# Seminars

The Laboratory of Complex Systems Modeling and Control kindly invites you to our climate change seminar, which is held online on Fridays at 14:40-16:00, Moscow time.

If you would like to participate, please contact Viktor Popov.

## 22.09.2023 Dr. A. Durga Devi "Isochronous Nonlinear Oscillators associated with Certain Classes of Lienard type equations"

In this talk, I am going to present a study of Isochronous properties associated with certain classes of Lienard type of equations including linear, quadratic, mixed quadratic linear Lienard type equation and their higher order generalizations which exhibiting Isochronous properties. Then I show a systematic procedure to identify a collective coordinate, which is conjugate to a given Hamiltonian in order to generate isochronous systems. By generalising this procedure for N-coupled systems in terms of omega, I modified Hamiltonians and identified suitable canonically conjugate coordinates such that the resultant form is non-singular and the corresponding Newton's equation of motion is constraint free. Further, a class of N-coupled mixed quadratic linear Lienard type equations can also be identified with the specific class of transformations that possess isochronous properties an studied their integrability properties.

## 11.08.2023 Manish Dev Shrimali "Dynamics under regulated Interaction and Noise"

In this talk, we discuss the dynamics under regulated interaction and noise in nonlinear oscillators. We introduce a time-evolving state-space-dependent interaction among an ensemble of identical coupled oscillators, where individual units are interacting only when the mean state of the system lies within a certain proximity of the phase space. The proposed design of dynamic intermittent interaction facilitates the onset of a plethora of asymptotic states including synchronous states, amplitude death states, oscillation death states, a mixed state, and bistable states. Interestingly due to this occasional interaction, we find that the system shows an abrupt explosive transition from oscillatory to death state. Besides the study on periodic oscillators, we present results for the chaotic oscillators, ecological and neuronal model systems with dynamic interaction.

We also discuss the enhanced synchronization of uncoupled nonlinear oscillators in the presence of regulated noise. The dynamic intermittent noise, which is applied only to a fraction of the state space, restricts the trajectories to evolve within the contraction region for a longer period of time. The basin stability of the synchronized states is found to be significantly enhanced compared to uncontrolled noise. Direction dependent noise also play an important role in synchronization of mobile oscillators. Another important application of intermittent noise is control of multistability. In contrast to the existing methods of unrestricted noise controls resulting predominantly in attractor hopping, space-dependent intermittent noise selectively annihilates undesired attractors to control multistability.

References:

1. Emergent rhythms in coupled nonlinear oscillators due to dynamic interactions, Shiva Dixit, Sayantan Nag Chowdhury, Awadhesh Prasad, Dibakar Ghosh and Manish Dev Shrimali, Chaos: An Interdisciplinary Journal of Nonlinear Science, 31, 011105 (2021).

2. Dynamic interaction induced explosive death, Shiva Dixit, Sayantan Nag Chowdhury, Dibakar Ghosh and Manish Dev Shrimali, Europhysics Letters, 133, 40003 (2021).

3. Enhanced synchronization due to intermittent noise, Emilda Shajan, Paul Asir M, Shiva Dixit, Juergen Kurths, and Manish Dev Shrimali, New Journal of Physics, 23, 112001 (2021)

4. Controlling multistability with intermittent noise, Emilda Shajan, and Manish Dev Shrimali, Chaos, Solitons and Fractals, 160, 112187 (2022).

5. Direction dependent noise-induced synchronization in mobile oscillators, Emilda Shajan, Dibakar Ghosh, Juergen Kurths, Manish Dev Shrimali, Chaos: An Interdisciplinary Journal of Nonlinear Science, 33, 053108 (2023).

## 28.07.2023 Mithun K "Application of GRU-Powered Echo State Networks to Predict the Hopf Bifurcation Dynamics of the FitzHugh-Nagumo Model"

The FitzHugh-Nagumo (FHN) model is a mathematical model used to describe the excitation of neurons. This model is governed by the following set of equations:

𝑣˙ = −𝑣(𝑣 − 𝑎)(𝑣 − 1) − 𝛾𝑤 + 𝐼(𝜔, 𝑡)

𝑤˙ = 𝑏 ( 𝛾𝑣 − 𝑓 𝜔 )

where 𝑣 determines the neuron’s activation and 𝑤 determines the inhibition of the neuron’s action potential. 𝛾 represents the direction of rotation of the oscillation cycle and 𝑎, 𝑏 and 𝑓 are parameters of the system.

As this model is a nonlinear dynamical system, various deep learning approaches are suitable for predicting such systems.Most notably, the Echo State Network (ESN) approach of Reservoir Computing is well-suited for the prediction of nonlinear dynamical systems2,3. While conventional Recurrent Neural Networks (RNNs) are useful for this use case, these networks suffer from the vanishing/exploding gradients problem. Additionally, conventional RNNs have limited information context, which makes it impractical for more complex systems. While Long Short-Term Memory (LSTM) networks implement information gates to regulate the flow of information, it is significantly more complex than a conventional RNN. LSTM networks also cannot handle temporal dependencies after a certain period. For this reason, we use a variant of LSTM, called Gated Recurrent Units (GRU)4, which is used to augment the ESN in order to model the bifurcation dynamics of the neuronal model. The characteristics of Hopf bifurcations in the single neuron variant of the FHN model are identified and studied5. Moreover, by implementing a GRU-powered ESN, we study and predict the oscillation cycles and the Hopf bifurcation delays. Since the identification of outliers and extreme events is of paramount importance in the field of nonlinear dynamics, we also use the ESN to predict the outliers in the Hopf bifurcation delays. In the future, this work includes the cross-examination of our deep learning model by utilizing a physical circuit implementation of the FHN model and testing the accuracy of theESN by using the data from the circuit.

References:

1. W.E. Sherwood, FitzHugh–Nagumo Model. In: Jaeger, D., Jung, R. (eds) Encyclopedia of Computational Neuroscience. Springer, New York, NY (2014).

2. H. Jaeger, The" echo state" approach to analysing and training recurrent neural networks-with an erratum note'. Bonn, Germany: German National Research Center for Information Technology GMD Technical Report. 148 (2001).

3. M. Lukoševičius, A Practical Guide to Applying Echo State Networks. In: Montavon, G., Orr, G.B., Müller, KR. (eds) Neural Networks: Tricks of the Trade. Lecture Notes in Computer Science, vol 7700. Springer, Berlin, Heidelberg (2012).

