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Robust topological oscillators govern a tunable phase transition to synchronized circadian rhythms
Authors:
Chongbin Zheng,
Peter Thomas,
Evelyn Tang
Abstract:
While synchronization has been well-studied in deterministic oscillators, most underlying oscillators are stochastic in both natural and man-made systems. Yet, the effects of intrinsic stochasticity remain poorly understood. Here, we develop a new mechanism for synchronizing circadian KaiC molecules that have topologically protected cycles. We find a phase transition to synchronization that depend…
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While synchronization has been well-studied in deterministic oscillators, most underlying oscillators are stochastic in both natural and man-made systems. Yet, the effects of intrinsic stochasticity remain poorly understood. Here, we develop a new mechanism for synchronizing circadian KaiC molecules that have topologically protected cycles. We find a phase transition to synchronization that depends only on the single-oscillator coherence, across a range of molecular changes that determine this coherence. Examining both mesoscopic and macroscopic numbers relevant for cellular and in vitro conditions respectively, we find different scaling properties above and below the phase transition. Our results shed light on several existing experiments and further predict that external changes can be offset by compensatory changes that improve the single-oscillator coherence - demonstrating a tunable pathway between stochastic single oscillators and their robust collective rhythms.
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Submitted 16 July, 2026; v1 submitted 14 July, 2026;
originally announced July 2026.
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Topological edge currents promote exploratory chromosome capture in microtubule dynamic instability
Authors:
Chongbin Zheng,
Jaime Agudo-Canalejo,
Jonathon Howard,
Evelyn Tang
Abstract:
Microtubules capture chromosomes during mitosis by stochastically switching between growth and shrinkage at catastrophe events. They display strikingly rich biochemistry and dynamics, regulated by a stabilizing cap with distinct conformational states. Microtubule lengths at catastrophe are observed to follow a peaked distribution, while their growth "stutters" briefly before catastrophe. Such comp…
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Microtubules capture chromosomes during mitosis by stochastically switching between growth and shrinkage at catastrophe events. They display strikingly rich biochemistry and dynamics, regulated by a stabilizing cap with distinct conformational states. Microtubule lengths at catastrophe are observed to follow a peaked distribution, while their growth "stutters" briefly before catastrophe. Such complexity makes it hard to capture all these observations without a large number of tunable parameters. Here, we introduce a topological model of the microtubule cap that reproduces the features above through dynamical edge states, that provides a minimal description with just two free parameters. Our approach further provides an analytical description of catastrophes and allows the same features to persist over a wide range of tubulin concentration, consistent with experimental observations.
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Submitted 5 April, 2026; v1 submitted 15 October, 2025;
originally announced October 2025.
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Topology of the simplest gene switch
Authors:
Aleksandra Nelson,
Peter Wolynes,
Evelyn Tang
Abstract:
Complex gene regulatory networks often display emergent simple behavior. Sometimes this simplicity can be traced to a nearly equivalent energy landscape, but not always. Here, we show how a topological theory for stochastic and biochemical networks can predict phase transitions between dynamical regimes, where the simplest landscape paradigm would fail. We demonstrate the utility of this topologic…
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Complex gene regulatory networks often display emergent simple behavior. Sometimes this simplicity can be traced to a nearly equivalent energy landscape, but not always. Here, we show how a topological theory for stochastic and biochemical networks can predict phase transitions between dynamical regimes, where the simplest landscape paradigm would fail. We demonstrate the utility of this topological approach for a simple gene network, revealing a new oscillatory regime in addition to previously recognized multimodal stationary phases. We show how local winding numbers predict the steady-state locations in the single-mode and bimodal phases, and a flux analysis predicts the respective strengths of the steady-state peaks.
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Submitted 29 October, 2025; v1 submitted 3 March, 2025;
originally announced March 2025.
