Related papers: Is the K-matrix approach adequate for describing o…
A new cluster analysis method, $K$-quantiles clustering, is introduced. $K$-quantiles clustering can be computed by a simple greedy algorithm in the style of the classical Lloyd's algorithm for $K$-means. It can be applied to large and…
Bifurcation theory and continuation methods are well-established tools for the analysis of nonlinear mechanical systems subject to periodic forcing. We illustrate the added value and the complementary information provided by singularity…
The randomized Kaczmarz (RK) method is an iterative method for approximating the least-squares solution of large linear systems of equations. The standard RK method uses sequential updates, making parallel computation difficult. Here, we…
In this paper, some properties of resonances for multi-dimensional quantum walks are studied. Resonances for quantum walks are defined as eigenvalues of complex translated time evolution operators in the pseudo momentum space. For some…
We obtain a class of parametric oscillation modes that we call K-modes with damping and absorption that are connected to the classical harmonic oscillator modes through the "supersymmetric" one-dimensional matrix procedure similar to…
We propose a variational scheme to represent composite quantum systems using multiple parameterized functions of varying accuracies on both classical and quantum hardware. The approach follows the variational principle over the entire…
J. Eells and L. Lemaire introduced k-harmonic maps, and Wang Shaobo showed the first variational formula. When, k=2, it is called biharmonic maps (2-harmonic maps). There have been extensive studies in the area. In this paper, We study…
Scattering resonances play a crucial role in understanding wave behavior in various physical systems. While significant progress has been made in analyzing resonances in high-contrast and nonlinear media, a general characterization of…
We demonstrate the use of spatially encoded magnetic resonance to quantify ensemble dynamics of microscopic particles below the spatial resolution. By evaluating time series of k-space data-points, k-dependent motion patterns can be…
In this work, the possibility of clustering correlated random variables was examined, both because of their mutual similarity and because of their similarity to the principal components. The k-means algorithm and spectral algorithms were…
The importance of $S$-matrix unitarity in realistic meson spectroscopy is reviewed, both its historical development and more recent applications. First the effects of imposing $S$-matrix unitarity on meson resonances is demonstrated in both…
In a standard cluster analysis, such as k-means, in addition to clusters locations and distances between them, it's important to know if they are connected or well separated from each other. The main focus of this paper is discovering the…
This paper reviews Kunchenko's polynomials using as template matching method to recognize template in one-dimensional input signal. Kunchenko's polynomials method is compared with classical methods - cross-correlation and sum of squared…
Experimental observation of the decoherence of macroscopic objects is of fundamental importance to the study of quantum collapse models and the quantum to classical transition. Optomechanics is a promising field for the study of such models…
This work focuses on the limitations about the insufficient fitting capability of current quantum machine learning methods, which results from the over-reliance on a single data embedding strategy. We propose a novel quantum machine…
Random unitaries are an important resource for quantum information processing. While their universal properties have been thoroughly analyzed, it is not known what happens to these properties when the unitaries are sampled on the…
We verify a conjecture on the structure of higher-rank numerical ranges for a wide class of unitary and normal matrices. Using analytic and geometric techniques, we show precisely how the higher-rank numerical ranges for a generic unitary…
We study a quantum-mechanical system of three particles in a one-dimensional box with two-particle harmonic interactions. The symmetry of the system is described by the point group $D_{3d}$. Group theory greatly facilitates the application…
We show that the method of distributed noise-shaping beta-quantization offers superior performance for the problem of spectral super-resolution with quantization whenever there is redundancy in the number of measurements. More precisely, if…
A limitation of many clustering algorithms is the requirement to tune adjustable parameters for each application or even for each dataset. Some techniques require an \emph{a priori} estimate of the number of clusters while density-based…