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Cooperativity is a hallmark of proteins, many of which show a modular architecture comprising discrete structural domains. Detecting and describing dynamic couplings between structural regions is difficult in view of the many-body nature of…
Efficiently computable stability and performance analysis of nonlinear systems becomes increasingly more important in practical applications. Dissipativity can express stability and performance jointly, but existing results are limited to…
Masked Diffusion Models (MDMs) offer flexible, non-autoregressive generation, but this freedom introduces a challenge: final output quality is highly sensitive to the decoding order. We are the first to formalize this issue, attributing the…
We study theoretically the denaturation of single RNA molecules by mechanical stretching, focusing on signatures of the (un)folding pathway in molecular fluctuations. Our model describes the interactions between nucleotides by incorporating…
Understanding how time delays impact the stability of a delay differential equation is important for modeling many natural and technological systems that experience time delays. Here we introduce a new stability criterion for…
Stein's unbiased risk estimator (SURE) has been shown to be an effective metric for determining optimal parameters for many applications. The topic of this article is focused on the use of SURE for determining parameters for blind…
This paper studies double/debiased machine learning (DML) methods applied to weakly dependent data. We allow observations to be situated in a general metric space that accommodates spatial and network data. Existing work implements…
The damage spreading method (DS) provided a useful tool to obtain analytical results of the thermodynamics and stability of the 2D Ising model --amongst many others--, but it suffered both from ambiguities in its results and from large…
This paper considers robust stability analysis of a large network of interconnected uncertain systems. To avoid analyzing the entire network as a single large, lumped system, we model the network interconnections with integral quadratic…
A variety of algorithms have been proposed to address the power system state estimation problem in the presence of uncertainties in the data. However, less emphasis has been given to handling perturbations in the model. In the context of…
The dislocation core is an important region as it controls many important properties of materials. Elasticity breaks down in the core and the stress, force, and energy diverge at the dislocation line. We consider three commonest methods…
Several results regarding the stability and the stabilization of linear impulsive positive systems under arbitrary, constant, minimum, maximum and range dwell-time are obtained. The proposed stability conditions characterize the pointwise…
In medical research, often, genomic or proteomic data are collected, with measurements frequently subject to uncertainties or errors, making it crucial to accurately separate the signals of the genes or proteins, respectively, from the…
The flexibility of the DPG methodology is exposed by solving the linear elasticity equations under different variational formulations, including some with non-symmetric functional settings (different infinite-dimensional trial and test…
Estimating the values of unknown parameters from corrupted measured data faces a lot of challenges in ill-posed problems. In such problems, many fundamental estimation methods fail to provide a meaningful stabilized solution. In this work,…
The protein folding problem must ultimately be solved on all length scales from the atomic up through a hierarchy of complicated structures. By analyzing the stability of the folding process using physics and mathematics, this paper shows…
Classical optimization theory requires a small step-size for gradient-based methods to converge. Nevertheless, recent findings challenge the traditional idea by empirically demonstrating Gradient Descent (GD) converges even when the…
We study the conformational freedom of a protein made by two rigid domains connected by a flexible linker. The conformational freedom is represented as an unknown probability distribution on the space of allowed states. A new algorithm for…
In different fields of applications including, but not limited to, behavioral, environmental, medical sciences and econometrics, the use of panel data regression models has become increasingly popular as a general framework for making…
In this paper, we study networks of positive linear systems subject to time-invariant and random uncertainties. We present linear matrix inequalities for checking the stability of the whole network around the origin with prescribed…