Related papers: Limitation for linear maps in a class for detectio…
To gain insight into the mechanisms behind machine learning methods, it is crucial to establish connections among the features describing data points. However, these correlations often exhibit a high-dimensional and strongly nonlinear…
We apply random matrix and free probability techniques to the study of linear maps of interest in quantum information theory. Random quantum channels have already been widely investigated with spectacular success. Here, we are interested in…
Promoting the connectivity of curvilinear structures, such as neuronal processes in biomedical scans and blood vessels in CT images, remains a key challenge in semantic segmentation. Traditional pixel-wise loss functions, including…
Loss-induced transmission in waveguides, and reversed pump dependence in lasers, are two prominent examples of counter-intuitive effects in non-Hermitian systems with patterned gain and loss. By analyzing the eigenvalue dynamics of complex…
Identifying low-dimensional latent structures within high-dimensional data has long been a central topic in the machine learning community, driven by the need for data compression, storage, transmission, and deeper data understanding.…
We propose a hierarchical correlation clustering method that extends the well-known correlation clustering to produce hierarchical clusters applicable to both positive and negative pairwise dissimilarities. Then, in the following, we study…
We propose a novel approach for density estimation with exponential families for the case when the true density may not fall within the chosen family. Our approach augments the sufficient statistics with features designed to accumulate…
We show that if $E$ is a closed convex set in $\mathbb C^n$ $(n>1)$ contained in a closed halfspace $H$ such that $E\cap bH$ is nonempty and bounded, then the concave domain $\Omega = \mathbb C^n\setminus E$ contains images of proper…
Visualizing spatial data on small-screen devices such as smartphones and smartwatches poses new challenges in computational cartography. The current interfaces for map exploration require their users to zoom in and out frequently. Indeed,…
Non-Hermitian systems can manifest rich static and dynamical properties at their exceptional points (EPs). Here, we identify yet another class of distinct phenomena that is hinged on EPs, namely, the emergence of a series of non-Hermitian…
Image classification is a challenging problem for computer in reality. Large numbers of methods can achieve satisfying performances with sufficient labeled images. However, labeled images are still highly limited for certain image…
Linear constraints for a matrix polytope with no fractional vertex are investigated as intersecting research among permutation codes, rank modulations, and linear programming methods. By focusing the discussion to the block structure of…
Quadratic eigenvalue problems (QEP) and more generally polynomial eigenvalue problems (PEP) are among the most common types of nonlinear eigenvalue problems. Both problems, especially the QEP, have extensive applications. A typical approach…
This paper presents an overview of the derivation and significance of recently derived conservation laws for the matrix moments of Hermitean random matrices with dominant exponential weights that may be either even or odd. This is based on…
We consider a discrete, non-Hermitian random matrix model, which can be expressed as a shift of a rank-one perturbation of an anti-symmetric matrix. We show that, asymptotically almost surely, the real parts of the eigenvalues of the…
Over the past decade, deep learning has proven to be a highly effective tool for learning meaningful features from raw data. However, it remains an open question how deep networks perform hierarchical feature learning across layers. In this…
Conventional mode tracking operates in the dark: it traces dispersion branches on the non-Hermitian eigenvalue manifold using only local continuity, unaware of the global Riemann-sheet topology. When exceptional points (EPs) lie close to…
Understanding the linear response of any system is the first step towards analyzing its linear and nonlinear dynamics, stability properties, as well as its behavior in the presence of noise. In non-Hermitian Hamiltonian systems, calculating…
The non-Hermitian skin effect (NHSE) and nonlinearity can both delocalize topological modes (TMs) from the interface. However, the NHSE requires precise parameter tuning, while nonlinearity in Hermitian systems results in partial…
The variance of the number of particles in a set is an important quantity in understanding the statistics of non-interacting fermionic systems in low dimensions. An exact map of their ground state in a harmonic trap in one and two…