scholarly journals Alignment of time series with use of the generalized Legendre's transformation and methods of idempotenty mathematics

2021 ◽  
Vol 16 (3) ◽  
pp. 75-82
Author(s):  
Maria V. Kurkina ◽  
Sergey P. Semenov ◽  
Viktor V. Slavsky ◽  
Olga V. Samarina ◽  
Olga A. Petuhova ◽  
...  
Keyword(s):  
Time Series ◽  
Riemannian Metrics ◽  
Digital Processing ◽  
Conformally Flat ◽  
Idempotent Algebra ◽  
Program Complex ◽  
Tropical Mathematics ◽  
Main Tendency ◽  
And Mathematics ◽  
Under Construction

Alignment of time series [time-series smoothing] identification of the main tendency of development (временнго a trend) by "cleaning" of a time series of the accidental deviations distorting this tendency. At a research of time series of economy (bioinformation science) apply for detection of patterns [1-3]. In this work it is offered to use for this purpose Legendre's transformation well-known in physics and mathematics. Its direct application to poorly regular objects is difficult therefore in work its idempotent analog is defined previously and on its basis the concept of the TRACK for a time series is defined. In recent years within the international center "Cuofus Li" the new field of mathe-matics idempotent or "tropical" mathematics gained intensive development that is reflected in works of the academician V.P. Maslov and his pupils: G.L. Litvinov, A.N. Sobolevsky, etc. The purpose of this work to be beyond duality of the theory of linear vector spaces, using similar concepts of duality of conformally flat Riemannian geometry and of idempotent algebra. By analogy with the polar transformation of a conformally flat Riemannian metrics entered in E.D. Rodionov and V.V. Slavsky's works the abstract idempotent analog of transformation of Legendre is under construction. In the MATLAB system the program complex for calculation the TRACK of a time series is created. It is in-vestigated its opportunities for digital processing of time series.

scholarly journals Idempotent Analog of the Legendre Transformation and lts Application in Digital Processing of Signals

2020 ◽  
pp. 96-101
Author(s):  
M.V. Kurkina ◽  
S.P. Semenov ◽  
V.V. Slavsky ◽  
O.V. Samarina ◽  
O.A. Petuhova ◽  
...  
Keyword(s):  
Convex Functions ◽  
Riemannian Geometry ◽  
Duality Theory ◽  
Digital Processing ◽  
Riemannian Metric ◽  
Theoretical Physics ◽  
Vector Spaces ◽  
Legendre Transformation ◽  
Conformally Flat ◽  
Tropical Mathematics

In recent years, a new area of mathematics — idempotent or “tropical” mathematics — has been intensively developed within the framework of the Sofus Lee international center, which is reflected in the works of V.P. Maslov, G.L. Litvinov, and A.N. Sobolevsky. The Legendre transformation plays an important role in theoretical physics, classical and statistical mechanics, and thermodynamics. In mathematics and its applications, the Legendre transformation is based on the concept of duality of vector spaces and duality theory for convex functions and subsets of a vector space. The purpose of this paper is to go beyond linear vector spaces using similar notions of duality in conformally flat Riemannian geometry and in idempotent algebra.An abstract idempotent analog of the Legendre transformation is constructed in a way similar to the polar transformation of the conformally flat Riemannian metric introduced in the works of E.D. Rodionov and V.V. Slavsky. Its capabilities for digital processing of signals and images are being investigated

scholarly journals Low-Pass Filtering Method for Poisson Data Time Series

2021 ◽  
Vol 11 (10) ◽  
pp. 4524
Author(s):  
Victor Getmanov ◽  
Vladislav Chinkin ◽  
Roman Sidorov ◽  
Alexei Gvishiani ◽  
Mikhail Dobrovolsky ◽  
...  
Keyword(s):  
Time Series ◽  
Finite Impulse Response ◽  
Digital Processing ◽  
Distributed Data ◽  
Gaussian Filter ◽  
Experimental Physics ◽  
Filtering Method ◽  
Filter Synthesis ◽  
Low Pass ◽  
Poisson Data

Problems of digital processing of Poisson-distributed data time series from various counters of radiation particles, photons, slow neutrons etc. are relevant for experimental physics and measuring technology. A low-pass filtering method for normalized Poisson-distributed data time series is proposed. A digital quasi-Gaussian filter is designed, with a finite impulse response and non-negative weights. The quasi-Gaussian filter synthesis is implemented using the technology of stochastic global minimization and modification of the annealing simulation algorithm. The results of testing the filtering method and the quasi-Gaussian filter on model and experimental normalized Poisson data from the URAGAN muon hodoscope, that have confirmed their effectiveness, are presented.

scholarly journals SUBSIDENCE EVALUATION OF HIGH-SPEED RAILWAY IN SHENYANG BASED ON TIME-SERIES INSAR

2018 ◽  
Vol IV-3 ◽  
pp. 273-276
Author(s):  
Yun Zhang ◽  
Lianhuan Wei ◽  
Jiayu Li ◽  
Shanjun Liu ◽  
Yachun Mao ◽  
...  
Keyword(s):  
Time Series ◽  
High Speed ◽  
Cross Validation ◽  
Surface Deformation ◽  
Local Environment ◽  
Local Area ◽  
Safe Operation ◽  
High Speed Rail ◽  
High Speed Railway ◽  
Under Construction

