Related papers: Geometric conditions for saturating the data proce…
Numerous industrial thermal processes and fluid processes can be described by distributed parameter systems (DPSs), wherein many process parameters and variables vary in space and time. Early internal abnormalities in the DPS may develop…
Extended Vision techniques are ubiquitous in physics. However, the data cubes steaming from such analysis often pose a challenge in their interpretation, due to the intrinsic difficulty in discerning the relevant information from the…
Depth completion involves estimating a dense depth image from sparse depth measurements, often guided by a color image. While linear upsampling is straight forward, it results in artifacts including depth pixels being interpolated in empty…
The quantum relative entropy is a measure of the distinguishability of two quantum states, and it is a unifying concept in quantum information theory: many information measures such as entropy, conditional entropy, mutual information, and…
We introduce an information-theoretic quantity with similar properties to mutual information that can be estimated from data without making explicit assumptions on the underlying distribution. This quantity is based on a recently proposed…
Computing spectra is a central problem in computational mathematics with an abundance of applications throughout the sciences. However, in many applications gaining an approximation of the spectrum is not enough. Often it is vital to…
Roughness determines many functional properties of surfaces, such as adhesion, friction, and (thermal and electrical) contact conductance. Recent analytical models and simulations enable quantitative prediction of these properties from…
Given an orthonormal basis in a $d$-dimensional Hilbert space and a unital quantum operation $\cal E$ acting on it one can define a non-linear mapping that associates to $\cal E$ a $d\times d$ real-valued matrix that we call the Coherence…
Solving image inverse problems (e.g., super-resolution and inpainting) requires generating a high fidelity image that matches the given input (the low-resolution image or the masked image). By using the input image as guidance, we can…
Operator learning has emerged as a new paradigm for the data-driven approximation of nonlinear operators. Despite its empirical success, the theoretical underpinnings governing the conditions for efficient operator learning remain…
In this paper, we aim to establish a range of numerical radius inequalities. These discoveries will bring us to a recently validated numerical radius inequality and will present numerical radius inequalities that exhibit enhanced precision…
The Double Operator Integral (DOI) framework provides a powerful tool for analyzing perturbations and interactions between self-adjoint operators in functional analysis and spectral theory. However, most existing DOI formulations rely on…
Polynomial and rational functions are the number one choice when it comes to modeling of radial distortion of lenses. However, several extrapolation and numerical issues may arise while using these functions that have not been covered by…
Comparison-based algorithms are algorithms for which the execution of each operation is solely based on the outcome of a series of comparisons between elements. Comparison-based computations can be naturally represented via the following…
We consider a matrix completion problem that exploits social or item similarity graphs as side information. We develop a universal, parameter-free, and computationally efficient algorithm that starts with hierarchical graph clustering and…
Multi-parameter statistical models may depend only on some functions of the parameters that are fewer than the number of initial parameters themselves. Such \emph{sloppy} statistical models are characterized by a degenerate Fisher…
We address the problem of merging graph and feature-space information while learning a metric from structured data. Existing algorithms tackle the problem in an asymmetric way, by either extracting vectorized summaries of the graph…
Data depth is a concept in multivariate statistics that measures the centrality of a point in a given data cloud in $\IR^d$. If the depth of a point can be represented as the minimum of the depths with respect to all one-dimensional…
Neural networks represent more features than they have dimensions via superposition, forcing features to share representational space. Current methods decompose activations into sparse linear features but discard geometric structure. We…
The remarkable performance of deep neural networks (DNNs) currently makes them the method of choice for solving linear inverse problems. They have been applied to super-resolve and restore images, as well as to reconstruct MR and CT images.…