only the target speech. Unlike simulated read-speech benchmarks, REAL-TSE evaluates Mandarin and English recordings that contain natural overlap, reverberation, noise, channel mismatch, and conversational dynamics. The challenge defines two complementary tracks: an Online track for low-latency streaming extraction and an Offline track for full-context processing. Systems are evaluated with Token Error Rate (TER), Speaker Similarity (SpkSim), DNSMOS, and target-speaker activity F1. This overview paper describes the task definition, datasets, baselines, evaluation protocol, submitted systems, condition-wise findings, and lessons for future real-world TSE benchmarks.
arXiv:2607.15233v1 Announce Type: cross
Abstract: The undamped Duffing oscillator is a nonlinear dynamical system with broad applications in physics, engineering and biological system. We present a comprehensive analysis of this system using the Lindstedt Poincare method (LPM) and its modifications and make comparison with numerical solution obtained using higher order Runge-Kutta. It is also shown the method suggested in this article converges better than the standard LPM and Lindstedt Poincare method with Burton's modification.
arXiv:2607.15256v1 Announce Type: cross
Abstract: Computer-assisted proofs of self-similar singularity formation for fluid equations often rely on numerically constructed approximate profiles. One effective approach to establishing stability of perturbations around a numerically constructed profile is to perform weighted energy estimates with singular weights near the singularity. However, the weighted norms require exact local vanishing conditions that are not automatically preserved by the equations nor the numerical construction. In this paper, we review an analytic low-rank correction method first developed in [ChenHou2023a,ChenHou2023b] to overcome this difficulty. The numerical step determines coefficients, rigorous bounds, and low-order defect modes in explicit global basis representations, while the required vanishing conditions are enforced analytically through low-rank corrections derived from Taylor expansions of the relevant quantities represented in a smooth basis. For completeness, we briefly review the singularly weighted estimates and a quantitative finite-rank perturbation method in the 2D Boussinesq / 3D Euler stability argument, where singular weights and the required vanishing order arise. Against this background, we formulate the local correction principle in a simplified setting, explain the correction of the residual error in numerical constructions of approximate space-time solutions and the stream function, and discuss its broader applicability to computer-assisted stability analysis for nonlocal PDEs.
arXiv:2201.02137v3 Announce Type: replace
Abstract: Extreme space weather events on Earth occur during intervals of strong solar wind driving. The solar wind drives plasma convection and currents in the near-Earth space environment. For low values of the driver, the Earth's response is linear, estimated by parameters such as the polar cap index based on ground magnetometer activity. Curiously, for extreme solar wind driving, the Earth's response appears not to increase beyond a saturation limit. Theorists have advanced a host of explanations for this saturation effect, but there is no consensus. Here, we demonstrate that this saturation is a manifestation of the regression to the mean effect arising from random uncertainty in the timing and magnitude of solar wind measurements. Our results reveal that data analysis underpinning the saturation theories is non-linearly biased, thereby challenging the validity of the theories. Correcting for the uncertainties reveals that the Earth's response to solar wind driving is linear throughout, and that the impact of extreme geomagnetic storms can be twice as large as previously thought. We show that regression to the mean is a fundamental property of the relationship between measurement and the truth, where the truth corresponding to the measurement is closer to the mean. This effect is particularly pronounced for uncertain measurements of extreme values and is likely to manifest across various fields, from extreme climate studies to chronic medical pain.
arXiv:2201.04868v3 Announce Type: replace
Abstract: Recent advances in large language models (LLMs) have made natural language interfaces (NLIs) widely accessible for data exploration, yet analysts who have a broad analytical objective still face the challenge of decomposing it into effective step-by-step queries, especially over unfamiliar, multi-table relational databases. Rather than generating high-level analytical agendas, we investigate how to augment an NLI with semantic- and context-aware next-step query recommendations that act as analytical scaffolding for relational database exploration. Our approach goes beyond interestingness-only methods by jointly integrating semantic relevance, data interestingness, and context coherence to guide exploration toward coherent, topic-focused analyses and potentially insightful subsets. We evaluate QRec-NLI with NL2SQL benchmarking, LLM-enhanced description validation, agentic comparisons against interestingness-only and LLM-based prompting baselines, and a 12-participant user study. In the agentic comparison, QRec-NLI yields more topically relevant and locally coherent query sequences than both baselines. In the user study against the interestingness-only baseline, it receives stronger ratings for insight-generation support and decision support.
