arXiv subjects

Michael C. Abbott

Publications and source records attributed to Michael C. Abbott.

At least 19 recordsLinked to original sources

arXiv2026

On the Information Required for Feedback Control

Biological systems across scales, along with many engineering problems, must control noisy systems with limited information. Here we study information-limited feedback control of stochastic systems to achieve target steady states, and derive a lower bound on the information rate from controlled system to controller. This framework allows us to obtain performance-information Pareto frontiers for wide-ranging control problems with limited information. For systems with state-independent passive dynamics, the bound is saturated by an explicit optimal control protocol which probabilistically time-reverses the passive dynamics. We showcase these results through applications to nonlinear particle localization, microbial navigation, and experimentally realized information engines.

cond-mat.stat-mech↗

arXiv2026

Discrete turn strategies emerge in information-limited navigation

Navigation up a smooth sensory gradient is one of the simplest behavioural tasks, and some organisms solve it by making continuous adjustments to their course. Bacteria instead employ a variety of discrete strategies, including run and tumble motion, direction reversals, and turns by specific angles. Here we ask what drives the choice of these strategies, framing the problem as maximising up-gradient speed with a given amount of sensory information per unit time. We find that, without directional information on which way to turn, behavioural strategies that take discrete actions perform better than gradual steering. As the amount of information is increased, we see a series of transitions between optimal strategies, including a shift from direction reversals to fully re-orienting tumbles. Among more complex re-orientation strategies, we show that discrete turn angles are best, and observe transitions in the number of angles employed by the optimal strategy. More broadly, such emergent simplicity in behaviour is a tractable example of a widespread phenomenon in which biology chooses a discrete solution, despite the underlying physics being continuous.

physics.bio-ph↗

arXiv2026

In-vivo entropy production of A. subaru

Entropy production is often used as a proxy for energy consumption of a non-equilibrium system. Lower bounds can be estimated from coarse-grained observations, and this has been done for various biological systems. Here, we apply these tools to a more macroscopic system whose true energy consumption is also known. We find that while entropy production does give a lower bound, it is some 25 orders of magnitude away from being saturated. To be certain of this result, we survey different methods of estimating irreversibility, and write down a novel kNN estimator.

physics.bio-ph↗

arXiv2026

On the Analytic Origin of Two Species of Cochlear Eigenmodes

After entering the ear, sound waves propagate as surface waves along the cochlea's basilar membrane. In recent work, we showed numerically that the system supports two types of modes: localized resonant modes, which underpin the modern understanding of cochlear mechanics, and a novel class of spatially extended modes. Here, we develop an analytic framework that explains the emergence of this mode structure. We show that extended modes arise from globally continuous standing-wave solutions, whereas localized modes result from internal resonance requiring matching across a singular point. These results clarify the generic structure of cochlear wave equations.

physics.bio-ph↗

arXiv2024

Hair cells in the cochlea must tune resonant modes to the edge of instability without destabilizing collective modes

Sound produces surface waves along the cochlea's basilar membrane. To achieve the ear's astonishing frequency resolution and sensitivity to faint sounds, dissipation in the cochlea must be canceled via active processes in hair cells, effectively bringing the cochlea to the edge of instability. But how can the cochlea be globally tuned to the edge of instability with only local feedback? To address this question, we use a discretized version of a standard model of basilar membrane dynamics, but with an explicit contribution from active processes in hair cells. Surprisingly, we find the basilar membrane supports two qualitatively distinct sets of modes: a continuum of localized modes and a small number of collective extended modes. Localized modes sharply peak at their resonant position and are largely uncoupled. As a result, they can be amplified almost independently from each other by local hair cells via feedback reminiscent of self-organized criticality. However, this amplification can destabilize the collective extended modes; avoiding such instabilities places limits on possible molecular mechanisms for active feedback in hair cells. Our work illuminates how and under what conditions individual hair cells can collectively create a critical cochlea.

physics.bio-ph↗

arXiv2023

Far from Asymptopia

Inference from limited data requires a notion of measure on parameter space, most explicit in the Bayesian framework as a prior. Here we demonstrate that Jeffreys prior, the best-known uninformative choice, introduces enormous bias when applied to typical scientific models. Such models have a relevant effective dimensionality much smaller than the number of microscopic parameters. Because Jeffreys prior treats all microscopic parameters equally, it is from uniform when projected onto the sub-space of relevant parameters, due to variations in the local co-volume of irrelevant directions. We present results on a principled choice of measure which avoids this issue, leading to unbiased inference in complex models. This optimal prior depends on the quantity of data to be gathered, and approaches Jeffreys prior in the asymptotic limit. However, this limit cannot be justified without an impossibly large amount of data, exponential in the number of microscopic parameters.

