scholarly journals Relative distances between homology groups to assess persistent defects in time series

2019 ◽  
Author(s):  
Juan G. Diaz Ochoa
Keyword(s):  
Time Series ◽  
Data Structure ◽  
Large Datasets ◽  
Mobile Sensors ◽  
Patient Stratification ◽  
Good Strategy ◽  
Homology Groups ◽  
Data Intensive ◽  
Persistent Anomalies ◽  
Definition Of

AbstractIt is common to consider a data-intensive strategy to be an appropriate way to develop systemic analyses in biology and physiology. Therefore, options for data collection, sampling, standardization, visualization, and interpretation determine how causes are identified in time series to build mathematical models. However, there are often biases in the collected data that can affect the validity of the model: while collecting enough large datasets seems to be a good strategy for reducing the bias of the collected data, persistent and dynamical anomalies in the data structure can affect the overall validity of the model. In this work we present a methodology based on the definition of homological groups to evaluate persistent anomalies in the structure of the sampled time series. In this evaluation relevant patterns in the combination of different time series are clustered and grouped to customize the identification of causal relationships between parameters. We test this methodology on data collected from patients using mobile sensors to test the response to physical exercise in real-world conditions and outside the lab. With this methodology we plan to obtain a patient stratification of the time series to customize models in medicine.

scholarly journals Observability of Complex Systems by Means of Relative Distances Between Homological Groups

2020 ◽  
Vol 8 ◽  
Author(s):  
Juan G. Diaz Ochoa
Keyword(s):  
Time Series ◽  
Data Structure ◽  
Quantitative Analysis ◽  
Complex Systems ◽  
Large Datasets ◽  
Mobile Sensors ◽  
Good Strategy ◽  
Data Intensive ◽  
Persistent Topology ◽  
Definition Of

It is common to consider using a data-intensive strategy as a way to develop systemic and quantitative analysis of complex systems so that data collection, sampling, standardization, visualization, and interpretation can determine how causal relationships are identified and incorporated into mathematical models. Collecting enough large datasets seems to be a good strategy in reducing bias of the collected data; but persistent and dynamic anomalies in the data structure, generated from variations in intrinsic mechanisms, can actually induce persistent entropy thus affecting the overall validity of quantitative models. In this research, we are introducing a method based on the definition of homological groups that aims at evaluating this persistent entropy as a complexity measure to estimate the observability of the systems. This method identifies patterns with persistent topology, extracted from the combination of different time series and clustering them to identify persistent bias in the data. We tested this method on accumulated data from patients using mobile sensors to measure the response of physical exercise in real-world conditions outside the lab. With this method, we aim to better stratify time series and customize models in complex biological systems.

T-Cube: A Data Structure for Fast Extraction of Time Series from Large Datasets

2007 ◽  
Author(s):  
Maheshkumar Sabhnani ◽  
Andrew W. Moore ◽  
Artur W. Dubrawski
Keyword(s):  
Time Series ◽  
Data Structure ◽  
Large Datasets ◽  
Fast Extraction

scholarly journals Path homology theory of edge-colored graphs

2021 ◽  
Vol 19 (1) ◽  
pp. 706-723
Author(s):  
Yuri V. Muranov ◽  
Anna Szczepkowska
Keyword(s):  
Spectral Sequence ◽  
Edge Coloring ◽  
Homology Theory ◽  
Homotopy Category ◽  
Homology Groups ◽  
Colored Graphs ◽  
Natural Filtration ◽  
Definition Of ◽  
Exact Sequences

Abstract In this paper, we introduce the category and the homotopy category of edge-colored digraphs and construct the functorial homology theory on the foundation of the path homology theory provided by Grigoryan, Muranov, and Shing-Tung Yau. We give the construction of the path homology theory for edge-colored graphs that follows immediately from the consideration of natural functor from the category of graphs to the subcategory of symmetrical digraphs. We describe the natural filtration of path homology groups of any digraph equipped with edge coloring, provide the definition of the corresponding spectral sequence, and obtain commutative diagrams and braids of exact sequences.

IDENTIFYING DISTINCT STOCHASTIC DYNAMICS FROM CHAOS: A STUDY ON MULTIMODAL NEURAL FIRING PATTERNS

2009 ◽  
Vol 19 (02) ◽  
pp. 453-485 ◽  
Author(s):  
MINGHAO YANG ◽  
ZHIQIANG LIU ◽  
LI LI ◽  
YULIN XU ◽  
HONGJV LIU ◽  
...  
Keyword(s):  
Time Series ◽  
Limit Cycle ◽  
Stochastic Dynamics ◽  
Nonlinear Time Series ◽  
Special Importance ◽  
Neuronal System ◽  
Neural Firing ◽  
Firing Patterns ◽  
Theoretical Simulation ◽  
Definition Of