4. X. Wang, Y. Jin and K. Hao, "A Gated Recurrent Unit based Echo State Network," International Joint Conference on Neural Networks (IJCNN), Glasgow, UK, 2020, pp. 1-7, doi: 10.1109/IJCNN48605.2020.9206786 (2020).

5. V. Varshney, S. Kumarasamy, B. Biswal. et al. Bifurcation delay, travelling waves and chimera-like states in a network of coupled oscillators. Eur. Phys. J. Spec. Top. 229, 2307–2325 (2020).

## 21.07.2023 Awadhesh Prasad "Understanding the short-time synchronization and the phase-slip in unsynchronized region of coupled oscillators"

Synchronization of coupled nonlinear dynamical systems has been studied extensively in previous works [1]. Although many techniques have been developed to understand the synchronized behavior of coupled systems, the unsynchronized domain is left relatively unexplored [2,3]. Notably, one can think of many natural and engineering systems which do not exhibit any synchronized motion. Yet, very few studies have explored this regime of unsynchronized behavior. Therefore, there is a need to develop theories and methods to understand such unsynchronized dynamics of coupled systems.

In this talk, we will demonstrate that the coupled systems may exhibit short-time synchronization in the unsynchronized regime [4]. We will also talk about the phenomenon of phase-slips present in this unsynchronized domain [2,5]. We will then show how both these phenomena, the short-time synchronization [4] and the phase-slips [5], related to the presence of perpetual points [6].

[1] A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization: A Universal Concept in Nonlinear Science(Cambridge University Press, Cambridge, 2001).

[2] Z. Zheng, G. Hu, and B. Hu, Phys. Rev. Lett. 81, 5318 (1998).

[3] D. Pazo, M. A. Zaks, J. Kurths, Chaos 13, 309 (2003).

[4] S. Kumarasamy, D. Dudkowski, A. Prasad, and T. Kapitaniak, Chaos 31, 081102 (2021).

[5] P. B. Gogoi, S. Kumarasamy, A. Prasad, and R. Amaswamy, (2023).

[6] A. Prasad, Int. J. Bifurcation Chaos 25, 1530005 (2015).

## 30.06.2023 Menghui Chen "Machine Learning Prediction on Sunspot"

In this presentation, I will deliver our preliminary results on the sunspot predictions using various machine-learning algorithms to find the best method for the sunspot prediction. I will give a brief introduction about sunspot data and its arrangements and gives the important link for sunspot databases. Moreover, I will describe the simple RNN, LSTM and GRU algorithms and their operational principles. Finally, I will show the results of the sunspot predictions using the above-mentioned algorithms. We have found R-squared, MAE etc through this sunspot data sets.

References:

1. Velasco Herrera, Victor Manuel, Willie Soon, Douglas V. Hoyt, and Judit Muraközy. "Group sunspot numbers: a new reconstruction of sunspot activity variations from historical sunspot records using algorithms from Machine Learning." Solar Physics 297, no. 1 (2022): 8.

2. Herrera, VM Velasco, W. Soon, and D. R. Legates. "Does Machine Learning reconstruct missing sunspots and forecast a new solar minimum?." Advances in Space Research 68, no. 3 (2021): 1485-1501.

3. Nguyen, Trung Thanh, Claire P. Willis, Derek J. Paddon, Sinh Hoa Nguyen, and Hung Son Nguyen. "Learning sunspot classification." Fundamenta Informaticae 72, no. 1-3 (2006): 295-309.

4. Pala, Zeydin, and Ramazan Atici. "Forecasting sunspot time series using deep learning methods." Solar Physics 294, no. 5 (2019): 50.

## 16.06.2023 Dr. Vaibhav Varshney "Emergence of different dynamics in counter-rotating coupled oscillators "

In this talk, we focus on the study of the novel dynamics emerging from coupled conter-rotating oscillators.

First, we will discuss a new scheme which does not disturb any internal parameter of the system and forces the coupled systems to either oscillation death or oscillating state simply by changing the sense of rotation of the augmented system. Next, we will discuss the novel bifurcation delays and chimera-like states in a network of driven FitHugh-Nagumo (FHN) oscillators, where each oscillator can rotate either clockwise or anticlockwise. Slow variation of the time-dependent parameter of FHN oscillator near the bifurcation point leads to a delay in the bifurcation. When the FHN oscillators are coupled via dissimilar variables, then bifurcation delay in the anticlockwise rotating oscillator changes, creating chimera-like structures and also travelling waves at certain coupling strengths.

Finally, we will discuss the emergence of extreme events and their propagation in a network of coupled nonlinear oscillators, where counter-rotating oscillators play the role of malfunctioning agents. We observe that the extreme events occur only in the counter oscillating pair of oscillators through the saddle-node bifurcation. We present a detailed study of the propagation and destruction of the extreme events and show how these events depend on the strength of the coupling.

## 07.04.2023 T. Fonzin Fozin "Analysis of coexisting dynamics and their control in some nonlinear systems"

The phenomenon of multistability has been uncovered in several nonlinear systems throughout this last decade. Although still intriguing and not well understood, intensive efforts are being made by researchers to better understand its mechanism while providing diagnostic techniques so as control one’s. Therefore, this lecture reports both the coexistence various dynamics and their control based on invasive and noninvasive feedback methods for attractor selection some nonlinear systems. Dynamical behaviors are harness through bifurcation diagrams, spectrum of Lyapunov exponents, phase portraits and demarcation regions of initial states. For some systems, the rare phenomenon of the coexistence of hyperchaos and chaos has been uncovered. Feedback control methods are further exploited to annihilate the coexisting phenomenon in some nonlinear systems in case they are undesired. For invasive control approaches, the dynamics of the survived attractor is distorted while non-invasive approaches preserve the intrinsic dynamic of the survived attractor. Our numerical results are confirmed either through PSpice analysis or laboratory measurements.

## 31.03.2023 Chittaranjan Hens "Signal propagation in complex networks"

It is now essential to understand complex networks to comprehend how spreading phenomena occur in various real-world scenarios. For example, a local infection may spread in the entire network within a shorter time scale. In most cases, the characteristic path lengths of the underlying network determine the propagation pattern. In others, however, characteristic path lengths cannot be the sole predicting element to visualize the propagation pattern. In this situation, the spreading phenomena occur more complicated way as the propagation depends not only on the network path lengths but also on the network heterogeneity and underlying oscillatory states of each node.

