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Amir Erez

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cond-mat.stat-mech Biological Physics cond-mat.supr-con cond-mat.dis-nn math.DS Molecular Networks Quantitative Methods

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preprint2026arXiv

Non-Monotone Response Modules and Cascades from the EML Operator for Reduced Models of Biological Dynamics

Standard saturating response functions, such as the Hill function, are monotone and therefore cannot represent recruitment-induced overshoot or adaptive transients with a single block. Reproducing such non-monotone responses from saturating primitives requires at least a difference of two blocks with opposing amplitudes, doubling the static-block parameter count. Here, building on a recent mathematical result that a single binary operator, EML, generates all standard elementary functions, we use EML as a structured grammar for reduced nonlinear ODEs. This yields an activation-suppression module that captures overshoot directly. We validate the framework in three settings. First, on PKA-R relocalization data, the EML grammar discovers a reduced surrogate consistent with established mechanistic biology. Second, on Rho-GTPase recruitment data, an exhaustive search over EML expression trees selects the same compositional form across all four perturbation-response traces. Third, a 50-state simulated network is compressed by an EML cascade acting as a fixed temporal basis. Thus we demonstrate the power and potential of EML for reduced models of biological dynamics.

preprint2020arXiv

Cell-to-cell information at a feedback-induced bifurcation point

A ubiquitous way that cells share information is by exchanging molecules. Yet, the fundamental ways that this information exchange is influenced by intracellular dynamics remain unclear. Here we use information theory to investigate a simple model of two interacting cells with internal feedback. We show that cell-to-cell molecule exchange induces a collective two-cell critical point and that the mutual information between the cells peaks at this critical point. Information can remain large far from the critical point on a manifold of cellular states, but scales logarithmically with the correlation time of the system, resulting in an information-correlation time tradeoff. This tradeoff is strictly imposed, suggesting the correlation time as a proxy for the mutual information.

preprint2013arXiv

How to measure the spatial correlations in disordered Berezinski-Kosterlitz-Thouless transition ?

The Berezinski-Kosterlitz-Thouless transition is a unique two dimensional phase transition, separating two phases with exponentially and power-law decaying correlations, respectively. In disordered systems, these correlations propagate along favorable paths, with the transition marking the point where global coherence is lost. Here we propose an experimental method to probe locally these particular paths in superconducting thin films, which exhibit this transition, and demonstrate theoretically that close to the transition the coherence propagate along a ramified network, reminiscent of a percolation transition. We suggest and calculate experimentally accessible quantities that can shed light on the spatial correlations in the system as it approaches the critical point.

preprint2013arXiv

The effect of amplitude fluctuations on the BKT transition

The Berezinskii-Kosterlitz-Thouless (BKT) transition is a generic transition describing the loss of coherence in two dimensional systems, and has been invoked, for example, to describe the superconductor-insulator transition in thin films. However, recent experiments have shown that the BKT transition, driven by phase fluctuations, is not sufficient to describe the loss of superconducting order, and amplitude fluctuations have also to be taken into account. The standard models that are extensively used to model two-dimensional superconductors are the Hubbard and XY models. Whereas the XY model allows only phase fluctuations, the Hubbard model has an extra degree of freedom: amplitude fluctuations. In this paper we compare two Hubbard models with the same critical temperature but with different interaction, and deduce the role of the amplitude fluctuations in the superconducting transition. For this purpose, a novel approximation is presented and used. We derive an effective phase-only (XY) Hamiltonian, incorporating amplitude fluctuations in an explicit temperature dependence of the phase rigidity. We study the relation between amplitude fluctuations and coupling strength. Our results support existing claims about the suppression of phase rigidity due to amplitude fluctuations not present in the XY model.

preprint2012arXiv

The Kibble-Zurek Problem: Universality and the Scaling Limit

Near a critical point, the equilibrium relaxation time of a system diverges and any change of control/thermodynamic parameters leads to non-equilibrium behavior. The Kibble-Zurek problem is to determine the dynamical evolution of the system parametrically close to its critical point when the change is parametrically slow. The non-equilibrium behavior in this limit is controlled entirely by the critical point and the details of the trajectory of the system in parameter space (the protocol) close to the critical point. Together, they define a universality class consisting of critical exponents-discussed in the seminal work by Kibble and Zurek-and scaling functions for physical quantities, which have not been discussed hitherto. In this article, we give an extended and pedagogical discussion of the universal content in the Kibble-Zurek problem. We formally define a scaling limit for physical quantities near classical and quantum transitions for different sets of protocols. We report computations of a few scaling functions in model Gaussian and large-N problems and prove their universality with respect to protocol choice. We also introduce a new protocol in which the critical point is approached asymptotically at late times with the system marginally out of equilibrium, wherein logarithmic violations to scaling and anomalous dimensions occur even in the simple Gaussian problem.