Protocol learns k-local Lindbladians to ε accuracy with Õ(n^{2k}/ε²) samples and projects to valid generators; improves to log n under sparsity assumptions.
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Scale-Free Networks: Complex Webs in Nature and Technology
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Stochastic inflation emerges as GKLS open-system dynamics from tracing entangled modes entering a coarse-grained de Sitter patch, reproducing the classical phase-space Fokker-Planck equation.
Transformer residual layers are approximated as an explicit Euler scheme for a controlled hidden-state flow whose mean-field limit is a first-order transport control problem with Pontryagin terminal condition given by the softmax residual.
First integrated spiking controller combining bipedal locomotion and arm control on a full-scale humanoid via NEF, SPA, and basal ganglia, validated in Nengo-Isaac Sim co-simulation.
DeepPolaron ML-MD simulations show rutile electrons form Ti-localized polarons hopping along [001] with 39 meV barrier and 4.4e-2 cm2/Vs mobility, while anatase holes form O-localized polarons hopping to second neighbors with 139 meV barrier and 1.4e-3 cm2/Vs mobility.
Training-language dominance, not English inherent properties, determines brain-LLM alignment across English, Chinese, and French, with additional independent effects from typological distance concentrated in syntactic brain regions.
Proposes a scale-calibrated median-of-means estimator for robust aggregation of distributed PCA estimates on the product of Euclidean space and Grassmann manifold.
Introduces De Simone laws over Kleisli categories that guarantee compositionality of coalgebraic trace equivalence and recovers the classical De Simone format while adding a probabilistic variant.
Aggregation mechanisms for surjective classifications are nearly dictatorial with high probability unless functions are nearly constant, with a full characterization of always-surjective mechanisms.
Derives covariant quadratic expansion in extrinsic curvature of the nonlocal effective action for a massless scalar field on manifolds with boundary, extending Monge-patch results to general surfaces.
The paper presents randomized tests with explicit query bounds for properties including number of leaves, maximum degree, typical distance, and diameter in tree-structured graphical models.
A solvable hierarchical model with power-law feature strengths yields explicit power-law scaling of prediction error through sequential recovery of latent directions by a layer-wise spectral algorithm.
Bayesian PLSs are special cases of non-stationary affine PIMs which are proven calibrated, and affine tracing automates construction of probabilistic iterative methods from classical code.
Moonflowers are introduced as set families with per-set unique elements, yielding near-optimal extremal bounds that enable logarithmic code sparsification with a matching lower bound.
Projective Kummer-type manifolds with finite-order symplectic birational self-maps acting nontrivially on H² are twisted modular except for Picard rank 3 cases characterized by their NS lattices; specific Mukai vectors are identified for finite-order wall-crossing maps on modular examples.
SGD, approximations of Newton's method, natural gradient descent, and Adam are proven compatible with evolutionary dynamics when augmented with DLS noise, turning them into valid in silico simulations of asexual Darwinian evolution.
Polynomial-time algorithm samples the Sherrington-Kirkpatrick Gibbs measure at beta < 1/2 with o(1) TVD error by combining potential Hessian ascent, stochastic localization, covariance estimates, and Jarzynski equality with rejection sampling.
The profile maximum likelihood estimator for the location in anisotropic hyperbolic wrapped normal models is strongly consistent, asymptotically normal, and attains the Hájek-Le Cam minimax lower bound under squared geodesic loss.
Introduces anytime-valid e-processes for first- and higher-order stochastic dominance that achieve power one and remain valid under continuous monitoring.
In open quantum systems, environmental coupling turns deterministic Krylov phase-space trajectories into stochastic ones by adding diffusion, destroying the hyperbolic mechanism for exponential complexity growth beyond a controlled scale.
Continuous focus groups enable repeated dialogue with autism care professionals across robot therapy phases to integrate evolving clinical insights and serve as an ethical safeguard.
A 2D neural cellular automaton spontaneously self-organizes into a Proto-CKY representation that exhibits syntactic processing capabilities for context-free grammars when trained on membership problems.
A 3D morphoelastic rod model with local Stokes hydrodynamics predicts flutter instability and self-sustained 2D or 3D oscillations in clamped elliptic hydrogel filaments under constant axial electric field, with a secondary bifurcation to large-amplitude motions.
Existence of self-similar finite-mass solutions is proved for the time-fractional porous-medium equation in the optimal range m > (d-2)_+/d for all d ≥ 1, with compact support for m > 1 and heavy tails for m_c < m < 1.
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