arXiv:2607.14238v1 Announce Type: cross
Abstract: The Beck--Fiala conjecture asserts that every matrix $A\in\{0,1\}^{n\times T}$ with at most $d$ nonzero entries in each column has discrepancy $O(\sqrt d)$. A major breakthrough result of Bansal and Jiang recently established the validity of the conjecture for $d \ge \log(T)^2$. The present article extends the validity of the classical \textit{offline} Beck--Fiala conjecture to $d \ge \log(T)^{1+o(1)}$; moreover, the main thrust of the result is that it is actually obtained by an efficient \textit{online} algorithm that minimizes prefix discrepancy. The result is also essentially optimal, since online prefix discrepancy is known to scale as $\omega(\sqrt{d})$ for $d =o(\log T)$. As an immediate corollary, the open question of online vector balancing in the Spencer setting is also resolved.
The algorithm is based on a compactly supported Metropolis fixed-point walk, constructed by combining ideas from several recent works on the online Koml\'os problem. The proof was generated in conversation with ChatGPT 5.6 Pro; the authors provided high-level guidance in several rounds of prompting, followed by manual checking and rewriting of the proof.
arXiv:2310.07211v2 Announce Type: replace
Abstract: Regularization is a cornerstone of modern reinforcement learning. Regularized policy iteration (RPI) provides a fundamental scheme for solving regularized Markov decision processes (RMDPs), and the widely used soft actor-critic algorithm arises as a special case when the regularizer is Shannon entropy. Despite its empirical success, the theoretical underpinnings of RPI remain unclear. In this paper, we address this gap by proving that RPI is formally equivalent to the standard Newton-Raphson method applied to the Bellman equation smoothed by strongly convex regularizers. This equivalence enables a unified convergence analysis of existing methods and supports the development of accelerated algorithms. We show that RPI enjoys local quadratic convergence; notably, for Shannon entropy, the guarantee is dimension-free. We further study RPI with inexact policy evaluation, establishing its equivalence to an inexact Newton method in which each Newton step is solved via truncated iterations, and derive an asymptotic linear convergence rate of $\gamma^{M}$, where $M$ denotes the number of operator steps used in policy evaluation. Finally, motivated by higher-order Newton schemes, we propose a new algorithm for RMDPs that achieves third-order local convergence. Numerical experiments corroborate our theory and demonstrate the practical advantages of the proposed algorithm. Overall, our results advance the theoretical understanding of regularization in reinforcement learning and suggest new directions for efficient algorithm design.
arXiv:2403.01977v5 Announce Type: replace
Abstract: Navigation in the natural world is a feat of adaptive inference, where biological organisms maintain goal-directed behaviour despite noisy and incomplete sensory streams. Central to this ability is the Free Energy Principle (FEP), which posits that perception is a generative process where the brain minimises Variational Free Energy (VFE) to maintain accurate internal models of the world. While Deep Neural Networks (DNNs) have served as powerful analogues for biological brains, they typically lack the real-time plasticity required to handle abrupt sensory shifts. We introduce FEP-Nav, a biologically inspired framework for real-time perceptual adaptation in robust visual navigation. Motivated by the decomposition of VFE into prediction error and Bayesian surprise, FEP-Nav combines a Top-down Decoder, which provides an internal expectation of uncorrupted sensory input, with Adaptive Normalisation, which adjusts shifted feature distributions toward prior statistics. We interpret reconstruction and normalisation as approximate mechanisms for reducing the corresponding VFE-related terms during inference without gradient-based updates. Experiments across simulated and real-world visual corruptions show that FEP-Nav restores performance lost under visual corruption, outperforming non-adaptive baselines and strong adaptive methods. These results suggest that variational principles can provide a useful design perspective for robust autonomous behaviour under degraded sensory conditions.
arXiv:2403.09742v2 Announce Type: replace
Abstract: This manuscript provides a comprehensive review of the Maximum Clique Problem, a computational problem that involves finding subsets of vertices in a graph that are all pairwise adjacent to each other. As such, this review is a continuation of the series of previous reviews from 1994, 1999 and 2014. The manuscript covers in a simple way classical algorithms and includes a review of recent developments in graph neural networks and quantum algorithms.
