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    Application of Hierarchical Bayesian Model in Ophtalmological Study
    (Springer, 2019)
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    Ljubic, Antonela
    The problems with statistical results based on p-values, together with multiple comparisons have been criticized often in the literature. Many authors argue that this way of reporting scientific research creates unreliable results. This issue is especially important in the era of Big Data, when many tests are done on the same data sets, which are often openly available. A way to overcome these problems is offered by Bayesian analysis. In our previous research we have used traditional statistical approach to conduct multiple hypothesis tests on our data in ophtalmological study. The goal of this paper is to apply the hierarchical Poisson exponential model on the data and test the dependence of congenital heart disease and Brusfield spots. We give detailed description of the model, analyze the generated Markov chains and the posterior distributions for the simulated parameters and discuss the results from Bayesian perspective. The results are original and have not been published yet.
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    General decay stability analysis of coupled systems of stochastic neural networks
    (2019)
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    This paper covers the topic of the pth moment (p ≥ 2) stability of coupled systems of stochastic Cohen-Grossberg neural networks with time delays, impulses and Markovian switching. This model generalises many models in the literature and to the best of our knowledge has not been analyzed before. The methods are based on results from graph theory, Lyapunov operator, Dini derivative and some known inequality techniques. Additionally, we consider the stability with respect to a general decay function which includes exponential, but also more general lower rate decay functions as the polynomial and the logarithmic ones. This fact gives us the opportunity to study general decay stability, even when the exponential one cannot be discussed. The presented theoretical results are supported by a numerical example.
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    Ophthalmic manifestations in children and young adults with Down syndrome and congenital heart defects
    (Informa Healthcare, USA, 2015)
    Ljubic, Antonela
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    Tesic, Milorad
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    Stankovic, Branislav
    Purpose: To investigate whether different types of ocular manifestations are associated with congenital heart disease (CHD) in a large Caucasian population of children and young adults with Down syndrome (DS). Methods: Population-based, case-control study which included 185 subjects with DS (mean age 13.2 ± 7.9 years), who reported presence or absence of CHD; DS with CHD group (51 subjects, mean age 10.6 ± 5.6 years) and DS without CHD (134 subjects, mean age 14.2 ± 8.4 years). Results: In our sample with DS and CHD, strabismus was found in 15 subjects (29.4%), nystagmus in 1 (2.0%), epiblepharon in 21 (41.2%) and Brushfield spots in 15 (31.3%). In the DS without CHD group, strabismus was found in 38 participants (28.4%), nystagmus in 13 (9.7%), epiblepharon in 31 (23.5%) and Brushfield spots in 21 (16.0%). Only the variables epiblepharon and presence of Brushfield spots differed significantly between the two groups (p = 0.02 and p = 0.03, respectively). Hyperopia was present in 26 participants (53.1%) in the DS with CHD group, and in 65 (57.0%) in the DS without CHD group. Oblique astigmatism was present in 25 (52.1%) in the DS with CHD group and in 61 (53.5%) in the DS without CHD group. Conclusions: Frequencies of DS participants presenting with strabismus, nystagmus, hyperopia and oblique astigmatism were not statistically different between those with CHD and those without CHD in this sample. Further studies are needed to confirm if there are associations between the presence of Brushfield spots or epiblepharon and CHD in patients with DS.
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    Digital Shift: Assessment of Mental States Through Passive Mobile Sensing
    (Springer International Publishing, 2022)
    Krajchevska, Evgenija
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    Petreska, Nina
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    Handjiski, Ognen
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    Andovska, Sandra
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    General decay stability analysis of impulsive neural networks with mixed time delays
    (Elsevier, 2014)
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    Jankovic, Svetlana
    To the best of our knowledge, there are only few results on general decay stability applied to stochastic neural networks. In the paper, we study both the pth moment (p>=2) and the almost sure stability on a general decay rate for impulsive stochastic Cohen–Grossberg neural networks with mixed time delays. The presented theory allows us to study the pth moment stability even if the exponential stability cannot be valid. Some examples are given to support and illustrate the theory.
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    Graph theoretical approach for construction of Lyapunov function for a coupled stochastic neural network
    (2017)
    In this paper, we describe a new model of coupled stochastic neural network given by a system of stochastic functional differential equations (SFDE’s) and give a way for construction of a Lyapunov function of the system. The considered coupled system is in fact a large system of SFDEs driven by n-dimensional Brownian motion, with impulses and Markovian switching. This complex system consists of large number of interconnected, mutually interacting neural networks with their own dynamics. The considered model is more complex than the ones presented in the literature and thus it is more difficult to analyze its stability properties. We take an approach from the graph theory which will give us an elegant way to construct the Lyapunov function. The result is important since the function can be effectively used to analyze the stability properties of the coupled system.
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    Synchronisation of coupled Neural networks
    (2019)
    Jovanovski, Petar
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    In this paper we discuss the problem of synchronization of neural networks and present it on the Izhikevich model of spiky neurons and define it on the Cohen-Grossberg model of coupled neural network. We simulate the models, discuss which parameteres influence the synchronization and refer to different results from the literature.
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    On a general decay stability of stochastic Cohen–Grossberg neural networks with time-varying delays
    (Elsevier, 2012)
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    Jankovic, Svetlana
    To the best of our knowledge, there are only few results on general decay stability applied to stochastic neural networks. For stochastic Cohen–Grossberg neural networks with time-varying delays, we study in the present paper both the pth moment and almost sure stability on a general decay rate and partly generalize and improve some known results referring to the exponential stability. We also extend the usual notion on a general decay function, which allows us to study both the pth moment and almost sure stability even if the exponential stability cannot be shown. Some examples are presented to support and illustrate the theory.