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Topological phases in discrete stochastic systems
Authors:
Jaime Agudo-Canalejo,
Evelyn Tang
Abstract:
Topological invariants have proved useful for analyzing emergent function as they characterize a property of the entire system, and are insensitive to local details, disorder, and noise. They support boundary states, which reduce the system response to a lower dimensional space and, in 2D systems, offer a mechanism for the emergence of global cycles within a large phase space. Topological invarian…
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Topological invariants have proved useful for analyzing emergent function as they characterize a property of the entire system, and are insensitive to local details, disorder, and noise. They support boundary states, which reduce the system response to a lower dimensional space and, in 2D systems, offer a mechanism for the emergence of global cycles within a large phase space. Topological invariants have been heavily studied in quantum electronic systems and have been observed in other classical platforms such as mechanical lattices. However, this framework largely describes equilibrium systems within an ordered crystalline lattice, whereas biological systems are often strongly non-equilibrium with stochastic components. We review recent developments in topological states in discrete stochastic models in 1D and 2D systems, and initial progress in identifying testable signature of topological states in molecular systems and ecology. These models further provide simple principles for targeted dynamics in synthetic systems and in the engineering of reconfigurable materials. Lastly, we describe novel theoretical properties of these systems such as the necessity for non-Hermiticity in permitting edge states, as well as new analytical tools to reveal these properties. The emerging developments shed light on fundamental principles for non-equilibrium systems and topological protection enabling robust biological function.
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Submitted 9 October, 2025; v1 submitted 6 June, 2024;
originally announced June 2024.
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Non-reciprocity is necessary for robust dimensional reduction and strong responses in stochastic topological systems
Authors:
Aleksandra Nelson,
Evelyn Tang
Abstract:
Topological theory predicts the necessary conditions for robust dimensional reduction in a host of quantum and classical systems. Models have recently been proposed for stochastic systems which describe many biological and chemical phenomena. However, general theoretical principles are lacking for this class of systems, exemplified by the breakdown of the celebrated bulk-edge correspondence. We pr…
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Topological theory predicts the necessary conditions for robust dimensional reduction in a host of quantum and classical systems. Models have recently been proposed for stochastic systems which describe many biological and chemical phenomena. However, general theoretical principles are lacking for this class of systems, exemplified by the breakdown of the celebrated bulk-edge correspondence. We prove that contrary to topological phases in quantum and many classical systems, stochastic systems require non-reciprocal (or non-Hermitian) transitions for robust edge responses, which holds across all dimensions and geometries. We propose a novel explanation of hybridization that destroys edge responses in reciprocal (Hermitian) stochastic systems. Further, we show that stochastic steady states grow dramatically with non-reciprocity, in contrast to their quantum counterparts which plateaus. We analyze the resulting theoretical and physical consequences and how non-reciprocity mitigates the effects of hybridization towards robust edge states in equilibrium and non-equilibrium steady states. These results establish the crucial role of non-reciprocal interactions for responses that are robust to random perturbations in active and living matter.
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Submitted 11 October, 2024; v1 submitted 25 October, 2023;
originally announced October 2023.
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A topological mechanism for robust and efficient global oscillations in biological networks
Authors:
Chongbin Zheng,
Evelyn Tang
Abstract:
Long and stable timescales are often observed in complex biochemical networks, such as in emergent oscillations. How these robust dynamics persist remains unclear, given the many stochastic reactions and shorter time scales demonstrated by underlying components. We propose a topological model that produces long oscillations around the network boundary, reducing the system dynamics to a lower-dimen…
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Long and stable timescales are often observed in complex biochemical networks, such as in emergent oscillations. How these robust dynamics persist remains unclear, given the many stochastic reactions and shorter time scales demonstrated by underlying components. We propose a topological model that produces long oscillations around the network boundary, reducing the system dynamics to a lower-dimensional current in a robust manner. Using this to model KaiC, which regulates the circadian rhythm in cyanobacteria, we compare the coherence of oscillations to that in other KaiC models. Our topological model localizes currents on the system edge, with an efficient regime of simultaneously increased precision and decreased cost. Further, we introduce a new predictor of coherence from the analysis of spectral gaps, and show that our model saturates a global thermodynamic bound. Our work presents a new mechanism and parsimonious description for robust emergent oscillations in complex biological networks.
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Submitted 6 June, 2024; v1 submitted 22 February, 2023;
originally announced February 2023.
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Optimal navigation strategies for microswimmers on curved manifolds
Authors:
Lorenzo Piro,
Evelyn Tang,
Ramin Golestanian
Abstract:
Finding the fastest path to a desired destination is a vitally important task for microorganisms moving in a fluid flow. We study this problem by building an analytical formalism for overdamped microswimmers on curved manifolds and arbitrary flows. We show that the solution corresponds to the geodesics of a Randers metric, which is an asymmetric Finsler metric that reflects the irreversible charac…
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Finding the fastest path to a desired destination is a vitally important task for microorganisms moving in a fluid flow. We study this problem by building an analytical formalism for overdamped microswimmers on curved manifolds and arbitrary flows. We show that the solution corresponds to the geodesics of a Randers metric, which is an asymmetric Finsler metric that reflects the irreversible character of the problem. Using the example of a spherical surface, we demonstrate that the swimmer performance that follows this "Randers policy" always beats a more direct policy. A study of the shape of isochrones reveals features such as self-intersections, cusps, and abrupt nonlinear effects. Our work provides a link between microswimmer physics and geodesics in generalizations of general relativity.