Some chaotic and a series of stochastic neural firings are multimodal. Stochastic multimodal firing patterns are of special importance because they indicate a possible utility of noise. A number of previous studies confused the dynamics of chaotic and stochastic multimodal firing patterns. The confusion resulted partly from inappropriate interpretations of estimations of nonlinear time series measures. With deliberately chosen examples the present paper introduces strategies and methods of identification of stochastic firing patterns from chaotic ones. Aided by theoretical simulation we show that the stochastic multimodal firing patterns result from the effects of noise on neuronal systems near to a bifurcation between two simpler attractors, such as a point attractor and a limit cycle attractor or two limit cycle attractors. In contrast, the multimodal chaotic firing trains are generated by the dynamics of a specific strange attractor. Three systems were carefully chosen to elucidate these two mechanisms. An experimental neural pacemaker model and the Chay mathematical model were used to show the stochastic dynamics, while the deterministic Wang model was used to show the deterministic dynamics. The usage and interpretation of nonlinear time series measures were systematically tested by applying them to firing trains generated by the three systems. We successfully identified the distinct differences between stochastic and chaotic multimodal firing patterns and showed the dynamics underlying two categories of stochastic firing patterns. The first category results from the effects of noise on the neuronal system near a Hopf bifurcation. The second category results from the effects of noise on the period-adding bifurcation between two limit cycles. Although direct application of nonlinear measures to interspike interval series of these firing trains misleadingly implies chaotic properties, definition of eigen events based on more appropriate judgments of the underlying dynamics leads to accurate identifications of the stochastic properties.

Efficient Time Series Clustering and Its Application to Social Network Mining

2014 ◽  
Vol 23 (2) ◽  
pp. 213-229 ◽  
Author(s):  
Cangqi Zhou ◽  
Qianchuan Zhao
Keyword(s):  
Time Series ◽  
Social Network ◽  
Information Diffusion ◽  
Time Series Data ◽  
Online Social Network ◽  
Dissimilarity Measure ◽  
Series Data ◽  
Formation Mechanisms ◽  
Network Analyses ◽  
Definition Of

AbstractMining time series data is of great significance in various areas. To efficiently find representative patterns in these data, this article focuses on the definition of a valid dissimilarity measure and the acceleration of partitioning clustering, a common group of techniques used to discover typical shapes of time series. Dissimilarity measure is a crucial component in clustering. It is required, by some particular applications, to be invariant to specific transformations. The rationale for using the angle between two time series to define a dissimilarity is analyzed. Moreover, our proposed measure satisfies the triangle inequality with specific restrictions. This property can be employed to accelerate clustering. An integrated algorithm is proposed. The experiments show that angle-based dissimilarity captures the essence of time series patterns that are invariant to amplitude scaling. In addition, the accelerated algorithm outperforms the standard one as redundancies are pruned. Our approach has been applied to discover typical patterns of information diffusion in an online social network. Analyses revealed the formation mechanisms of different patterns.

Distributed data structure templates for data-intensive remote sensing applications

2012 ◽  
Vol 25 (12) ◽  
pp. 1784-1797 ◽  
Author(s):  
Yan Ma ◽  
Lizhe Wang ◽  
Dingsheng Liu ◽  
Tao Yuan ◽  
Peng Liu ◽  
...  
Keyword(s):  
Remote Sensing ◽  
Data Structure ◽  
Distributed Data ◽  
Data Intensive ◽  
Sensing Applications ◽  
Remote Sensing Applications

An Algorithm to Slice 3-D Shapes for Reconstruction in Prototyping Systems

1991 ◽  
Author(s):  
K. L. Chalasani ◽  
B. Grogan ◽  
A. Bagchi ◽  
C. C. Jara-Almonte ◽  
A. A. Ogale ◽  
...  
Keyword(s):  
Data Structure ◽  
Rapid Prototyping ◽  
Surface Finish ◽  
Cyclic Order ◽  
Contour Tracing ◽  
Building Process ◽  
Dense Grid ◽  
A Chain ◽  
Definition Of

Abstract Rapid Prototyping (RP) processes reduce the time consumed in the manufacture of a prototype by producing parts directly from a CAD representation, without tooling. The StereoLithography Apparatus (SLA), and most other recent RP processes build a 3-D object from 2.5-D layers. Slicing is the process of defining layers to be built by the system. In this paper a framework is proposed for the development of algorithms for the representation and definition of layers for use in the SLA, with a view to determine if the slicing algorithms will affect surface finish in any significant manner. Currently, it is not possible to automatically vary slice thicknesses within the same object, using the existent algorithm. Also, it would be useful to use a dense grid for hatching or skin filling any given layer, or to change the hatch-pattern if desired. In addition, simulation of the layered building process would be helpful, so that the user can prespecify parameters that need to be varied during the process. The proposed framework incorporates these and other features. Two approaches for determining contours on each slice are suggested and their implementation is discussed. In the first, the layers are defined by the intersections of a plane with the surfaces defining the object. The plane is moved up from the base of the object as it is being built in increments. All intersections found are stored in a data structure, and sorted in head to tail fashion to define a contour for all closed areas on a layer. The second approach uses a scanline-type search to look for an intersection that will trigger a contour-tracing procedure. The contour-tracer is invoked whenever an unused edge is found in the search. This saves storage and sorting times, because the contour is determined as a chain of edges, in cyclic order. It is envisaged that results of this work on the SLA can be applied to other RP processes entailing layered building.

