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Related Articles from SNS

On the Maximal Length of MDS Elliptic Codes

arXiv:2605.29439v2 Announce Type: replace Abstract: The determination of the maximal length of maximum distance separable (MDS) codes arising from elliptic curves is a central problem in coding theory. For an elliptic curve $E$ over $\mathbb{F}_q$, let $\operatorname{MEC}(k,q)$ denote the maximal length of a $q$-ary MDS elliptic code of dimension $k$. It was recently shown that $\operatorname{MEC}(k,q)\le\frac{q+1}{2}+\sqrt{q}$ for $q\ge289$ and $3\le k\le(q+1-2\sqrt{q})/10$, with equality...

arXiv CS 5d ago

A Temporal Spatial Minimax Rate for Smoothly-Varying Distributions in Wasserstein Space

arXiv:2606.07325v1 Announce Type: cross Abstract: We study the minimax rate of estimating a future value $\mu_{t_n+h}$ of a curve $t\mapsto\mu_t$ in the $2$-Wasserstein space $\mathcal{P}_2(\mathbb{R}^d)$ from finitely many noisy snapshots of its past, under an adiabatic bound $\|\nabla_t^k v\|\le\varepsilon$ on the $k$-th covariant derivative of the velocity field. Our central result is a unified temporal-spatial minimax lower bound: over regular, locally transport-rich subclasses, every...

arXiv CS 2d ago

Dielectric formalism of the 2D uniform electron gas at finite temperatures

arXiv:2601.14989v2 Announce Type: replace-cross Abstract: We present a comprehensive analysis of the two-dimensional uniform electron gas (2D-UEG or more commonly 2DEG) at finite temperature, spanning a broad range of densities / coupling strengths ($0.01\le{r}_s\le20$) and temperatures / degeneracy parameters ($0.01\le\Theta= k_B Within the self-consistent dielectric formalism, we construct two-dimensional versions of the Singwi-Tosi-Land-Sj\"olander (STLS) and hypernetted-chain (HNC)...

arXiv Physics 9d ago

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.

arXiv CS 6d ago

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...

arXiv CS 1d ago

On the Duke--Erd\H{o}s--R\"odl Problem at the One-Third Threshold

Announce Type: cross Abstract: Let $G$ be an $n$-vertex graph with $e(G)\ge n^2/ k$. We prove a self-contained internal short-cycle core theorem at the threshold $k\le n^{1/3}$: the graph $G$ contains a subgraph $H_6$ with $\Omega(n^2/ k^3)$ edges in which every two distinct edges lie together on a cycle of length at most $6$ contained in $H_6$, and a subgraph $H_8$ with $\Omega(n^2/k^2)$ edges in which every two distinct edges lie together on a cycle of length at most $8$ contained in...

arXiv CS 2d ago

Blow-ups of order types of positive density

Announce Type: cross Abstract: Order types are an equivalence relation between point configurations that capture their combinatorial and convexity properties. Let $P$ be a $\kappa$-colored sequence of $n \ge d+1$ points in general position in $\mathbb{R}^d$. Let $\rho$ be a $\kappa$-colored order type on $k \le d+1$ points that has positive density on $P$; that is, for some constant $\delta >0$, there are $\delta \cdot \binom{n}{k}$ $k$-point subsequences of $P$ that have the same order type...

arXiv CS 1d ago

Tough cookies: How pop group Le Sserafim overcame band tensions and internet trolls

The K-pop band say accepting their flaws and embracing humour took them to a new level of success.

BBC Arts 5d ago

Tough cookies: How pop group Le Sserafim overcame internal conflict and internet trolls

The K-pop band say accepting their flaws and embracing humour took them to a new level of success.

BBC World 5d ago

Tough cookies: How pop group Le Sserafim overcame band tensions and internet trolls

The K-pop band say accepting their flaws and embracing humour took them to a new level of success.

BBC Entertainment 5d ago