Related papers: On Random Unitary Channels
The distance transform (DT) and its many variations are ubiquitous tools for image processing and analysis. In many imaging scenarios, the images of interest are corrupted by noise. This has a strong negative impact on the accuracy of the…
In the setting of CAT(k) spaces, common fixed point iterations built from prox mappings (e.g. prox-prox, Krasnoselsky-Mann relaxations, nonlinear projected-gradients) converge locally linearly under the assumption of linear metric…
This chapter develops a theoretical analysis of the convex programming method for recovering a structured signal from independent random linear measurements. This technique delivers bounds for the sampling complexity that are similar with…
Consider a set $P$ of $n$ points picked uniformly and independently from $[0,1]^d$ for a constant dimension $d$ -- such a point set is extremely well behaved in many aspects. For example, for a fixed $r \in [0,1]$, we prove a new…
Compact sets in constructive mathematics capture our intuition of what computable subsets of the plane (or any other complete metric space) ought to be. A good representation of compact sets provides an efficient means of creating and…
Local feature matching aims at establishing sparse correspondences between a pair of images. Recently, detector-free methods present generally better performance but are not satisfactory in image pairs with large scale differences. In this…
For many completely positive maps repeated compositions will eventually become entanglement breaking. To quantify this behaviour we develop a technique based on the Schmidt number: If a completely positive map breaks the entanglement with…
M. Christandl conjectured that the composition of any trace preserving PPT map with itself is entanglement breaking. We prove that Christandl's conjecture holds asymptotically by showing that the distance between the iterates of any unital…
Conformal prediction, a post-hoc, distribution-free, finite-sample method of uncertainty quantification that offers formal coverage guarantees under the assumption of data exchangeability. Unfortunately, the resulting uncertainty regions…
Recently [Phys. Rev. Lett. {\bf 106}, 093902 (2011)] it has been shown that $\mathcal{PT}$-symmetric scattering systems with balanced gain and loss, undergo a transition from $\mathcal{PT}$-symmetric scattering eigenstates, which are norm…
Generalized Chinese Remainder Theorem (CRT) is a well-known approach to solve ambiguity resolution related problems. In this paper, we study the robust CRT reconstruction for multiple numbers from a view of statistics. To the best of our…
We give a short proof that the coherent information is an achievable rate for the transmission of quantum information through a noisy quantum channel. Our method is to produce random codes by performing a unitarily covariant projective…
Spectrum cartography aims at estimating power propagation patterns over a geographical region across multiple frequency bands (i.e., a radio map)---from limited samples taken sparsely over the region. Classic cartography methods are mostly…
Necessary and sufficient conditions for convexity and strong convexity, respectively, of sublevel sets that are defined by finitely many real-valued $C^{1,1}$-maps are presented. A novel characterization of strongly convex sets in terms of…
Suppose a given observation matrix can be decomposed as the sum of a low-rank matrix and a sparse matrix (outliers), and the goal is to recover these individual components from the observed sum. Such additive decompositions have…
Conformal prediction (CP) constructs uncertainty sets for model outputs with finite-sample coverage guarantees. A candidate output is included in the prediction set if its non-conformity score is not considered extreme relative to the…
For better learning, large datasets are often split into small batches and fed sequentially to the predictive model. In this paper, we study such batch decompositions from a probabilistic perspective. We assume that data points (possibly…
The transmission matrix (TM) is a representation to describe the light scattering process through a scattering medium. The degree of control elements in TM is correlated with the capacity of evaluating enormous equations with tremendous…
The classical randomization criterion is an important result of statistical decision theory. Recently, a quantum analogue has been proposed, giving equivalent conditions for two sets of quantum states, ensuring existence of a quantum…
For a family of random intermittent dynamical systems with a superattracting fixed point we prove that a phase transition occurs between the existence of an absolutely continuous invariant probability measure and infinite measure depending…