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Valence Ionization Of Water Clusters Formed Inside Helium Nanodroplets

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arXiv Physics 7d ago

Faster algorithms for k-Orthogonal Vectors in low dimension

Announce Type: replace Abstract: In the Orthogonal Vectors problem (OV), we are given two families $A, B$ of subsets of $\{1,\ldots,d\}$, each of size $n$, and the task is to decide whether there exists a pair $a \in A$ and $b \in B$ such that $a \cap b = \emptyset$. Straightforward algorithms for this problem run in $\mathcal{O}(n^2 \cdot d)$ or $\mathcal{O}(2^d \cdot n)$ time, and assuming SETH, there is no $2^{o(d)}\cdot n^{2-\varepsilon}$ time algorithm that solves this problem for any...

arXiv CS 6d ago

Relaxation Kernel, Spectral Dissipation, and Global Convergence of Blahut--Arimoto Dynamics

arXiv:2604.25106v3 Announce Type: replace Abstract: We develop a spectral theory for continuous- and discrete-time Blahut--Arimoto (BA) dynamics, centered on the relaxation kernel $ \G = \E_p[K^*_X \otimes K^*_X] $. Five main results are established. Along the continuous-time BA flow, the free energy satisfies the exact $ \chi^2 $-dissipation identity $ \dot F_\beta = -\D(q) $, where $ \D(q)=\chi^2(\T q \| q) $ is the Pearson $ \chi^2 $-divergence.

arXiv CS 8d ago

Global Convergence of Adaptive Sensing for Principal Eigenvector Estimation

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arXiv CS 8d ago

Infinite sequences with optimal diaphony, periodic $L_2$-discrepancy, and beyond

arXiv:2606.05482v1 Announce Type: new Abstract: We investigate the periodic $L_2$-discrepancy of infinite sequences $\S_d$ in $[0,1)^d$ and its analytic counterpart, the diaphony. We prove that infinite order-2 digital sequences over $\mathbb{F}_2$ attain the optimal order $L_{2,N}^{{\rm per}}(\S_d) \le C_d (\log N)^{d/2}/N$ for all $N \in \mathbb{N}\setminus \{1\}$, matching known lower bounds for infinitely many $N \in \mathbb{N}$.

arXiv CS 5d ago

One-Shot Klein Cutting Planes for Lipschitz Geodesically Convex Optimization in Hyperbolic Space

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arXiv CS 9d ago

Information-Theoretic Bounds for Sparse Covariance Estimation in the Vertical-Split Distributed Model

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arXiv CS 2d ago

Optical Memory Optimization Across Rubidium Isotopes and Transitions

arXiv:2606.00199v1 Announce Type: cross Abstract: We investigate optical memory efficiency and storage time across $^{85}\mathrm{Rb}$ and $^{87}\mathrm{Rb}$ isotopes on both the D$_1$ and D$_2$ transitions. Maximum efficiency of up to $44\%$ was achieved using the D$_1$ line in both isotopes, with up to 1.5 ms storage time. %Maximum efficiencies of $44\%$ were measured for both isotopes on the D$_1$ line, in agreement within $1\sigma$, while the longest storage time reached is $1.5$ ms.

arXiv Physics 8d ago

Optical Memory Optimization Across Rubidium Isotopes and Transitions

Announce Type: replace-cross Abstract: We investigate optical memory efficiency and storage time across $^{85}\mathrm{Rb}$ and $^{87}\mathrm{Rb}$ isotopes on both the D$_1$ and D$_2$ transitions. Maximum efficiency of up to $44\%$ was achieved using the D$_1$ line in both isotopes, with up to 1.5 ms storage time. %Maximum efficiencies of $44\%$ were measured for both isotopes on the D$_1$ line, in agreement within $1\sigma$, while the longest storage time reached is $1.5$ ms.

arXiv Physics 7d ago

Stable full-field simulation of a multiscale elliptic equation by means of Quantized Tensor Trains

Announce Type: replace Abstract: In this article, we design an original solver based on Quantized Tensor Trains (QTT) for linear elliptic equations with heterogeneous coefficient field, that allows for extremely fine meshes. It can achieve full-field simulations in dimensions $d=2$ and $d=3$ with a number of Degrees of Freedom (DoFs) up to $20$ orders of magnitude beyond the classical solvers, recovering accurately the solution as well as its gradient in the $\LL^2$ norm. For treating such...

arXiv CS 2d ago