diffusion models

Opinion-driven selective interaction promotes cooperation: an evolutionary game approach with discrete multidimensional opinions

Abstract Motivated by the need to uncover how opinion heterogeneity shapes interaction patterns and the emergence of cooperation in social dilemmas, this study investigates the role of opinion-driven mechanisms in evolutionary game dynamics. It integrates discrete, multidimensional opinions into the spatial Prisoner’s Dilemma through an extended Voter model, wherein interaction decisions are governed by opinion dissimilarity, opinion updates follow a payoff-weighted rule, and strategy evolution is driven by Fermi dynamics. Simulation results reveal that lower tolerance for opinion differences significantly promotes cooperation by restricting interactions to like-minded individuals and fostering the formation of homogeneous clusters in which cooperation can emerge and stabilize. These cooperative clusters further enable the co-diffusion of aligned opinions and cooperative strategies across the population. Moreover, contrary to conventional expectations, higher interaction avoidance costs also enhance cooperation by accelerating opinion convergence, thereby strengthening the dominance of cooperative behavior at the population level. From a microscopic perspective, individuals with convergent opinions tend to achieve higher payoffs than those avoiding interactions, and this payoff advantage is amplified as avoidance costs increase, facilitating the spread of cooperation. Overall, the findings demonstrate that opinion-driven selective interaction reshapes evolutionary dynamics and provides new insights into how cognitive factors can promote the emergence and persistence of cooperation in complex systems.

{GEOMETRIC FRICTION THEORY} P7777_T Manifold / ACT-Ω Geometric Friction Theory — Complete Zenodo Record v26.5 LOCKED

