This study presents a novel approach utilizing deep neural networks to address the inverse line-source scattering problem in dielectric cylinders. By employing Multi-layer Perceptron models, we intend to identify the number, positions, and strengths of hidden internal sources. This is performed by using single-frequency phased data, from limited measurements of real electric and real magnetic surface fields. Training data are generated by solving corresponding direct problems, using an exact solution representation. Through extended numerical experiments, we demonstrate the efficiency of our approach, including scenarios involving noise, reduced sample sizes, and fewer measurements. Additionally, we examine the empirical scaling laws governing model performance and conduct a local analysis to explore how our neural networks handle the inherent ill-posedness of the considered inverse problems.

The direct problem of exciting a multilayered spherical medium by a distribution of arbitrarily located (internal and external) electric dipoles is considered. A formulation based on excitation operators is adopted. The solution of the direct problem is obtained by means of an overall superposition method that combines elements of the T‐matrix approach, the Sommerfeld's method, and Green's functions' techniques. Approximations are extracted for the obtained far‐field patterns in the long‐wavelength (low‐frequency) regime. A set of source‐localization inverse problems is considered. Analytical algorithms are devised in which nonlinear systems are obtained from specifically selected low‐frequency far‐field measurements. These systems are subsequently solved explicitly including all special cases. The developed algorithms are noninvasive and can determine accurately the characteristics of internal sources.

The quantum phase estimation algorithm has been utilized by a variety of quantum algorithms, most notably Shor’s algorithm, to obtain information regarding the period of a function that is appropriately encoded into a unitary operator. In many cases, it is desired to estimate whether a specific state exhibits a certain pattern quickly. In this paper, we exhibit a methodology based on the QPE algorithm to identify certain patterns. In particular, starting from a properly encoded state, we demonstrate how to construct unitary operators whose eigenvectors correspond to states with proper diagonals. QPE will then output an eigenphase equal to zero with certainty for these states, thereby identifying this class of matrices. For partial matches, our algorithm, based on the tolerance threshold used, will show areas of high similarity, and it will outperform classical ones when the number of mismatches defined by the tolerance is significantly low when compared to the size of the diagonal.

Vast amounts of genomic, proteomic, transcriptomics and other forms, commonly referred to as -omics data, are generated daily in an unprecedented way thanks to high-throughput Next Generation Sequencing technologies. One of the main processes to generate value and insights from this data in bioinformatics is “sequence alignment”, an algorithmic routine that matches a “reference” sequence to a larger sequence. Despite the plethora of approaches, pairwise and multiple sequence alignment remain a complex problem that requires high computational power. In this article, the most prominent sequence alignment approaches of the past three decades are reviewed and categorized, examining different aspects, such as their overall algorithmic synthesis, alignment quality and performance benchmarking tests in a uniform way. The latest trends reveal an increased specialization on biology-based directions, the need for alternative heuristic approaches and a promise in optics-enabled approaches and the quantum computing paradigm shift.