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Explicit Factorization of $x^{p+1}-1$ over $\mathbb{Z}_{p^e}$: A Structural Approach via Dickson Polynomials

arXiv:2604.19038v2 Announce Type: replace Abstract: Let $p$ be an odd prime. The factorization of the polynomial $x^{p+1}-1$ over the integer residue ring $\mathbb{Z}_{p^e}$ is pivotal for constructing cyclic codes with Hermitian symmetry, a critical resource for Linear Complementary Dual (LCD) codes and Entanglement-Assisted Quantum Error-Correcting Codes (EAQECC). Traditionally, lifting factorizations relies on the generic Hensel's Lemma, masking the underlying algebraic structure.

arXiv CS 9d ago

DTop-p MoE: Sparsity-Controlled Dynamic Top-p MoE for Foundation Model Pre-training

arXiv:2512.13996v2 Announce Type: replace Abstract: Sparse Mixture-of-Experts architectures are essential for scaling model capacity efficiently, yet the standard Top-$k$ routing imposes a rigid sparsity pattern that ignores the intrinsic variance in token difficulty and layer-specific computational needs. Top-$p$ routing is more adaptive because it selects experts until their cumulative routing probability reaches a threshold, allowing confident tokens to use fewer experts and ambiguous...

arXiv CS 9d ago

DTop-p MoE: Sparsity-Controlled Dynamic Top-p MoE for Foundation Model Pre-training

arXiv:2512.13996v3 Announce Type: replace Abstract: Sparse Mixture-of-Experts architectures are essential for scaling model capacity efficiently, yet the standard Top-$k$ routing imposes a rigid sparsity pattern that ignores the intrinsic variance in token difficulty and layer-specific computational needs. Top-$p$ routing is more adaptive because it selects experts until their cumulative routing probability reaches a threshold, allowing confident tokens to use fewer experts and ambiguous...

arXiv CS 7d ago

Strategyproof Mechanisms for Euclidean Facility Location Problems under $L_p$-norm Social Cost

arXiv:2606.08621v1 Announce Type: new Abstract: We study strategyproof mechanisms for eliciting agents' location preferences truthfully in the Euclidean plane $\mathbb R^2$ and locating a facility so as to minimize the $L_p$-norm social cost, defined as the $L_p$-norm of the vector of distances from the facility to the agents' preferred locations, for any $p \ge 1$. While the cases $p=1$ and $p=\infty$ have been well-studied, open questions remain about the optimal approximation ratios...

arXiv CS 1d ago

Explainer-Why SpaceX faces a longer wait to join S&P 500

Explainer-Why SpaceX faces a longer wait to join S&P 500 June 5 : SpaceX's entry into the S&P 500 will take longer after S&P Dow Jones Indices declined to relax rules for megacap IPOs, delaying billions in passive fund inflows from the potential inclusion. The decision keeps several barriers intact. To join the S&P 500, a company must trade publicly for at least 12 months, be profitable under U.S. accounting standards and hold a free float of at least 10 per cent.

Channel News Asia 5d ago

Empirical Approximation of $L_p$ Norms

arXiv:2606.00347v1 Announce Type: cross Abstract: We study empirical $L_p$ moments of a random vector $\pmb\varphi$ based on its i.i.d.\ copies $\pmb\varphi^1,\ldots,\pmb\varphi^m$, that is, $\frac1m\sum_{j=1}^m |\langle \pmb\varphi^j,y\rangle|^p$. Our main result is a new estimate for the expected uniform deviation \[ \mathbb{E}\sup_{y\in D}\biggl| \frac1m\sum_{j=1}^m |\langle \pmb\varphi^j,y\rangle|^p -\mathbb{E}|\langle \pmb\varphi,y\rangle|^p \biggr| \] over an arbitrary index set $D$....

arXiv CS 8d ago

SpaceX blocked from early US benchmark index entry as S&P reaffirms existing rules

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Channel News Asia 5d ago

Rule-based autocorrection of Piping and Instrumentation Diagrams (P&IDs) on graphs

arXiv:2502.18493v2 Announce Type: replace Abstract: A piping and instrumentation diagram (P&ID) is a central reference document in chemical process engineering. Currently, chemical engineers manually review P&IDs through visual inspection to find and rectify errors. However, engineering projects can involve hundreds to thousands of P&ID pages, creating a significant revision workload.

arXiv CS 1d ago

Set-Preserving Calibration from Conformal P-Values to E-Values

arXiv:2606.03600v1 Announce Type: cross Abstract: Standard conformal prediction (CP) procedures are typically formulated in terms of p-values, but reliance on p-values alone limits flexibility, for example, when combining dependent evidence across models or data splits. Recent work has explored e-value formulations for conformal inference, yet a direct connection between p- and e-value formulations in CP has been missing, especially regarding their statistical efficiency. We first identify...

arXiv CS 7d ago

Extreme $L_p$ discrepancy, numerical integration and the curse of dimensionality

arXiv:2602.19760v3 Announce Type: replace Abstract: The classical notion of extreme $L_p$ discrepancy is a quantitative measure for the irregularity of distribution of finite point sets in the $d$-dimensinal unit cube. In this paper we find a dual integration problem whose worst-case error is exactly the extreme $L_p$ discrepancy of the underlying integration nodes. Studying this integration problem we show that the extreme $L_p$ discrepancy suffers from the curse of dimensionality for all...

arXiv CS 9d ago