Coexistence of extended and localized states in the one-dimensional non-Hermitian Anderson model

In one-dimensional Hermitian tight-binding models, mobility edges separating extended and localized states can appear in the presence of properly engineered quasiperiodical potentials and coupling constants. On the other hand, mobility edges do not exist in a one-dimensional Anderson lattice since localization occurs whenever a diagonal disorder through random numbers is introduced. Here we consider a nonreciprocal non-Hermitian lattice and show that the coexistence of extended and localized states appears with or without diagonal disorder in the topologically nontrivial region. We discuss that the mobility edges appear basically due to the boundary condition sensitivity of the nonreciprocal non-Hermitian lattice

Robust Exceptional Points in Disordered Systems

We construct a theory to introduce the concept of topologically robust exceptional points (EP). Starting from an ordered system with $N$ elements, we find the necessary condition to have the highest order exceptional point, namely $N^\text{th}$ order EP. Using symmetry considerations, we show an EP associated with an order system is very sensitive to the disorder. Specifically, if the EP associated with the ordered system occurs at the fixed degree of non-Hermiticity $\gamma_{EP}$, the disordered system will not have EP at the same $\gamma_{PT}$ which puts an obstacle in front of the observation and applications of EPs. To overcome this challenge, by incorporating an asymmetric coupling we propose a disordered system that has a robust EP which is extended all over the space. While our approach can be easily realized in electronic circuits and acoustics, we propose a simple experimentally feasible photonic system to realize our robust EP. Our results will open a new direction to search for topologically robust extended states (as opposed to topological localized states) and find considerable applications in direct observation of EPs, realizing topological sensors and designing robust devices for metrology

Stabilization of zero-energy skin modes in finite non-Hermitian lattices

The zero energy of a one-dimensional semi-infinite non-Hermitian lattice with nontrivial spectral topology may disappear when we introduce boundaries to the system. While the corresponding zero-energy state can be considered as a quasi-edge state for the finite lattice with a long survival time, any small disruption (noise) in the initial form of the quasi-edge state can significantly shorten the survival time. Here, by tailoring the couplings at one edge we form an exceptional point allowing for a topological phase transition and the stabilization of the quasi-edge state in a finite-size lattice with open edges. Such a small modification in the lattice does not require closing and opening of the band gap and opens the door for experimental realization of such robust zero-energy edge states

A Review on the Applications of Machine Learning for Tinnitus Diagnosis Using EEG Signals

Tinnitus is a prevalent hearing disorder that can be caused by various factors such as age, hearing loss, exposure to loud noises, ear infections or tumors, certain medications, head or neck injuries, and psychological conditions like anxiety and depression. While not every patient requires medical attention, about 20% of sufferers seek clinical intervention. Early diagnosis is crucial for effective treatment. New developments have been made in tinnitus detection to aid in early detection of this illness. Over the past few years, there has been a notable growth in the usage of electroencephalography (EEG) to study variations in oscillatory brain activity related to tinnitus. However, the results obtained from numerous studies vary greatly, leading to conflicting conclusions. Currently, clinicians rely solely on their expertise to identify individuals with tinnitus. Researchers in this field have incorporated various data modalities and machine-learning techniques to aid clinicians in identifying tinnitus characteristics and classifying people with tinnitus. The purpose of writing this article is to review articles that focus on using machine learning (ML) to identify or predict tinnitus patients using EEG signals as input data. We have evaluated 11 articles published between 2016 and 2023 using a systematic literature review (SLR) method. This article arranges perfect summaries of all the research reviewed and compares the significant aspects of each. Additionally, we performed statistical analyses to gain a deeper comprehension of the most recent research in this area. Almost all of the reviewed articles followed a five-step procedure to achieve the goal of tinnitus. Disclosure. Finally, we discuss the open affairs and challenges in this method of tinnitus recognition or prediction and suggest future directions for research