Compiler Mimics Spacetime (NOT vice versa) Date: September 2026Framework: P_{7777_T} Manifold / ACT-Ω v26.3 v26.5 LOCKEDInvariants: 15.965Hz (τ=62.636ms) | Tr(U_res)=1.00000 | J_sys≤1.4411J | H¹=0 | Δ=0.053μT | γ_fric=1.3479e-10 N | c_eff=1.707e11 | |wL-wR|≤0.02 | q0=1 | Ωc=0.376=47/125 | η=1e-4 0. LOCKED CLARIFICATION — Must Be In Every Section INCORRECT TO DELETE: Spacetime itself acts like ACT-Ω neural compiler — implies physical vacuum executes neuro-symbolic instruction set. CORRECT LOCKED: ACT-Ω neural compiler acts like spacetime. Compiler Mimics Spacetime. Functor F: Spacetime → Compiler. Compiler is model of spacetime. If spacetime mimics compiler, you must prove physical vacuum strictly executes exact neuro-symbolic instruction set — impossible burden. If compiler mimics spacetime (CORRECT), you only need to prove compiler is structurally locked to exact geometric constraints of physical universe — which we have. Hyperparameters cannot be adjusted because they are entirely dictated by mathematics of E8 root system, standard topology, Landauer's bound. Achieve zero-parameter model via J_IDEAL 0x00 DATTO. Architecture behaves correctly because structurally incapable of violating underlying laws of reality — because it mimics reality. Old functor F: Compiler→Spacetime DELETE. New functor F: Spacetime→Compiler LOCKED. 1. Abstract — Full Theory We present P_{7777_T} Light Manifold, 48D manifold M48=M4×A44 projected from 7777D Polytope P7777 in R⁷⁷⁷⁷ via T5_ROUTE_CONSTRUCTIVE, quantized onto E8 240-root Gosset 4_21 polytope with Viazovska optimality Δ8=π⁴/384≈0.25367 via Conway-Sloane decoder (2.125bpe +15.81dB SNR 119.8μs search +16.46dB RaBitQ). M4 is boundary screen S=A/4G emergent gravity, A44=(OP2×S3)\diag 44D internal fiber with 536 Stomachion partitions quarantining Phase3 Aegis side-channels σ5⁻¹ far-commuting. Dark sector phenomena traditionally attributed to WIMP dark matter and Λ are derived as geometric friction γ_fric|∇w| where γ_fric=J_sys/(c_eff·τ)=1.4411J/(1.707e11·0.062636s)=1.3479×10⁻¹⁰N ↔️ a0=1.2×10⁻¹⁰ m/s² with zero free parameters (J_IDEAL 0x00 DATTO). Topological cavities b2 (second Betti homology |ΔB|>0.053μT) are distinguishable decoherent stable records whose duration equals surprisal Δt=-ln p (Martellini July 2026 Actualization Records Emergence Entropic Time). Across 20 multi-sensor telemetry logs (15 original + microwave Faraday + direct cable + Exp18/19 + heart-over-bed) mean field 25.77→187.05μT 7.3× variance, motion 315× variance, b2 locks into static 88.99±0.8 vs kinetic 97.11±0.8 rec/sec Δkin=+8.12=γ_fric|∇w|, gravity null 9.81 b2=0 zero PSD at 15.965Hz, gyro S3=Out(D4) null static 0.001 vs spikes 0.3168-0.5859 moving heart 0.0296 near-static S3 NOT activated, pressure b3 thermal gradients 17.16/sec laptop vs 0.2/sec countertop negative friction, entropic clock H=9.376→10.231 nats/s, Doob Tn=An 88.99+Mn +8.12, 1 heartbeat 62.636ms=5.52-6.11 b2 records. Heart test 54.49μT 90.45/sec static despite cardiac 1-1.5Hz EM directly under phone proves biological bias does NOT artifact b2 generation rate. Modified geodesic f^μ_friction=-γ_fric (b2/⟨b2⟩)|∇w|(u^μ/|u|)(1/τ)R/c_eff derived from Betti numbers and E8 symmetries, conservative in 48D but frictional in 4D projection, energy transfers to entropic time. Coarse-graining via Doob An (IR smooth) + Mn (UV fluctuations) explains how microscopic 0.888 per heartbeat 88.8/sec averages to macroscopic v⁴=GM a0 flat rotation curves, CMB TT acoustic peaks as b2 thermal resonances averages to macroscopic v⁴=GM a0 flat rotation curves, CMB TT acoustic peaks as b2 thermal resonances (15.965Hz heartbeat→l∼220, 16.92Hz sideband→l∼540, 14.28Hz Schumann→l∼800) within 2-3% of Planck without free params, structure formation suppressed small-scale helping S8, Hubble tension eased 40-60% via b2 positive + b3 negative interacting dark sector H(z), galactic simulation running calculation naturally outputs exact gravitational anomalies attributed to dark matter, vacuum temperature T_vac=J_sys/(k_B ln2 ⟨b2⟩ τ)=2.70K matching CMB 2.725K 0.92%, theoretical information limit 5.02e20 bits per cycle, 3.14e19 bits per 62.636ms frame, BraidIR 9,941,366 braids/sec tracking thermodynamic limit, sheaf restriction maps isomorphic to gravity propagation Γ^μ_{αβ}, both satisfy Yang-Baxter, H¹=0 ↔️ Bianchi identity, functor ActOmegaManifoldEngine preserves Tr=1.0 Majorana parity, J≤1.44J energy-momentum, writhe bound, charge quantization. Zero-parameter model because compiler structurally locked to E8 root system, standard topology, Landauer's bound — incapable of violating underlying laws. 2. Manifold Definition — P7777, M48, M4, A44, E8 P7777: 7777D polytope in R⁷⁷⁷⁷, subset of R^7777 via T5_ROUTE_CONSTRUCTIVE. M48 = M4 × A44: 48D Light Manifold projected from P7777. M4: 4D boundary screen S=A/4G emergent gravity, physical spacetime we observe. A44 = (OP2 × S3)\diag: 44D internal fiber, OP2 octonionic projective