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This study presents new estimates for fractional derivatives without singular kernels defined by some specific functions. Based on obtained inequalities, we give a useful method to establish the global stability of steady states for…
We provide performance guarantees for a variant of simulation-based policy iteration for controlling Markov decision processes that involves the use of stochastic approximation algorithms along with state-of-the-art techniques that are…
Stability selection is a popular method for improving feature selection algorithms. One of its key attributes is that it provides theoretical upper bounds on the expected number of false positives, E(FP), enabling false positive control in…
Refined stability estimates are derived for classical mixed problems. The novel emphasis is on the importance of semi norms on data functionals, inspired by recent progress on pressure-robust discretizations for the incompressible…
The structural and dynamical properties of ultra-soft colloids - star polymers - exposed to a uniform external force field are analyzed applying the multiparticle collision dynamics approach, a hybrid coarse-grain mesoscale simulation…
Stochastic bilevel optimization (SBO) has been integrated into many machine learning paradigms recently, including hyperparameter optimization, meta learning, and reinforcement learning. Along with the wide range of applications, there have…
It is classical that, when the small deformation is assumed, the incremental analysis problem of an elastoplastic structure with a piecewise-linear yield condition and a linear strain hardening model can be formulated as a convex quadratic…
In this paper, we focus on providing convergence guarantees for stochastic subgradient methods in minimizing nonsmooth nonconvex functions. We first investigate the global stability of a general framework for stochastic subgradient methods,…
A molecular understanding of how protein function is related to protein structure will require an ability to understand large conformational changes between multiple states. Unfortunately these states are often separated by high free energy…
In this paper, we consider Steiner forest and its generalizations, prize-collecting Steiner forest and k-Steiner forest, when the vertices of the input graph are points in the Euclidean plane and the lengths are Euclidean distances. First,…
The proper biological functioning of proteins often relies on the occurrence of coordinated fluctuations around their native structure, or of wider and sometimes highly elaborated motions. Coarse-grained elastic-network descriptions are…
Schoenberg transformations, mapping Euclidean configurations into Euclidean configurations, define in turn a transformed inertia, whose minimization produces robust location estimates. The procedure only depends upon Euclidean distances…
Using lattice approximations of Euclidean space, we develop a way to approximate stable processes that are represented by stochastic integrals over Euclidean space. Via a stable version of the Lindeberg-Feller Theorem we show that the…
This work proposes a framework for multistage adjustable robust optimization that unifies the treatment of three different types of endogenous uncertainty, where decisions, respectively, (i) alter the uncertainty set, (ii) affect the…
Optimization over the Stiefel manifold is a fundamental computational problem in many scientific and engineering applications. Despite considerable research effort, high-dimensional optimization problems over the Stiefel manifold remain…
Discovering relationships between materials' microstructures and mechanical properties is a key goal of materials science. Here, we outline a strategy exploiting Bayesian optimization to efficiently search the multidimensional space of…
An approach is proposed to improve the efficiency of fourth-order algorithms for numerical integration of the equations of motion in molecular dynamics simulations. The approach is based on an extension of the decomposition scheme by…
Revealing the functional sites of biological sequences, such as evolutionary conserved, structurally interacting or co-evolving protein sites, is a fundamental, and yet challenging task. Different frameworks and models were developed to…
This paper presents a novel framework for the modeling of biological networks. It makes use of recent tools analyzing the robust satisfaction of properties of (hybrid) dynamical systems. The main challenge of this approach as applied to…
Approximation theory for Lyapunov and Sacker-Sell spectra based upon QR techniques is used to analyze the stability of a one-step method solving a time-dependent, linear, ordinary differential equation (ODE) initial value problem in terms…