arXiv:2403.10360v2 Announce Type: replace
Abstract: Lagrangian methods continue to stand at the forefront of the analysis of time-dependent dynamical systems. Most Lagrangian methods have criteria that must be fulfilled by trajectories as they are followed throughout a given finite flow duration. This key strength of Lagrangian methods can also be a limitation in more complex evolving environments. It places a high importance on selecting a time window that produces useful results, and these results may vary significantly with changes in the flow duration. We show how to overcome this drawback in the tracking of coherent flow features. Finite-time coherent sets (FTCS) are material objects that strongly resist mixing in complicated nonlinear flows. Like other materially coherent objects, by definition they must retain their coherence properties throughout the specified flow duration. Recent work [Froyland and Koltai, CPAM, 2023] introduced the notion of semi-material FTCS, whereby a balance is struck between the material nature and the coherence properties of FTCS. This balance provides the flexibility for FTCS to come and go, merge and separate, or undergo other changes as the governing unsteady flow experiences dramatic shifts. The purpose of this work is to illustrate the utility of the inflated dynamic Laplacian introduced in [Froyland and Koltai, CPAM, 2023] in a range of dynamical systems that are challenging to analyse by standard Lagrangian means, and to provide an efficient meshfree numerical approach for the discretisation of the inflated dynamic Laplacian.
arXiv:2405.00549v4 Announce Type: replace
Abstract: A Confirmation Rule is an algorithm run by network nodes to determine whether a block will remain permanently in the canonical chain. The only Confirmation Rule currently available in Ethereum's consensus protocol, Gasper, is FFG finalization. While it tolerates asynchronous network conditions, it is slow: in the best case, a transaction takes 13 to 19 minutes to confirm, depending on when it is submitted.
We devise a Fast Confirmation Rule (FCR) for Gasper that, under synchrony and the assumptions stated in this paper, achieves a best-case confirmation time of 12 seconds, a single slot, providing an order-of-magnitude improvement over FFG finalization. The rule is complementary to finalization: users who trust synchrony obtain fast confirmations, while finalization remains available as a fallback that tolerates asynchrony. Gasper is an ebb-and-flow protocol: it combines LMD-GHOST, a fork-choice rule providing fast progress under synchrony, with FFG-Casper, a finality gadget providing finality under partial synchrony. The main technical difficulty is to reason jointly about these two components, so that a block confirmed by LMD-GHOST cannot be filtered out by FFG-Casper's rules. We prove that the rule satisfies both safety, confirmed blocks remain canonical, and monotonicity, a confirmed block remains confirmed at all future times.
arXiv:2405.03529v5 Announce Type: replace
Abstract: This paper contributes to the study of optimal experimental design for Bayesian inverse problems governed by partial differential equations (PDEs). We derive estimates for the parametric regularity of multivariate double integration problems over high-dimensional parameter and data domains arising in Bayesian optimal design problems. We provide a detailed analysis for these double integration problems using two approaches: a full tensor product and a sparse tensor product combination of quasi-Monte Carlo (QMC) cubature rules over the parameter and data domains. Specifically, we show that the latter approach significantly improves the convergence rate, exhibiting performance comparable to that of QMC integration of a single high-dimensional integral. Furthermore, we numerically verify the predicted convergence rates for an elliptic PDE problem with an unknown diffusion coefficient in two spatial dimensions, offering empirical evidence supporting the theoretical results and highlighting practical applicability.
arXiv:2405.10703v5 Announce Type: replace
Abstract: Safe control in unknown environments is a key challenge in mobile robotics. Control Barrier Functions (CBFs) provide a principled framework for guaranteeing safety constraint satisfaction. State-of-the-art CBF approaches assume either known environments with predefined obstacles, or rely only on obstacles currently within the robot's Field of View (FoV). However, practical robots in a priori unknown environments can observe their surroundings only partially, and therefore can violate safety due to limited FoV, sensor range, or occlusion. This paper incorporates the memory of previously observed obstacles of arbitrary shape that have left the robot's FoV into CBF-based safe control. In particular, we couple the Signed Distance Function (SDF)-based CBF formulation to an occupancy grid map built online during the system's operation. Furthermore, the lack of steering authority induced by the SDF gradient degeneracy when facing obstacles head-on is addressed by constructing a Gaussian pyramid of the SDF, yielding a multi-level CBF. The efficacy of the proposed approach is evaluated against memory unaware baselines in the CARLA simulator. Moreover, we demonstrate the generalizability of the proposed approach in real deployments on a small warehouse robot and a large, articulated frame steering autonomous wheel loader.