scholarly journals The Gender Outcomes International Group: to Further Well-being Development (Going-fwd) Methodology on Identification and Inclusion of Gender Factors in Retrospective Cohort Studies

2020 ◽  
Author(s):  
Valeria Raparelli Raparelli ◽  
Colleen M. Norris ◽  
Uri Bender ◽  
Maria Trinidad Herrero ◽  
Alexandra Kautzky-Willer ◽  
...  
Keyword(s):  
Data Structure ◽  
Meta Analysis ◽  
Synthetic Data ◽  
Well Being ◽  
Pooled Analysis ◽  
Research Network ◽  
Local Analysis ◽  
Related Factors ◽  
Individual Level ◽  
Definition Of

Abstract Background: Gender refers to the socially constructed roles, behaviors, expressions, and identities of girls, women, boys, men, and gender diverse people. It influences self-perception, individual’s actions and interactions, as well as the distribution of power and resources in society. Gender-related factors are seldom assessed as determinants of health outcomes, despite their powerful contribution.Methods: Investigators of the GOING-FWD project developed a standard methodology applicable for observational studies to retrospectively identify gender-related factors to assess their relationship to outcomes and applied this method to selected cohorts of non-communicable chronic diseases from Austria, Canada, Spain, Sweden.Results: The following multistep process was applied. Step 1 (Identification of Gender-related Variables): Based on the gender framework of the Women Health Research Network (i.e. gender identity, role, relations, and institutionalized gender), and available literature for a certain disease, an optimal “wish-list” of gender-related variables/factors was created and discussed by experts. Step 2 (Definition of Outcomes): each of the cohort data dictionaries were screened for clinical and patient relevant outcomes, using the ICHOM framework. Step 3 (Building of Feasible Final List): A cross-validation between gender-related and outcome variables available per database and the “wish-list” was performed. Step 4 (Retrospective Data Harmonization): The harmonization potential of variables was evaluated. Step 5 (Definition of Data Structure and Analysis): Depending on the database data structure, the following analytic strategies were identified: (1) local analysis of data not transferable followed by a meta-analysis combining study-level estimates; (2) centrally performed federated analysis of anonymized data, with the individual-level participant data remaining on local servers; (3) synthesizing the data locally and performing a pooled analysis on the synthetic data; and (4) central analysis of pooled transferable data.Conclusion: The application of the GOING-FWD systematic multistep approach can help guide investigators to analyze gender and its impact on outcomes in previously collected data.

scholarly journals Determination of the Starting Point in Time Series for Trend Detection Based on Overlapping Trend

2016 ◽  
Vol 16 (6) ◽  
pp. 98-110
Author(s):  
Gao Xuedong ◽  
Gu Kan
Keyword(s):  
Time Series ◽  
Piecewise Linear ◽  
Negative Influence ◽  
Trend Detection ◽  
Computational Accuracy ◽  
Starting Point ◽  
Time Series Studies ◽  
Definition Of ◽  
Stage Characteristic

Abstract The traditional time series studies consider the time series as a whole while carrying on the trend detection; therefore not enough attention is paid to the stage characteristic. On the other hand, the piecewise linear fitting type methods for trend detection are lacking consideration of the possibility that the same node belongs to multiple trends. The above two methods are affected by the start position of the sequence. In this paper, the concept of overlapping trend is proposed, and the definition of milestone nodes is given on its base; these way not only the recognition of overlapping trend is realized, but also the negative influence of the starting point of sequence is effectively reduced. The experimental results show that the computational accuracy is not affected by the improved algorithm and the time cost is greatly reduced when dealing with the processing tasks on dynamic growing data sequence.

ANALYSIS OF SPACECRAFT TELEMETRY INFORMATION USING THE KNOWLEDGE BASE, REPLENISHED DURING THEIR OPERATION

2021 ◽  
pp. 12-17
Author(s):  
S. V. Soloviev
Keyword(s):  
Time Series ◽  
Flight Control ◽  
Control Process ◽  
State Control ◽  
Mathematical Apparatus ◽  
Analysis Algorithm ◽  
Intelligent Analysis ◽  
Flight Controls ◽  
Basic Concepts ◽  
Definition Of

The method for intellectualizing the analysis of telemetric information from spacecraft arriving at ground-based flight controls is discusses. The features of state control during the spacecraft operation are formulated. The basic concepts, terms and basic properties of time series are presented, the definition of the physical meaning of the characteristic quantities for the spacecraft flight control process is given. The use of the mathematical apparatus for the analysis of time radars is substantiated in solving problems of telemetry support in the process of controlling the flight of spacecraft. A mathematical apparatus for analyzing time series is proposed to identify the actual trend. An approach to solving the problem of predicting the state of a spacecraft based on a comparative version is presented. Requirements for the intelligent analysis algorithm are presented and an integrated algorithm is proposed, a method based on time series.

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