|10:00 to 11:00||Partha Sharathi Dutta (IIT Ropar, India)||Dynamical systems and Tipping (Lecture 1)|
|11:30 to 12:30||Partha Sharathi Dutta (IIT Ropar, India)||Dynamical systems and Tipping (Lecture 2)|
|14:00 to 15:00||Partha Sharathi Dutta (IIT Ropar, India)||Early warning signals|
|15:30 to 17:30||--||Tutorial/Lab (EWS)|
|09:00 to 10:00||Sudipta Kumar Sinha (IIT Ropar, India)||Stochastic Dynamics (Lecture 1)|
|10:00 to 11:00||Sudipta Kumar Sinha (IIT Ropar, India)||Stochastic Dynamics (Lecture 2)|
|11:30 to 12:30||Sudipta Kumar Sinha (IIT Ropar, India)||Stochastic Dynamics (Lecture 3)|
|14:00 to 15:00||Debabrata Biswas (Bankura Univ, India)||Delay Dynamical Systems (Lecture 1)|
|15:30 to 17:30||--||Tutorial/Lab (SD)|
|09:00 to 10:00||Vishwesha Guttal (IISc, India)||Tipping in Spatial Systems (Lecture 1)|
|10:00 to 11:00||Vishwesha Guttal (IISc, India)||Tipping in Spatial Systems - 2|
|11:30 to 12:30||Vishwesha Guttal (IISc, India)||Tipping in Spatial Systems (Lecture 3)|
|14:00 to 15:00||Debabrata Biswas (Bankura Univ, India)||Delay Dynamical Systems (Lecture 2)|
|15:30 to 17:30||--||Tutorial/Lab (SEWS)|
|09:00 to 10:00||Mohit Kumar Jolly (IISc, India)||Cellular systems|
|10:00 to 11:00||Mohit Kumar Jolly (IISc, India)||CT in cellular systems|
|11:30 to 12:30||R. I. Sujith * (IIT Madras, India)||Tipping in thermoacoustic systems and their early warning signals|
|14:00 to 15:00||Sebastian Wieczorek * (UCC, Ireland)||TBA|
|10:00 to 11:00||Vishwesha Guttal (IISc, India)||Tipping in Spatial Systems - 4|
|11:30 to 12:30||Narayanan Krishnan (IIT Palakkad, India)||A gentle introduction to machine learning - 1|
|14:00 to 15:00||Narayanan Krishnan (IIT Palakkad, India)||A gentle introduction to machine learning - 2|
|15:30 to 17:30||--||Tutorial/Lab (ML)|
|09:30 to 10:00||Induja Pavithran (IIT Madras, India)||Hyperexponential growth and log-periodicity precede extreme COVID-19 waves|
|10:00 to 11:00||R. I. Sujith (IIT Madras, India)||Rate dependent transition to thermoacoustic instability|
|11:30 to 12:30||Amit Apte (IISER Pune, India)||
Dynamical and Statistical models of Indian monsoon rainfall
The Indian summer monsoon rainfall varies on timescales ranging from days to months to years and on spatial scales from sub-kilometer to continental. I will describe a simple dynamical model and some data-based statistical models that aim to capture the qualitative aspects of the Indian monsoon and its variability. The underlying feedbacks or processes that drive this variability are not yet well understood but are essential to predict the evolution of the monsoon in the future changing climate and to try to answer the question: is there a tipping point which will change the monsoon system drastically?
|14:00 to 15:00||Chunhe Li * (Shanghai Center for Mathematical Sciences, China)||
Stochastic analysis and applications in gene networks
Cellular functions in biological systems are regulated by the underlying gene regulatory networks. How to investigate the global properties of gene networks is a challenging problem. In this talk, I will present some approaches we recently developed, i.e., the potential landscape and flux framework, as well as the dimension reduction approach based on landscape theory, to study the stochastic dynamics of gene networks. The basins on the landscape characterize different cell states. The landscape topography in terms of barrier heights between stable states quantifies the global stability of the gene regulatory system. The kinetic paths based on the minimum action principles quantify the transition processes between different cell states. I will also discuss some applications of this approach in specific biological systems, including EMT and cancer system.
|15:00 to 16:00||Sebastian Wieczorek * (UCC, Ireland)||
Rate-Induced Tipping in Asymptotically Autonomous Dynamical Systems: Theory and Examples
Many systems are subject to external disturbances or changing external conditions. For a system near a stable state (an attractor) we might expect that, as external conditions change over time, the stable state will change too. In many cases the system may adapt to changing external conditions and track the moving stable state. However, some systems can be particularly sensitive to how fast the external conditions change and have critical rates: they suddenly and unexpectedly move to a different state if the external input changes slowly but too fast. This happens even though the moving stable state never loses stability in the classical autonomous sense. We describe this phenomenon as rate-induced tipping or R-tipping. Being a genuine non-autonomous instability, R-tipping is not captured by the classical bifurcation theory and requires an alternative framework.
In the first part of the talk, we illustrate R-tipping using a simple ecosystem model where environmental changes are represented by time-varying parameters . We then introduce the concept of basin instability and show how to complement the classical bifurcation diagram with information on nonautonomous R-tipping that cannot be captured by the classical bifurcation analysis. In the second part of the talk, we develop a general mathematical framework for R-tipping with decaying inputs based on the concepts of thresholds, edge states and special compactification  of the nonautonomous system. This allows us to transform the R-tipping problem into a connecting heteroclinic orbit problem in the compactified system, which greatly simplifies the analysis. We explain the key concept of threshold instability and give rigorous testable criteria for R-tipping to occur in arbitrary dimension .
 P. O'Keeffe, S. Wieczorek, Tipping phenomena and points of no return in ecosystems: beyond classical bifurcations, https://epubs.siam.org/doi/10.1137/19M1242884
|16:30 to 17:00||Ankan Banerjee (IIT Madras, India)||Imprints of log-periodicity and the prediction to blowout in a turbulent thermoacoustic system|
|17:00 to 17:30||Taranjot Kaur (IIT Ropar, India)||Critical rates of climate warming and abrupt collapse of ecosystems|
|17:30 to 18:30||Kenneth J. Pienta * (Johns Hopkins University, USA)||
Tipping points in the development of cancer as a complex adaptive system.
Our understanding of how cancer arises is intimately tied to understanding how it first arises as a new unicellular species (a tipping point) in the host patient and then evolves to a “multicellular” organism (a tipping point). Between the events of origination and diversification lies complex tissue organization that gave rise to novel functionality for organisms that need to be overcome by the new unicellular cancer species but then, also, utilized by the malignant transformed multicellularity. Tissue specialization with distinctly separated cell fates allowed novel functionality at organism level, such as for vertebrate animals, but also involved trade-offs at the cellular level that are potentially disruptive and need to be overcome. These trade-offs may contribute to cancer evolution by (a) how factors can reverse differentiated cells into a window of phenotypic plasticity, (b) the reversal to phenotypic plasticity coupled with asexual reproduction occurs in a way that the host cannot adapt, and (c) the power of the transformation factor correlates to the power needed to reverse tissue specialization. The role of reversed cell fate separation for cancer evolution is strengthened by how some tissues and organisms maintain high cell proliferation and plasticity without developing tumors at a corresponding rate. This demonstrates a potential proliferation paradox that requires further explanation. The development of cancer requires a sweet spot of phenotypic and reproductive versatility.