We here analytically derive the response propagation, obtaining its dependence on the degree distribution, the distance from the perturbation and the intrinsic dynamics of each network. Our results uncover a deep universality in the propagation patterns crossing domains of inquiry, from ecological system to gene regulatory dynamics. More specifically we uncover how disease spread in arbitrary complex networks [1-2]. We aim to comprehend the spread of epidemics (Influenza like disease) in meta-population networks. We also provide the suitable intervention strategy to reduce the severity disease based on the human movements [2].

References:

1. Spatiotemporal signal propagation in complex networks, Chittaranjan Hens, Uzi Harush, Simi Haber, Reuven Cohen, Baruch Barzel. Nature Physics, 15, 403–412 (2019).

2. Optimal test-kit based intervention strategy of epidemic spreading in heterogeneous complex networks, Subrata Ghosh, Abhishek Senapati, Joydeb Chattopadhyay, Chittaranjan Hens, D Ghosh. Chaos 31 (7), 071101, (2021).

3. Identifying Influential Pandemic Regions Using Graph Signal Variation, S Darapu, S Ghosh, A Senapati, C Hens, S Nannuru, arXiv:2211.05517,(2022).

4. Emergent stability in complex network dynamics, Chandrakala Meena, Chittaranjan Hens, Suman Acharyya, Simcha Haber, Stefano Boccaletti, & Baruch Barzel. Nature Physics Revision submitted (2023).

## 17.03.2023 Dibakar Ghosh "Dynamics of swarmalators"

Swarmalators are entities with the simultaneous presence of swarming and synchronization that reveal emergent collective behavior due to the fascinating bidirectional interplay between phase and spatial dynamics. Although different coupling topologies have already been considered, recently we introduce time-varying competitive phase interaction among swarmalators where the underlying connectivity for attractive and repulsive coupling varies depending on the vision (sensing) radius. In this talk, we will discuss some systematic approaches and review the collective dynamics of swarmalators analytically and/or numerically. Some of the states (the phase wave and split phase wave) resemble those seen in systems of Janus matchsticks or Japanese tree frogs. The others (such as the sync and unsteady states) may be observable in systems of vinegar eels, electrorotated Quincke rollers, or other swarmalators moving in disordered environments. Long-term states of position aggregation and phase synchronization will be discussed with some future problems.

References:

1 Swarmalators under competitive time-varying phase interactions. Gourab K Sar, Sayantan Nag Chowdhury, Matjaz Perc, and Dibakar Ghosh. New Journal of Physics 24, 043004 (2022)

2 Dynamics of swarmalators: A pedagogical review. Gourab K Sar, and Dibakar Ghosh. Europhysics, Letters 139, 53001 (2022)

3 Pinning in a system of swarmalators. Gourab K Sar, Dibakar Ghosh, and Kevin O’Keeffe. arXiv:2211.02353 (Accepted for publication in Phys. Rev. E 2023)

## 03.03.2023 Dr. R.Gopal "Collective dynamical states: Reviews and Perspectives"

Understanding the various collective dynamical states in the networks of coupled nonlinear oscillators is one of the significant challenges in dynamic systems theory. Considering an array of nonlinear oscillators under different couplings, for example, global, nonlocal or local, one is interested to know the underlying collective dynamical states. The systems can include a variety of physically exciting situations, such as neuronal systems, Josephson-junction arrays, and chemical and mechanical oscillators.

In this talk, I will bring out the existence of various collective states, including synchronized, desynchronized, chimera (partially coherent/incoherent) states, and so on, in typical nonlinear systems. More interestingly, I will also discuss the chimera-like states in a small-world network of oscillators by adding randomly switching nonlocal links.

References:

1. Y. Kuramoto and D. Battogtokh, Nonlinear. Phen. Complex. Sys. 5, 380 (2002).

2. D. M. Abrams and S. H. Strogatz, Phys. Rev. Lett. 93,174102 (2004)

3. G. C. Sethia and A. Sen, Phys. Rev. Lett. 112, 114101 (2014)

4. R. Gopal, V. K.Chandrasekar, A. Venkatesan and M. Lakshmanan, Phys. Rev. E 89, 052914 (2014).

5. V. K.Chandrasekar, R. Gopal, A. Venkatesan and M. Lakshmanan, Phys. Rev. E 90, 062913 (2014)

6. R. Gopal, V. K.Chandrasekar, D. V. Senthilkumar, A. Venkatesan and M. Lakshmanan, Phys. Rev. E 91, 062916 (2015).

7. P. Chandran, R. Gopal, V. K. Chandrasekar and N. Athavan, Chaos 29, 053125 (2019).

8. P. Chandran, R. Gopal, V. K. Chandrasekar and N. Athavan, Chaos 30, 063106 (2020).

## 17.02.2023 Dr. Premraj Durairaj "Emergence of Extreme events in a Quasiperiodic Oscillator"

Extreme events are unusual and rare large-amplitude fluctuations that occur can unexpectedly in nonlinear dynamical systems. Events above the extreme event threshold of the probability distribution of a nonlinear process characterize extreme events. Different mechanisms for the generation of extreme events and their prediction measures have been reported in the literature. Based on the properties of extreme events, such as rare in the frequency of occurrence and extreme in amplitude, various studies have shown that extreme events are both linear and nonlinear in nature. Interestingly, in this work, we report on a special class of extreme events which are nonchaotic and nonperiodic. These nonchaotic extreme events appear in between the quasi-periodic and chaotic dynamics of the system. We report the existence of such extreme events with various statistical measures and characterization techniques.

References:

1. Premraj Durairaj, Sathiyadevi Kanagaraj, Suresh Kumarasamy, and Karthikeyan Rajagopal, “Emergence of extreme events in a quasiperiodic oscillator”, Phys. Rev. E, (2023).

2. Premraj Durairaj, Suresh, K., Pawar, S. A., Kabiraj, L., Prasad, A., & Sujith, R. I. Dragon-king extreme events as precursors for catastrophic transition. Europhysics Letters, 134(3), 34006, (2021).

3. Chowdhury SN, Ray A, Dana SK, Ghosh D. Extreme events in dynamical systems and random walkers: a review. Phys Rep. 966:1–52 (2022) .

