Cohomology of parallelized n-manifolds carries a natural homotopy involutive n-Frobenius structure extending the rational homotopy type, via Quillen equivalence to n-Poisson cooperad comodules.
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- background for gravitating objects. For comprehensive reviews of effective field theory in a variety of physical contexts relevant to the current problem, see the recent textbook by Burgess [110], as well as the review articles by Pich [111], Donoghue [112, 113], Kaplan [114], Rothstein [115-117], Burgess [118], Goldberger [119-121], Porto [122], Manohar [123], Levi [124], and Penco [125]. A note on language: The EFT approach was pioneered in particle physics. In particle physics the expansion parameter is
- background r= 3r s/2−ϵwithϵgoing quickly to zero with increasingℓ, as we see from only the first two modes. 3.2. Kerr 3.2.1. Geometry Black holes in the real world rotate, which is not accounted for in the spherically-symmetric Schwarzschild solution (3.1). Schwarzschild had derived his metric within months of the publication of Einstein's field equations, while it took nearly a half century for Kerr to find its spinning generalization [235]. Here we will summarize salient features of the Kerr solution; se
- background Importantly, the sum of all angular momenta,ℓ1 +ℓ2 +ℓ3 +···, must be even. Starting fromO(E4), however, for a fixed set of angular momenta(ℓ1ℓ2···ℓn+1), multiple independent coefficients may arise. The precise counting of inequivalent contractions and independent Wilson coefficients follows from standard group-theoretic arguments, see e.g., Refs. [183, 189, 190]. 2.3. Examples of EFT calculations and matching The effective field theory(2.9) is completely general and, as long as one is concerned
- method and all upper bounds at the 95 % CL. The e ffectiveχ2 value of model n is given relative to model n− 1. Parameters Prior type Prior range N Discrete uniform [0 , 8] ln V∗ Uniform [ −25,−15] d ln V∗/dφ Log-uniform [10 −3, 10−0.3] d2ln V1/dφ2,..., d2ln VN/dφ2 Uniform [ −0.5, 0.5] φ1,...,φ N Sorted uniform [ ˜φmin, ˜φmax ] ln 1010PR(k) Indirect constraint [2 , 4] Table 9. Parameters of the free-form potential reconstruction analysis and details of the priors. There is a further prior con- straint in
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Parallel algorithm for matroid basis computation with O(n^{1/3} log^{1/3} n) round complexity, nearly matching the KUW lower bound.
A Master Theorem supplies explicit formulas for topological zeta functions of matroids and solves multiple conjectures.
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PAL uses the classical Preisach hysteresis operator with learned thresholds and an extrema stack to model sequences, proving O(1)-depth Turing completeness via two-stack PDA simulation and incomparability with standard transformers on rate-independent vs. random-access functions.
Categorical univalence of a universe does not entail function extensionality, as shown by polynomial models of type theory that refute the latter while satisfying the former.
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Introduces separable and essentially separable graphs as a broad class for mixed graphical models, provides multiple characterizations of the graphs and their separation equivalence, and develops an identification algorithm for equivalence classes.
In the subcritical regime m = m_c(1-ε) with ε→0 and ε³n→∞, the largest component L1 satisfies L1 = (1+o_p(1)) * [2(α+2)/(α+1)] ε^{-2} log(ε³ n) for fixed α>0 (and analogous limits when α(n)→a).
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Sound and complete axiomatizations are provided for path-reachability logic with Cantor derivative in T1 topologies and metric spaces, with decidability via neighborhood semantics that yields the finite model property.
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Quantum corrections suppress the symmetron fifth force by order 10% within a Compton wavelength of a thick planar source and enhance it at larger distances.
Unifilarisation of stochastic Mealy machines is an instance of coalgebraic determinisation over monads with support structure, producing causal stochastic behaviours rather than Moore-style output distributions.
Mazur and Jester manifolds have pairwise nonhomeomorphic boundaries via an octahedral hyperbolic structure, Dehn filling, and systolic geodesics, distinguishing their contractible 4-manifolds.
Seiberg-Witten instanton expansions combined with exact WKB period integrals allow analytic computation and continuation of quasinormal modes from large q to q=0.
An active learning method based on E-SINDy identifies governing ODEs and PDEs accurately with significantly fewer data samples than random sampling across tested systems.
Effective scalaron-photon coupling in f(R) gravity vanishes in the light-scalaron limit due to cancellation of anomaly-induced and diagrammatic contributions.
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Diagonal EP under variance-profile Gaussian matrices produces Gaussian-process dynamics with profile-dependent memory instead of conventional scalar state evolution.
LSD extends speculative sampling to second-order Langevin dynamics, achieving 3-9x speedup in MD while exactly sampling from the target distribution without relative error.
Introduces Δ-VFE pivoted Cholesky, a pivot rule maximizing the one-step gain in a VFE functional for kernel matrices via closed-form decomposition and batch sampling, yielding improved GP objective values and accuracy at low ranks.
DAML is a new dynamic modal logic that derives conditional obligations in multi-agent settings by combining action models with deontic value maximization over outcomes.
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citing papers explorer
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Variational Free Energy Pivot Selection for Pivoted Cholesky
Introduces Δ-VFE pivoted Cholesky, a pivot rule maximizing the one-step gain in a VFE functional for kernel matrices via closed-form decomposition and batch sampling, yielding improved GP objective values and accuracy at low ranks.
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Layer Potential Methods for Doubly-Periodic Harmonic Functions
Develops and analyzes single- and double-layer potential operators for doubly-periodic harmonic functions on finitely-connected tori, proves compactness and boundary limits, constructs the null space for multiply-connected cases, and demonstrates spectral convergence for Dirichlet, Neumann, and Stek
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A Mixed Virtual Element Method for the p-Laplace equation
Mixed VEM with novel non-linear stabilization for p-Laplace equation, establishing non-Hilbertian inf-sup stability, continuity, coercivity, and a priori error estimates.
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Cut Finite Element Methods for Convection-Diffusion in Mixed-Dimensional Domains
A CutFEM is developed and analyzed for convection-diffusion on hierarchical mixed-dimensional manifolds, with a priori error estimates in energy and L2 norms that hold for reduced regularity solutions.
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Neural network parametrized level sets for image segmentation
Neural networks parametrize level sets for Chan-Vese segmentation via equivalence to polygonal approximations, with unsupervised training providing data-driven geometric priors that improve initialization and convergence.
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Singularities in phase separation models: a spectral element approach for the nonlocal Cahn-Hilliard equation
A pseudospectral multishape method is developed to accurately approximate singular convolution operators in the nonlocal Cahn-Hilliard equation, enabling efficient high-resolution phase separation simulations.
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Low-Rank Solvers for Energy-Conserving Hamiltonian Boundary Value Methods
Low-rank structure in HBVM stage equations is exploited via Krylov projection for linear cases and Newton-Krylov with adaptive time-stepping for nonlinear cases, shown efficient on semi-discretized wave equations.