相关论文: Inequality, uncertainty principles and their struc…
We demonstrate that the recently developed Optimal Uncertainty Quantification (OUQ) theory, combined with recent software enabling fast global solutions of constrained non-convex optimization problems, provides a methodology for rigorous…
In the field of applied mathematics the Fourier transform has developed into an important tool. It is a powerful method for solving partial differential equations. The Fourier transform provides also a technique for signal analysis where…
Quaternion-valued signals along with quaternion Fourier transforms (QFT)provide an effective framework for vector-valued signal and image processing. However, the sampling theory of quaternion valued signals has not been well developed. In…
This paper addresses the limitations of standard uncertainty models, e.g., robust (norm-bounded) and stochastic (one fixed distribution, e.g., Gaussian), and proposes to model uncertainty via Optimal Transport (OT) ambiguity sets. These…
We have recently proposed a rigorous framework for Uncertainty Quantification (UQ) in which UQ objectives and assumption/information set are brought into the forefront, providing a framework for the communication and comparison of UQ…
In recent years, Orthogonal Recurrent Neural Networks (ORNNs) have gained popularity due to their ability to manage tasks involving long-term dependencies, such as the copy-task, and their linear complexity. However, existing ORNNs utilize…
In recent years there has been a renewed interest in finding fast algorithms to compute accurately the linear canonical transform (LCT) of a given function. This is driven by the large number of applications of the LCT in optics and signal…
Quantum analogues of the transient fluctuation theorem(TFT) and steady-state fluctuation theorem(SSFT) are investigated for a harmonic oscillator linearly coupled with a harmonic reservoir. The probability distribution for the work done…
Uncertainty estimation is critical for cost-sensitive deep-learning applications (i.e. disease diagnosis). It is very challenging partly due to the inaccessibility of uncertainty groundtruth in most datasets. Previous works proposed to…
The aim of this paper is to derive a new uncertainty principle for the generalized $q$-Bessel wavelet transform studied earlier in \cite{Rezguietal}. In this paper, an uncertainty principle associated with wavelet transforms in the…
Recently, it was realized that use of the properties of quantum mechanics might speed up certain computations dramatically. Interest in quantum computation has since been growing. One of the main difficulties of realizing quantum…
The concept of balancedly splittable orthogonal designs is introduced along with a recursive construction. As an application, equiangular tight frames over the real, complex, and quaternions meeting the Delsarte-Goethals-Seidel upper bound…
In this paper, we generalize the continuous quaternion shearlet transform on $\mathbb{R}^{2}$ to $\mathbb{R}^{2d}$, called the multivariate two sided continuous quaternion shearlet transform. Using the two sided quaternion Fourier…
We develop a bottom-up, statistics-first framework in which the full probabilistic content of an operational theory is encoded in its matrix of conditional outcome probabilities of events (COPE). Within this setting, five model classes…
We present a new method to calculate formation of cosmological structure in the Newtonian limit. The method is based on Lagrangian perturbation theory plus two key theoretical extensions. One advance involves identifying and fixing a…
We review the field of Optical Quantum Computation, considering the various implementations that have been proposed and the experimental progress that has been made toward realizing them. We examine both linear and nonlinear approaches and…
In this paper, the space complexity of nonuniform quantum computations is investigated. The model chosen for this are quantum branching programs, which provide a graphic description of sequential quantum algorithms. In the first part of the…
Inequalities for the transformation operator kernel $A(x,y)$ in terms of $F$-function are given, and vice versa. These inequalities are applied to inverse scattering on half-line. Characterization of the scattering data corresponding to the…
Conformal prediction is a framework that provides valid uncertainty quantification for general models with exchangeable data. However, in the online learning and time-series settings, exchangeability is not satisfied. Existing online…
Conformal prediction (CP) quantifies the uncertainty of machine learning models by constructing sets of plausible outputs. These sets are constructed by leveraging a so-called conformity score, a quantity computed using the input point of…