An official website of the United States government
Epithelial-to-mesenchymal transition (EMT) is a fundamental cellular process and plays an essential role in development, tissue regeneration, and cancer metastasis. Interestingly, EMT is not a binary process but instead proceeds with multiple partial intermediate states. However, the functions of these intermediate states are not fully understood. Here, we focus on a general question about how the number of partial EMT states affects cell transformation. First, by fitting a hidden Markov model of EMT with experimental data, we propose a statistical mechanism for EMT in which many unobservable microstates may exist within one of the observable macrostates. Furthermore, we find that increasing the number of intermediate states can accelerate the EMT process and that adding parallel paths or transition layers may accelerate the process even further. Last, a stabilized intermediate state traps cells in one partial EMT state. This work advances our understanding of the dynamics and functions of EMT plasticity during cancer metastasis.
more »
« less
This content will become publicly available on February 1, 2026
What Is a Macrostate? Subjective Observations and Objective Dynamics
We consider the question of whether thermodynamic macrostates are objective consequences of dynamics, or subjective reflections of our ignorance of a physical system. We argue that they are both; more specifically, that the set of macrostates forms the unique maximal partition of phase space which (1) is consistent with our observations (a subjective fact about our ability to observe the system) and (2) obeys a Markov process (an objective fact about the system’s dynamics). We review the ideas of computational mechanics, an information-theoretic method for finding optimal causal models of stochastic processes, and argue that macrostates coincide with the “causal states” of computational mechanics. Defining a set of macrostates thus consists of an inductive process where we start with a given set of observables, and then refine our partition of phase space until we reach a set of states which predict their own future, i.e. which are Markovian. Macrostates arrived at in this way are provably optimal statistical predictors of the future values of our observables.
more »
« less
- Award ID(s):
- 2310834
- PAR ID:
- 10608907
- Publisher / Repository:
- Springer-Nature
- Date Published:
- Journal Name:
- Foundations of Physics
- Volume:
- 55
- Issue:
- 1
- ISSN:
- 0015-9018
- Page Range / eLocation ID:
- 2
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
This paper revisits the parametric analysis of semidefinite optimization problems with respect to the perturbation of the objective function along a fixed direction. We review the notions of invariancy set, nonlinearity interval, and transition point of the optimal partition, and we investigate their characterizations. We show that the set of transition points is finite and the continuity of the optimal set mapping, on the basis of Painlevé–Kuratowski set convergence, might fail on a nonlinearity interval. Under a local nonsingularity condition, we then develop a methodology, stemming from numerical algebraic geometry, to efficiently compute nonlinearity intervals and transition points of the optimal partition. Finally, we support the theoretical results by applying our procedure to some numerical examples.more » « less
-
Abstract Objective. Improvements in recording technology for multi-region simultaneous recordings enable the study of interactions among distinct brain regions. However, a major computational challenge in studying cross-regional, or cross-population dynamics in general, is that the cross-population dynamics can be confounded or masked by within-population dynamics. Approach. Here, we propose cross-population prioritized linear dynamical modeling (CroP-LDM) to tackle this challenge. CroP-LDM learns the cross-population dynamics in terms of a set of latent states using a prioritized learning approach, such that they are not confounded by within-population dynamics. Further, CroP-LDM can infer the latent states both causally in time using only past neural activity and non-causally in time, unlike some prior dynamic methods whose inference is non-causal. Results. First, through comparisons with various LDM methods, we show that the prioritized learning objective in CroP-LDM is key for accurate learning of cross-population dynamics. Second, using multi-regional bilateral motor and premotor cortical recording during a naturalistic movement task, we demonstrate that CroP-LDM better learns cross-population dynamics compared to recent static and dynamic methods, even when using a low dimensionality. Finally, we demonstrate how CroP-LDM can quantify dominant interaction pathways across brain regions in an interpretable manner. Significance. Overall, these results show that our approach can be a useful framework for addressing challenges associated with modeling dynamics across brain regions.more » « less
-
A bstract In the AdS/CFT correspondence, amplitudes associated to connected bulk manifolds with disconnected boundaries have presented a longstanding mystery. A possible interpretation is that they reflect the effects of averaging over an ensemble of boundary theories. But in examples in dimension D ≥ 3, an appropriate ensemble of boundary theories does not exist. Here we sharpen the puzzle by identifying a class of “fixed energy” or “sub-threshold” observables that we claim do not show effects of ensemble averaging. These are amplitudes that involve states that are above the ground state by only a fixed amount in the large N limit, and in particular are far from being black hole states. To support our claim, we explore the example of D = 3, and show that connected solutions of Einstein’s equations with disconnected boundary never contribute to these observables. To demonstrate this requires some novel results about the renormalized volume of a hyperbolic three-manifold, which we prove using modern methods in hyperbolic geometry. Why then do any observables show apparent ensemble averaging? We propose that this reflects the chaotic nature of black hole physics and the fact that the Hilbert space describing a black hole does not have a large N limit.more » « less
-
In this paper, we study a sampling problem where a source takes samples from a Wiener process and transmits them through a wireless channel to a remote estimator. Due to channel fading, interference, and potential collisions, the packet transmissions are unreliable and could take random time durations. Our objective is to devise an optimal causal sampling policy that minimizes the long-term average mean square estimation error. This optimal sampling problem is a recursive optimal stopping problem, which is generally quite difficult to solve. However, we prove that the optimal sampling strategy is, in fact, a simple threshold policy where a new sample is taken whenever the instantaneous estimation error exceeds a threshold. This threshold remains a constant value that does not vary over time. By exploring the structure properties of the recursive optimal stopping problem, a low-complexity iterative algorithm is developed to compute the optimal threshold. This work generalizes previous research by incorporating both transmission errors and random transmission times into remote estimation. Numerical simulations are provided to compare our optimal policy with the zero-wait and age-optimal policies.more » « less
