Modeling Active Non-Markovian Oscillations

Tucci, Gennaro; Roldán, Édgar; Gambassi, Andrea; Belousov, Roman; Berger, Florian; Gogui, Alonso, Rodrigo; Hudspeth, A. J.

doi:10.1103/physrevlett.129.030603

Cited by 17 publications

(13 citation statements)

References 69 publications

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“…where P 1 (x 1 , t) and P 2 (x 2 , t) are the distributions that correspond to the processes x 1 (t) and x 2 (t), respectively, and are each exactly known (x 1 (t) being the confined 1D RTP studied in [44] as described above, and x 2 (t) being an Ornstein-Uhlenbeck process). This decomposition can be generalized, in 1D, to the sum of any number of noise terms of any type [70,74].…”

Section: Diffusionmentioning

confidence: 99%

Exact position distribution of a harmonically-confined run-and-tumble particle in two dimensions

Smith¹,

Doussal²,

Majumdar³

et al. 2022

Preprint

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We consider an overdamped run-and-tumble particle in two dimensions, with self propulsion in an orientation that stochastically rotates by 90 degrees at a constant rate, clockwise or counterclockwise with equal probabilities. In addition, the particle is confined by an external harmonic potential of stiffness µ, and possibly diffuses. We find the exact time-dependent distribution P (x, y, t) of the particle's position, and in particular, the steady-state distribution Pst (x, y) that is reached in the long-time limit. We also find P (x, y, t) for a "free" particle, µ = 0. We then extend these results in several directions, to two such run-and-tumble particles with a harmonic interaction, to analogous systems of dimension three or higher, and by taking diffusion into account.

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Section: Diffusionmentioning

confidence: 99%

Exact position distribution of a harmonically-confined run-and-tumble particle in two dimensions

Smith¹,

Doussal²,

Majumdar³

et al. 2022

Preprint

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“…Instead, we consider a two-layer model with one hidden position variable for the active membrane-cortex in-teraction that is linearly coupled to the membrane outer layer x (probe) (materials and methods S7). Similar active models have been proposed in the study of hair-cell bundle dynamics (14,34,35). The two-layer active model leads to a reduced VSR of the form (Eq.…”

Section: Red Blood Cellsmentioning

confidence: 88%

“…By fitting the experimental data to a single function, the total variance scriptVTt over several decades, the contribution of dissipative processes over multiple timescales is appropriately weighted in the sum balance. This distinguishes our approach from plain model fitting of the experimental power spectrum to derive the model parameters ( 35 ) that may lead to inaccurate estimations (materials and methods S14). In this regard, the VSR links modeling with energetics.…”

Section: Discussionmentioning

confidence: 99%

Variance sum rule for entropy production

Di Terlizzi,

Gironella,

Herraez-Aguilar

et al. 2024

Science

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Entropy production is the hallmark of nonequilibrium physics, quantifying irreversibility, dissipation, and the efficiency of energy transduction processes. Despite many efforts, its measurement at the nanoscale remains challenging. We introduce a variance sum rule (VSR) for displacement and force variances that permits us to measure the entropy production rate σ in nonequilibrium steady states. We first illustrate it for directly measurable forces, such as an active Brownian particle in an optical trap. We then apply the VSR to flickering experiments in human red blood cells. We find that σ is spatially heterogeneous with a finite correlation length, and its average value agrees with calorimetry measurements. The VSR paves the way to derive σ using force spectroscopy and time-resolved imaging in living and active matter.

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“…We can understand the root of this difficulty by studying the variance of the distribution p(x t , c t ). Using the tools introduced by Tucci et al [31], we can calculate these correlations analytically for any integer k. As we describe in more detail in appendix A.2, we find that…”

Section: The Interplay Between Sequence Memory and Model Architecture...mentioning

confidence: 93%

“…Another exciting avenue would be to apply neural networks to noisy non-Markovian signals extracted from experiments in physical or biological systems [57][58][59][60][61][62][63]. Examples include the recent application of the SSOU to infer the mitigation of the effects of non-Markovian noise [64,65] and the underlying heat dissipation of spontaneous oscillations of the hair-cell bundles in the ear of the bullfrog [31]. Applying our techniques to such a biological system could be fruitful to decipher the hidden mechanisms and statistics of switching in hearing and infer thermodynamic quantities beyond energy dissipation.…”

Section: Concluding Perspectivesmentioning

confidence: 99%

The impact of memory on learning sequence-to-sequence tasks

Seif,

Loos,

Tucci

et al. 2024

Mach. Learn.: Sci. Technol.

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The recent success of neural networks in natural language processing has drawnrenewed attention to learning sequence-to-sequence (seq2seq) tasks. While thereexists a rich literature that studies classification and regression tasks usingsolvable models of neural networks, seq2seq tasks have not yet been studied fromthis perspective. Here, we propose a simple model for a seq2seq task that hasthe advantage of providing explicit control over the degree of memory, ornon-Markovianity, in the sequences -- the stochasticswitching-Ornstein-Uhlenbeck (SSOU) model. We introduce a measure ofnon-Markovianity to quantify the amount of memory in the sequences. For aminimal auto-regressive (AR) learning model trained on this task, we identifytwo learning regimes corresponding to distinct phases in the stationary state ofthe SSOU process. These phases emerge from the interplay between two differenttime scales that govern the sequence statistics. Moreover, we observe that whileincreasing the integration window of the AR model always improves performance,albeit with diminishing returns, increasing the non-Markovianity of the inputsequences can improve or degrade its performance. Finally, we performexperiments with recurrent and convolutional neural networks that show that ourobservations carry over to more complicated neural network architectures.

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Modeling Active Non-Markovian Oscillations

Abstract: Modeling noisy oscillations of active systems is one of the current challenges in physics and biology.

Cited by 17 publications

References 69 publications

Exact position distribution of a harmonically-confined run-and-tumble particle in two dimensions

Exact position distribution of a harmonically-confined run-and-tumble particle in two dimensions

Variance sum rule for entropy production

The impact of memory on learning sequence-to-sequence tasks

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