stat.OT↗

arXiv2022

Information geometry for multiparameter models: New perspectives on the origin of simplicity

Complex models in physics, biology, economics, and engineering are often sloppy, meaning that the model parameters are not well determined by the model predictions for collective behavior. Many parameter combinations can vary over decades without significant changes in the predictions. This review uses information geometry to explore sloppiness and its deep relation to emergent theories. We introduce the model manifold of predictions, whose coordinates are the model parameters. Its hyperribbon structure explains why only a few parameter combinations matter for the behavior. We review recent rigorous results that connect the hierarchy of hyperribbon widths to approximation theory, and to the smoothness of model predictions under changes of the control variables. We discuss recent geodesic methods to find simpler models on nearby boundaries of the model manifold -- emergent theories with fewer parameters that explain the behavior equally well. We discuss a Bayesian prior which optimizes the mutual information between model parameters and experimental data, naturally favoring points on the emergent boundary theories and thus simpler models. We introduce a `projected maximum likelihood' prior that efficiently approximates this optimal prior, and contrast both to the poor behavior of the traditional Jeffreys prior. We discuss the way the renormalization group coarse-graining in statistical mechanics introduces a flow of the model manifold, and connect stiff and sloppy directions along the model manifold with relevant and irrelevant eigendirections of the renormalization group. Finally, we discuss recently developed `intensive' embedding methods, allowing one to visualize the predictions of arbitrary probabilistic models as low-dimensional projections of an isometric embedding, and illustrate our method by generating the model manifold of the Ising model.

cond-mat.stat-mech↗

arXiv2021

Resurgence in the O(4) sigma model

We analyze the free energy of the integrable two dimensional O(4) sigma model in a magnetic field. We use Volin's method to extract high number (2000) of perturbative coefficients with very high precision. The factorial growth of these coefficients are regulated by switching to the Borel transform, where we perform several asymptotic analysis. High precision data allowed to identify Stokes constants and alien derivatives with exact expressions. These reveal a nice resurgence structure which enables to formulate the first few terms of the ambiguity free trans-series. We check these results against the direct numerical solution of the exact integral equation and find complete agreement.

hep-th↗

arXiv2021

From perturbative to non-perturbative in the O(4) sigma model

We study the resurgent trans-series for the free energy of the two-dimensional O(4) sigma model in a magnetic field. Exploiting integrability, we obtain very high-order perturbative data, from which we can explore non-perturbative sectors. We are able to determine exactly the leading real-valued exponentially small terms, which we check against the direct numerical solution of the exact integral equation, and find complete agreement.

hep-th↗

arXiv2020

Integrable Field Theories with an Interacting Massless Sector

We present the first known integrable relativistic field theories with interacting massive and massless sectors. And we demonstrate that knowledge of the massless sector is essential for understanding of the spectrum of the massive sector. Terms in this spectrum polynomial in the spatial volume (the accuracy for which the Bethe ansatz would suffice in a massive theory) require not just Lüscher-like corrections (usually exponentially small) but the full TBA integral equations. We are motivated by the implications of these ideas for AdS/CFT, but present here only field-theory results.

hep-th↗

arXiv2019

A scaling law from discrete to continuous solutions of channel capacity problems in the low-noise limit

An analog communication channel typically achieves its full capacity when the distribution of inputs is discrete, composed of just K symbols, such as voltage levels or wavelengths. As the effective noise level goes to zero, for example by sending the same message multiple times, it is known that optimal codes become continuous. Here we derive a scaling law for the optimal number of symbols in this limit, finding a novel rational scaling exponent. The number of symbols in the optimal code grows as $\log K \sim I^{4/3}$, where the channel capacity I increases with decreasing noise. The same scaling applies to other problems equivalent to maximizing channel capacity over a continuous distribution.

cond-mat.stat-mech↗

arXiv2018

Maximizing the information learned from finite data selects a simple model

We use the language of uninformative Bayesian prior choice to study the selection of appropriately simple effective models. We advocate for the prior which maximizes the mutual information between parameters and predictions, learning as much as possible from limited data. When many parameters are poorly constrained by the available data, we find that this prior puts weight only on boundaries of the parameter manifold. Thus it selects a lower-dimensional effective theory in a principled way, ignoring irrelevant parameter directions. In the limit where there is sufficient data to tightly constrain any number of parameters, this reduces to Jeffreys prior. But we argue that this limit is pathological when applied to the hyper-ribbon parameter manifolds generic in science, because it leads to dramatic dependence on effects invisible to experiment.

