Related papers: Comment on "Maximum likelihood reconstruction of C…
Given a redundant dictionary $\Phi$, represented by an $M \times N$ matrix ($\Phi \in \mathbb{R}^{M \times N}$) and a target signal $y \in \mathbb{R}^M$, the \emph{sparse approximation problem} asks to find an approximate representation of…
Optimization is ubiquitous in quantum information science and technology, however, the corresponding optimization landscape can encounter false traps, i.e., local but not global optima, likely to prevent used optimizers from finding optimal…
We present a new distributed model of probabilistically checkable proofs (PCP). A satisfying assignment $x \in \{0,1\}^n$ to a CNF formula $\varphi$ is shared between two parties, where Alice knows $x_1, \dots, x_{n/2}$, Bob knows…
We analyze the security of recently proposed image encryption scheme [1]. We show that the scheme is insecure and the methods used to evaluate its security are insufficient. By designing the Deliberately Weak Cipher, a completely vulnerable…
The incompatibility of the measurements constraints the achievable precisions in multi-parameter quantum estimation. Understanding the tradeoff induced by such incompatibility is a central topic in quantum metrology. Here we provide an…
Withdrawn due to an incompleteness of the main results.
Within the task of collaborative filtering two challenges for computing conditional probabilities exist. First, the amount of training data available is typically sparse with respect to the size of the domain. Thus, support for higher-order…
We consider the problem of covering hypersphere by a set of spherical hypercaps. This sort of problem has numerous practical applications such as error correcting codes and reverse k-nearest neighbor problem. Using the reduction of non…
Plastino and Rocca [Physica A 491, 1023 (2018)] recently criticized our work [Phys. Lett. A 381, 207 (2017)] on the ground that one should use functional calculus instead of the ordinary calculus adopted by us in the entropy maximization…
In quantum-state tomography on sources with quantum degrees of freedom of large Hilbert spaces, inference of quantum states of light for instance, a complete characterization of the quantum states for these sources is often not feasible…
The calculation of the error threshold of quantum error correcting codes typically proceeds as follows. First, syndromes are measured. Then, a decoder infers the error chain and the corresponding correction is applied. The threshold is then…
We analyse the reconstruction error of principal component analysis (PCA) and prove non-asymptotic upper bounds for the corresponding excess risk. These bounds unify and improve existing upper bounds from the literature. In particular, they…
This paper addresses the class of continuous-time nonlinear programming problems with equality and inequality constraints. The paper presents necessary optimality conditions of the sequential form. To be more precise, a sequence of…
We commend the authors for an exciting paper which provides a strong contribution to the emerging field of probabilistic numerics (PN). Below, we discuss aspects of prior modelling which need to be considered thoroughly in future work.
A recent work of the authors on the analysis of pairwise comparison matrices that can be made consistent by the modification of a few elements is continued and extended. Inconsistency indices are defined for indicating the overall quality…
The standard quadratic optimization problem (StQP) consists of minimizing a quadratic form over the standard simplex. Without convexity or concavity of the quadratic form, the StQP is NP-hard. This problem has many relevant real-life…
Reliable confidence measures of metrics derived from medical imaging reconstruction pipelines would improve the standard of decision-making in many clinical workflows. Conformal Prediction (CP) provides a robust framework for producing…
Conformal prediction (CP) is a powerful framework for quantifying uncertainty in machine learning models, offering reliable predictions with finite-sample coverage guarantees. When applied to classification, CP produces a prediction set of…
In the light of recent experimental results on $\theta_{13}^{pmns}$, we re-investigate the complementarity between the quark and lepton mixing matrices and obtain predictions for most unsettled neutrino mixing parameters like…
Accuracy thresholds of quantum error correcting codes, which exploit topological properties of systems, defined on two different arrangements of qubits are predicted. We study the topological color codes on the hexagonal lattice and on the…