scholarly journals Asymptotics of the number of 2-threshold functions

2021 ◽  
pp. 104742
Author(s):  
Elena Zamaraeva ◽  
Joviša Žunić
Keyword(s):  
Threshold Functions

scholarly journals Hybrid Model for Time Series of Complex Structure with ARIMA Components

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1122
Author(s):  
Oksana Mandrikova ◽  
Nadezhda Fetisova ◽  
Yuriy Polozov
Keyword(s):  
Neural Network ◽  
Time Series ◽  
Hybrid Model ◽  
Complex Structure ◽  
Arima Model ◽  
Ionospheric Parameter ◽  
Arima Models ◽  
Complicated Structure ◽  
Threshold Functions ◽  
Anomalous Component

A hybrid model for the time series of complex structure (HMTS) was proposed. It is based on the combination of function expansions in a wavelet series with ARIMA models. HMTS has regular and anomalous components. The time series components, obtained after expansion, have a simpler structure that makes it possible to identify the ARIMA model if the components are stationary. This allows us to obtain a more accurate ARIMA model for a time series of complicated structure and to extend the area for application. To identify the HMTS anomalous component, threshold functions are applied. This paper describes a technique to identify HMTS and proposes operations to detect anomalies. With the example of an ionospheric parameter time series, we show the HMTS efficiency, describe the results and their application in detecting ionospheric anomalies. The HMTS was compared with the nonlinear autoregression neural network NARX, which confirmed HMTS efficiency.

scholarly journals The Coupling Method for Inhomogeneous Random Intersection Graphs.

10.37236/5186 ◽  
2017 ◽  
Vol 24 (2) ◽  
Author(s):  
Katarzyna Rybarczyk
Keyword(s):  
Coupling Method ◽  
Intersection Graphs ◽  
New Approach ◽  
Threshold Functions ◽  
Wide Family

We present new results concerning threshold functions for a wide family of random intersection graphs. To this end we improve and generalize  the coupling method introduced for random intersection graphs so that it may be used for a wider range of parameters. Using the new approach we are able to tighten the best known results concerning random intersection graphs and establish threshold functions for some monotone properties of inhomogeneous random intersection graphs. Considered properties are: $k$-connectivity, matching containment and hamiltonicity.

scholarly journals Sharp Threshold Functions for Random Intersection Graphs via a Coupling Method

10.37236/523 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Katarzyna Rybarczyk
Keyword(s):  
Perfect Matching ◽  
Hamilton Cycle ◽  
Coupling Method ◽  
New Method ◽  
Intersection Graphs ◽  
Sharp Threshold ◽  
Threshold Functions

We present a new method which enables us to find threshold functions for many properties in random intersection graphs. This method is used to establish sharp threshold functions in random intersection graphs for $k$–connectivity, perfect matching containment and Hamilton cycle containment.

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