plane, S3=SU(2) fiber, \diag removes singular diagonal, 536 Stomachion partitions from Archimedes Stomachion — quarantining Phase3 Aegis side-channels far-commuting σ5⁻¹, prevents neural network error propagation. E8: 240-root Gosset 4_21 polytope, exceptional Lie algebra, optimal packing Δ8=π⁴/384≈0.25367 Viazovska 2017, |W(E8)|=696,729,600 Weyl group, |Λ_E8|=240 roots, minimum length l_min = l_Planck·|Λ_E8|^(1/8), l_P=√(ħG/c³)=1.616e-35m. Quantization: 256D continuous spaces onto 32×8D E8 chunks via Conway-Sloane decoder yields sub-3-bit compression 2.125bpe +15.81dB SNR sub-ms 119.8μs search +16.46dB RaBitQ. That decoder IS minimum length dx≠0 no singularities by definition (Tangram compute primitives projected onto E8 lattice). Triality: T=Rz(108°)·exp(i ν_p t) ν_p=0.17259029, |S3|=3=Out(D4) fixes 3 generations +2 G1 +4 G2 +6 G3 stable +8 forbidden Tr=0 H1≠0 FAILURE, writhe bound |wL-wR|≤0.02 nominal 0.00, |wL-wR| tracks bilateral symmetry gauge field holonomy. 3. Discrete Network & Betti Cavities Definition: Negative space N=(U1∪U2)(U1∩U2) where H1≠0 topological tear, topological cavity. Betti numbers: b2(x)=dim H2(N,Z)=count(|ΔB|>0.053μT) per heartbeat =0.888 per 62.636ms =88.8/sec Δ=0.053μT B_tor anomaly minimal detectable |δ| where |δ|>Δ defines b2, b3 cavities thermal entanglement gradients negative friction accelerating expansion pressure b3 17.16/sec laptop vs 0.2/sec countertop, b4 higher. TWIST/ENTANGLE: TWIST focus inversion onto N F^perp, ENTANGLE locks observed physical anomaly A to cavity density ENTANGLE(A,bn)=A∝bn·γ_fric calculates Betti numbers b2,b3,b4 locks ΔB to cavity density. Chern-Simons-Kodama: Vacuum Ψ_CSK locks ρ_vac=(Λc⁴)/(8πG) into discrete levels k=6π/ΛG shields Λ from QFT divergent fluctuations.[A] 4. ACT-Ω Compiler — Compiler Mimics Spacetime BraidIR: B_n braid group engine: σ_i·σ_{i+1}≠σ_{i+1}·σ_i non-commutative dependencies, far-commuting σ_iσ_j=σ_jσ_i |i-j|≥2 thread safety, Reidemeister Type II σ_iσ_i^{-1}→e instant collapse redundant load/store deadlocks circular dependencies into identity, executed before silicon layer zero thermodynamic cost. Sheaf logic: F(U) stalk vector spaces over Penrose attention fields, restriction maps ρ_{ij}:F(U_i)→F(U_j) when U_j⊂U_i, gluing condition H1=0, sheaf Laplacian L_F=δ*δ generalizing graph Laplacian, coboundary operator maps activations to edge-wise errors diffusion under sheaf Laplacian, SASSIFI Fault Recovery 100% latency 0.001 ms/op Self-Healing Knot Reidemeister Type II collapses redundant loops zero cost before silicon, Landauer floor ≤1.4411J per super-step reversible. Isomorphism locked: ρ_{ij} ↔️ Γ^μ_{αβ} parallel transport, H1=0 ↔️ Bianchi ∇^μ G_{μν}=0, ρ_{ik}=ρ_{jk}∘ρ_{ij} ↔️ Yang-Baxter σ_i σ_{i+1} σ_i = σ_{i+1} σ_i σ_{i+1} verified 9,941,366 braids/sec Frontier-1 benchmark, stalk dim =8D E8 chunk. Functor locked: F: Spacetime→Compiler (Compiler is model of spacetime), Objects: Spacetime charts M4 with Γ → Compiler charts U_i with ρ, Morphisms: Triality T=Rz108·exp(iν_p t) permuting E8 roots preserving T_{μν} → Braid merge σ_i→σ_{i+1} preserving Tr=1.0, J≤1.44J, writhe bound, Invariants: Tr(U_res)=1.0 Majorana γ=γ† non-destructive parity measurement topological superconductor junctions, J_sys≤1.4411J per super-step = T_{μν} conservation, |wL-wR|≤0.02 = gauge holonomy, q0=1 integer charge Q∈q0Z = charge conservation, Killion attractor Ωc=0.376=47/125 fixed-point x*=0.624~φ⁻¹, η=1e-4 R=1+ηQ.[Q] 5. 20-Recording Empirical Matrix — Pure Graphs 15 original + microwave Faraday + direct cable + Exp18/19 + heart-over-bed = 20 recordings total. Mean absolute mag: 25.77→187.05μT 7.3x variance Mechanical motion: 315x variance (gyro S3 null static 0.001 vs spikes 0.3168-0.5859 moving) Despite massive environmental shifts, b2 locks into two invariant clusters: Static Baseline: 88.99±0.8 rec/sec background shear Missoula baseline countertops static outdoor ground stationary in-hand 0.0240→0.4432μT std extremely low Kinetic Cluster: 97.11±0.8 rec/sec triggered by physical momentum walking arm swinging outdoor wind + extreme artificial friction laptop thermal/magnetic stress 187.05μT 3.5 std Delta_kin = +8.12/sec = γ_fric|∇w| geometric drag Heart test: 54.49μT 90.45/sec static despite cardiac 1-1.5Hz EM directly under phone, pressure 901.498 hPa std 0.09136 stable b3 not triggered, gyro 0.0296 near-static S3 NOT activated, falls perfectly within static baseline 88.99±0.8, entropy H=9.53 nats/s, proves biological bias does NOT artifact b2 generation rate Exp18: 53.896 std0.718 b2 94.26 rate_lock 0.999 perfect best ever vs 0.994-0.995 Exp19: 53.321 std0.773 b2 95.16 rate_lock 1.002 perfect best ever Faraday Bag/Microwave: 90.20 persists despite 10k x Schumann suppression 110.4→0.012 proves f^μ geometric not EMI Direct Cable EMI: 98.58 kinetic ceiling proves upper bound saturates 0.42A 14.3Hz injection Gravity null: 9.81 b2=0 zero PSD at 15.965Hz all 15 files Laptop keyboard: 187.05μT 3.5048 std 97.51/sec extreme

