20 papers · ranked by Valyu relevance
Zijian Wang, Tao Peng, Jifan Shi, Rui Bao + 2 more
- 1 Key Laboratory of Systems Health Science of Zhejiang Province, School of Life Science, Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences, Hangzhou 310024, China - 2 School of Mathematical Sciences and School of AI, Shanghai Jiao Tong University, Shanghai 200240, China. - 3 Research…
Yiting Duan, Zhikun Zhang, Yi Guo
Time-delay embedding is a powerful technique for reconstructing the state space of nonlinear time series. However, the fidelity of reconstruction relies on the assumption that the time-delay map is an embedding, which is implicitly justified by Takens' embedding theorem but rarely scrutinised in practice. In this work…
Jonah Botvinick-Greenhouse, Maria Oprea, Romit Maulik, Yunan Yang
The celebrated Takens' embedding theorem provides a theoretical foundation for reconstructing the full state of a dynamical system from partial observations. However, the classical theorem assumes that the underlying system is deterministic and that observations are noise-free, limiting its applicability in real-world…
A. T. Lin, Adrian Wong, Robert Martin, Stanley Osher + 1 more
'Daniel Eckhardt'] We provide a method to identify system parameters of dynamical systems, called ID-ODE – Inference by Differentiation and Observing Delay Embeddings. In this setting, we are given a dataset of trajectories from a dynamical system with system parameter labels. Our goal is to identify system parameters…
Jiaxi Hu, Bowen Zhang, Qingsong Wen, Fugee Tsung + 1 more
In various scientific and engineering fields, the primary research areas have revolved around physics-based dynamical systems modeling and data-driven time series analysis. According to the embedding theory, dynamical systems and time series can be mutually transformed using observation functions and physical…
Zijian Wang, Peng Tao, Luonan Chen
Predicting time series is of great importance in various scientific and engineering fields. However, in the context of limited and noisy data, accurately predicting the dynamics of all variables in a high-dimensional system is a challenging task due to their nonlinearity and complex interactions. This study introduces…
Daniel Wüstner, Henrik Helge Gundestrup, Katja Thaysen
Metabolic oscillations are a common phenomenon in cell biology. They are based on non-linear coupling of biochemical reactions and can show rich dynamic behavior including sustained and damped oscillations, as found, for example, in glycolysis of yeast and other eukaryotic cells. Metabolic oscillations are often…
Mitchell Ostrow, Adam Eisen, Ila Fiete
To generate coherent responses, language models infer unobserved meaning from their input text sequence. One potential explanation for this capability arises from theories of delay embeddings in dynamical systems, which prove that unobserved variables can be recovered from the history of only a handful of observed…
Tao Wu, Xiangyun Gao, Feng An, Xiaotian Sun + 5 more
'Shraddha Gupta' 'Jianxi Gao' 'Jürgen Kurths'] Forecasting all components in complex systems is an open and challenging task, possibly due to high dimensionality and undesirable predictors. We bridge this gap by proposing a data-driven and model-free framework, namely, feature-and-reconstructed manifold mapping (FRMM)…
Maximilian Topel, Andrew L. Ferguson
Embedding theorems can be used to provide theoretical guarantees about the relation between low-dimensional observations of a system and its full-dimensional state and dynamics. Such theorems do not, however, provide guidance on observable choice, embedding construction, or methodologies to learn the mapping between…
Debdipta Goswami
This paper considers the problem of data-driven prediction of partially observed systems using a recurrent neural network. While neural network based dynamic predictors perform well with full-state training data, prediction with partial observation during training phase poses a significant challenge. Here a predictor…
Jonnel Jaurigue, Joshua Robertson, Antonio Hurtado, Lina Jaurigue + 1 more
'Kathy Lüdge'] Reservoir computing is a machine learning method that is well-suited for complex time series prediction tasks. Both delay embedding and the projection of input data into a higher-dimensional space play important roles in enabling accurate predictions. We establish simple post-processing methods that…
Richard E Rosch, Brittany Scheid, Kathryn A Davis, Brian Litt + 1 more
Many biological systems display circadian and slow multi-day rhythms, such as hormonal and cardiac cycles. In patients with epilepsy, these cycles also manifest as slow cyclical fluctuations in seizure propensity. However, such fluctuations in symptoms are consequences of the complex interactions between the underlying…
Hao Peng, Pei Chen, Na Yang, Kazuyuki Aihara + 2 more
The enormous computational requirements and unsustainable resource consumption associated with massive parameters of large language models and large vision models have given rise to challenging issues. Here, we propose an interpretable ‘small model’ framework characterized by only a single core-neuron, i.e. the…
Hanhuai Zhu, Jingjing Huang, Stanisław Drożdż, Jae Woo Lee
Identification of embedding dimension is helpful to the reconstruction of phase space. However, it is difficult to calculate the proper embedding dimension for the financial time series of dynamics. By this Letter, we suggest a new method based on Manhattan distance and recurrence quantification analysis for…
Jalim Singh, Jeremy Copperman, Laura M. Heiser, Daniel M. Zuckerman
Quantification of the temporal sequence of molecular behavior in live individual cells holds promise for improving causal and mechanistic models of cell biology. In recent years, different methods for inferring molecular labeling from microscopy data have been developed, especially in the context of “virtual…
Xiang Huang, Noah Cohen Kalafut, Sayali Anil Alatkar, Athan Z. Li + 3 more
Studying the temporal dynamics of neural activities is essential for understanding how neurons function. These dynamics often involve temporal delays between neurons that vary over time, revealing both their functions and how they interact within circuits. Recent techniques such as Neuropixels, depth electrodes, and…
Authors not listed
Obtaining quantitative information about residence time behavior (i.e., the residence time distribution function) in realistic experimental systems is oftentimes experimentally challenging and numerically complex. The conventional way is to conduct very simple pulse or step tracer experiments or construct elaborate…
MohammadAmin Farajzadeh, Mehdi Sanayei
Whether different timing tasks utilize the same brain processes is still debated. To approach this question, we investigated how working memory affects two different timing tasks: time reproduction and time discrimination. We found that delay interval led to an overestimation in the reproduction task but did not lead…
Authors not listed
Real-world datasets in chemical engineering and bioengineering processes--such as those from catalytic reactors, multiphase flows, polymerization reactors, bioreactors, and clinical trials--can often be unlabelled or disorganized, rendering the training of existing supervised learning models ineffective at learning the…