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Erd\H{o}s Rado Sunflower Theorem for Shifted Families

Combinatorics [Submitted on 1 Jun 2026 (v1), last revised 8 Jun 2026 (this version, v2)] Title:Erdős Rado Sunflower Theorem for Shifted Families View PDF HTML (experimental)Abstract:Let $f(k,s)$ denote the minimum integer $m$ such that any family $\mathcal{F}$ consisting of $k$-sized sets of cardinality at least $m$ always contain a sunflower of size $s$. The Erdős-Rado Sunflower Conjecture states that for every $s >2$, there is an constant $C=C(s)$ such that $f(k,s) \leq C^k$.

arXiv CS 1d ago

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...

arXiv CS 9d ago

Inverse Critical Experiment Design via Gradient Optimization and a Multigroup Attention-Based Neural Network Architecture

arXiv:2606.04033v1 Announce Type: new Abstract: The validation of advanced nuclear reactor designs and fuel concepts requires critical experiments with high neutronic similarity to the target technology. Neutronic similarity is quantified by the correlation coefficient $c_k$, which captures the shared bias in $k_\text{eff}$ induced by uncertainties in nuclear data. Generally, a $c_k\geq0.9$ is needed for an experiment to be sufficiently similar to a target technology.

arXiv CS 6d ago

Counting Distinct (Non-)Crossing Substrings in Optimal Time

Announce Type: replace Abstract: Let $w$ be a string of length $n$. The problem of counting factors crossing a position -- Problem 64 from the textbook ``125 Problems in Text Algorithms'' [Crochemore, Lecroq, and Rytter, 2021] -- asks to count the number $\mathcal{C}(w,k)$ (resp. $\mathcal{N}(w,k)$) of distinct substrings in $w$ that have occurrences containing (resp.

arXiv CS 5d ago

Distributed Instrument Simulation with Quantum Side Information in the One-Shot Regime

arXiv:2109.12586v5 Announce Type: replace-cross Abstract: Three distributed parties, two transmitters (Txs) and a receiver (Rx), hold one component each of a tripartite quantum state \(\rho^{A_1A_2C}\). The goal is to simulate the action of a separable instrument acting on the \(A_1\) and \(A_2\) components, with the Rx recovering the classical outcome. To enable this, each Tx \(k\) can transfer bits on a noiseless bit pipe and share randomness at rates \(R_k\) and \(C_k\), respectively,...

arXiv CS 2d ago

Do Transformers Need Three Projections? Systematic Study of QKV Variants

arXiv:2606.04032v2 Announce Type: replace Abstract: Transformers have become the standard solution for various AI tasks, with the query, key, and value (QKV) attention formulation playing a central role. However, the individual contribution of these three projections and the impact of omitting some remain poorly understood. We systematically evaluate three projection sharing constraints: a) Q-K=V (shared key-value), b) Q=K-V (shared query-key), and c) Q=K=V (single projection).

arXiv CS 5d ago

Do Transformers Need Three Projections? Systematic Study of QKV Variants

Announce Type: new Abstract: Transformers have become the standard solution for various AI tasks, with the query, key, and value (QKV) attention formulation playing a central role. However, the individual contribution of these three projections and the impact of omitting some remain poorly understood. We systematically evaluate three projection sharing constraints: a) Q-K=V (shared key-value), b) Q=K-V (shared query-key), and c) Q=K=V (single projection).

arXiv CS 6d ago

AIADMK faces fresh exodus as 3 ex-ministers, 10 ex-MLAs head to TVK

CHENNAI: The exodus from the AIADMK continued on Saturday, with several senior leaders making a beeline for the ruling TVK. Former AIADMK ministers Udumalai K Radhakrishnan, Kadambur C Raju and M C Sampath are the latest to join the growing list of defectors. The trio, along with their supporters, arrived at the TVK headquarters in Panaiyur to formally join the ruling party.

Times of India 4d ago

Homomorphic encryption schemes based on coding theory and polynomials

arXiv:2509.13788v2 Announce Type: replace Abstract: Homomorphic encryption is a powerful cryptographic tool that enables secure computations on the private data. It evaluates any function for any operation securely on the encrypted data without knowing its corresponding plaintext. For original data $p$, $c$ denotes the ciphertext of the original plaintext $p$, i.e. $c = Encrypt_k(p)$.

arXiv CS 6d ago

Majorization and Gaussian-Mass Maximality for Construction-A Lattices from Binary Self-Dual Codes

Announce Type: replace-cross Abstract: Regev and Stephens-Davidowitz conjectured that the integer lattice maximizes Gaussian mass among integral lattices of a given rank. We prove this, including the equality case, for all unimodular Construction-A lattices arising from binary self-dual codes. The proof reduces the theta-series inequality to a sharp majorization statement for codes: if $C$ is a binary self-dual $[2k,k]$ code, then the half-weight distribution of $C$ is dominated in convex...

arXiv CS 6d ago