4. Seneviratne S, Nicholls N, Easterling D, Goodess C, Kanae S, Kossin J, et al. Changes in Climate Extremes and Their Impacts on the Natural Physical Environment. (2012).

## 03.02.2023 Dr. R. Arun "Spin Torque Nano Oscillator: As a candidate for microwave oscillations"

Spin torque nano oscillator (STNO) is a nanoscaled device which can be used to generate microwave oscillations by applying current and/or magnetic field. It consists of two ferromagnetic layers seperated by a nonmagnetic conductive or insulative layer. Among two ferromagnetic layers one is relatively thick and called pinned layer in which the magnetization is fixed or polarized in a particular direction. Another ferromagnetic layer is thin and called free layer in which the magnetization is allowed to change its direction or oscillate by means of incoming polarized electrons due to pinned layer and externally applied magnetic field. In the spin torque nano oscillator the persistent oscilaltions of the free layer’s magnetization is achieved by the transfer of spin angular momentum between the incoming spin polarized electrons and the local magnetic moments in the free layer. The oscillations in the magnetization of the free layer is converted into voltage oscillations due to magnetoresistive effect. In this talk, I will introduce about the STNO and discuss the different approaches to enhance the frequency, power and Q-factor of the STNO by solving Landau-Lifshitz-Gilbert-Slonczewski equation.

References:

[1] Effect of interlayer exchange coupling in spin-torque nano oscillator, R. Arun, R. Gopal, V.K.Chandrasekar and M. Lakshmanan, J. Appl. Phys. 132, 094301 (2022).

[2] Spin torque oscillations triggered by in-plane field, R. Arun, R. Gopal, V.K. Chandrasekar and M. Lakshmanan, J. Phys.: Condens. Matter 34, 125803 (2022).

[3] Large Amplitude Spin-Hall Oscillations due to Field-like Torque, R. Arun, R. Gopal, V.K. Chandrasekar and M. Lakshmanan, J. Phys.: Condens. Matter 33, 165402 (2021).

[4] Enhancement of frequency by tuning in-plane magnetic field in spin-torque oscillator, R. Arun, R. Gopal, V.K. Chandrasekar and M. Lakshmanan, J. Magn. Magn. Mater. 532, 167989 (2021).

[5] Frequency enhancement and power tunability in tilted polarizer spin-torque nano oscillator, R. Arun, R. Gopal, V.K. Chandrasekar and M. Lakshmanan, J. Appl. Phys. 127, 153903 (2020).

[6] Influence of field-like torque in synchronization of spin torque oscillators, R. Arun, R. Gopal, V. K. Chandrasekar and M. Lakshmanan, IEEE Transaction on Magnetics 56(9), 1400310 (2020).

## 19.01.2023 Dr. Sanjay Dutta "Decision Making Under Uncertainty"

Uncertainty governs everything in the universe, from small particle to big system. The process of unwrapping the uncertainty is a most important part in such problems. The uncertainty such as fuzziness, randomness, multi-choice and deep uncertainty are the growing areas in Operations Research. So, in this talk, a gentle introduction to the above-mentioned uncertainties are discussed.

Fuzzy theory deals on how to handle the impreciseness within the data, language, and processes, where one knows the data but not clearly. On the other-hand, randomness can be in the data or process where the decision- makers cannot make a precise decision due to the nature of the data or process. Multi-choice is process, which an individual does every time when it comes to make a best selection from the given alternatives. Lastly, deep uncertainty exists beyond the level of the previous three uncertainties, where the decision-makers cannot agree on the future states of the problems or do not have any information how the future will unfold.

References

1. Decision Making under Deep Uncertainty: From Theory to Practice (Springer International Publishing: New York, 2019).

2. https://www.rand.org/topics/robust-decision-making.html

3. Developing Robust Strategies for Climate Change and Other Risks: A Water Utility Framework, RAND Corporation, 2014.

4. Dutta, S., and Ramya V. Nair. "Multi-choice Programming with Benefits Using Kriging Interpolation Method." Proceedings of the International Conference on Computational Intelligence and Sustainable Technologies. Springer, Singapore, 2022.

5. Dutta, Sanjay, et al. "Fuzzy stochastic price scenario based portfolio selection and its application to BSE using genetic algorithm." Applied Soft Computing 62 (2018): 867-891.

6. Dutta, S., et al. "Fuzzy stochastic genetic algorithm for obtaining optimum crops pattern and water balance in a farm." Water Resources Management 30.12 (2016): 4097-4123.

## 22.12.2022 Dr J. B. Sudharsan "Optical solitons management in a harmonic Gaussian PT-symmetric potential with space dependent higher order nonlinearities"

The existence of stable optical soliton in collisionally inhomogeneous cubic, quintic and septimal nonlinear Schrödinger equation with the presence of a PT -symmetric harmonic-Gaussian potential with unbounded gain-loss distributions is studied. For the various strengths of PT -symmetric potential, stable optical soliton for a particular range of propagation constant is obtained. The intensity distributions and the conserved power of the soliton in the stable regime are managed by collisional inhomogeneity strength. The intensity and the conserved power of the optical soliton get saturated when the strength of collisional inhomogeneity exceeds a critical value.

## 10.11.2022 Dr. D. Aravinthan "Magnetization Switching in Pentalayer Nanopillar Alloys with Oscillatory Interlayer Exchange Coupling"

Recently spin transfer magnetization switching in nanopillar device has been a continuously growing topic, because of its potential applications in ultrahigh density recording media, magnetic random access memories, read/write heads, microwave frequency generators, logic gates and sensors. The interlayer coupling between the ferromagnetic layers in the nanopillar devices control the manipulation of local magnetization assisted by spin-polarised currents. In this talk, I will present details about magnetization switching, various methods to achieve switching and the important interlayer couplings so far reported. I will discuss in detail about the influence of oscillatory interlayer exchange coupling aka Ruderman-Kittel-Kasyua-Yosida (RKKY) coupling on STT-assisted magnetization switching in a pentalayer nanaopillar structure.

