arXiv subjects

Hadas Abraham

Publications and source records attributed to Hadas Abraham.

4 recordsLinked to original sources

arXiv2026

Analyzing Collection Strategies: A Computational Perspective on the Coupon Collector Problem

The Coupon Collector Problem (CCP) is a well-known combinatorial problem that seeks to estimate the number of random draws required to complete a collection of $n$ distinct coupon types. Various generalizations of this problem have been applied in numerous engineering domains. However, practical applications are often hindered by the computational challenges associated with deriving numerical results for moments and distributions. In this work, we present three algorithms for solving the most general form of the CCP, where coupons are collected under any arbitrary drawing probability, with the objective of obtaining $t$ copies of a subset of $k$ coupons from a total of $n$. The First algorithm provides the base model to compute the expectation, variance, and the second moment of the collection process. The second algorithm utilizes the construction of the base model and computes the same values in polynomial time with respect to $n$ under the uniform drawing distribution, and the third algorithm extends to any general drawing distribution. All algorithms leverage Markov models specifically designed to address computational challenges, ensuring exact computation of the expectation and variance of the collection process. Their implementation uses a dynamic programming approach that follows from the Markov models framework, and their time complexity is analyzed accordingly.

cs.DS↗

arXiv2025

An Analysis of Hyper-Parameter Optimization Methods for Retrieval Augmented Generation

Optimizing Retrieval-Augmented Generation (RAG) configurations for specific tasks is a complex and resource-intensive challenge. Motivated by this challenge, frameworks for RAG hyper-parameter optimization (HPO) have recently emerged, yet their effectiveness has not been rigorously benchmarked. To fill this gap, we present a comprehensive study involving five HPO algorithms over five datasets from diverse domains, including a newly curated real-world product documentation dataset. Our study explores the largest RAG HPO search space to date that includes full grid-search evaluations, and uses three evaluation metrics as optimization targets. Analysis of the results shows that RAG HPO can be done efficiently, either greedily or with random search, and that it significantly boosts RAG performance for all datasets. For greedy HPO approaches, we show that optimizing model selection first is preferable to the common practice of following the RAG pipeline order during optimization.

cs.CL↗

arXiv2024

Beyond the Alphabet: Deep Signal Embedding for Enhanced DNA Clustering

The emerging field of DNA storage employs strands of DNA bases (A/T/C/G) as a storage medium for digital information to enable massive density and durability. The DNA storage pipeline includes: (1) encoding the raw data into sequences of DNA bases; (2) synthesizing the sequences as DNA \textit{strands} that are stored over time as an unordered set; (3) sequencing the DNA strands to generate DNA \textit{reads}; and (4) deducing the original data. The DNA synthesis and sequencing stages each generate several independent error-prone duplicates of each strand which are then utilized in the final stage to reconstruct the best estimate for the original strand. Specifically, the reads are first \textit{clustered} into groups likely originating from the same strand (based on their similarity to each other), and then each group approximates the strand that led to the reads of that group. This work improves the DNA clustering stage by embedding it as part of the DNA sequencing. Traditional DNA storage solutions begin after the DNA sequencing process generates discrete DNA reads (A/T/C/G), yet we identify that there is untapped potential in using the raw signals generated by the Nanopore DNA sequencing machine before they are discretized into bases, a process known as \textit{basecalling}, which is done using a deep neural network. We propose a deep neural network that clusters these signals directly, demonstrating superior accuracy, and reduced computation times compared to current approaches that cluster after basecalling.

q-bio.GN↗

arXiv2024

Covering All Bases: The Next Inning in DNA Sequencing Efficiency

DNA emerges as a promising medium for the exponential growth of digital data due to its density and durability. This study extends recent research by addressing the \emph{coverage depth problem} in practical scenarios, exploring optimal error-correcting code pairings with DNA storage systems to minimize coverage depth. Conducted within random access settings, the study provides theoretical analyses and experimental simulations to examine the expectation and probability distribution of samples needed for files recovery. Structured into sections covering definitions, analyses, lower bounds, and comparative evaluations of coding schemes, the paper unveils insights into effective coding schemes for optimizing DNA storage systems.

cs.IT↗