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We demonstrate that a knowledge of the density-of-states and the eigenstates of a random system without gain, in conjunction with the frequency profile of the gain, can accurately predict the mode that will lase first. Its critical pumping…
Stationary points (SPs) of the potential energy landscapes can be classified by their Morse index, i.e., the number of negative eigenvalues of the Hessian evaluated at the SPs. In understanding chemical clusters through their potential…
Prevalence mapping in low resource settings is an increasingly important endeavor to guide policy making and to spatially and temporally characterize the burden of disease. We will focus our discussion on consideration of the complex design…
A stochastic algorithm for simulation of fluctuation-induced kinetics of H$_2$ formation on grain surfaces is suggested as a generalization of the technique developed in our recent studies where this method was developed to describe the…
Many applications of Gaussian random fields and Gaussian random processes are limited by the computational complexity of evaluating the probability density function, which involves inverting the relevant covariance matrix. In this work, we…
The traditional way of tackling discrete optimization problems is by using local search on suitably defined cost or fitness landscapes. Such approaches are however limited by the slowing down that occurs when the local minima that are a…
We consider the localization problem of multiple wideband sources in a multi-path environment by coherently taking into account the attenuation characteristics and the time delays in the reception of the signal. Our proposed method leaves…
Gradient flow in the 2-Wasserstein space is widely used to optimize functionals over probability distributions and is typically implemented using an interacting particle system with $n$ particles. Analyzing these algorithms requires showing…
This paper proposes a novel low-rank approximation to the multivariate State-Space Model. The Stochastic Partial Differential Equation (SPDE) approach is applied component-wise to the independent-in-time Mat\'ern Gaussian innovation term in…
Multidimensional scaling (MDS) is a popular dimensionality reduction techniques that has been widely used for network visualization and cooperative localization. However, the traditional stress minimization formulation of MDS necessitates…
Energy landscapes provide a valuable means for studying the folding dynamics of short RNA molecules in detail by modeling all possible structures and their transitions. Higher abstraction levels based on a macro-state decomposition of the…
The complexity and unpredictability of postbuckling responses in even simple thin shells have raised great challenges to emerging technologies exploiting buckling transitions. Here we comprehensively survey the buckling landscapes to show…
We propose efficient preconditioning algorithms for an eigenvalue problem arising in quantum physics, namely the computation of a few interior eigenvalues and their associated eigenvectors for the largest sparse real and symmetric…
In this paper we propose an algorithm for recovering sparse orthogonal polynomials using stochastic collocation. Our approach is motivated by the desire to use generalized polynomial chaos expansions (PCE) to quantify uncertainty in models…
In this paper we present a combinatorial optimisation view on the routing problem for connectionless packet networks by using the metaphor of a landscape. We examine the main properties of the routing landscapes as we define them and how…
We present a formalism of the transition matrix Monte Carlo method. A stochastic matrix in the space of energy can be estimated from Monte Carlo simulation. This matrix is used to compute the density of states, as well as to construct…
We introduce LDL, a fast and robust algorithm that localizes a panorama to a 3D map using line segments. LDL focuses on the sparse structural information of lines in the scene, which is robust to illumination changes and can potentially…
We discuss explicit landscape functions for quantum graphs. By a "landscape function" $\Upsilon(x)$ we mean a function that controls the localization properties of normalized eigenfunctions $\psi(x)$ through a pointwise inequality of the…
The semiclassical Schr\"{o}dinger equation with multiscale and random potentials often appears when studying electron dynamics in heterogeneous quantum systems. As time evolves, the wavefunction develops high-frequency oscillations in both…
In this paper, we investigate the localization properties of optical waves in disordered systems with multifractal scattering potentials. In particular, we apply the localization landscape theory to the classical Helmholtz operator and,…