References:

1. D. Aravinthan and P. Sabareesan, Eur. Phys. J. Plus 137, 994 (2022).

2. D. Aravinthan et al., Appl. Phys. A 128, 910 (2022).

3. D. Aravinthan et al., J. Supercond. Nov. Magn. 35, 2831 (2022).

4. P. Ogrodnik et al., ACS Appl. Mater. Interfaces 13, 47019 (2021)

5. B. Dieny et al., Nat. Electron. 3, 446 (2020)

6. J.Z. Sun, Physical principles of spin torque, in Handbook of Spintronics. (Eds.) by Y. Xu, D.D. Awschalom, J. Nitta (Springer, Netherlands, Dordrecht, 2016), pp. 1339–1385.

## 27.10.2022 R. Mahendran "Impacts of Global Climate Change - 2022: Eagle's Eye View"

Climate change has resulted from an increase in global temperatures due to enhanced emissions of anthropogenic greenhouse gases (GHGs). Statistically, climate change (CC) represents the average weather over a period of 30 years. The main anthropogenic sources of GAGs emissions are fossil fuel burning, from chemical industries, and deforestation. Since 1900, the GHG emissions have increased the global temperature by 1°C. By 2050, it is estimated that the Earth's temperature will increase drastically, if the emission of GHGs continue at the current rate. The CC cause many extreme weather events, such as sea level rise, floods, droughts, desertification, melting of glaciers, forest fires, loss of biodiversity, ocean acidification, and shrinking Arctic ice [1]. The Intergovernmental Panel on Climate Change (IPCC) report (Climate Change 2022: Impacts, Adaptation and Vulnerability) warned that the human-induced CC is the root cause for extensive interruption in nature and affect the livelihood of billions of people around the world [2]. Specifically, the CC affects our physical and mental health, interruption to family functioning, induce food shortages, and increase intergroup conflict. Hence, in this talk, I am going to emphasize the current and future impacts of CC worldwide.

References

1. Lyon et al. Climate change research and action must look beyond 2100. Global change biology. 28 (2022) 349-361.

2. J. Tollefson, IPCC climate report: Earth is warmer than it’s been in 125,000 years, Nature. 596 (2021) 171.

## 13.10.2022 K. Sakkaravarthi "Management of Localized Waves in Inhomogeneous Media"

The dynamics of nonlinear systems feature several exciting phenomena that find multifaceted applications in different fields of science, engineering, and technology. Various nonlinear coherent structures like bright-bright, bright-dark, and dark-dark type solitons/solitary waves, Akhmediev & Ma breathers, rogue waves, etc. associated with such scalar and vector models are of considerable physical significance. The characteristics of nonlinear waves are explored through different analytic/numeric investigations and experimental realization.

In this talk, we will discuss the impact of nonlinearity modulation in the dynamics of localized waves arising in inhomogeneous Kerr-type optical media. For this purpose, we consider a coherently coupled nonlinear Schrödinger equation consisting of varying dispersion, incoherent (self-phase and cross-phase modulations), and coherent (four-wave mixing) nonlinearities. We obtain explicit solutions by designing an appropriate similarity transformation and explore the dynamics of stable bright solitons along with bright-dark and bright-bright type Akhmediev-Ma breathers and rogue waves possessing different localized coherent structures. We study their manipulation mechanism for appropriately chosen forms of modulated nonlinearities by incorporating elliptic functions. We demonstrate phenomena such as soliton amplification, compression, tunnelling through a localized barrier, superposition/interaction of breather-soliton, transition from soliton/rogue wave to breather, and existence on modulated background with significant characteristics. The present results will be helpful for a better understanding of the dynamics of nonlinear waves in various inhomogeneous media.

## 16.06.2022 Dr. Jagadeesan Palanivel "Fractional order complex systems"

In my talk, I will discuss about fractional order complex systems with a focus on my research article titled “Chaos in a low dimensional fractional order nonautonomous nonlinear oscillator “. Studies on nonlinear dynamical system and their complex behavior have gained a great research attraction in recent days. Fractional order differential equations describe nonlinear systems more precisely compared to its integer order counterpart. In the above mentioned work, the dynamics of a fractional order forced series LCR circuit is studied numerically and experimentally. The circuit implementation of oscillator was done using fractional frequency domain approximation 1/s^{q}. For a set of system parameters, the forced series LCR circuit exhibited period doubling route to chaos. We have taken both derivative of voltage and current as fractional derivatives. When the fractional order of the derivatives is decreased, the system exhibited interesting dynamical behavior. The chaotic regime in the system decreased, as the fractional order corresponding to the voltage in the circuit is reduced from 1. But in the case of current, when the order is decreased, chaotic regime in the system increased initially and after a certain value of the fractional order, the chaotic regime decreased. It is interesting to note that the distance between the two bifurcation points has followed a fourth order polynomial with different coefficients. Also we found that lowest order at which the nonautonomous fractional order nonlinear system exhibited chaotic behavior and the lowest order is 2.1. The lowest order has also been confirmed with the help of eigen values. The results obtained from the experimental study are compared with numerical simulation and it is found that they match closely with each other.

Describing nonlinear systems with fractional differential equations will allow us to characterize those nonlinear systems in a better way. Fractional derivative representation of extreme events may help us even to identify the precursors of the extreme events. This will have a significant impact on disaster management and medicine.

## 09.06.2022 Dr. Nallappan Gunasekaran "Networked Control Systems and Its Applications"

Network control systems (NCS) consists of sensors, actuators, and controllers whose operations are geographically distributed and coordinated by the exchange of information passed over the communication network. Network control systems, on the other hand, are used for remote control of distributed systems where control loops are closed over communication links or systems that are not co-located. Remote access to industrial robotic systems is one of the application areas where closed-loop robustness and reliability play an important role. Network control systems have the advantages of cost savings, system diagnostics and flexibility, wiring minimization, and relatively easy addition and replacement of individual elements. Efficient data sharing facilitates globally intelligent control decisions using NCS. Due to the communication chain within the control-loop, there are difficult constraints that can affect the stability and performance of the closed-loop. This type of control system considers many issues, such as unknown delays.

The objectives of this NCS are: (a) to design controllers that guarantee stability and stabilization of the system for a desired sampling period; (b) to design observers that guarantee exponential convergence of the estimation error to the origin for a desired sampling period; and (c) given a controller, to find the maximum allowable network-induced delay that guarantees exponential stability of the sampled-data networked control system. Lyapunov-Krasovskii based approaches are used to propose sufficient stability and stabilization conditions for sampled-data networked control systems. Convex relaxation techniques are employed to cast the proposed stability analysis and controller synthesis criteria in terms of linear matrix inequalities that can be solved efficiently.

