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Related Articles from SNS
Strong Polarization and Entropy
arXiv:2606.02567v1 Announce Type: cross Abstract: We show that for any set of $n$ unit vectors $v_1,\ldots,v_n$ in a real Hilbert space and positive numbers $p_1,\ldots,p_n$ satisfying $\sum_j p_j = 1$, there exists a unit vector $u$ such that \[ \sum_{j=1}^n \frac{p_j^2}{\langle v_j, u\rangle^2}\leq 1. This inequality is a weighted version of the strong polarization inequality. As immediate corollaries, it yields a polarization inequality for products of powers of linear functionals and a...
Approximation by short exponential sums with geometric error decay based on Gauss quadrature
Announce Type: new Abstract: We present new short exponential sum approximations of length $N$ for $f_1(x)=\frac{1}{a+x}$ with $a>0$ on $[0, \infty)$ and for $f_2(x)= {\mathrm e}^{-x^2/2\sigma}$ with $\sigma>0$ on ${\mathbb R}$ with geometric error decay ${\rho}^{-2N}$ for user-defined $N \ge 2$ and $\rho > The approximations are built over consecutive intervals $[b_j, \, b_{j+1}) \subset [0, \infty)$, $j \in {\mathbb N}_{0}$, with interval lengths that depend on $\rho$ and grow...
Revisiting $O(n \log \log n)$ chaining for anchored edit distance
arXiv:2606.03929v1 Announce Type: new Abstract: Colinear chaining is a classical heuristic for sequence alignment: it enables scalable genome comparison and is a main component of many state-of-the-art read mappers based on seed-chain-extend. The earliest $O(n \log \log n)$ time algorithms by Eppstein et al. (J. ACM, 1992) chained $n$ fragments between two sequences $T$ and $Q$ while minimizing a gap cost based on the diagonal distance $\Delta_{\text{diag}}$ between consecutive fragments.
Deterministic Monotone Min-Plus Product and Convolution
arXiv:2605.07150v2 Announce Type: replace Abstract: The Monotone Min-Plus Product problem is a useful primitive that has seen many algorithmic applications over the past decade. In this problem, we are given two $n\times n$ integer matrices $A$ and $B$, where each row of $B$ is a monotone non-decreasing sequence of integers from $\{1,\dots,n\}$, and the goal is to compute their Min-Plus product, defined as the $n\times n$ matrix $C$ with $C_{i,j} = \min_{k}\{A_{i,k} + B_{k,j}\}$. The fastest...
Classification of independent sets in signed Johnson graphs and applications to kissing arrangements
Announce Type: new Abstract: Johnson graph are a family of graphs that play an important role in the theory of constant-weight codes, extremal combinatorics, and combinatorial geometry. We study signed analogues of classical Johnson graphs, denoted by $J_\pm(n,k)$, whose vertices are vectors of the form $\pm e_{i_1}\pm\cdots\pm e_{i_k}$, where two vertices are adjacent whenever their dot product equals $k-1$. We are particularly interested in maximum independent sets in the case $k=4$. An...
DAVID MARCUS: 5 blatant lies Democrats are spreading about Delaney Hall and ICE
Democratic elected officials and far-left agitators have teamed up in the past week to manufacture a chaotic crisis at Delaney Hall, an ICE detention facility in Newark, New Jersey, and it is a conflagration fueled almost entirely by blatant lies. It began with Sen. Andy Kim, D-N.J., being pepper sprayed when he decided to spend his Memorial Day marching with Antifa thugs, under their flag, while pretending he just wanted to visit the facility. Less than two days later, Reps. Jerry Nadler...
Mitochondria directly interact with the nuclear pore complex
Abstract Mitochondria regulate cellular processes through direct and indirect interactions with other organelles. A well-studied example has been contact with the endoplasmic reticulum at mitochondrial-associated endoplasmic reticulum membranes1, which control pathways including redox and calcium homeostasis2,3. Recent studies have also reported direct mitochondria–nuclear membrane contacts in cancer cells and yeast that promote pro-survival signalling4,5.
Structural basis for chaperone-guided assembly of RNA-induced silencing complex
Abstract The RNA-induced silencing complex (RISC), comprising an Argonaute (AGO) protein and a small RNA, is the central effector in RNA silencing. Small RNAs are loaded onto AGO as bulky duplexes in an HSP70- and HSP90-dependent process1,2,3, but the molecular mechanism remains poorly understood. Here we identify the human AGO–HSP90–p23 complex, which captures AGO in an RNA-free state, termed the AGO maturation complex (AMC).
Dems pick challenger for GOP congressman who vanished from public view amid health mystery
Democrat Rebecca Bennett will face Rep. Tom Kean Jr., R-N.J., an embattled lawmaker sidelined for months by an undisclosed health issue, in November’s general election. Bennett, a former Navy helicopter pilot, won the Democratic nomination in a crowded primary for a battleground New Jersey House seat, according to The Associated Press. Kean, who has not appeared in public since early March, ran unopposed for the GOP nomination.
Dems pick challenger for GOP congressman who vanished from public view amid health mystery
Democrat Rebecca Bennett will face Rep. Tom Kean Jr., R-N.J., an embattled lawmaker sidelined for months by an undisclosed health issue, in November’s general election. Bennett, a former Navy helicopter pilot, won the Democratic nomination in a crowded primary for a battleground New Jersey House seat, according to The Associated Press. Kean, who has not appeared in public since early March, ran unopposed for the GOP nomination.