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Lightning Plus Polynomial Approximation: Optimal Root-Exponential Convergence for Singular Functions in Corner Domains

Announce Type: replace Abstract: This paper presents a rigorous convergence analysis for the lightning plus polynomial approximation scheme, which employs rational approximations constructed with preassigned tapered, exponentially clustered poles. This pole placement strategy was originally introduced by Trefethen and his collaborators for the resolution of corner singularities. Ample numerical results indicate that this scheme achieves root-exponential convergence, and in particular attains...

arXiv CS 6d ago

Lightning Plus Polynomial Approximation: Optimal Root-Exponential Convergence for Singular Functions in Corner Domains

Announce Type: new Abstract: This work presents a rigorous convergence analysis for the lightning plus polynomial approximation scheme, which employs rational approximations constructed with tapered, exponentially clustered poles. This pole placement strategy was originally introduced by Trefethen and his collaborators for the resolution of corner singularities.

arXiv CS 9d ago

Late-Time Cosmology and Structure Formation in Quadratic $f(Q)$ Gravity

arXiv:2606.02660v1 Announce Type: new Abstract: We investigate the cosmological evolution associated with the quadratic symmetric teleparallel gravity framework, \( f(Q)=Q+\alpha Q^{2}+\beta \) where the relation \(Q\propto H^{2}\) generates an additional \(H^{4}\) contribution to the Friedmann equation. Using the exact algebraic solution for $H(z)$, we reconstruct the effective dark-energy sector and compare the background evolution with $\Lambda$CDM using Type Ia supernovae, BAO, and...

arXiv Physics 7d ago

Whole-genome duplication shaped cell-type evolution in the vertebrate brain

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Nature 21h ago

A first-in-class pulsatile FXR agonist for bile-acid-related liver diseases

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A prognostic human brain network for diffuse midline glioma

Abstract Diffuse midline gliomas (DMGs) are near-universally lethal tumours of the childhood central nervous system1,2. In animal models, DMGs form brain-wide integrated networks through neuron-to-glioma synapses3,4,5,6 and glioma-to-glioma gap junctional coupling3. This extensive connectivity robustly promotes the growth and invasion of DMG3,4,5,6,7,8,9 and other glial malignancies10,11,12 through paracrine mechanisms and direct neuron-to-glioma synapses.

Nature 21h ago