Related papers: Central Limit Theorem for Mutation Systems
In response to the evolving landscape of data storage, researchers have increasingly explored non-traditional platforms, with DNA-based storage emerging as a cutting-edge solution. Our work is motivated by the potential of in-vivo DNA…
Due to its longevity and enormous information density, DNA is an attractive medium for archival storage. In this work, we study the fundamental limits and tradeoffs of DNA-based storage systems under a simple model, motivated by current…
Due to its longevity and enormous information density, DNA is an attractive medium for archival storage. In this work, we study the fundamental limits and trade-offs of DNA-based storage systems by introducing a new channel model, which we…
Recent work in dynamic causal inference introduced a class of discrete-time stochastic processes that generalize martingale difference sequences and arrays as follows: the random variates in each sequence have expectation zero given certain…
We develop a central limit theorem (CLT) for a non-parametric estimator of the transition matrices in controlled Markov chains (CMCs) with finite state-action spaces. Our results establish precise conditions on the logging policy under…
We provide an overview of current approaches to DNA-based storage system design and accompanying synthesis, sequencing and editing methods. We also introduce and analyze a suite of new constrained coding schemes for both archival and random…
Under the high-dimensional setting that data dimension and sample size tend to infinity proportionally, we derive the central limit theorem (CLT) for linear spectral statistics (LSS) of large-dimensional sample covariance matrix. Different…
DNA-based storage is an emerging technology that enables digital information to be archived in DNA molecules. This method enjoys major advantages over magnetic and optical storage solutions such as exceptional information density, enhanced…
DNA is an attractive medium for digital data storage. When data is stored on DNA, errors occur, which makes error-correcting coding techniques critical for reliable DNA data storage. To reduce the errors, a common technique is to include…
DNA is emerging as an increasingly attractive medium for data storage due to a number of important and unique advantages it offers, most notably the unprecedented durability and density. While the technology is evolving rapidly, the…
DNA strands serve as a storage medium for $4$-ary data over the alphabet $\{A,T,G,C\}$. DNA data storage promises formidable information density, long-term durability, and ease of replicability. However, information in this intriguing…
We prove two theorems related to the Central Limit Theorem (CLT) for Martin-L\"of Random (MLR) sequences. Martin-L\"of randomness attempts to capture what it means for a sequence of bits to be "truly random". By contrast, CLTs do not make…
DNA exhibits remarkable potential as a data storage solution due to its impressive storage density and long-term stability, stemming from its inherent biomolecular structure. However, developing this novel medium comes with its own set of…
Sample covariance matrices are widely used in multivariate statistical analysis. The central limit theorems (CLT's) for linear spectral statistics of high-dimensional non-centered sample covariance matrices have received considerable…
The Central Limit Theorem (CLT) establishes that sufficiently large sequences of independent and identically distributed random variables converge in probability to a normal distribution. This makes the CLT a fundamental building block of…
DNA data storage offers a high-density, long-term alternative to traditional storage systems, addressing the exponential growth of digital data. Composite DNA extends this paradigm by leveraging mixtures of nucleotides to increase storage…
Recent theoretical works have characterized the dynamics of wide shallow neural networks trained via gradient descent in an asymptotic mean-field limit when the width tends towards infinity. At initialization, the random sampling of the…
As a medium for cold data storage, DNA stands out as it promises significant gains in storage capacity and lifetime. However, it comes with its own data processing challenges to overcome. Constrained codes over the DNA alphabet…
DNA is a leading candidate as the next archival storage media due to its density, durability and sustainability. To read (and write) data DNA storage exploits technology that has been developed over decades to sequence naturally occurring…
This paper provides a Central Limit Theorem (CLT) for a process $\{\theta_n, n\geq 0\}$ satisfying a stochastic approximation (SA) equation of the form $\theta_{n+1} = \theta_n + \gamma_{n+1} H(\theta_n,X_{n+1})$; a CLT for the associated…