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Submitted 15 October, 2020;
originally announced October 2020.
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Topology protects chiral edge currents in stochastic systems
Authors:
Evelyn Tang,
Jaime Agudo-Canalejo,
Ramin Golestanian
Abstract:
Constructing systems that exhibit time-scales much longer than those of the underlying components, as well as emergent dynamical and collective behavior, is a key goal in fields such as synthetic biology and materials self-assembly. Inspiration often comes from living systems, in which robust global behavior prevails despite the stochasticity of the underlying processes. Here, we present two-dimen…
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Constructing systems that exhibit time-scales much longer than those of the underlying components, as well as emergent dynamical and collective behavior, is a key goal in fields such as synthetic biology and materials self-assembly. Inspiration often comes from living systems, in which robust global behavior prevails despite the stochasticity of the underlying processes. Here, we present two-dimensional stochastic networks that consist of minimal motifs representing out-of-equilibrium cycles at the molecular scale and support chiral edge currents in configuration space. These currents arise in the topological phase due to the bulk-boundary correspondence and dominate the system dynamics in the steady-state, further proving robust to defects or blockages. We demonstrate the topological properties of these networks and their uniquely non-Hermitian features such as exceptional points and vorticity, while characterizing the edge state localization. As these emergent edge currents are associated to macroscopic timescales and length scales, simply tuning a small number of parameters enables varied dynamical phenomena including a global clock, dynamical growth and shrinkage, and synchronization. Our construction provides a novel topological formalism for stochastic systems and fresh insights into non-Hermitian physics, paving the way for the prediction of robust dynamical states in new classical and quantum platforms.
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Submitted 21 July, 2021; v1 submitted 6 October, 2020;
originally announced October 2020.
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Effect of an electric field on liquid helium scintillation produced by fast electrons
Authors:
N. S. Phan,
V. Cianciolo,
S. M. Clayton,
S. A. Currie,
R. Dipert,
T. M. Ito,
S. W. T. MacDonald,
C. M. O'Shaughnessy,
J. C. Ramsey,
G. M. Seidel,
E. Smith,
E. Tang,
Z. Tang,
W. Yao
Abstract:
The dependence on applied electric field ($0 - 40$ kV/cm) of the scintillation light produced by fast electrons and $α$ particles stopped in liquid helium in the temperature range of 0.44 K to 3.12 K is reported. For both types of particles, the reduction in the intensity of the scintillation signal due to the applied field exhibits an apparent temperature dependence. Using an approximate solution…
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The dependence on applied electric field ($0 - 40$ kV/cm) of the scintillation light produced by fast electrons and $α$ particles stopped in liquid helium in the temperature range of 0.44 K to 3.12 K is reported. For both types of particles, the reduction in the intensity of the scintillation signal due to the applied field exhibits an apparent temperature dependence. Using an approximate solution of the Debye-Smoluchowski equation, we show that the apparent temperature dependence for electrons can be explained by the time required for geminate pairs to recombine relative to the detector signal integration time. This finding indicates that the spatial distribution of secondary electrons with respect to their geminate partners possesses a heavy, non-Gaussian tail at larger separations, and has a dependence on the energy of the primary ionization electron. We discuss the potential application of this result to pulse shape analysis for particle detection and discrimination.
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Submitted 14 September, 2020; v1 submitted 6 May, 2020;
originally announced May 2020.
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Quantifying configurational information for a stochastic particle in a flow-field
Authors:
Evelyn Tang,
Ramin Golestanian
Abstract:
Flow-fields are ubiquitous systems that are able to transport vital signalling molecules necessary for system function. While information regarding the location and transport of such particles is often crucial, it is not well-understood how to quantify the information in such stochastic systems. Using the framework of nonequilibrium statistical physics, we develop theoretical tools to address this…
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Flow-fields are ubiquitous systems that are able to transport vital signalling molecules necessary for system function. While information regarding the location and transport of such particles is often crucial, it is not well-understood how to quantify the information in such stochastic systems. Using the framework of nonequilibrium statistical physics, we develop theoretical tools to address this question. We observe that rotation in a flow-field does not explicitly appear in the generalized potential that governs the rate of system entropy production. Specifically, in the neighborhood of a flow-field, rotation contributes to the information content only in the presence of strain -- and then with a comparatively weaker contribution than strain and at higher orders in time. Indeed, strain and especially the flow divergence, contribute most strongly to transport properties such as particle residence time and the rate of information change. These results shed light on how information can be analyzed and controlled in complex artificial and living flow-based systems.
