![The parity-check tensor [latex]H_{2-D}[/latex] is defined for [latex]p=3[/latex], utilizing shifts where [latex]\phi(i) = i[/latex], [latex]\psi(j) = j[/latex], and [latex]\eta(k) = k[/latex], thereby establishing a foundational element for error correction within a two-dimensional system.](https://arxiv.org/html/2601.08927v1/stack.png)
Researchers have developed a new family of quantum error-correcting codes designed to significantly improve data storage and transmission by addressing burst errors with enhanced cycle-free structures.
Researchers have developed a method to maintain the safety and performance of powerful AI models even after they’ve been adapted for specific tasks.
![The study demonstrates that bit decoding failure probability transitions across distinct availability regimes-linear, polylogarithmic, and sub-logarithmic-as evidenced by the comparison of empirical and theoretical results with a failure probability of [latex] p_f = 0.2 [/latex] and redundancy of [latex] r = 4 [/latex].](https://arxiv.org/html/2601.08765v1/photos/bit_dec_prob.png)
A new analysis demonstrates that locally repairable codes, when paired with majority-logic decoding, can achieve near-perfect data recovery even with significant data loss.
New research reveals a surprisingly straightforward method for accurately replicating European and Asian option payoffs without the complexities of rough-path theory.
A novel framework utilizes Ethereum smart contracts to establish a decentralized and tamper-proof system for verifying the integrity of critical firmware in Cyber-Physical Systems.
New analysis of constant entropy contours offers a precise location for the QCD critical point and a corresponding equation of state.
A novel family of error-correcting codes, optimized for maximizing toroidal distance, promises to enhance the security and efficiency of lattice cryptography.
A new theoretical result connects the computational power of randomized queries with the size of the shortest possible proofs for recursively defined Boolean functions.
A new analysis reveals that violations of Bell inequalities, long considered proof of quantum entanglement, may be replicated by alternative, non-quantum models.
A novel algebraic construction using dyadic matrices enhances the performance of quantum low-density parity-check codes for reliable quantum communication.