相关论文: Differential equations for real-structured (and un…

With the help of a given distance matrix of size $n$, we construct an infinite family of distances $d_p$ (where $p \geq 2$) on the complex projective space $\mathbb{P}(\mathbb{C}^n)$ modelling the space of pure states of an $n$-level…

Existing structural analysis methods may fail to find all hidden constraints for a system of differential-algebraic equations with parameters if the system is structurally unamenable for certain values of the parameters. In this paper, for…

The larger the distance to instability from a matrix is, the more robustly stable the associated autonomous dynamical system is in the presence of uncertainties and typically the less severe transient behavior its solution exhibits.…

Given a positive integer k, it is natural to ask for a formula for the distance between a given density matrix (i.e., mixed quantum state) and the set of density matrices of rank at most k. This problem has already been solved when…

A k-dissimilarity map on a finite set X is a function D : X \choose k \rightarrow R assigning a real value to each subset of X with cardinality k, k \geq 2. Such functions, also sometimes known as k-way dissimilarities, k-way distances, or…

In the fields of quantum mechanics and quantum information science, the traces of reduced density matrix powers play a crucial role in the study of quantum systems and have numerous important applications. In this paper, we propose a…

A distance matrix $A \in \mathbb R^{n \times m}$ represents all pairwise distances, $A_{ij}=\mathrm{d}(x_i,y_j)$, between two point sets $x_1,...,x_n$ and $y_1,...,y_m$ in an arbitrary metric space $(\mathcal Z, \mathrm{d})$. Such matrices…

We study private matrix analysis in the sliding window model where only the last $W$ updates to matrices are considered useful for analysis. We give first efficient $o(W)$ space differentially private algorithms for spectral approximation,…

Sliced Wasserstein (SW) distance suffers from redundant projections due to independent uniform random projecting directions. To partially overcome the issue, max K sliced Wasserstein (Max-K-SW) distance ($K\geq 1$), seeks the best…

Let $\mathbf{P}=\{ p_1, p_2, \ldots p_n \}$ and $\mathbf{Q} = \{ q_1, q_2 \ldots q_m \}$ be two point sets in an arbitrary metric space. Let $\mathbf{A}$ represent the $m\times n$ pairwise distance matrix with $\mathbf{A}_{i,j} = d(p_i,…

The aim of this paper is to introduce new statistical criterions for estimation, suitable for inference in models with common continuous support. This proposal is in the direct line of a renewed interest for divergence based inference tools…

In quantum information, trace distance is a basic metric of distinguishability between quantum states. However, there is no known efficient approach to estimate the value of trace distance in general. In this paper, we propose efficient…

This article presents a new distance for measuring shape dissimilarity between objects. Recent publications introduced the use of eigenvalues of the Laplace operator as compact shape descriptors. Here, we revisit the eigenvalues to define a…

Finding the distance to singularity for a matrix is a ubiquitous problem in numerical linear algebra, and is elegantly solved by the Eckart-Young-Mirsky theorem. Its structured variant naturally emerges when one considers structured…

When both the difference between two quantities and their individual values can be measured or computational predicted, multiple quantities can be determined from the measurements or predictions of select individual quantities and select…

We consider the discretization y(t+\epsilon)=y(t-\epsilon)+2\epsilon\big(1-y(t)^{2}\big), $\epsilon>0$ a small parameter, of the logistic differential equation $y'=2\big(1-y^{2}\big)$, which can also be seen as a discretization of the…

We present a simple, accurate method for solving consistent, rank-deficient linear systems, with or without addi- tional rank-completing constraints. Such problems arise in a variety of applications, such as the computation of the…

Applications in machine learning and data mining require computing pairwise Lp distances in a data matrix A. For massive high-dimensional data, computing all pairwise distances of A can be infeasible. In fact, even storing A or all pairwise…

In many robotics applications, it is necessary to compute not only the distance between the robot and the environment, but also its derivative - for example, when using control barrier functions. However, since the traditional Euclidean…

Reachability analysis is a fundamental problem for safety verification and falsification of Cyber-Physical Systems (CPS) whose dynamics follow physical laws usually represented as differential equations. In the last two decades, numerous…