NCS applications range from large-scale factory automation and plant monitoring to small but complex networks of modern automobiles, locations, and autonomous robot computers. The network control system presents the latest results in the analysis of stability and robustness and new developments related to the fuzzy and optimal control of networked Takagi-Sugeno fuzzy system. With the increasing interest in the industry these days, with numerous methods and approaches for dealing with NCS problems, many methods are still being developed to improve the functionality of closed loops on telecommunications networks. Overall, this area of study will learn about NCS stability and stabilization analysis applicable to control, electrical, computer and mechanical engineering, and computer science.

## 02.06.2022 Dr. R. Vadivel "Neural networks and its application"

The Artificial Neural network (ANN) is a functional imitation of a simplified model of the biological neurons, and its goal is to construct useful computers for real-world problems. ANN and their various generalizations have attracted the attention of the scientific community due to their promising potential for tasks of classification, knowledge acquisition, automatic control, and their ability to solve difficult optimization problems. The key features of ANNs are asynchronous parallel processing, continuous-time dynamics and global interaction of network elements. Moreover, Lyapunov functions are an essential tool in the stability analysis of dynamical systems, both in theory and applications. They provide sufficient conditions for the stability of equilibria. Because of their importance in stability analysis, numerous computational construction methods have been developed within the Engineering, Informatics, and Mathematics community. Finally, regarding the stability analysis some numerical examples are presented in this talk.

## 26.05.2022 Dr. Suresh Kumarasamy "Birth of Strange nonchaotic Attractors Nonlinear Dynamical Systems"

Strange Nonchaotic Attractors (SNAs) are well known to appear in periodic and quasi-periodically forced smooth dynamical systems and autonomous nonsmooth dynamical systems. The SNAs possess a complex geometrical structure, which shows them to be truly fractal in nature. However, they do not have any sensitive dependence on initial conditions, as is seen from the negative maximal Lyapunov exponent. It was identified by Grebogi et al. Following the pioneering work, many researchers have found the existence of SNAs in several physically important systems and have beenclassified the different mechanisms for their occurrence. To mention a few systems such as pulsating star, quasi-periodically forced pendulum, the quantum particles in quasi-periodic potentials, biological oscillators, Duﬃng-type oscillators, velocity-dependent oscillators, electronic circuits, and forced buckled ribbon neon glow-discharge experiment. The presence of SNAs in a wide range of dynamical systems shows the robustness of this phenomenon. The talk will deal with strange nonchaotic attractors in different dynamical systems and demonstrate their experimental observations and numerical techniques.

## 11.11.2021 S. Srinivasan "Existence of Extreme event: Understanding the mechanism via simple complex system"

In this presentation, I will start to explain my research background and my research motivations. Then, I will present my recently published article entitled “extreme event in a simple dynamical system”. The existence of extreme events in the well known Bonhoeffer-van der Pol (BVP) oscillator under the excitation of a periodically forced voltage is studied. From this study, I will explain the detection and characterization of such rare event. Our investigations involve both laboratory experiments and numerical simulations. To the best of our knowledge, we believe that it is for the first time that the occurrence of extreme event has been reported using both real time experimental and numerical studies on this forced BVP system.

For a long time, the occurrence of extreme event (EE) (sudden increase or burst in the amplitude of one or more state variable) in complex systems were known, but were dismissed to be rare and unexpected and hence as of no consequence. However, they have gained increasing attention by researchers nowadays. This is because they are found to arise commonly in nature as well as from man made events. For example, they are observed in tsunamis, floods, earthquakes, rouge waves, seismic activities, wildfires, valcanos, etc,.

The reason is the extreme events display large magnitude deviations from normal behaviors under certain conditions. The study of these events are carried out by setting up mathematical models and applying the principles of statistics to the time series of state variables to detect sudden and large deviations in the behavior of the systems.

## 28.10.2021 Dmitrii Kolotkov, Ph.D, University of Warwick, UK "Measuring waves and oscillations in the Sun's corona. How and why?"

The outermost layer of the Sun's atmosphere, the corona, is a natural laboratory of a fully ionized plasma in which fundamental physical processes such as magnetic reconnection, acceleration of charged particles, heating and cooling, and magnetic confinement of plasma are open to direct study. In addition to the academic interest, understanding the processes in the solar corona is necessary for timely and adequate prediction of space weather conditions in the near-Earth space. One of the modern and promising approaches for studying the solar corona is the method of coronal MHD seismology - the use of direct observations of waves and oscillations in the corona for local plasma diagnostics.

Wave phenomena in the solar corona are regularly and confidently observed by many modern space-borne and ground-based telescopes. The continuously increasing amount and precision of observational data require the development and application of new methods for their processing and analysis. In this lecture, we will consider several original and state-of-the-art methods for measuring the parameters of waves and oscillations in the solar corona, which are actively used by the research community worldwide. In particular, a method for measuring the oscillation period, propagation speed, and damping law of waves using time-distance maps will be shown, based on the images of the Sun's corona in the extreme UV with high spatial and temporal resolution. We will also demonstrate the advantages and capabilities of the method of motion magnification for detection and subsequent analysis of oscillations of essentially small amplitude both in the solar corona and in other fields such as medicine and industry. We will discuss the use of Bayesian analysis with Monte Carlo Markov Chain (MCMC) sampling to fit observational data by low-dimensional multi-parametric models. The pros and cons of the traditional Fourier-based methods for the analysis of quasi-periodic processes with pronounced non-stationary properties (for example, in the lightcurves of solar flares) will be pointed out, and more recent and suitable approaches based, for example, on the method of the Empirical Mode Decomposition (EMD) and the Hilbert-Huang Transform (HHT) will be discussed.

Despite significant progress in the understanding, application, continuous development and improvement of methods for measuring the parameters of waves and oscillations in the solar corona, it is already crystal clear that the colossal amounts of data (hundreds of TB) collected over the last few decades require the integration of existing approaches with methods of big data analysis and machine learning principles, traditionally used in business intelligence. Such a mutually beneficial transfer of knowledge and application of an interdisciplinary approach in the future would allow us to consider the question of data processing from a new and more advanced point of view, and thereby significantly expand the horizons of understanding the intrinsic processes both in solar physics and in more practical problems of econometrics, medicine, and geophysics.