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Submitted 1 September, 2020; v1 submitted 2 November, 2019;
originally announced November 2019.
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Monte Carlo calculation and verification of the geometrical factors for the NPDGamma experiment
Authors:
Kyle B. Grammer,
David Blyth,
James D. Bowman,
Nadia Fomin,
Geoffrey L. Greene,
Matthew Musgrave,
Elise Tang,
Zhaowen Tang
Abstract:
The NPDGamma experiment measures the parity-violating asymmetry in $γ$-ray emission in the capture of polarized neutrons on liquid parahydrogen. The sensitivity to the asymmetry for each detector in the array is used as a parameter in the extraction of the physics asymmetry from the measured data. The detector array is approximately cylindrically symmetric around the target and a step-wise sinusoi…
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The NPDGamma experiment measures the parity-violating asymmetry in $γ$-ray emission in the capture of polarized neutrons on liquid parahydrogen. The sensitivity to the asymmetry for each detector in the array is used as a parameter in the extraction of the physics asymmetry from the measured data. The detector array is approximately cylindrically symmetric around the target and a step-wise sinusoidal function has been used for the sensitivity in the previous iteration of the NPDGamma experiment, but deviations from cylindrical symmetry necessitate the use of a Monte Carlo model to determine corrections to the geometrical factors. For the calculations, source code modifications to MCNPX were done in order to calculate the sensitivity of each cesium iodide detector to the physics asymmetry. We describe the MCNPX model and results from calculations and how the results are validated through measurement of the parity violating asymmetry of $γ$-rays from neutron capture on chlorine.
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Submitted 9 July, 2019;
originally announced July 2019.
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Measurement of the absolute neutron beam polarization from a supermirror polarizer and the absolute efficiency of a neutron spin rotator for the NPDGamma experiment using a polarized $^{3}$He neutron spin-filter
Authors:
M. M. Musgrave,
S. Baessler,
S. Balascuta,
L. Barron-Palos,
D. Blyth,
J. D. Bowman,
T. E. Chupp,
V. Cianciolo,
C. Crawford,
K. Craycraft,
N. Fomin,
J. Fry,
M. Gericke,
R. C. Gillis,
K. Grammer,
G. L. Greene,
J. Hamblen,
C. Hayes,
P. Huffman,
C. Jiang,
S. Kucuker,
M. McCrea,
P. E. Mueller,
S. I. Penttila,
W. M. Snow
, et al. (4 additional authors not shown)
Abstract:
Accurately measuring the neutron beam polarization of a high flux, large area neutron beam is necessary for many neutron physics experiments. The Fundamental Neutron Physics Beamline (FnPB) at the Spallation Neutron Source (SNS) is a pulsed neutron beam that was polarized with a supermirror polarizer for the NPDGamma experiment. The polarized neutron beam had a flux of $\sim10^9$ neutrons per seco…
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Accurately measuring the neutron beam polarization of a high flux, large area neutron beam is necessary for many neutron physics experiments. The Fundamental Neutron Physics Beamline (FnPB) at the Spallation Neutron Source (SNS) is a pulsed neutron beam that was polarized with a supermirror polarizer for the NPDGamma experiment. The polarized neutron beam had a flux of $\sim10^9$ neutrons per second per cm$^2$ and a cross sectional area of 10$\times$12~cm$^2$. The polarization of this neutron beam and the efficiency of a RF neutron spin rotator installed downstream on this beam were measured by neutron transmission through a polarized $^{3}$He neutron spin-filter. The pulsed nature of the SNS enabled us to employ an absolute measurement technique for both quantities which does not depend on accurate knowledge of the phase space of the neutron beam or the $^{3}$He polarization in the spin filter and is therefore of interest for any experiments on slow neutron beams from pulsed neutron sources which require knowledge of the absolute value of the neutron polarization. The polarization and spin-reversal efficiency measured in this work were done for the NPDGamma experiment, which measures the parity violating $γ$-ray angular distribution asymmetry with respect to the neutron spin direction in the capture of polarized neutrons on protons. The experimental technique, results, systematic effects, and applications to neutron capture targets are discussed.
