相关论文: A data-driven method for quantifying the impact of…
Transcriptional regulation of gene expression is one of the main processes that affect cell diversification from a single set of genes. Regulatory proteins often interact with DNA regions located distally from the transcription start sites…
A numerical framework is proposed for identifying partial differential equations (PDEs) governing dynamical systems directly from their observation data using Chebyshev polynomial approximation. In contrast to data-driven approaches such as…
Approaches based on Koopman operators have shown great promise in forecasting time series data generated by complex nonlinear dynamical systems (NLDS). Although such approaches are able to capture the latent state representation of a NLDS,…
We present a data-driven method for spectral analysis of the Koopman operator based on direct construction of the pseudo-resolvent from time-series data. Finite-dimensional approximation of the Koopman operator, such as those obtained from…
Spectral decomposition of dynamical systems is a popular methodology to investigate the fundamental qualitative and quantitative properties of these systems and their solutions. In this chapter, we consider a class of nonlinear cooperative…
Generative Control Policies (GCPs) show immense promise in robotic manipulation but struggle to simultaneously model stable global motions and high-frequency local corrections. While modern architectures extract multi-scale spatial…
The Koopman and Perron Frobenius transport operators are fundamentally changing how we approach dynamical systems, providing linear representations for even strongly nonlinear dynamics. Although there is tremendous potential benefit of such…
Gene-gene interactions play a crucial role in the manifestation of complex human diseases. Uncovering significant gene-gene interactions is a challenging task. Here, we present an innovative approach utilizing data-driven computational…
Heterologous gene expression draws resources from host cells. These resources include vital components to sustain growth and replication, and the resulting cellular burden is a widely recognised bottleneck in the design of robust circuits.…
Koopman operator theory is a key tool in data assimilation of complex dynamical systems, with the potential to be applied to multimodal data. We formulate the problem of learning Koopman eigenfunctions from observations at arbitrary,…
Time series forecasting plays a vital role across scientific, industrial, and environmental domains, especially when dealing with high-dimensional and nonlinear systems. While Transformer-based models have recently achieved state-of-the-art…
Stochastic reaction networks (SRNs) are a general class of continuous-time Markov jump processes used to model a wide range of systems, including biochemical dynamics in single cells, ecological and epidemiological populations, and queueing…
The paper presents a framework for online learning of the Koopman operator using streaming data. Many complex systems for which data-driven modeling and control are sought provide streaming sensor data, the abundance of which can present…
This paper reports a theory of Koopman operators for a class of hybrid dynamical systems with globally asymptotically stable periodic orbits, called hybrid limit-cycling systems. We leverage smooth structures intrinsic to the hybrid…
The field of dynamical systems is being transformed by the mathematical tools and algorithms emerging from modern computing and data science. First-principles derivations and asymptotic reductions are giving way to data-driven approaches…
Data-driven neural Koopman operator theory has emerged as a powerful tool for linearizing and controlling nonlinear robotic systems. However, the performance of these data-driven models fundamentally depends on the trade-off between sample…
The modeling of nonlinear dynamics based on Koopman operator theory, which is originally applicable only to autonomous systems with no control, is extended to non-autonomous control system without approximation to input matrix B. Prevailing…
For every non-autonomous system, there is the related family of Koopman operators $\mathcal{K}^{(t,t_0)}$, parameterized by the time pair $(t,t_0)$. In this paper we are investigating the time dependency of the spectral properties of the…
Cells receive a wide variety of cellular and environmental signals, which must be processed combinatorially to generate specific and timely genetic responses. We present here a theoretical study on the combinatorial control and integration…
Reconstructing transcriptional regulatory networks is an important task in functional genomics. Data obtained from experiments that perturb genes by knockouts or RNA interference contain useful information for addressing this reconstruction…