20 papers · ranked by Valyu relevance
Sebastian Wallot, Dan Mønster
Using the method or time-delayed embedding, a signal can be embedded into higher-dimensional space in order to study its dynamics. This requires knowledge of two parameters: The delay parameter τ, and the embedding dimension parameter D. Two standard methods to estimate these parameters in one-dimensional time series…
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…
Zhifei Zhang, Song Yang, Wei Wang, Hairong Qi
The staggering amount of streaming time series coming from the real world calls for more efficient and effective online modeling solution. For time series modeling, most existing works make some unrealistic assumptions such as the input data is of fixed length or well aligned, which requires extra effort on…
Seth M. Hirsh, Sara M. Ichinaga, Steven L. Brunton, J. Nathan Kutz + 1 more
Time-delay embedding and dimensionality reduction are powerful techniques for discovering effective coordinate systems to represent the dynamics of physical systems. Recently, it has been shown that models identified by dynamic mode decomposition on time-delay coordinates provide linear representations of strongly…
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…
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…
Michael X Cohen
The number of simultaneously recorded electrodes in neuroscience is steadily increasing, providing new opportunities for understanding brain function, but also new challenges for appropriately dealing with the increase in dimensionality. Multivariate source-separation analysis methods have been particularly effective…
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…
Kristina Enes, Hassan Errami, Moritz Wolter, Tim Krake + 3 more
'Bernhard Eberhardt' 'Andreas Weber' 'Jörg Zimmermann'] Various neural network based methods are capable of anticipating human body motions from data for a short period of time. What these methods lack are the interpretability and explainability of the network and its results. We propose to use Dynamic Mode…
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…
Quoc Hoan Tran, Yoshihiko Hasegawa
Identifying the qualitative changes in time-series data provides insights into the dynamics associated with such data. Such qualitative changes can be detected through topological approaches, which first embed the data into a high-dimensional space using a time-delay parameter and subsequently extract topological…
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…
Aniruddha Tamma, Bhaskar Khubchandani
A new and accurate method to determine the time delay and embedding dimension for state space reconstruction of a high dimensional system from a scalar time series using time delay embedding is presented. The time delay is obtained to unprecedented accuracy by evaluating the minima of a newly defined dimension…
Christopher J. Cueva, Encarni Marcos, Alex Saez, Aldo Genovesio + 5 more
Our decisions often depend on multiple sensory experiences separated by time delays. The brain can remember these experiences and, simultaneously, estimate the timing between events. To understand the mechanisms underlying working memory and time encoding we analyze neural activity recorded during delays in four…
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…