arXiv subjects

Evelyn Tang

Publications and source records attributed to Evelyn Tang.

At least 19 recordsLinked to original sources

arXiv2026

Robust topological oscillators govern a tunable phase transition to synchronized circadian rhythms

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.

physics.bio-ph↗

arXiv2026

The unique control features of topological stochastic and quantum systems

Topological phases support edge states that can be robust to material deformations and other perturbations. While well-studied in quantum systems, topological phases have also been observed in stochastic and biochemical systems, yet it remains unclear which of their properties remain similar or different from those in quantum systems. In this paper, we derive analytical expressions for the spectral properties of simple quantum and stochastic models on the same lattice to rigorously characterize these complex systems. Intriguingly, we find that non-reciprocity moves states away from the steady-state in stochastic systems while clustering states at zero-energy in quantum systems. In contrast, making the system more topological does the opposite: it clusters more states around the steady-state in stochastic systems but moves states away from the zero-energy state in quantum systems. These results provide control parameters for selection and modulation of different purposes while quantifying the size of gap which protects the longest-lived states. Lastly, we discover a mode unique to stochastic systems that we dub the topologically emerging state, which persists across different models and dimensions, including in the presence of non-equilibrium currents.

cond-mat.stat-mech↗

arXiv2026

Analytical topological invariants for 2D non-Hermitian phases using Morse theory

As energy dissipation and gain are ubiquitous in the real world, such phenomena demand the generalization of Hermitian methods such as the analysis of topological properties for non-Hermitian systems. However, as non-Hermitian systems typically contain more degrees of freedom, this poses a challenge for analytical approaches to understand their topology and invariants. In this work, we analytically calculate the 2D Zak phase for a 2D non-Hermitian SSH-type Hamiltonian that supports a rich structure and edge currents. Closed-form expressions for eigenstates and divisions of the phase diagram are obtained, including for regions in the phase diagram where different types of exceptional points exist. We use Morse theory to determine the topology of exceptional points in momentum space. Although the band structure breaks down at exceptional points, we show that a specific phase-based topological invariant remains well-defined. Furthermore, our work yields an analytic derivation for counting edge states in the Hermitian limit. These results provide new conceptual and analytical tools for the study of complex topological systems.

cond-mat.mes-hall↗

arXiv2025

Topological edge currents promote exploratory chromosome capture in microtubule dynamic instability

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.

physics.bio-ph↗

arXiv2025

Topology of the simplest gene switch

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.

physics.bio-ph↗

arXiv2024

Topological edge flows drive macroscopic re-organization in magnetic colloids

Magnetic colloids can be driven with time-varying fields to form clusters and voids that re-organize over vastly different timescales. However, the driving force behind these non-equilibrium dynamics is not well-understood. Here, we introduce a topological framework that predicts protected edge flows despite strong thermal motion. Notably, these edge flows produce shear stress that creates global rotation of clusters but not of voids. We verify this theory experimentally using micron-sized super-paramagnetic colloids to demonstrate these emergent physical predictions and show how they drive system re-organization differentially at long timescales. Our results elucidate fundamental principles that shape and control non-equilibrium colloidal aggregates.

cond-mat.soft↗

arXiv2024

A topological mechanism for robust and efficient global oscillations in biological networks

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.

physics.bio-ph↗

arXiv2024

Topological phases in discrete stochastic systems

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.

cond-mat.stat-mech↗

arXiv2023

Non-reciprocity is necessary for robust dimensional reduction and strong responses in stochastic topological systems

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.

cond-mat.stat-mech↗

arXiv2021

A topological fluctuation theorem

Fluctuation theorems specify the non-zero probability to observe negative entropy production, contrary to a naive expectation from the second law of thermodynamics. For closed particle trajectories in a fluid, Stokes theorem can be used to give a geometric characterization of the entropy production. Building on this picture, we formulate a topological fluctuation theorem that depends only by the winding number around each vortex core and is insensitive to other aspects of the force. The probability is robust to local deformations of the particle trajectory, reminiscent of topologically protected modes in various classical and quantum systems. We demonstrate that entropy production is quantized in these strongly fluctuating systems, and it is controlled by a topological invariant. We demonstrate that the theorem holds even when the probability distributions are non-Gaussian functions of the generated heat.

cond-mat.stat-mech↗

arXiv2021

Topology protects chiral edge currents in stochastic systems

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.

cond-mat.stat-mech↗

arXiv2020

Optimal navigation strategies for microswimmers on curved manifolds

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.

physics.bio-ph↗

arXiv2020

Quantifying configurational information for a stochastic particle in a flow-field

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.

