Tipping the Balance: A Criticality Perspective

Bose, Indrani

doi:10.3390/e24030405

Cited by 3 publications

(3 citation statements)

References 47 publications

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“…We now show that the same method, as proposed earlier, can be used in the case of a noiseinduced transition with the starting equation being different (Bose 2022). In the deterministic case, one starts with the steady state equation, 𝐹(𝑥 * ) = 0, obtained from the rate equation, 𝑑𝑥 𝑑𝑡 = 𝐹(𝑥), with 𝑥 * representing the steady states.…”

Section: Box 3 Phase Transitions and Critical Phenomenamentioning

confidence: 85%

Emergent phenomena in living systems: A statistical mechanical perspective

Bose

2022

J Biosci

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A natural phenomenon occurring in a living system is an outcome of the dynamics of the specific biological network underlying the phenomenon. The collective dynamics have both deterministic and stochastic components. The stochastic nature of the key processes like gene expression and cell differentiation give rise to fluctuations (noise) in the levels of the biomolecules and this combined with nonlinear interactions give rise to a number of emergent phenomena. In this review, we describe and discuss some of these phenomena which have the character of phase transitions in physical systems. We specifically focus on noise-induced transitions in a stochastic model of gene expression and in a population genetics model which have no analogs when the dynamics are solely deterministic in nature. Some of these transitions exhibit critical-point phenomena belonging to the mean-field Ising universality class of equilibrium phase transitions. A number of other examples, ranging from biofilms to homeostasis in adult tissues, are also discussed which exhibit behavior similar to critical phenomena in equilibrium and nonequilbrium phase transitions. The examples illustrate how the subject of statistical mechanics provides a bridge between theoretical models and experimental observations.

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Section: Box 3 Phase Transitions and Critical Phenomenamentioning

confidence: 85%

Emergent phenomena in living systems: A statistical mechanical perspective

Bose

2022

J Biosci

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“…In our study on the stochastic Solow model, we have demonstrated the existence of two such signatures of an approaching tipping point, A c , which is not a bifurcation point, at which the states of poverty and well-being are evenly balanced but away from which a tilt favouring one or the other regime (economic decline versus economic progress) occurs. The bifurcation point transitions are analogous to equilibrium phase transitions and have been discussed/analysed utilising the criticality perspective [41,44,45]. In economics and the social sciences, opportunities for field experiments are limited, but cross-disciplinary perspectives could facilitate in identifying the universal features, opening up in the process new pathways for exploration.…”

Section: J Stat Mech (2024) 083401mentioning

confidence: 99%

Growth, poverty trap and escape

Bose

2024

J. Stat. Mech.

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The well-known Solow growth model is the workhorse model of the theory of economic growth, which studies capital accumulation in a model economy as a function of time with capital stock, labour and technology-based production as the basic ingredients. The capital is assumed to be in the form of manufacturing equipment and materials. Two important parameters of the model are: the saving fraction s of the output of a production function and the technology efficiency parameter A , appearing in the production function. The saved fraction of the output is fully invested in the generation of new capital and the rest is consumed. The capital stock also depreciates as a function of time due to the wearing out of old capital and the increase in the size of the labour population. We propose a stochastic Solow growth model assuming the saving fraction to be a sigmoidal function of the per capita capital k p . We derive analytically the steady state probability distribution P ( k p ) and demonstrate the existence of a poverty trap, of central concern in development economics. In a parameter regime, P ( k p ) is bimodal with the twin peaks corresponding to states of poverty and well-being, respectively. The associated potential landscape has two valleys with fluctuation-driven transitions between them. The mean exit times from the valleys are computed and one finds that the escape from a poverty trap is more favourable at higher values of A . We identify a critical value of A c below (above) which the state of poverty (well-being) dominates and propose two early signatures of the regime shift occurring at A c . The economic model, with conceptual foundations in nonlinear dynamics and statistical mechanics, shares universal features with dynamical models from diverse disciplines like ecology and cell biology.

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“…According to recent results [34], this means a direct relationship with the reaction of the immune system and variations in the dynamics of the system, either in the time it takes for the populations involved to reach the steady state (we will see it deeply in section 5) and its consequent reduction in the number of cancer cells [35]. Likewise, the variation in the amplitude of the multiplicative noise reflects changes in the microenvironments of the tissues where cancer is generated, and its progression takes place [36].…”

Section: The Effect Of Multiplicative Noise In the Systemmentioning

confidence: 99%

Stochastic and parameter analysis for an integrative cancer model

Reale¹,

Margarit²,

Scagliotti³

et al. 2022

Phys. Scr.

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In previous work, we presented a model that integrates cancer cell differentiation and immunotherapy, analysing a particular therapy against cancer stem cells by cytotoxic cell vaccines. As every biological system is exposed to random fluctuations, is important to incorporate stochasticity in the models to adequate their behaviour to experimental observations. Thus, we propose a necessary upgrade to the former model incorporating fluctuations in it. On the one hand, we added multiplicative noise throughout the proposed system, and on the other, we specifically analysed the influence of demographic and multiplicative noise on the parameters of reproduction and death in cancer cells. In both cases, we studied the dynamics for different values of the parameters involved. It was observed that the final number of cancer cells decreases for different combinations of these parameters and noise intensity.

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Tipping the Balance: A Criticality Perspective

Cited by 3 publications

References 47 publications

Emergent phenomena in living systems: A statistical mechanical perspective

Emergent phenomena in living systems: A statistical mechanical perspective

Growth, poverty trap and escape

Stochastic and parameter analysis for an integrative cancer model

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