相关论文: Bandgap Extremization: Some Exact Results
Accurate approximation of probability measures is essential in numerical applications. This paper explores the quantization of probability measures using the maximum mean discrepancy (MMD) distance as a guiding metric. We first investigate…
Topological mapping of a large physical system on a graph, and its decomposition using universal measures is proposed. We find inherent limits to the potential for optimization of a given system and its approximate representations by…
The problem of capacity achieving (optimal) input probability measures has been widely investigated for several channel models with constrained inputs. So far, no outstanding generalizations have been derived. This paper does a forward step…
The principle of maximum entropy is a broadly applicable technique for computing a distribution with the least amount of information possible constrained to match empirical data, for instance, feature expectations. We seek to generalize…
This paper considers a distributionally robust chance constraint model with a general ambiguity set. We show that a sample based approximation of this model converges under suitable sufficient conditions. We also show that upper and lower…
The act of measuring optical emissions from two remote qubits can entangle them. By demanding that a photon from each qubit reaches the detectors, one can ensure than no photon was lost. But the failure rate then rises quadratically with…
We derive the exact analytic form of the potential experienced by a magnetic dipole trapped between two infinite parallel superconducting plates using the method of image dipoles, providing a benchmark for numerical methods and a foundation…
Works, briefly surveyed here, are concerned with two basic methods: Maximum Probability and Bayesian Maximum Probability; as well as with their asymptotic instances: Relative Entropy Maximization and Maximum Non-parametric Likelihood.…
In this paper, we study a maximization and a minimization problem associated with a Poisson boundary value problem. Optimal solutions in a set of rearrangements of a given function define stationary and stable flows of an ideal fluid in two…
We consider the problem of estimating a probability distribution that maximizes the entropy while satisfying a finite number of moment constraints, possibly corrupted by noise. Based on duality of convex programming, we present a novel…
We establish the optimal nonergodic sublinear convergence rate of the proximal point algorithm for maximal monotone inclusion problems. First, the optimal bound is formulated by the performance estimation framework, resulting in an infinite…
Recently, Shih et al. [Phys. Rev. Lett. 105, 146401 (2010)] published a theoretical band gap for wurtzite ZnO, calculated with the non-selfconsistent GW approximation, that agreed surprisingly well with experiment while deviating strongly…
We derive an extremal equation for optimal completely-positive map which most closely approximates a given transformation between pure quantum states. Moreover, we also obtain an upper bound on the maximal mean fidelity that can be attained…
Peak estimation of hybrid systems aims to upper bound extreme values of a state function along trajectories, where this state function could be different in each subsystem. This finite-dimensional but nonconvex problem may be lifted into an…
In this letter we present band gaps of II-VI semiconductors, calculated by the full potential linearized augmented plane wave (FP-LAPW) method with the modified Becke-Johnson (mBJ) potential. The accuracy of the calculated results is…
Confidence intervals are a standard technique for analyzing data. When applied to time series, confidence intervals are computed for each time point separately. Alternatively, we can compute confidence bands, where we are required to find…
Transmission-constrained problems in power systems can be cast as polynomial optimization problems whose coefficients vary over time. We consider the complications therein and suggest several approaches. On the example of the…
We address periodic-image errors arising from the use of periodic boundary conditions to describe systems that do not exhibit full three-dimensional periodicity. The difference between the periodic potential, as straightforwardly obtained…
In this work, we will investigate the question of optimal control for bilinear systems with constrained endpoint. The optimal control will be characterized through a set of unconstrained minimization problems that approximate the former.…
A mixed-integer linear programming (MILP) formulation is presented for parameter estimation of the Potts model. Two algorithms are developed; the first method estimates the parameters such that the set of ground states replicate the…