## 15.04.2021 Prof S. C. Chapman «Historical datasets- implications for space weather risk over multiple solar cycles»

By obtaining the analytic signal of daily sunspot numbers since 1818 we construct a new solar cycle phase clock that maps each of the last 18 solar cycles onto a single normalized epoch. This clock orders solar coronal activity and can be used to order observations that exist on multiple solar cycles. The aa index tracks geomagnetic storms at the Earth's surface over the last 14 Schwabe cycles, and 'space age' observations are available over several Schwabe cycles: e.g. F10.7 solar radio flux, galactic cosmic ray flux and the GOES flare catalog. We will construct 'clocks' for the (on average) 11 year Schwabe and 22 year Hale cycles to discern systematic Schwabe and Hale cycle variations in these quantities. Analysis of the aa index is desirable given its extent in time, however it is a discretized quantity rather than a well sampled timeseries. New methods to quantify the occurrence rates of extreme events in aa (amplitude information) and in its 27 day recurrence (phase information) are applied in the context of these solar cycle clocks.

S. C. Chapman, S. W. McIntosh, R. J. Leamon, N. W. Watkins, The Sun's magnetic (Hale) cycle and 27 day recurrences in the aa geomagnetic index. Ap. J. submitted (2021) arXiv:2101.02569[astro-ph.SR]

S. C. Chapman, S. W. McIntosh, R. J. Leamon, N. W. Watkins, Quantifying the solar cycle modulation of extreme space weather, Geophysical Research Letters, (2020) doi:10.1029/2020GL087795

S. C. Chapman, R. Horne, N. W. Watkins, Using the aa index over the last 14 solar cycles to characterize extreme geomagnetic activity. Geophys. Res. Lett.(2020) doi: 10.1029/2019GL086524

## 01.04.2021 Vladimir Fufaev "Application of Machine Learning Methods in Recurrent Sunspot Groups Identification"

Sunspots – observable patches on the Sun where intense magnetic fields loop up through the surface – play significant role in research of solar activity. One of the difficulties faced by researcher is restricted visibility of the Sun – one can see only half of the solar surface from the Earth. Especially strong solar activity is connected with large sunspot groups that are supposed to be visible during more than one solar rotation. Hence continuous observation of such groups is impossible and the problem of long-lived (recurrent) sunspot groups identification arises. Today exist applications of data analysis and machine learning methods to this problem. The most prolonged database of sunspot group areas is the Royal Greenwich Observatory catalogue began in 1874 (it contains also descriptions of some groups supposed to be recurrent). We will show one of the identification algorithms, results of its application and comparison with other approaches.

## 18.03.2021 Roman Kislov "Quasi-stationary current sheets in the solar wind"

According to the classic models (Parker, ApJ, 1958; Weber & Davis, ApJ, 1967) the interplanetary magnetic field (IMF) has a dipole structure. The regions with different polarity of IMF are separated by heliospheric current sheet which is a tangential discontinuity. The solar wind and IMF are isotropic in both hemispheres, IMF is twisted into an Archimedean spiral due to violation of corotation of the plasma and the Sun. Over the past half-century a lot of observational data has been obtained indicating that the structure of the inner heliosphere is much more complex than it is in old models. Despite this, there are still any deviations from the dipole and/or isotropic description are perceived as nontrivial, the self-consistent structure of the current sheet is not considered, the problem of the type of discontinuity in the current sheet is not solved completely.

You will see in this report the heliosphere with multiple IMF, MHD-structure of the heliospheric current sheet, nonisotropic solar wind and cone-shaped polar current sheets are recently discovered in Ulysses data.

## 22.01.2021 Edith Elkind (Oxford University) "Keeping Your Friends Close: Land Allocation with Friends"

We examine the problem of assigning plots of land to prospective buyers who prefer living next to their friends. In this setting, each agent's utility depends on the plot she receives and the identities of the agents who receive the adjacent plots. We are interested in mechanisms without money that guarantee truthful reporting of both land values and friendships, as well as Pareto optimality and computational efficiency. We explore several modifications of the Random Serial Dictatorship (RSD) mechanism, and identify one that performs well according to these criteria, We also study the expected social welfare of the assignments produced by our mechanisms when agents' values for the land plots are binary; it turns out that we can achieve good approximations to the optimal social welfare, but only if the agents value the friendships highly. Based on joint work with Neel Patel, Alan Tsang and Yair Zick.

## 21.04.2020. Igor Rouzine "An evolution-based measurement of the fitness landscape from genetic sequences"

Fitness landscape is the most important input parameter required to predict the trajectory of pathogen's evolution. Here we present two methods, which in combination allow to measure fitness landscape from genetic data. Also, an intriguing fact long defying explanation is the observation of a universal exponential distribution of beneficial mutations in fitness effect for different microorganisms. Here we use a general and straightforward analytic model to demonstrate that, regardless of the inherent distribution of mutation fitness effect across genomic sites, an observed exponential distribution of fitness effects emerges naturally, as a consequence of the evolutionary process. Our results demonstrate the difference between the distribution of fitness effects experimentally observed for naturally occurring mutations and the inherent distribution obtained in directed-mutagenesis experiments. The technique will enable researchers to measure fitness effects of mutations across the genome from a single DNA sample, which is important for predicting the evolution of a population.

Linkage effects in a multi-locus population strongly influence its evolution. Recent models based on the traveling wave approach enable us to predict the speed of evolution and the statistics of phylogeny. However, predicting the evolution of specific sites and pairs of sites in the multi-locus context remains a mathematical challenge. In particular, the effect of epistasis, the interaction of gene regions contributing to phenotype, is difficult both to predict theoretically and detect experimentally in sequence data. A large number of false interactions arising from linkage and indirect interactions which mask true interactions. Here we develop a method to clean false-positive interactions. We start by demonstrating that averaging of the two-way haplotype frequencies over a hundred of independent populations is not enough to clear false interactions. Then, to address this problem, we develop analytically and use a triple-way haplotype test, which isolates true interactions. Next, the fidelity of the test is confirmed on simulated genetic sequences, where the epistatic network known in advance. Finally, we apply the test to a large database on influenza A H1N1 virus sequences of neurominidase from various geographic locations to predict the epistatic network responsible for the transition from the pre-pandemic virus to the pandemic strain. We predict a primary mutation and 15-22 secondary compensatory mutations of variable strength, as many as typically observed for drug resistance and immune escape mutations in HIV. These results present a simple and reliable method to measure epistatic interaction from sequence data.