arXiv:2405.20983v3 Announce Type: replace
Abstract: Goal-oriented communication (GoC) is a form of semantic communication where the effectiveness of information transmission is measured by its impact on achieving the desired goal. In Internet-of-Things (IoT) networks, GoC can enable sensors to selectively transmit data relevant to the intended goals of the receiver, thereby facilitating timely decision-making, reducing network congestion, and enhancing spectral efficiency. In this paper, we consider an IoT scenario where an edge node polls sensors monitoring the state of a non-linear dynamic system (NLDS) to respond to the queries of several clients. This work delves into the foregoing GoC problem and solution, which we termed goal-oriented scheduling (GoS). The latter utilizes deep reinforcement learning (DRL) with meticulously devised action space, state space, and reward function. A long short-term memory network is used to estimate the inter-query duration and the corresponding estimation standard deviation. This empowers the proposed DRL scheduler to make judicious decisions, even when no queries are posed. Numerical analysis demonstrates that the proposed GoS reduces the mean square error (MSE) of the query responses compared to the benchmark scheduling methods even as the number of clients and DRL action space increase, which proves its scalability. Moreover, this is attained without polling sensors during $70\% - 87\%$ of the testing phase, thus promoting energy efficiency. Lastly, the complexity of the proposed GoS is relatively lower than the benchmark scheduling methods.
arXiv:2607.15079v1 Announce Type: new
Abstract: Understanding the brain increasingly depends on integrating evidence across scales, modalities, and disciplines. Addressing a single research question therefore requires a coordinated sequence of operations, from surveying prior work to executing analyses and interpreting results in light of domain knowledge. AI agents promise to accelerate this process, but current agents lack domain expertise in brain science, may fabricate claims, drift during multi-step reasoning, and offer few defined points for expert intervention. These failures are especially costly in brain science, where conclusions feed into downstream scientific claims and depend on laboratory-specific expertise and careful human judgment. We present \textbf{BrainPilot} a \textbf{fully open-source} multi-agent system that accelerates brain science research with traceable logs and agent-verified results. A principal investigator (PI) agent coordinates specialist agents grounded in curated domain knowledge: a unified brain science knowledge base containing 7{,}233 indexed items and a skill library of 72 reusable methodology units across seven research domains. Every major step is recorded in the Graph of Trace, an auditable record that links subgoals, tool use, evidence, and claims and allows researchers to follow and inspect the workflow. An Auditor agent further integrates fabrication checking into the workflow. For evaluation, we run three brain science tasks from Agents' Last Exam, introduce our own benchmark, \textbf{BrainPilotBench-v0}, and present additional end-to-end case studies. Across these evaluations, BrainPilot with an open-source backbone model attains performance comparable to state-of-the-art agent framework with less costs.
arXiv:2604.02429v2 Announce Type: replace
Abstract: Convolutional neural networks (CNNs) have transformed image processing, but the energy consumption and inference latency of electronic based implementations remain fundamental bottlenecks. These limitations have motivated the search for alternative hardware architectures beyond Complementary metal-oxide-semiconductor (CMOS) chips. Optical systems can perform linear matrix operations at the speed of light with extremely low energy dissipation, making them attractive for CNN acceleration. However, building a fully coherent photonic CNN that performs both linear and nonlinear operations and training it efficiently remains an open challenge. Here we present a fully photonic convolutional neural network (PCNN) that executes image classification in the optical domain, including convolution, max-pooling, nonlinear activation, and fully connected layers. The network achieves 94.49 percent accuracy on the MNIST dataset distributed across Mach Zehnder Interferometer (MZI) meshes, weighted Multimode Interferometer (MMI) trees, and a microring resonator based nonlinearity. A mathematically exact differentiable digital twin, enables backpropagation for ex situ pre training, reaches 97.45 percent digital accuracy. Trained phases are transferred one-to-one to the photonic hardware and refined via a gradient free algorithm that estimates the full gradient with only two forward passes. The architecture exhibits inherent robustness to non idealities, under the compound effect of propagation loss, MZI insertion loss, fabrication disorder, and thermal crosstalk. A bottom-up power analysis yields 10.83 W static chip consumption and 843 ns inference latency, translating to 220 to 330 times greater energy efficiency than state of the art electronic GPUs for single-image inference.
