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This paper presents a novel phase-field-based methodology for solving minimum compliance problems in topology optimization under fixed external loads and body forces. The proposed framework characterizes the optimal structure through an…
The reduced-rank regression model is a popular model to deal with multivariate response and multiple predictors, and is widely used in biology, chemometrics, econometrics, engineering, and other fields. In the reduced-rank regression…
The uncertainties in material and other properties of structures are usually spatially correlated. We introduce an efficient technique for representing and processing spatially correlated random fields in robust topology optimisation of…
This work proposes a new a framework for determining robust periodic invariant sets and their associated control laws for constrained uncertain linear systems. Necessary and sufficient conditions for stabilizability by periodic controllers…
We advance a combined filtered/phase-field approach to topology optimization in the setting of linearized elasticity. Existence of minimizers is proved and rigorous parameter asymptotics are discussed by means of variational convergence…
We have previously shown that Good-Turing statistics can be applied to molecular dynamics trajectories to estimate the probability of observing completely new (thus far unobserved) biomolecular structures, and showed that the method is…
We present a sequence-based probabilistic formalism that directly addresses co-operative effects in networks of interacting positions in proteins, providing significantly improved contact prediction, as well as accurate quantitative…
Fixed-time stable dynamical systems are capable of achieving exact convergence to an equilibrium point within a fixed time that is independent of the initial conditions of the system. This property makes them highly appealing for designing…
This paper analyses a $(1,\lambda)$-Evolution Strategy, a randomised comparison-based adaptive search algorithm, on a simple constraint optimisation problem. The algorithm uses resampling to handle the constraint and optimizes a linear…
Experimentally obtained X-ray diffraction (XRD) patterns can be difficult to solve, precluding the full characterization of materials, pharmaceuticals, and geological compounds. Herein, we propose a method based upon a multi-objective…
We propose a novel approach for navigating in polygonal environments by synthesizing controllers that take as input relative displacement measurements with respect to a set of landmarks. Our algorithm is based on solving a sequence of…
The Euclidean Steiner tree problem seeks the min-cost network to connect a collection of target locations, and it underlies many applications of wireless networks. In this paper, we present a study on solving the Euclidean Steiner tree…
A computational method is developed to work on an inverse equilibrium problem with an interest towards applications with protein folding. In general, we are given a set of equilibrium confgiurations and want to derive the most probable…
We analyze the one-step method TR-BDF2 from the point of view of monotonicity, strong stability and positivity. All these properties are strongly related and reviewed in the common framework of absolute monotonicity. The radius of absolute…
Metabolites, small molecules that are involved in cellular reactions, provide a direct functional signature of cellular state. Untargeted metabolomics experiments usually relies on tandem mass spectrometry to identify the thousands of…
Stochastic optimization of the Area Under the Precision-Recall Curve (AUPRC) is a crucial problem for machine learning. Although various algorithms have been extensively studied for AUPRC optimization, the generalization is only guaranteed…
This paper integrates two strands of the literature on stability of general state Markov chains: conventional, total variation based results and more recent order-theoretic results. First we introduce a complete metric over Borel…
We study the performance of Stochastic Cubic Regularized Newton (SCRN) on a class of functions satisfying gradient dominance property with $1\le\alpha\le2$ which holds in a wide range of applications in machine learning and signal…
A microscopic theory of the free energy barriers and folding routes for minimally frustrated proteins is presented, greatly expanding on the presentation of the variational approach outlined previously [J. J. Portman, S. Takada, P. G.…
Lyapunov functions play a fundamental role in analyzing the stability and convergence properties of optimization methods. In this paper, we propose a novel and straightforward approach for constructing Lyapunov functions for first-order…