cond-mat.stat-mech↗

arXiv2020

The control of brain network dynamics across diverse scales of space and time

The human brain is composed of distinct regions that are each associated with particular functions and distinct propensities for the control of neural dynamics. However, the relation between these functions and control profiles is poorly understood, as is the variation in this relation across diverse scales of space and time. Here we probe the relation between control and dynamics in brain networks constructed from diffusion tensor imaging data in a large community based sample of young adults. Specifically, we probe the control properties of each brain region and investigate their relationship with dynamics across various spatial scales using the Laplacian eigenspectrum. In addition, through analysis of regional modal controllability and partitioning of modes, we determine whether the associated dynamics are fast or slow, as well as whether they are alternating or monotone. We find that brain regions that facilitate the control of energetically easy transitions are associated with activity on short length scales and slow time scales. Conversely, brain regions that facilitate control of difficult transitions are associated with activity on long length scales and fast time scales. Built on linear dynamical models, our results offer parsimonious explanations for the activity propagation and network control profiles supported by regions of differing neuroanatomical structure.

q-bio.NC↗

arXiv2018

Network architecture of energy landscapes in mesoscopic quantum systems

Mesoscopic quantum systems exhibit complex many-body quantum phenomena, where interactions between spins and charges give rise to collective modes and topological states. Even simple, non-interacting theories display a rich landscape of energy states --- distinct many-particle configurations connected by spin- and energy-dependent transition rates. The collective energy landscape is difficult to characterize or predict, especially in regimes of frustration where many-body effects create a multiply degenerate landscape. Here we use network science to characterize the complex interconnection patterns of these energy-state transitions. Using an experimentally verified computational model of electronic transport through quantum antidots, we construct networks where nodes represent accessible energy states and edges represent allowed transitions. We then explore how physical changes in currents and voltages are reflected in the network topology. We find that the networks exhibit Rentian scaling, which is characteristic of efficient transportation systems in computer circuitry, neural circuitry, and human mobility, and can be used to measure the interconnection complexity of a network. Remarkably, networks corresponding to points of frustration in quantum transport (due, for example, to spin-blockade effects) exhibit an enhanced topological complexity relative to networks not experiencing frustration. Our results demonstrate that network characterizations of the abstract topological structure of energy landscapes can capture salient properties of quantum transport. More broadly, our approach motivates future efforts to use network science in understanding the dynamics and control of complex quantum systems.

cond-mat.mes-hall↗

arXiv2018

Effective learning is accompanied by high dimensional and efficient representations of neural activity

A fundamental cognitive process is the ability to map value and identity onto objects as we learn about them. Exactly how such mental constructs emerge and what kind of space best embeds this mapping remains incompletely understood. Here we develop tools to quantify the space and organization of such a mapping, thereby providing a framework for studying the geometric representations of neural responses as reflected in functional MRI. Considering how human subjects learn the values of novel objects, we show that quick learners have a higher dimensional geometric representation than slow learners, and hence more easily distinguishable whole-brain responses to objects of different value. Furthermore, we find that quick learners display a more compact embedding of their neural responses and hence have a higher ratio of their task-based dimension to their embedding dimension -- consistent with a greater efficiency of cognitive coding. Lastly, we investigate the neurophysiological drivers of high dimensional patterns at both regional and voxel levels, and we complete our study with a complementary test of the distinguishability of associated whole-brain responses. Our results demonstrate a spatial organization of neural responses characteristic of learning, and offer a suite of geometric measures applicable to the study of efficient coding in higher-order cognitive processes more broadly.

q-bio.NC↗

arXiv2018

Control of Dynamics in Brain Networks

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.

q-bio.QM↗

arXiv2018

Sex differences in network controllability as a predictor of executive function in youth

Executive function emerges late in development and displays different developmental trends in males and females. Sex differences in executive function in youth have been linked to vulnerability to psychopathology as well as to behaviors that impinge on health. Yet, the neurobiological basis of these differences is not well understood. Here we test the hypothesis that sex differences in executive function in youth stem from sex differences in the controllability of structural brain networks as they rewire over development. Combining methods from network neuroscience and network control theory, we characterize the network control properties of structural brain networks estimated from diffusion imaging data acquired in males and females in a sample of 882 youth aged 8-22 years. We summarize the control properties of these networks by estimating average and modal controllability, two statistics that probe the ease with which brain areas can drive the network towards easy- versus difficult-to-reach states. We find that females have higher modal controllability in frontal, parietal, and subcortical regions while males have higher average controllability in frontal and subcortical regions. Furthermore, average controllability values in the medial frontal cortex and subcortex, both higher in males, are negatively related to executive function. Finally, we find that average controllability predicts sex-dependent individual differences in activation during an n-back working memory task. Taken together, our findings support the notion that sex differences in the controllability of structural brain networks can partially explain sex differences in executive function. Controllability of structural brain networks also predicts features of task-relevant activation, suggesting the potential for controllability to represent context-specific constraints on network state more generally.

q-bio.NC↗