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Microstructure reconstruction is a key enabler of process-structure-property linkages, a central topic in materials engineering. Revisiting classical optimization-based reconstruction techniques,they are recognized as a powerful framework…
Recent advancements in information technology and the widespread use of the Internet have led to easier access to data worldwide. As a result, transmitting data through noisy channels is inevitable. Reducing the size of data and protecting…
The process of DNA-based data storage (DNA storage for short) can be mathematically modelled as a communication channel, termed DNA storage channel, whose inputs and outputs are sets of unordered sequences. To design error correcting codes…
Tomography deals with the reconstruction of objects from their projections, acquired along a range of angles. Discrete tomography is concerned with objects that consist of a small number of materials, which makes it possible to compute…
With the emergence of new storage and communication methods, the insertion, deletion, and substitution (IDS) channel has attracted considerable attention. However, many topics on the IDS channel and the associated Levenshtein distance…
We consider error-correcting coding for DNA-based storage. We model the DNA storage channel as a multi-draw IDS channel where the input data is chunked into $M$ short DNA strands, which are copied a random number of times, and the channel…
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…
This study presents a novel model for invertible sentence embeddings using a residual recurrent network trained on an unsupervised encoding task. Rather than the probabilistic outputs common to neural machine translation models, our…
Mean-based reconstruction is a fundamental, natural approach to worst-case trace reconstruction over channels with synchronization errors. It is known that $\exp(O(n^{1/3}))$ traces are necessary and sufficient for mean-based worst-case…
In the trace reconstruction problem, one seeks to reconstruct a binary string $s$ from a collection of traces, each of which is obtained by passing $s$ through a deletion channel. It is known that $\exp(\tilde O(n^{1/5}))$ traces suffice to…
Currently, most deep learning methods cannot solve the problem of scarcity of industrial product defect samples and significant differences in characteristics. This paper proposes an unsupervised defect detection algorithm based on a…
Despite the rapid progress of neuromorphic computing, inadequate capacity and insufficient representation power of spiking neural networks (SNNs) severely restrict their application scope in practice. Residual learning and shortcuts have…
An insdel refers to a deletion or an insertion, and an edit refers to an insdel or a substitution. In this paper, we consider the segmented single-insdel (resp. single-edit) channel, where the channel's input bit stream is partitioned into…
In the trace reconstruction problem, the goal is to reconstruct an unknown string $x$ of length $n$ from multiple traces obtained by passing $x$ through the deletion channel. In the relaxed problem of $approximate$ trace reconstruction, the…
Inverse problems arise in a multitude of applications, where the goal is to recover a clean signal from noisy and possibly (non)linear observations. The difficulty of a reconstruction problem depends on multiple factors, such as the ground…
In this paper we consider the problem of sparse signal recovery in Multiple Measurement Vectors (MMVs) case. Recently, ample researches have been conducted to solve this problem and diverse methods are proposed, one of which is deep neural…
We consider the problem of correcting insertion and deletion errors in the $d$-dimensional space. This problem is well understood for vectors (one-dimensional space) and was recently studied for arrays (two-dimensional space). For vectors…
In dense retrieval, deep encoders provide embeddings for both inputs and targets, and the softmax function is used to parameterize a distribution over a large number of candidate targets (e.g., textual passages for information retrieval).…
\ac{fl} proposed a distributed \ac{ml} framework where every distributed worker owns a complete copy of global model and their own data. The training is occurred locally, which assures no direct transmission of training data. However, the…
Particularly motivated by DNA storage channels, we consider channels with synchronization errors modeled as insertions and deletions, along with substitutions. We focus on the case where the synchronization error process has memory and…