## 05/02/2020 Machine learning methods for identification of long-lived sunspot groups

Vladimir Fufaev, Research Assistant (MCCS lab)

The size and number of sunspots are visible indicators of solar activity. Catalogues containing daily information about sunspots were created by different observers. Studies of sunspot groups are hampered by the rotation of the Sun. Sunspots disappear from the visible part of the Sun, but some of them have a sufficient lifetime to become visible from the Earth again. This is the problem of long-lived sunspot group identification. Machine learning methods are effective at finding such patterns in data. The algorithm for identification of long-lived sunspot groups will be shown in the presentation. Also, nontrivial properties of long-lived sunspots found in well-known catalogues will be demonstrated.

## 18/12/2019 Nonparametric welfare analysis for discrete choice using convex duality

Grigory Franguridi, Department of Economics, University of Southern California

I suggest a semi/nonparametric, computationally attractive procedure to evaluate counterfactual welfare in a general class of discrete choice models, for which a consistent estimator of in-sample conditional choice probabilities and mean utilities is available. This class includes semiparametric dynamic discrete choice models under conditional independence as in Buchholz et al. (2016) and semiparametric random utility models with additively separable heterogeneity as in Allen and Rehbeck (2019). The estimating procedure does not require any prior knowledge of the distribution of the utility shock (as in multinomial logit) or the distribution of the random coefficients (as in mixed logit); instead, the only information used in estimation is convexity of welfare as a function of mean utilities. The estimators are based on the convex dual representation of the welfare function, are nonparametrically consistent (as long as the demand can be identified) and enjoy an array of properties implied by rational behavior of the consumer. To the best of my knowledge, this is the first consistent procedure for counterfactual evaluation in the aforementioned class of discrete choice models.

## 13/11/2019 How to create a mobile app for Android (master class)

Ekaterina Samorodova, Research Assistant (MCCS lab)

Have you always wanted to make mobile apps, but don't know how to start?

At the upcoming master class, anyone can create his first mobile app and launch it on the smartphone!

## 06/11/2019 Epsilon-equilibrium

Dmitry Dagaev, Head of Laboratory of Sports Studies, Faculty of Economic Sciences

In 2015, the solution of he simplest version of poker was published in Science (Bowling et al., 2015). Even in the simplest version of the game it is extremely difficult to find an analytical solution. The authors use the concept of Epsilon-equilibrium to find an approximate, in some sense, equilibrium. This concept is convenient because it allows to use computing methods to find an approximate equilibrium. In the talk we will introduce the essential definitions and look at examples of how Epsilon-equilibrium helps to solve difficult game problems.

## 30/10.2019 Features of synchronization of two Van der Pol oscillators

Anton Savostyanov, Research Assistant (MCCS lab), Senior Lecturer

We consider the systems of coupled oscillators where the cases of phase and frequency synchronization are of particular interest. In contrast to simple linear models of connected pendulums (such as the Kuramoto model), in the case of dissipatively connected Van der Pol oscillators, phase transitions (bifurcations) of the system can be detected with respect to changes in the coupling coefficient. In the talk several similar features will be described for cases of symmetric and asymmetric coupling.

## 16/10/2019 Application of machine learning methods in data processing and storage problems in high energy physics experiments

Michail Gushchin, Faculty of Computer Sciences

In experimental high-energy physicis the fundamental properties of elementary particles are studied. The data obtained from the experiment detectors go through several processing steps and are stored for further physical analysis. During the talk solutions to several problems of data processing and storage using machine learning methods are presented.

In particular, the problems of recognition of charged particle tracks in the tube spectrometer of the SHiP experiment at CERN and optimization of parameters of its geometry are considered. The problem of global particle identification for the LHCb experiment at CERN is discussed. In addition, algorithms for diagnosing failures in storage systems are mentioned.

Moscow, 11 Pokrovsky Boulevard, Room D102, 16:00 - 18.20

## 25/09/2019 Super-diffusion and other problems of statistical physics

Dr. Sergei Nechaev, Center Poncelet, CNRS & Independent University of Moscow

Some statements of educational and scientific problems of statistical physics of disordered systems, random walks, some aspects of the graph theory and extreme statistics were discussed.

Moscow, 11 Pokrovsky Boulevard, Room T906, 16:40 - 18.00

## 28/11/2018 Composite synthesis of Petri nets using the algorithm of the regions

Joint seminar with the Laboratory of Process-Aware Information Systems (PAIS lab)

Anna Kalenkova, Senior Research Fellow (PAIS lab), Professor

Finite automata model sequential processes. However, there are algorithms, such as the algorithm of regions, which allow to synthesize equivalent Petri nets using finite automata, detecting latent parallelism. Unfortunately, the task of synthesizing equivalent Petri nets over finite automata is NP-complete. The paper presents the algorithm of compositional synthesis, which allows to perform the synthesis "in parts", thereby reducing the size of the input data of the algorithm of the regions.

The properties of the composite synthesis algorithm are investigated and it is proved that it also allows preserving the equivalence of the original state machine and the synthesized Petri net.

__3 Kochnovsky Proezd, room 622 __

__Time 16:40-18:00__

## 21/11/2018 The inverse problem of the Kuramoto model as applied to the solar dynamo

Anton Savostyanov, Research Assistant (MCCS lab), Senior Lecturer

The presence of a sufficiently large set of various indices of solar activity associated both with the magnetic field and with the external observable features (the number and area of sunspot groups, etc.) leads to a natural desire to build an exhaustive analytical model. Attempts to use classical oscillators did not reveal the ability to qualitatively reflect the phenomena of phase and frequency synchronization between different indices, one way or another observed in the data; however, at the same time, the Kuramoto model of linear oscillators with non-linear coupling specifically investigates such situations. The described synchronization can be achieved by including the connection between oscillators physically realized by the solar meridional flux into the model, which is consistent with the helioseismology data. In the story, the reverse procedure will be discussed: restoring a certain understanding of the intensity of the connection between them using these oscillators; It will also discuss the quality assessments of this procedure and the features of recovery errors caused by the connection characteristics and model correctness.

__3 Kochnovsky Proezd, room 311 __

__Time 16:40-18:00__

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