Fractional Extendibility
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Related Articles from SNS
No-Go Theorem for Gaussian Quantum Repeaters from Fractional Extendibility
Announce Type: cross Abstract: Photon loss in optical channels fundamentally limits long-range reliable quantum communication. A standard approach to overcoming this limitation is the use of quantum repeater nodes, which typically perform experimentally demanding non-Gaussian operations. However, whether Gaussian repeater protocols can enhance quantum communication rates over bosonic attenuation channels has remained open.
Rotation-Parameterized Graph Fractional Fourier Transform: Definition, Properties, and Optimal Filtering
Announce Type: replace-cross Abstract: Graph spectral representations are fundamental in graph signal processing, providing a rigorous frameworkforanalyzing graph-structured data. The graph fractional Fourier transform (GFRFT) extends the graph Fourier transform (GFT) through a fractional-order parameter, enabling flexible spectral analysis with mathematical consistency. The angular graph Fourier transform (AGFT) further introduces angular control by rotating GFT eigenvectors; however,...
Amplified Arctic iceberg traffic reshapes benthic biodiversity
Abstract The Arctic is undergoing rapid warming, resulting in retreating sea ice and glaciers1, yet how cryospheric changes propagate into the deep ocean remains poorly understood2. Here we identify a climate-driven mechanism linking accelerating glacier disintegration to an increase in deep-sea hard-bottom habitats far beyond calving fronts. Seafloor observations in Fram Strait show a localized increase in the density and patchiness of dropstones delivered by debris-laden icebergs.
SFMP: Fine-Grained, Hardware-Friendly and Search-Free Mixed-Precision Quantization for Large Language Models
arXiv:2602.01027v2 Announce Type: replace Abstract: Mixed-precision quantization is a promising approach for compressing large language models under tight memory budgets. However, existing mixed-precision methods typically suffer from one of two limitations: they either rely on expensive discrete optimization to determine precision allocation, or introduce hardware inefficiencies due to irregular memory layouts. We propose SFMP, a search-free and hardware-friendly mixed-precision...
Molecular glue degraders of HuR suppress BRAF-mutant colorectal cancer
Abstract BRAF gain-of-function mutations, particularly BRAF(V600E), affect roughly 10% of all patients with colorectal cancer (CRC), and portend poor prognosis with limited therapeutic interventions. BRAF inhibitors such as encorafenib are ineffective due to MAPK pathway reactivation driven by BRAF dimerization. Combined inhibition of BRAF and EGFR, although approved therapies, results in short survival benefits and frequent treatment resistance and relapse1,2,3.
Dimension Reduction via Sum-of-Squares and Improved Clustering Algorithms for Non-Spherical Mixtures
arXiv:2411.12438v2 Announce Type: replace Abstract: We develop a new approach for clustering non-spherical (i.e., arbitrary component covariances) Gaussian mixture models via a subroutine, based on the sum-of-squares method, that finds a low-dimensional separation-preserving projection of the input data. Our method gives a non-spherical analog of the classical dimension reduction, based on singular value decomposition, that, among several other applications, forms a key component of the...
Actually, the SAT Was Necessary After All
Zvezdelina Stankova has taught mathematics at UC Berkeley for nearly three decades. But in 2023, while teaching introductory calculus for the first time since the beginning of the coronavirus pandemic, she noticed that something was quite wrong. The bottom 25 percent of students were not just struggling with the coursework, Stankova told me; “people were in freefall.”
Fixed-Point Scaffolding in the Clef Programming Language
Announce Type: new Abstract: For fans of Gabriel's "Worse is Better" it may be ironic that C++, by way of MLIR, serves as the scaffold for compiling an ML-family language whose correctness properties are structural. A crucial intersection in our Composer compiler initiates its lowering with a fixed-point combinator that preserves the dimensional, grade, escape, and numeric-representation structure from the Program Semantic Graph. And the MLIR that's witnessed from the PSG is no passive host.
Improved Torn Paper Coding via Local Alignment
arXiv:2605.23076v2 Announce Type: replace Abstract: In the torn paper channel, a transmitted codeword is broken at random locations into fragments that arrive at the decoder in an unordered manner. A central theoretical challenge within this model is global alignment -- the task of determining each fragment's original position -- in order to faithfully reconstruct the entire codeword. Prior work by Shomorony and Vahid introduced an interleaved-pilot scheme that successfully achieved a...
Sharp lower error bounds for strong approximation of SDEs with a drift coefficient of H\"older or Sobolev regularity using a Weierstra{\ss} scale
arXiv:2504.20728v2 Announce Type: replace-cross Abstract: We study strong approximation of solutions of SDEs with bounded $\alpha$-H\"older continuous drift coefficient and constant diffusion coefficient at time point $1$. Recently, it was shown in [arXiv:1909.07961v4 (2021)] that for such SDEs the equidistant Euler scheme achieves an $L^p$-error rate of at least $(1+\alpha)/2$, up to an arbitrary small $\varepsilon$, for all $p\geq 1$ and $\alpha\in (0,1]$, in terms of the number of...