相关论文: Inequality, uncertainty principles and their struc…

The aim of the paper is two-fold. First, we provide an explicit form of the functions for which equality holds for the uncertainty inequalities studied in \cite{Fei}. Second, we establish an $L^p$-type Heisenberg-Pauli-Weyl uncertainty…

A novel framework for a unifying treatment of quaternion valued adaptive filtering algorithms is introduced. This is achieved based on a rigorous account of quaternion differentiability, the proposed I-gradient, and the use of augmented…

This paper revisits the notion of classical orthogonal polynomials from a broader functional-analytic point of view. It is intended neither as a survey of known results nor as a review of the literature, but rather as a conceptual…

Optimal transport (OT) is a powerful framework to compare probability measures, a fundamental task in many statistical and machine learning problems. Substantial advances have been made in designing OT variants which are either…

The log canonical threshold (lct) is a fundamental invariant in birational geometry, essential for understanding the complexity of singularities in algebraic varieties. Its real counterpart, the real log canonical threshold (rlct), also…

As the fundamental tool in quantum information science, the uncertainty principle is essential for manifesting nonclassical properties of quantum systems. Plenty of efforts on the uncertainty principle with two observables have been…

This report investigates the main definitions and fundamental properties of the fractional two-sided quaternionic Dunkl transform in two dimensions. We present key results concerning its structure and emphasize its connections to classical…

A new version of the so-called optimized perturbation (OPT), implementing consistently renormalization group properties, is used to calculate the nonperturbative ratio $F_\pi/\overline\Lambda$ of the pion decay constant and the basic QCD…

We demonstrate how quantum computation can provide non-trivial improvements in the computational and statistical complexity of the perceptron model. We develop two quantum algorithms for perceptron learning. The first algorithm exploits…

In this paper, we provide the Heisenberg's inequality and the Hardy's theorem for the two-sided quaternion Fourier transform.

Quantum Optical Coherence Tomography (Q-OCT) uses quantum properties of light to provide several advantages over its classical counterpart, OCT: it achieves a twice better axial resolution with the same spectral bandwidth and it is immune…

The conflict between Quantum Mechanics (QM) and the intuitive concepts of Locality and Realism (LR) is manifest in the correlation between measurements performed in remote regions of a spatially spread entangled state. In this paper, it is…

Operator learning enables fast surrogate modeling of high-dimensional dynamical systems, but existing approaches face two fundamental limitations: quadratic inference complexity and unreliable uncertainty quantification in safety-critical…

Orthogonal Monte Carlo (OMC) is a very effective sampling algorithm imposing structural geometric conditions (orthogonality) on samples for variance reduction. Due to its simplicity and superior performance as compared to its Quasi Monte…

Canonical duality-triality is a breakthrough methodological theory, which can be used not only for modeling complex systems within a unified framework, but also for solving a wide class of challenging problems from real-world applications.…

Many statistical estimation procedures lead to nonconvex optimization problems. Algorithms to solve these are often guaranteed to output a stationary point of the optimization problem. Oracle inequalities are an important theoretical…

This study proposes an econometric framework to interpret and empirically decompose the difference between IV and OLS estimates given by a linear regression model when the true causal effects of the treatment are nonlinear in treatment…

We explore the uncertainty relation for unitary operators in a new way and find two uncertainty equalities for unitary operators, which are minimized by any pure states. Additionally, we derive two sets of uncertainty inequalities that…

We prove global convergence of a bundle trust region algorithm for non-smooth non-convex optimization, where cutting planes are generated by oracles respecting four basic rules. The benefit is that convergence theory applies to a large…

Spatial resolution in optical microscopy has traditionally been treated as a fixed parameter of the optical system. Here, we present an approach to enhance transverse resolution in beam-scanned optical coherence tomography (OCT) beyond its…