The aim of this paper is to study the boundedness of different conical square functions that arise naturally from second order divergence form degenerate elliptic operators. More precisely, let $L_w=w^{-1}\,{\rm div}(w\,A\,\nabla)$ where $w\in A_2$ a...
Laplacian Bond Order This method is an extension of the QTAIM (Quantum Theory of Atoms In Molecules) concept of using the Laplacian of the electron density $\nabla^2\rho$ to characterize …
variables is the vector field (or vector-valued function) ∇ f {\displaystyle \nabla f} whose value at a point p {\displaystyle p} gives the direction and the
Let $(M^n,g,\nabla f)$, $n\geq 3$, be an expanding gradient Ricci soliton with nonnegative sectional curvature whose asymptotic cone is isometric to $C(\mathbb{S}^{n-1}(c))$ where $\mathbb{S}^{n-1}(c)$ is the standard $(n-1)$-sphere of curvature $1/c...
Points: 1528 | Comments: 823 | Author: nabla9
Points: 726 | Comments: 382 | Author: nabla9
We show that the gradient norm $\|\nabla f(x)\|$ for $x \sim \exp(-f(x))$, where $f$ is strongly convex and smooth, concentrates tightly around its mean. This removes a barrier in the prior state-of-the-art analysis for the well-studied Metropolized...
Points: 515 | Comments: 433 | Author: nabla9
Points: 425 | Comments: 157 | Author: nabla9
We consider first passage percolation (FPP) with passage times generated by a general class of models with long-range correlations on $\mathbb{Z}^d$, $d\geq 2$, including discrete Gaussian free fields, Ginzburg-Landau $\nabla φ$ interface models or...
In this paper we obtain results indicating that fine shape is tractable and "not too strong" even in the non-locally compact case, and can be used to better understand infinite-dimensional metrizable spaces and their homology theories. We show that...
We show that attempts to modify the force on a magnetic dipole by introducing either hidden momentum or internal forces are not correct. The standard textbook result ${\bf F=\nabla(\bmu\cdot B)}$ is correct even in the presence of time dependent elec...
We show that the 14 graphs obtained by $\nabla\mathrm{Y}$ moves on K_7 constitute a complete list of the minor minimal intrinsically knotted graphs on 21 edges. We also present evidence in support of a conjecture that the 20 graph Heawood family, obt...
Points: 335 | Comments: 147 | Author: nabla9
Points: 9 | Comments: 4 | Author: nabla9
AI is driving incredible innovation and actively reshaping care delivery. On March 18, join healthcare leaders from around the world for a virtual summit exploring how AI moves from vision to real-world impact across the healthcare landscape. Featuring a keynote fireside chat wit…
Context is everything in healthcare: from specialty and care setting to patient history and the real-world constraints that shape decisions every day. The next generation of AI models will be defined by their ability to understand and adapt to that clinical context. Yann LeCun an…