More and more high-speed railway are under construction in China. The slow settlement along high-speed railway tracks and newly-built stations would lead to inhomogeneous deformation of local area, and the accumulation may be a threat to the safe operation of high-speed rail system. In this paper, surface deformation of the newly-built high-speed railway station as well as the railway lines in Shenyang region will be retrieved by time series InSAR analysis using multi-orbit COSMO-SkyMed images. This paper focuses on the non-uniform subsidence caused by the changing of local environment along the railway. The accuracy of the settlement results can be verified by cross validation of the results obtained from two different orbits during the same period.

A CLASSIFICATION AND A NON-EXISTENCE THEOREM FOR CONFORMALLY FLAT HYPERSURFACES IN EUCLIDEAN 4-SPACE

2005 ◽  
Vol 16 (01) ◽  
pp. 53-85 ◽  
Author(s):  
YOSHIHIKO SUYAMA
Keyword(s):  
Existence Theorem ◽  
Fundamental Form ◽  
Riemannian Metrics ◽  
Equivalence Classes ◽  
Classification Theorem ◽  
Conformally Flat ◽  
Conformal Class ◽  
First Fundamental Form ◽  
Conformal Equivalence ◽  
Conformally Flat Hypersurface

We study generic conformally flat hypersurfaces in the Euclidean 4-space satisfying a certain condition on the conformal class of the first fundamental form. We first classify such hypersurfaces by determining all conformal-equivalence classes of generic conformally flat hypersurfaces satisfying the condition. Next, as an application of the classification theorem, we give some examples of flat Riemannian metrics which are not conformal to the first fundamental form of any generic conformally flat hypersurface. These flat Riemannian metrics seem to provide counter-examples to Hertrich–Jeromin's claim [3, 5].

scholarly journals Tuberculosis Case Finding in Benin, 2000–2014 and Beyond: A Retrospective Cohort and Time Series Study

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Serge Ade ◽  
Wilfried Békou ◽  
Mênonli Adjobimey ◽  
Omer Adjibode ◽  
Gabriel Ade ◽  
...  
Keyword(s):  
Time Series ◽  
Retrospective Cohort ◽  
Seasonal Pattern ◽  
Case Finding ◽  
Tuberculosis Case ◽  
Time Series Study ◽  
Tuberculosis Epidemiology ◽  
And Mathematics ◽  
Series Study ◽  
Best Fit

Objective. To determine any changes in tuberculosis epidemiology in the last 15 years in Benin, seasonal variations, and forecasted numbers of tuberculosis cases in the next five years.Materials and Methods. Retrospective cohort and time series study of all tuberculosis cases notified between 2000 and 2014. The “R” software version 3.2.1 (Institute for Statistics and Mathematics Vienna Austria) and the Box-Jenkins 1976 modeling approach were used for time series analysis.Results. Of 246943 presumptive cases, 54303 (22%) were diagnosed with tuberculosis. Annual notified case numbers increased, with the highest reported in 2011. New pulmonary bacteriologically confirmed tuberculosis (NPBCT) represented 78%  ± SD 2%. Retreatment cases decreased from 10% to 6% and new pulmonary clinically diagnosed cases increased from 2% to 8%. NPBCT notification rates decreased in males from 2012, in young people aged 15–34 years and in Borgou-Alibori region. There was a seasonal pattern in tuberculosis cases. Over 90% of NPBCT were HIV-tested with a stable HIV prevalence of 13%. The ARIMA best fit model predicted a decrease in tuberculosis cases finding in the next five years.Conclusion. Tuberculosis case notifications are predicted to decrease in the next five years if current passive case finding is used. Additional strategies are needed in the country.

scholarly journals Statistical analysis of music data

2011 ◽  
Vol 52 ◽  
Author(s):  
Mindaugas Kavaliauskas
Keyword(s):  
Time Series ◽  
Markov Chain ◽  
Statistical Analysis ◽  
Data Clustering ◽  
Mathematical Methods ◽  
Markov Chain Models ◽  
Tight Connection ◽  
Music And Mathematics ◽  
And Mathematics ◽  
Work Done

Connection of music and mathematics is known from Pythagoras. Music sounds are in harmony if it satisfies certain mathematical conditions. Despite tight connection between music and mathematics, the idea of using mathematical methods in musicology was used only in the 1950s. Last decade various methods of mathematical statistics, such as correlation analysis, time series analysis, analysis of variance, data clustering, Markov chain models was successfully applied in musiclogy. Though, there was no work done in this area in Lithuania. In this article musical data (notes) is analysed using statistical methods. Musical intervalas are analysed. Music compositions are classified. Analysis results are presented. Research uses works of a few Lithuanian composers.  

Sign in / Sign up

Export Citation Format

Share Document