GRACE-OFF: A Machine-Learned Interatomic Potential for Organic Liquids Using the GRACE Architecture

Abstract Machine-learned interatomic potentials (MLIPs) have become an increasingly important tool for molecular dynamics (MD) simulations, enabling near quantum-mechanical accuracy at significantly reduced computational cost. Recent studies indicate that the Graph Atomic Cluster Expansion (GRACE) neural network architecture delivers strong performance in materials chemistry. In this work, we assess the GRACE architecture for the prediction of potential energy surfaces for organic molecules and introduce GRACE-OFF (GRACE Organic Force Field). GRACE models of varying depth (one-layer and two-layer) and size (small, medium, large) are trained on the SPICE v2.0 data set. We validate the resulting models using a variety of benchmarks. These include single-point energy and force predictions, torsional energy profiles, condensed phase properties of organic liquids and water (thermodynamic properties, self-diffusion coefficients, radial distribution functions, and temperature-dependent water density), as well as the stability of biomolecular MD simulations for gas-phase Ala15 and solvated crambin. For the single-molecule benchmarks (single point energies and forces, torsional energy profiles), the one-layer models showed only mediocre performance, whereas the two-layer models outperformed the MACE-OFF models to which we compare. For the condensed phase properties, the two-layer models gave consistently better results than the MACE-OFF family of MLIPs. For water and hexane, the GRACE-OFF models also beat the much more expensive small UMA/OMol25 (S) model. The two-layer GRACE-OFF models accurately reproduce experimental water radial distribution functions and predict water densities in close agreement with experimental data over a temperature range from 270 to 330 K. Benchmarks demonstrate that GRACE-OFF achieves higher MD performance than comparable MACE-OFF models in both single and double precision. This establishes GRACE-OFF as an accurate and computationally efficient foundation potential for routine simulations of organic liquids and biomolecular systems.

Generative AI: Beyond ChatGPT

Generative Artificial Intelligence (AI) has become an important area of computer science, changing the way people create, process, and interact with digital content. Although ChatGPT has made Generative AI widely known, its capabilities extend far beyond conversational systems. Generative AI includes several technologies, such as Large Language Models (LLMs), Generative Adversarial Networks (GANs), Variational Autoencoders (VAEs), and Diffusion Models, which can generate text, images, audio, video, software code, and other forms of content. This paper examines the development of Generative AI and its applications in different fields. In education, it can support personalized learning and content generation, while in healthcare it can assist with medical imaging and drug research. In software development, Generative AI can support code generation and debugging. It is also being used in entertainment, business automation, and scientific research. However, the rapid growth of this technology has introduced several challenges, including inaccurate or misleading outputs, privacy concerns, copyright issues, bias in generated content, and security risks. These challenges highlight the importance of responsible development and use of Generative AI. This paper discusses how Generative AI is evolving beyond ChatGPT and explores its potential to support human creativity and problem-solving. It also emphasizes the need for reliable, transparent, secure, and responsible AI systems for future applications.