physics.data-an↗

arXiv2016

Massless Lüscher Terms and the Limitations of the AdS3 Asymptotic Bethe Ansatz

In AdS5/CFT4 integrability the Bethe ansatz gives the spectrum of long strings, accurate up to exponentially small corrections. This is no longer true in AdS3, as we demonstrate here by studying Luscher F-terms with a massless particle running in the loop. We apply this to the classic test of Hernandez & Lopez, in which the su(2) sector Bethe equations (including one-loop dressing phase) should match the semiclassical string theory result for a circular spinning string. These calculations did not agree in AdS3xS3xT4, and we show that the sum of all massless Luscher F-terms can reproduce the difference.

hep-th↗

arXiv2016

Fermionic T-Duality of $AdS_n \times S^n (\times S^n) \times T^m$ using IIA Supergravity

We show that the string backgrounds AdS2 x S2 x T6 and AdSd x Sd x Sd x T{10 - 3d} (d = 2, 3) are self-dual under a series of bosonic and fermionic T-dualities. We do this using the fermionic Buscher rules derived by Berkovits and Maldacena, thus working at the level of the supergravity fields. This allows us to explicitly track the behaviour of the RR fields, from which we see that we need T-duality along some torus directions. For the AdS x S x S cases, which contain cosets of D(2,1;alpha), it is necessary to perform bosonic T-duality along some complexified Killing spinors in one of the spheres.

hep-th↗

arXiv2015

T-Duality of Green-Schwarz Superstrings on AdS(d) x S(d) x M(10-2d)

We verify the self-duality of Green-Schwarz supercoset sigma models on AdS$_d \times S^d $ backgrounds (d=2,3,5) under combined bosonic and fermionic T-dualities without gauge fixing kappa symmetry. We also prove this property for superstrings on AdS$_d \times S^d \times S^d$ (d=2,3) described by supercoset sigma models with the isometries governed by the exceptional Lie supergroups $D(2,1;α)$ (d=2) and $D(2,1;α)\times D(2,1;α)$ (d=3), which requires an additional T-dualisation along one of the spheres. Then, by taking into account the contribution of non-supercoset fermionic modes (up to the second order), we provide evidence for the T-self-duality of the complete type IIA and IIB Green-Schwarz superstring theory on AdS$_d\times S^d \times T^{10-2d}$ (d=2,3) backgrounds with Ramond-Ramond fluxes. Finally, applying the Buscher-like rules to T-dualising supergravity fields, we prove the T-self-duality of the whole class of the AdS$_d\times S^d \times M^{10-2d}$ superbackgrounds with Ramond-Ramond fluxes in the context of supergravity.

hep-th↗

arXiv2015

Macroscopic (and Microscopic) Massless Modes

We study certain spinning strings exploring the flat directions of AdS3 x S3 x S3 x S1, the massless sector cousins of su(2) and sl(2) sector spinning strings. We describe these, and their vibrational modes, using the D(2,1;α)^2 algebraic curve. By exploiting a discrete symmetry of this structure which reverses the direction of motion on the spheres, and alters the masses of the fermionic modes s \to 1-s, we find out how to treat the massless fermions which were previously missing from this formalism. We show that folded strings behave as a special case of circular strings, in a sense which includes their mode frequencies, and we are able to recover this fact in the worldsheet formalism. We use these frequencies to calculate one-loop corrections to the energy, with a version of the Beisert-Tseytlin resummation.

hep-th↗

arXiv2014

An improved AFS phase for AdS3 string integrability

We propose a number of modifications to the classical term in the dressing phase for integrable strings in AdS3 x S3 x S3 x S1, and check these against existing perturbative calculations, crossing symmetry, and the semiclassical limit of the Bethe equations. The principal change is that the phase for different masses should start with a term Q_1 Q_2, like the one-loop AdS3 dressing phase, rather than Q_2 Q_3 as for the original AdS5 AFS phase.

hep-th↗

arXiv2013

Meromorphic Functions and the Topology of Giant Gravitons

Using Mikhailov's map from holomorphic functions to supersymmetric D3-brane solutions, we show how to construct giant gravitons in AdS5 x S5 with toroidal topologies. In the 1/4-BPS sector we show that these are always of the form #^K (S2 x S1), and in the limit in which this becomes a set of m+n perpendicular spherical giants re-connected near to their intersections, we find K in terms of m,n. In the 1/8-BPS sector we find a similar class of solutions.

hep-th↗