Related papers: Weakly Mutually Uncorrelated Codes
Conventional quantum mechanics describes a pre- and post-selected system in terms of virtual (Feynman) paths via which the final state can be reached. In the absence of probabilities, a weak measurement (WM) determines the probability…
In this paper, we study how often unique decoding from $t$ insertions or $t$ deletions occurs for error correcting codes. Insertions and deletions frequently occur in synchronization problems and DNA, a medium which is beginning to be used…
Composite DNA is a recent method to increase the base alphabet size in DNA-based data storage.This paper models synthesizing and sequencing of composite DNA and introduces coding techniques to correct substitutions, losses of entire…
Some mutually quasi-unbiased weighing matrices are constructed from binary codes satisfying certain conditions. Motivated by this, in this note, we study binary codes satisfying the conditions. The weight distributions of binary codes…
The alignment of biological sequences such as DNA, RNA, and proteins, is one of the basic tools that allow to detect evolutionary patterns, as well as functional/structural characterizations between homologous sequences in different…
In this paper we propose a novel transmit signal structure and an adjusted and optimized receiver for OFDM (orthogonal frequency division multiplexing). Instead of the conventional cyclic prefix we use a deterministic sequence, which we…
We consider the problem of assembling a sequence based on a collection of its substrings observed through a noisy channel. The mathematical basis of the problem is the construction and design of sequences that may be discriminated based on…
Modeling heterogeneous correlated time series requires the ability to learn hidden dynamic relationships between component time series with possibly varying periodicities and generative processes. To address this challenge, we formulate and…
Motivated by applications in DNA storage, we study a setting in which strings are affected by tandem-duplication errors. In particular, we look at two settings: disjoint tandem-duplication errors, and equal-length tandem-duplication errors.…
This paper presents prefix codes which minimize various criteria constructed as a convex combination of maximum codeword length and average codeword length or maximum redundancy and average redundancy, including a convex combination of the…
Pseudorandom sequences are used extensively in communications and remote sensing. Correlation provides one measure of pseudorandomness, and low correlation is an important factor determining the performance of digital sequences in…
Serializability is a well-understood correctness criterion that simplifies reasoning about the behavior of concurrent transactions by ensuring they are isolated from each other while they execute. However, enforcing serializable isolation…
Line codes make it possible to mitigate interference, to prevent short pulses, and to generate streams of bipolar signals with no direct-current (DC) power content through balancing. They find application in magnetic recording (MR) devices,…
A good understanding of how neurons use electrical pulses (i.e, spikes) to encode the signal information remains elusive. Analyzing spike sequences generated by individual neurons and by two coupled neurons (using the stochastic…
Multiple Sequences Alignment (MSA) of biological sequences is a fundamental problem in computational biology due to its critical significance in wide ranging applications including haplotype reconstruction, sequence homology, phylogenetic…
Motivation: Low-complexity (LC) DNA sequences are compositionally repetitive sequences that are often associated with spurious homologous matches and variant calling artifacts. While algorithms for identifying LC sequences exist, they…
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…
We derive theoretical upper and lower bounds on the maximum size of DNA codes of length n with constant GC-content w and minimum Hamming distance d, both with and without the additional constraint that the minimum Hamming distance between…
Quantum circuits that generate coherent superpositions of stochastic processes are key to many downstream quantum-accelerated tasks, such as risk analysis, importance sampling, and DNA sequencing. However, traditional methods for designing…
Fragment-based shape signature techniques have proven to be powerful tools for computer-aided drug design. They allow scientists to search for target molecules with some similarity to a known active compound. They do not require reference…