Related papers: Certified Real Eigenvalue Location
In this paper, using the linearization technique we write the Helmholtz transmission eigenvalue problem as an equivalent nonselfadjoint linear eigenvalue problem whose left-hand side term is a selfadjoint, continuous and coercive…
In this paper we discuss reduced order models for the approximation of parametric eigenvalue problems. In particular, we are interested in the presence of intersections or clusters of eigenvalues. The singularities originating by these…
We propose a real-time method to estimate spatiallyvarying indoor lighting from a single RGB image. Given an image and a 2D location in that image, our CNN estimates a 5th order spherical harmonic representation of the lighting at the given…
We consider the numerical approximations of the Cahn-Hilliard equation with dynamic boundary conditions (C. Liu et. al., Arch. Rational Mech. Anal., 2019). We propose a first-order in time, linear and energy stable numerical scheme, which…
We consider the verification of neural network policies for discrete-time stochastic systems with respect to reach-avoid specifications. We use a learner-verifier procedure that learns a certificate for the specification, represented as a…
The goal of this paper is to determine the spatio-temporal location of actions in video. Where training from hard to obtain box annotations is the norm, we propose an intuitive and effective algorithm that localizes actions from their class…
Robust and accurate localization is an essential component for robotic navigation and autonomous driving. The use of cameras for localization with high definition map (HD Map) provides an affordable localization sensor set. Existing methods…
Modern machine learning pipelines are built on numerical algorithms. Reliable numerical methods are thus a prerequisite for trustworthy machine learning and cyber-physical systems. Therefore, we contribute a framework for verified numerical…
One way to analyze Cyber-Physical Systems is by modeling them as hybrid automata. Since reachability analysis for hybrid nonlinear automata is a very challenging and computationally expensive problem, in practice, engineers try to solve the…
Hardware-firmware co-verification is critical to design trustworthy systems. While formal methods can provide verification guarantees, due to the complexity of firmware and hardware, it can lead to state space explosion. There are promising…
We consider the semiclassical asymptotic behaviour of the number of eigenvalues smaller than $E$ for elliptic operators in $L\sp 2 ({\bf R}\sp d)$. We describe a method of finding remainder estimates related to the volume of the region of…
The development of instruments for remote sensing applications (active or passive) requires in situ validation measurements. The equipments (radar or radiometer) must be tested on real geological profiles. We must have accurate information…
Studying the optoelectronic structure of materials can require the computation of several thousands of the smallest positive eigenpairs of a pseudo-hermitian Hamiltonian. Iterative eigensolvers may be preferred over direct methods for this…
Knowledge about the locations of keypoints of an object in an image can assist in fine-grained classification and identification tasks, particularly for the case of objects that exhibit large variations in poses that greatly influence their…
Certificates to a linear algebra computation are additional data structures for each output, which can be used by a---possibly randomized---verification algorithm that proves the correctness of each output. The certificates are essentially…
Numerical methods for the transmission eigenvalue problems are hot topics in recent years. Based on the work of Lin and Xie [Math. Comp., 84(2015), pp. 71-88], we build a multigrid method to solve the problems. With our method, we only need…
Characterizing increasingly complex quantum systems is a central task in quantum information science, yet experimental costs often scale prohibitively with system size. Certifying key properties using simple local measurements is highly…
High-performance deep learning methods typically rely on large annotated training datasets, which are difficult to obtain in many clinical applications due to the high cost of medical image labeling. Existing data assessment methods…
We describe a quantum algorithm for finding the smallest eigenvalue of a Hermitian matrix. This algorithm combines Quantum Phase Estimation and Quantum Amplitude Estimation to achieve a quadratic speedup with respect to the best classical…
It is shown in [10] that a regular and local Dirichlet form on an interval can be represented by so-called effective intervals with scale functions. This paper focuses on how to operate on effective intervals to obtain regular Dirichlet…