Browsing by Author "Borisenok, Sergey"

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Citation - WoS: 16
Citation - Scopus: 20
Parameter Investigation of Topological Data Analysis for EEG Signals
(Elsevier Sci Ltd, 2021) Altindis, Fatih; Yilmaz, Bulent; Borisenok, Sergey; Icoz, Kutay
Topological data analysis (TDA) methods have become appealing in EEG signal processing, because they may help the scientists explore new features of complex and large amount of data by simplifying the process from a geometrical perspective. Time delay embedding is a common approach to embed EEG signals into the state space. Parameters of this embedding method are variable and the structure of the state space can be entirely different depending on their selection. Additionally, extracted persistent homologies of the state spaces depend on filtration level and the number of points used. In this study, we showed how to adapt false nearest neighbor (FNN) test to find out the suitable/optimal time embedding parameters (i.e., time delay and embedding dimension) for EEG signals, and compared their effects on different types of artefacts and motor intention waves that are commonly used in brain-computer interfaces. We extracted and compared persistent homologies of state spaces that were reconstructed with four different sets of parameters. Later, the effect of filtration level on extracted persistent homologies was compared, and statistical significance levels were computed between leftand right-hand movement imaginations. Finally, computational cost of the discussed methods was found, and the adaptability of this method to a real-time application was evaluated. We demonstrated that the discussed parameters of the TDA approach were highly crucial to extract true topological features of the EEG signals, and the adapted testing approaches depicted the applicability of this approach on real-time analysis of EEG signals.
Target Attractor Formed via Fractional Feedback Control
(Yildiz Technical Univ, 2021) Borisenok, Sergey
We discuss here the stabilization problem for an ordinary differential equation (ODE) dynamical model. To make such a control, one can form a Kolesnikov's subset attracting the phase trajectories to its neighborhood in the phase space via defining the appropriate feedback signal. Kolesnikov's target attractor algorithm provides the exponential convergence, but at the same time it demands the permanent power supply pumping the energy to the system even if the control goal is achieved. To decrease the power cost of Kolesnikov's control, we re-formulate the feedback in the form of Caputo's fractional derivative. In this case the solution to the ODE together with the feedback control signal could be found with the Rida-Arafa method based on the generalized Mittag-Leffler function. We prove that for the certain constraints over the initial condition and the target stabilization level, the integer-dimensional Kolesnikov algorithm can be replaced with the fractional target attractor feedback to provide the minimal power cost.
Control of Collective Bursting in Small Hodgkinhuxley Neuron Clusters
(2018) Borisenok, Sergey; Catmabacak, Onder; Şenel, Zeynep
The speed gradient-based control algorithm for tracking the membranepotential of Hodgkin-Huxley neurons is applied to their small clusters modeling thebasic features of an epileptiform dynamics. One of the neurons plays a role of controlelement detecting the temporal hyper-synchronization among its network companionsand switching their bursting behavior to resting. The ‘toy’ model proposed in thepaper can serve as an algorithmic basement for developing special control elements atthe scale of one or few cells that may work autonomously and are able to detect andsuppress epileptic behavior in the networks of real biological neurons.
Citation - WoS: 8
Citation - Scopus: 13
Energy Control in a Quantum Oscillator Using Coherent Control and Engineered Environment
(Pergamon-Elsevier Science Ltd, 2022) Pechen, Alexander N.; Borisenok, Sergey; Fradkov, Alexander L.
We develop and analyze a new method for manipulation of energy in a quantum harmonic oscillator using coherent, e.g., electromagnetic, field and incoherent control. Coherent control is typically implemented by shaped laser pulse or tailored electromagnetic field. Incoherent control is implemented by engineered environment, whose mean number of excitations at the frequency of the oscillator is used as a control variable. An approach to coherent and incoherent controls design based on the speed gradient algorithms in general, finite and differential forms is proposed. It is proved that the differential form is able to completely manipulate the energy of the oscillator: an arbitrary energy can be achieved starting from any initial state of the oscillator. The key instrument which allows for complete energy manipulation in this case is the use of the engineered environment. A robustified speed-gradient control algorithm in differential form is also proposed. It is shown that the proposed robustified control algorithm ensures exponential stability of the closed loop system which is preserved for sampled-data control.
Target Attractor Tracking of Relative Phase in Bosonic Josephson Junction
(Amer Inst Physics, 2016) Borisenok, Sergey
The relative phase of Bosonic Josephson junction in the Josephson regime of Bose-Hubbard model is tracked via the target attractor ('synergetic') feedback algorithm with the inter-well coupling parameter presented as a control function. The efficiency of our approach is demonstrated numerically for Gaussian and harmonic types of target phases.
Hodgkin-Huxley Nöronlarının Küçük Populasyonunda Geri Bildirim İzleme için Kontrol Algoritmaları
(Abdullah Gül Üniversitesi, 2018) ŞENEL, ZEYNEP; Şenel, Zeynep; Borisenok, Sergey
Tezin amacı, 4 boyutlu dinamik sistemlerde gerçek biyolojik nöronların ani yükseliş ve fırlama davranışlarının izlenmesi ve modellenmesi için güçlü matematiksel kontrol algoritmaları tasarlamaktır. Bu amaçla 4 boyutlu Hodgkin-Huxley (HH) lineer olmayan diferansiyel denklemleri içeren dinamik sistem tercih edilir. Çünkü HH modeli gerçek nöronlar için gerçekçi bir matematik modeli temsil eder ve analitik olarak kabul edilmiştir. Bir kontrol sinyali olarak uygulanan dış akım, nöronal ağlardaki nöron hücrelerinin uyarılmasını başlatırken, membran eylem potansiyelleri çıkışlardır. HH nöron kümelerindeki kontrol sinyalinin yarattığı akson membran potansiyelinde ani yükseliş ve patlama rejiminin modellenmesi ve kontrol edilmesi için Fradkov'un hız gradyanı (SG) ve Kolesnikov'un hedef çekicisi (TA) geribildirimleri olmak üzere iki tane alternatif kontrol yöntemi kullanılmaktadır. Her iki algoritma da kontrollü HH dinamik nöron sisteminde yüksek verimlilik ve sağlamlık gösterir. Bu çalışma, ağın seçilmiş bir unsuru üzerindeki kontrol ile HH nöron kümelerinin çeşitli konfigürasyonlarında (doğrusal zincir ve halka tipi zincir) rastgele tek ani yükseliş (spike), bir ani yükseliş dizisi (spike train) ve fırlama (burst) formlarının oluşturulmasını sağlamaktadır. Bu çalışmada, geliştirilen algoritmalar küçük bir HH nöron kümesinde epileptik yapıdaki toplu fırlamalara baskılama yapmak için uygulanmıştır. Bu tezin amacı, gerçek nöronların kontrolüne yönelik matematiksel modelleme için yeni kontrol yöntemlerinin geliştirilmesi ve hesaplamalı nörobilimde ve HH nöron ağlarında epileptik yapı veya anormal davranış gibi nöral fonksiyon bozukluklarının tanısı veya tedavisinde etkin bir şekilde kullanılabilmesidir. Anahtar Kelimeler: Hodgkin-Huxley nöronu, hız gradyan metodu, hedef çekicisi geribeslemesi