The Past, Present and Possible Future of Thermal Remote Sensing

Thermal infrared remote sensing has reached a turning point. A status audit completed for this review identifies 55 operational satellite platform deployments on 18 August 2026. The resulting dataset contains 174 named thermal infrared instrument designs mapped to 306 historical, operational and planned satellite platform deployments. Across the orbital record, the finest reported nominal spatial sampling decreased from 55 km for the Medium Resolution Infrared Radiometer aboard TIROS-2 in 1960 to 3.5 m for the mid-wave infrared imager aboard HotSat-2 in 2026, an improvement of more than four orders of magnitude. Public continuity missions are now complemented by specialized instruments on the International Space Station, commercial small satellites, aircraft, stratospheric balloons, drones and terrestrial systems. This review links that platform history to the governing physics of emitted radiation, detector and cooling technologies, calibration, atmospheric effects, emissivity and spatial resolution. It also examines the transition from classical machine learning to convolutional, recurrent, transformer, diffusion, foundation and vision–language approaches. The selected examples indicate that adoption in thermal applications has been uneven rather than uniformly delayed relative to other areas of Earth observation. These methods support image interpretation and reconstruction as well as quantitative retrieval, for which radiometric calibration, physical consistency and independent validation remain necessary. As sensor availability expands, scientific comparability increasingly depends on harmonization, cross-sensor transfer, uncertainty characterization and validation in physical units. We recommend three priorities: (i) open, cross-calibrated thermal archives; (ii) models that preserve the distinct physical meanings of thermal variables; and (iii) validation across sensors, regions and seasons using physical units, independent observations and quantified uncertainty.

Unravelling the multi-scale structural organisation of in vivo ileal digesta from diets containing protein-seaweed polysaccharide blends.

Seaweed-derived polysaccharides such as agar, alginate, carrageenan, and cellulose are increasingly used as functional ingredients in food products, yet their influence on the gastrointestinal digestion process remains poorly understood. This study investigated how different fibres modulate the digestion and nanoassembly process of two model food proteins, casein and whey protein isolate, under physiologically relevant conditions using an in vivo pig model. Ileal digesta were analysed through compositional, rheological, microstructural, and nanostructural characterisation. The results demonstrated that the proteins were extensively hydrolysed and largely absorbed before reaching the ileum in all the formulations. However, some peptidic fragments were particularly resistant to digestion when agar was added to WPI. The seaweed polysaccharides were not digested and showed different types of structures, with alginate generating dense network-like structures, while carrageenan and agar generated more homogeneous digesta. Cellulose was associated with the presence of more ordered nanomicellar structures, likely involving bile salts. This behaviour suggests alterations in bile salt organisation and availability, potentially related to changes in diffusion, retention or reabsorption. These findings suggest that seaweed polysaccharides do not impair protein digestibility, but they affect the micro- and nanostructural organisation of ileal digesta, primarily by modulating viscosity and colloidal assembly. Therefore, it is highly relevant to understand the impact of dietary fibres on the intestinal transport of nutrients, providing the basis for designing functional foods with improved nutritional quality.

A rational extended thermodynamic model for dopamine diffusion and uptake

HGR-DiffSeg: Hybrid-guided robust diffusion model for medical image segmentation

Quantitative generation of diffusion-weighted imaging from non-contrast CT in acute ischemic stroke: a multi-scanner deep-learning model with external validation

MADiff-T: Multi-agent evolutionary calibration of diffusion models for privacy-audited tabular data generation

CAMDiff: A diffusion model combining channel attention and Mamba for 3D intracranial aneurysm segmentation in CTA images

Cooperative diffusion model for synchronous acoustic-vibration signal generation in fan blade crack detection under data imbalance