This paper derives bounds on the probability of incorrect clustering of noisy short sequences using statistically optimal rules, focusing on DNA storage decoders.

This paper proves space lower bounds for entropy-efficient random sampling using i.i.d. uniform bits.

This paper introduces a novel algorithm for generating k Hamming weight binary words in linear time while minimizing random bit consumption.

The paper proves a stochastic comparison for Gaussian maxima, resolving the Weak Simplex Conjecture and proving the Simplex Mean Width Conjecture.

The authors introduce a quantum empirical operator and use it to prove a universal achievability result for composite quantum hypothesis testing.

The paper derives new informational inequalities using Stam-like, moment-entropy-like inequalities, and a recently established Rényi entropy-based inequality. It obtains a Stam-like inequality connect…

This paper studies the existence of polynomial measures of dependence between two random variables that satisfy the data processing inequality and vanish on independence. It proves that no such polyno…

The paper improves Banaszczyk's inequality, providing a significantly better tail estimate for the discrete Gaussian measure on a lattice, which has applications in analyzing dual attacks against the…

This paper establishes a Coding Theorem in the context of symmetry groups and develops a connection between subgroups of a group and subsets of binary strings.

This paper measures the lower bound for the shortest program generating a sequence, proving a conservation law and providing a deterministic engine to recover generating programs for certain sequences…

This book provides a compact, derivation-oriented mathematical primer that connects major families of generative AI models, showing their underlying structural relationships.

The paper establishes information-theoretic lower bounds for stochastic optimization using low-bit gradients by reducing the problem to compressed Gaussian mean estimation, yielding sharp bounds on co…

This paper investigates the necessity of interaction for order-optimal 1-bit mean estimation in nonparametric finite-moment classes.

This paper presents an unconditional construction for a one-bit one-time private-key unclonable encryption scheme, which is information-theoretically secure, efficient, and has exponentially small unc…