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Monday, 19 September 2022
Time Speaker Title Resources
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)
Tuesday, 20 September 2022
Time Speaker Title Resources
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)
Wednesday, 21 September 2022
Time Speaker Title Resources
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)
Thursday, 22 September 2022
Time Speaker Title Resources
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
Friday, 23 September 2022
Time Speaker Title Resources
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)
Monday, 26 September 2022
Time Speaker Title Resources
10:00 to 11:00 Karen Abbott * (CWRU, USA) When and where can we expect to see early warning signals in multi-species systems approaching tipping points?

Multi-species communities (and other multi-dimensional ecological systems) have a high risk of "silent collapse" because early warning signals are not expected to appear with the same strength in all species.  If we monitor the wrong species, we may have no chance to detect early warning signals.  In this talk, I will discuss the reasons for this and some insights into how monitoring schemes can be designed to maximize early warning signal detection.

11:30 to 12:30 Valeria Livina (NPL, UK) Scaling and potentiality in tipping point analysis

System potential and temporal scaling in time series change when a dynamical system is experiencing tipping. We discuss how early warning signals are obtained from various scaling indicators and how system potential can be used for detection and forecast of tipping points. We consider applications in geophysics, climatology, structure health monitory, electric signals, and other records of dynamical systems.

14:00 to 15:00 Peter Cox * (University of Exeter, UK) Some new Research on Climate Tipping Points
15:00 to 16:00 Sonia Kefi * (Université de Montpellier, France) Spatial signatures of dryland resilience

Some ecosystems have a striking spatial structure. Drylands are an example of such ecosystems, where the vegetation cover is fragmented into patches. These structures have attracted attention and raised questions about their origin or the functional consequences of their presence on ecosystem functioning and resilience. In drylands, it has been suggested that the spatial structure of the vegetation may provide useful tools for predicting their level of degradation. After presenting an overview of the theory, I will discuss the challenges associated with the validation and applicability these indicators for real ecosystems.

16:30 to 17:00 Tanveen Randhawa (IISc, India) Role of trait variation in savanna-woodland bistable system
17:00 to 17:30 Smita Deb (IIT Ropar, India) Machine learning methods trained on simple models can predict critical transitions in complex natural systems
17:30 to 18:30 Corina Tarnita * (Princeton University, USA) Spatial Self-Organization and Its Implications for Ecosystem Robustness

Self-organized spatial vegetation patterning is widespread and has been described using models of scale-dependent feedback between plants and water on homogeneous substrates. As rainfall decreases, these models yield a characteristic sequence of patterns with increasingly sparse vegetation, followed by sudden collapse to desert. Thus, the final, spot-like pattern may provide early warning for such catastrophic shifts. In many arid ecosystems, however, termite nests impart substrate heterogeneity by altering soil properties, thereby enhancing plant growth. I will discuss how termite-induced heterogeneity interacts with scale-dependent feedbacks to produce vegetation patterns at different spatial grains. Although the coarse-grained patterning resembles that created by scale-dependent feedback alone, it does not indicate imminent desertification. Rather, mound-field landscapes are more robust to aridity, suggesting that termites may help stabilize ecosystems under global change.

Tuesday, 27 September 2022
Time Speaker Title Resources
09:00 to 10:00 Mercedes Pascual * (University of Chicago, USA) TBA
10:00 to 11:00 Jason George (Texas A&M University, USA) Stochastic tipping points in optimal tumor evasion and adaptation induced by fluctuating environments

Transitions and criticality play central roles in many important biological processes. Here, we will discuss our recent work in characterizing stochastic optimal decision-making of cancer utilizing dynamic programming. In our first application, we consider the random interaction between an evolving cancer population and an adaptive T cell repertoire comprised of many (10 8 ) distinct T cells. We frame cancer optimal evasion as a tradeoff between downregulating antigens detected by the immune system in the present and the generation of new tumor antigens susceptible to immune targeting in the future. The optimal evasion framework permits a critical immune detection rate around which cancer populations are driven either to highly antigenic or antigen-depleted states. We will also discuss our recent modeling effort to characterize stochastic optimal cellular decision-making when faced with a fluctuating metabolic environment and demonstrate the role of state variance on the optimal memory of prior states.

11:30 to 12:30 Sumanta Bagchi (IISc , India) TBA
14:00 to 15:00 Peter Ashwin * (University of Exeter, UK) Rate-induced tipping in non-autonomous systems
15:00 to 16:00 Vasilis Dakos * (Université de Montpellier, France) How do we operationalise resilience for decision-making?