arXiv:2607.13641v1 Announce Type: cross
Abstract: Particle Image Velocimetry (PIV) is the prime image-processing technique to measure and visualize velocity fields of laminar and turbulent flows. The velocity field vectors are obtained with sub-pixelaccuracy by analyzing cross-correlations, empowered by Fast Fourier Transforms (FFT). Here, we present a quantum algorithm with multidimensional quantum Fourier Transforms, termed Quantum-based PIV (QuPIV), to replace the classical computation of up to millions of velocity vectors. Our end-to-end quantum algorithm includes a novel state preparation, modified amplitude amplification, and the output extraction. We enhance amplitude amplification by a contracted ground-state projector, which allows a significant reduction of the number of gates in the quantum circuit. We justify the end-to-end capability with numerical studies on all stages of the algorithm on both synthetic and experimental data.
arXiv:2607.14304v1 Announce Type: cross
Abstract: We study sparse random geometric graphs generated by connecting pairs of high-dimensional vectors whose inner product exceeds a threshold. The latent vectors are sampled either uniformly from the sphere or from a standard Gaussian distribution. Although every edge appears with probability $p$, the edges are dependent through their shared latent vectors. For the spherical model, at the connectivity scale $np=\Omega(\log n)$, we prove $\|A-\mathbb E A\|=O\left(\sqrt{np\log n}+np\tau\right)$, with high probability, where $\tau$ is the cap threshold. This sharpens the spectral norm bound of Liu, Mohanty, Schramm, and Yang (2023) under weaker assumptions. An analogous result holds for the Gaussian model after removing the fluctuations of the vector norms, yielding improved global synchronization guarantees for the homogeneous Kuramoto model. We then recover the latent geometry from the leading eigenspace. When $np\gg\log n$, both the latent vector and relative Gram matrix errors vanish provided $d\ll np\log(1/p)/\log n$. The required lower dimension is only $d\gg\log(1/p)$ for the spherical model and $d\gg\log^2(1/p)\log n$ for the Gaussian model, improving the recovery guarantees of Li and Schramm (2023). Finally, we prove the first exact recovery result for the Gaussian mixture block model of Li and Schramm (2023). At the optimal connectivity scale $np=\Omega(\log n)$, a polynomial-time semidefinite program exactly recovers all labels in a moderate-separation regime, whereas larger separation makes exact recovery impossible because isolated vertices appear with high probability. Our proofs combine orthogonal polynomial expansions, decoupling, and matrix concentration, avoiding the trace-moment arguments used in previous work.
arXiv:2607.14360v1 Announce Type: cross
Abstract: Food webs have been extensively studied from both ecological and mathematical aspects. However, most of the models studied in this area do not capture the effects of infectious diseases simultaneously. Recently, the idea of including an infectious disease in a food web model has been investigated. We study and simulate a small food chain consisting of only prey, predators, and apex predators governed by the generalized Lotka-Volterra equations, and we implement the Susceptible-Infected-Recovered (SIR) model on only one of the species at a time in the food chain. To study the effects of an infectious disease on the food chain, we introduce a new parameter that increases the predation rate by a factor of $w$ and decreases the hunting rate by a factor of $1/w$ for infected species. When the infectious disease is present in predators, we observe that predators do not become extinct under any set of parameters; however, an oscillation in their population size occurs under some circumstances, which we do not observe in ordinary SIR or the generalized Lotka-Volterra equations alone. When an infectious disease is present in apex predators, oscillations in the population size do not happen; but if the set of parameters is in a specific range the apex predators may become extinct. Furthermore, the chance of survival of the community, known as community persistence, increases for the predators and decreases for the apex predators.