Difference between revisions of "My fist scientific paper"

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==Functional Data Analysis, 2024==  
 
==Functional Data Analysis, 2024==  
The statistical analysis of spatial time series requires additional methods of data analysis. First,  we suppose time is continuous, put to the state space changes <math>\frac{d\mathbf{x}}{dt}</math> and use neural ordinary and stochastic differential equations. Second, we analyze a multivariate and multidimensional time series and use the tensor representation and tensor analysis. Third, since the time series have significant cross-correlation we model them in the Riemannian space. Fourth, medical time series are periodic, the base model is the pendulum model, <math>\frac{d^2x}{dt^2}=-c\sin{x}</math>. We use physics-informed neural networks to approximate data. Fifth, the practical experiments involve multiple data sources. We use canonical correlation analysis with latent state space. This space aligns the source and target spaces and generates data in source and target manifolds.  
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The statistical analysis of spatial time series requires additional methods of data analysis. First,  we suppose time is continuous, put to the state space changes <math>\frac{d\mathbf{x}}{dt}</math> and use neural ordinary and stochastic differential equations. Second, we analyze a multivariate and multidimensional time series and use the tensor representation and tensor analysis. Third, since the time series have significant cross-correlation we model them in the Riemannian space. Fourth, medical time series are periodic, the base model is the pendulum model, <math>\frac{d^2x}{dt^2}=-c\sin{x}</math>. We use physics-informed neural networks to approximate data. Fifth, the practical experiments involve multiple data sources. We use canonical correlation analysis with latent state space. This space aligns the source and target spaces and generates data in source and target manifolds. [[Functional Data Analysis|See the course page]].
  
 
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Revision as of 22:44, 15 September 2024

Research management course

 

News and announcements

Fall 2024 on September 14 — The Art of Scientific Research

Fall 2024 on September 13 — Intelligent Data Analysis / FDA

Before January 2025 — My fist scientific paper: Suggest your project here

Spring 2025 on February 6th — My fist scientific paper starts

See results of 2024 —  on GitHub

The Art of Scientific Research

See you this Saturday (September 21, 2024) at 14:40 m1p.org/go_zoom

The goal is to prepare and select the research topic of your dream. We must be sure that the problem statement and project planning lead you to successful delivery.

m1p Course progress

This course produces student research papers. It gathers research teams. Each team joins a student, a consultant, and an expert. The student is a project driver who wants to plunge into scientific research activities. The graduate student consultant conducts the research and helps the student. The expert, a professor, states the problem and enlightens the road to the goal. The projects start in February and end in May, according to the schedule.

LINKS


HISTORY

Mathematical methods of forecasting, 2024

This course delivers methods of model selection in machine learning and forecasting. The modeling data are videos, audio, encephalograms, fMRIs, and other measurements in natural science. The models are linear, tensor, deep neural networks, and neural ODEs. The practical examples are brain-computer interfaces, weather forecasting, and various spatial-time series forecasting. The lab works are organized as paper-with-code reports. See the course page

Functional Data Analysis, 2024

The statistical analysis of spatial time series requires additional methods of data analysis. First, we suppose time is continuous, put to the state space changes \(\frac{d\mathbf{x}}{dt}\) and use neural ordinary and stochastic differential equations. Second, we analyze a multivariate and multidimensional time series and use the tensor representation and tensor analysis. Third, since the time series have significant cross-correlation we model them in the Riemannian space. Fourth, medical time series are periodic, the base model is the pendulum model, \(\frac{d^2x}{dt^2}=-c\sin{x}\). We use physics-informed neural networks to approximate data. Fifth, the practical experiments involve multiple data sources. We use canonical correlation analysis with latent state space. This space aligns the source and target spaces and generates data in source and target manifolds. See the course page.