There are many ways to estimate ecosystem resilience as signals to potential approaching tipping points. While the theory and empirical examples are plenty, there is still a gap in operationalising resilience metrics to a practice and decision-making. The reason is that such task is challenging, yet there is a new frontier of global assessments based on remote-sensing data that could prove fruitful. Here, I talk about the limitations and opportunities of such approaches through a series of examples from forests, lakes and the climate.

16:30 to 17:00 Francesco Cerini * (University in Bristol, UK) Timeline to collapse
17:00 to 17:30 Shuaib Palathingal (IISc, India) Impact of Seasonality on Bi-stable Ecosystem Dynamics
17:30 to 18:30 Chris Bauch * (University of Waterloo, Canada) Harnessing the universality of tipping points to improve early warning signal detection through deep learning

Many early warning indicators are based on mathematical theory that discards higher-order terms of the equations that are either too hard to solve by hand, or too hard to detect through statistical measures.  However, these higher-order terms leave signatures in time series that may provide information about an upcoming tipping point.  Deep learning algorithms excel at detecting subtle features in temporal data but must be trained on very large amounts of data from the study system, which we often lack for many experimental or field-based study systems.  However, the need for system-specific data could be circumvented by training the algorithms on a library of random dynamical systems passing through tipping points.  This would exploit the ‘universality’ of tipping points that can make their features so similar across diverse systems. Hence, training a deep learning algorithm on a library of random ordinary differential equations, phase transition models, or bifurcation normal forms could--in principle--provide early warning signals of upcoming regime shifts as well as provide information about what kind of state lies beyond the tipping point, all without the need for simulated or empirical data specific to the system.  This talk will illustrate applications of this approach to both simulated and empirical tipping points in systems including temporal transitions in paleo-climate shifts, thermoacoustics, lake sedimentation, and social shifts, and spatio-temporal phase transitions in ecological, physical, and climate systems. 

Wednesday, 28 September 2022
Time Speaker Title Resources
09:30 to 10:00 Swarnendu Banerjee (Utrecht University, Netherlands) Evading tippings in spatial ecosystems
10:00 to 10:30 Pranali Roy Chowdhury (IIT Kanpur, India) Dynamics of a slow-fast predator-prey model with a predator-dependent functional response
10:30 to 11:00 Pankaj Gautam (IIT Ropar, India) Anticipating response function in gene regulatory networks
11:30 to 12:30 Krishnapriya Tamma (APU Bangalore, India) Examining ecosystem resilience of forests in northeast India using remotely sensed and field data

The resilience of an ecosystem can be defined as the time taken for the system to recover from perturbation. In these times of climate and ecological crisis, measuring the resilience of ecosystems is important for their long term conservation. Using theory from complex systems, scientists have developed methods to measure resilience of ecosystems using time series data. Northeast India is home to an astounding diversity of ecosystems and biodiversity. In our study, we a) characterise the state-driver relationship for vegetation in northeast India, b) measure resilience using remotely sensed data for 2 protected areas, and c) link it to forest structure and composition from the two areas . From our work we find no support for the presence of alternate stable states in vegetation cover for northeast India. Our preliminary analysis also shows spatial variation in resilience across two protected areas in Meghalaya. We are currently analysing data from the field to link it to the measured resilience. Our approach allows for relatively easy monitoring of forest resilience at coarse scales.

14:00 to 15:00 Tim Lenton * (University of Exeter, UK) Climate tipping points
17:30 to 18:30 Madhur Anand * (University of Guelph, Canada) Tipping points in coupled human-environment systems

Humans and the environment form a single complex system where humans not only cause ecosystem impacts, but also react to them. Despite this, there are far fewer examples of coupled human-environment system (CHES) mathematical models than models of uncoupled ecosystems. These coupled models are essential to understand the impacts of social interventions and their potential to avoid catastrophic environmental events and support sustainable trajectories on multi-decadal timescales. They demonstrate how social parameters, as well as the degree of human influence on environmental systems profoundly affect the amount and type of tipping points that occur, through a focus on alternative stable states. Additionally, the efficacy of early warning signals can be altered through this coupling, with potential for the monitoring of environmental systems through social data. Coupled study systems presented here include forests and land use, coral reefs and fishing, and invasive species models.

Thursday, 29 September 2022
Time Speaker Title Resources
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 [1]. 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 [2] 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 [3].

[1] 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
[2] S. Wieczorek, Ch. Xie, C.K.R.T. Jones,   Compactification for asymptotically autonomous dynamical systems: theory, applications, and invariant manifolds, Nonlinearity, 34(5) (2020), 2970, https://iopscience.iop.org/article/10.1088/1361-6544/abe456
[3] S. Wieczorek, Ch. Xie, P. Ashwin,  Rate-induced tipping: Thresholds, edge states and connecting orbits, https://arxiv.org/abs/2111.15497

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.