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Submitted 3 April, 2018; v1 submitted 26 March, 2018;
originally announced March 2018.
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Benchmarking measures of network controllability on canonical graph models
Authors:
Elena Wu-Yan,
Richard F. Betzel,
Evelyn Tang,
Shi Gu,
Fabio Pasqualetti,
Danielle S. Bassett
Abstract:
Many real-world systems are composed of many individual components that interact with one another in a complex pattern to produce diverse behaviors. Understanding how to intervene in these systems to guide behaviors is critically important to facilitate new discoveries and therapies in systems biology and neuroscience. A promising approach to optimizing interventions in complex systems is network…
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Many real-world systems are composed of many individual components that interact with one another in a complex pattern to produce diverse behaviors. Understanding how to intervene in these systems to guide behaviors is critically important to facilitate new discoveries and therapies in systems biology and neuroscience. A promising approach to optimizing interventions in complex systems is network control theory, an emerging conceptual framework and associated mathematics to understand how targeted input to nodes in a network system can predictably alter system dynamics. While network control theory is currently being applied to real-world data, the practical performance of these measures on simple networks with pre-specified structure is not well understood. In this study, we benchmark measures of network controllability on canonical graph models, providing an intuition for how control strategy, graph topology, and edge weight distribution mutually depend on one another. Our numerical studies motivate future analytical efforts to gain a mechanistic understanding of the relationship between graph topology and control, as well as efforts to design networks with specific control profiles.
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Submitted 15 June, 2017;
originally announced June 2017.
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Control of Dynamics in Brain Networks
Authors:
Evelyn Tang,
Danielle S. Bassett
Abstract:
The ability to effectively control brain dynamics holds great promise for the enhancement of cognitive function in humans, and the betterment of their quality of life. Yet, successfully controlling dynamics in neural systems is challenging, in part due to the immense complexity of the brain and the large set of interactions that can drive any single change. While we have gained some understanding…
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The ability to effectively control brain dynamics holds great promise for the enhancement of cognitive function in humans, and the betterment of their quality of life. Yet, successfully controlling dynamics in neural systems is challenging, in part due to the immense complexity of the brain and the large set of interactions that can drive any single change. While we have gained some understanding of the control of single neurons, the control of large-scale neural systems -- networks of multiply interacting components -- remains poorly understood. Efforts to address this gap include the construction of tools for the control of brain networks, mostly adapted from control and dynamical systems theory. Informed by current opportunities for practical intervention, these theoretical contributions provide models that draw from a wide array of mathematical approaches. We present intriguing recent developments for effective strategies of control in dynamic brain networks, and we also describe potential mechanisms that underlie such processes. We review efforts in the control of general neurophysiological processes with implications for brain development and cognitive function, as well as the control of altered neurophysiological processes in medical contexts such as anesthesia administration, seizure suppression, and deep-brain stimulation for Parkinson's disease. We conclude with a forward-looking discussion regarding how emerging results from network control -- especially approaches that deal with nonlinear dynamics or more realistic trajectories for control transitions -- could be used to directly address pressing questions in neuroscience.
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Submitted 14 May, 2018; v1 submitted 5 January, 2017;
originally announced January 2017.
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Scaling Properties of Superoscillations and the Extension to Periodic Signals
Authors:
Eugene Tang,
Lovneesh Garg,
Achim Kempf
Abstract:
Superoscillatory wave forms, i.e., waves that locally oscillate faster than their highest Fourier component, possess unusual properties that make them of great interest from quantum mechanics to signal processing. However, the more pronounced the desired superoscillatory behavior is to be, the more difficult it becomes to produce, or even only calculate, such highly fine-tuned wave forms in practi…
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Superoscillatory wave forms, i.e., waves that locally oscillate faster than their highest Fourier component, possess unusual properties that make them of great interest from quantum mechanics to signal processing. However, the more pronounced the desired superoscillatory behavior is to be, the more difficult it becomes to produce, or even only calculate, such highly fine-tuned wave forms in practice. Here, we investigate how this sensitivity to preparation errors scales for a method for constructing superoscillatory functions which is optimal in the sense that it minimizes the energetic expense. We thereby also arrive at very accurate approximations of functions which are so highly superoscillatory that they cannot be calculated numerically. We then investigate to what extent the scaling and sensitivity results for superoscillatory functions on the real line extend to the experimentally important case of superoscillatory functions that are periodic.
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Submitted 30 November, 2015;
originally announced December 2015.