Cartesian
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Related Articles from SNS
A Cartesian-3j Framework for Machine Learning Interatomic Potentials
Announce Type: replace Abstract: Machine learning interatomic potentials (MLIPs) have brought substantial gains in the extrapolation capability in computational chemistry. However, most equivariant models are typically built with spherical tensors (STs), while Cartesian tensor formulations remain less developed despite their natural alignment with atomic coordinates and tensorial targets. In this work, we develop a Cartesian framework for irreducible Cartesian tensors (ICTs) by introduce the...
A Cartesian-3j Framework for Machine Learning Interatomic Potentials
Announce Type: replace-cross Abstract: Machine learning interatomic potentials (MLIPs) have brought substantial gains in the extrapolation capability in computational chemistry. However, most equivariant models are typically built with spherical tensors (STs), while Cartesian tensor formulations remain less developed despite their natural alignment with atomic coordinates and tensorial targets. In this work, we develop a Cartesian framework for irreducible Cartesian tensors (ICTs) by...
The Cartesian Shortcut: Re-evaluate Vision Reasoning in Polar Coordinate Space
Announce Type: replace Abstract: As current Multimodal Large Language Models rapidly saturate canonical visual reasoning benchmarks, a key question emerges: do these strong scores genuinely reflect robust visual understanding? We identify a pervasive vulnerability, the Cartesian Shortcut: visual reasoning benchmarks prevalently build on orthogonal grid-based layouts that can be readily discretized into explicit textual coordinates. Models systematically exploit this property, heavily...
Differentiable Particle-Mesh Ewald with Cartesian Tensor Message Passing for Learning Long-Range Electrostatics and Dipole Response
Announce Type: new Abstract: Machine learning interatomic potentials (MLIPs) can approach quantum accuracy for short-range chemistry, but most architectures remain local and fail to capture the long-range electrostatic and polarization interactions essential for ionic, polar, and interfacial systems. Recent Ewald-based MLIPs show that locally predicted electrostatic variables can recover important long-range physics, including multipolar response. However, many energy-based implementations...
Token-sliding realizability for complements, Cartesian-products, and grid graph families
Announce Type: cross Abstract: For an integer $k\ge 0$ and a graph $G$, the \emph{token-sliding reconfiguration graph $\mathsf{TS}_k(G)$} has the independent $k$-sets of $G$ as vertices. Two vertices are adjacent if one token can slide along an edge of $G$ and the resulting $k$-set is still independent. We study the following realizability problem: for fixed $k\ge 2$, which graphs are isomorphic to $\mathsf{TS}_k(G)$ for some graph $G$?
8-K - Cartesian Therapeutics, Inc. (0001453687) (Filer)
Filed: 2026-06-09 AccNo: 0001140361-26-024556 Size: 188 KB Item 7.01: Regulation FD Disclosure Item 9.01: Financial Statements and Exhibits
On graph products and multi-word-representability
arXiv:2603.29629v4 Announce Type: replace-cross Abstract: The multi-word-representation number $\mu(G)$ of a graph $G$ is the minimum number of word-representable graphs whose union is $G$. We study the behavior of $\mu$ under six standard graph products: the lexicographic, Cartesian, rooted, corona, tensor, and strong products. For the Cartesian and rooted products, we show that $\mu(G_1 \square G_2)=\mu(G_1 \diamond G_2)=\max\{\mu(G_1),\mu(G_2)\}$. For the corona product, we prove that...
On graph products and multi-word-representability
arXiv:2603.29629v3 Announce Type: replace-cross Abstract: The multi-word-representation number $\mu(G)$ of a graph $G$ is the minimum number of word-representable graphs whose union is $G$. We study the behavior of $\mu$ under four standard graph products: the lexicographic, Cartesian, rooted, and corona products.
On first-order definable operations on relational structures
Announce Type: new Abstract: We survey the definitions and main properties of first-order (FO) definable unary operations on relational structures, called FO-transductions, and of FO-definable binary operations based on disjoint union and Cartesian product. We focus our study on Backwards Translation Theorems and Splitting Theorems that permit to express FO properties of output structures in terms of finitely many FO properties of the corresponding input ones. In the particular cases where...
Element-Saving Hexahedral 3-Refinement Templates
arXiv:2512.14862v5 Announce Type: replace Abstract: Conforming hex meshes are widely regarded as an effective computational domain for simulation because of their nice numerical properties, yet automatically decomposing a general 3D volume into a conforming hex mesh remains a formidable challenge. Among existing approaches, methods that construct an adaptive Cartesian grid and subsequently convert it into a conforming mesh stand out for their robustness. However, topological conversion...