History-dependent Dynamics Research Articles

Experimental photonic quantum memristor

Memristive devices are a class of physical systems with history-dependent dynamics characterized by signature hysteresis loops in their input–output relations. In the past few decades, memristive devices have attracted enormous interest in electronics. This is because memristive dynamics is very pervasive in nanoscale devices, and has potentially groundbreaking applications ranging from energy-efficient memories to physical neural networks and neuromorphic computing platforms. Recently, the concept of a quantum memristor was introduced by a few proposals, all of which face limited technological practicality. Here we propose and experimentally demonstrate a novel quantum-optical memristor (based on integrated photonics) that acts on single-photon states. We fully characterize the memristive dynamics of our device and tomographically reconstruct its quantum output state. Finally, we propose a possible application of our device in the framework of quantum machine learning through a scheme of quantum reservoir computing, which we apply to classical and quantum learning tasks. Our simulations show promising results, and may break new ground towards the use of quantum memristors in quantum neuromorphic architectures.

History-dependent dopamine release increases cAMP levels in most basal amygdala glutamatergic neurons to control learning.

Dopaminergic inputs to basal amygdala (BA) instruct learning of motivational salience. This learning depends on intracellular plasticity signals such as cyclic adenosine monophosphate (cAMP), which is regulated by activation of dopamine receptors. We examine the dynamics of dopamine release and downstream signaling during multiple salient events occurring within tens of seconds. We perform real-time tracking and manipulation of cAMP in BA neurons invitro and invivo. Optogenetically evoked release of dopamine drives proportional increases in cAMP in almost all BA glutamatergic neurons, suggesting widespread actions of dopamine across neurons preferring positive or negative valence. This cAMP response decreases across trials with short intertrial intervals owing to depression of dopamine release. No such depression is evident when photostimulating cAMP production directly. cAMP and protein kinase A responses to repeated appetitive or aversive stimuli also exhibit pronounced depression. Thus, history-dependent dynamics of dopamine and cAMP may regulate learning of temporally clustered, salient stimuli.

Generalized entropies, density of states, and non-extensivity

The concept of entropy connects the number of possible configurations with the number of variables in large stochastic systems. Independent or weakly interacting variables render the number of configurations scale exponentially with the number of variables, making the Boltzmann–Gibbs–Shannon entropy extensive. In systems with strongly interacting variables, or with variables driven by history-dependent dynamics, this is no longer true. Here we show that contrary to the generally held belief, not only strong correlations or history-dependence, but skewed-enough distribution of visiting probabilities, that is, first-order statistics, also play a role in determining the relation between configuration space size and system size, or, equivalently, the extensive form of generalized entropy. We present a macroscopic formalism describing this interplay between first-order statistics, higher-order statistics, and configuration space growth. We demonstrate that knowing any two strongly restricts the possibilities of the third. We believe that this unified macroscopic picture of emergent degrees of freedom constraining mechanisms provides a step towards finding order in the zoo of strongly interacting complex systems.

Environmental deformations dynamically shift human spatial memory.

Place and grid cells in the hippocampal formation are commonly thought to support a unified and coherent cognitive map of space. This mapping mechanism faces a challenge when a navigator is placed in a familiar environment that has been deformed from its original shape. Under such circumstances, many transformations could plausibly serve to map a navigator's familiar cognitive map to the deformed space. Previous empirical results indicate that the firing fields of rodent place and grid cells stretch or compress in a manner that approximately matches the environmental deformation, and human spatial memory exhibits similar distortions. These effects have been interpreted as evidence that reshaping a familiar environment elicits an analogously reshaped cognitive map. However, recent work has suggested an alternative explanation, whereby deformation-induced distortions of the grid code are attributable to a mechanism that dynamically anchors grid fields to the most recently experienced boundary, thus causing history-dependent shifts in grid phase. This interpretation raises the possibility that human spatial memory will exhibit similar history-dependent dynamics. To test this prediction, we taught participants the locations of objects in a virtual environment and then probed their memory for these locations in deformed versions of this environment. Across three experiments with variable access to visual and vestibular cues, we observed the predicted pattern, whereby the remembered locations of objects were shifted from trial to trial depending on the boundary of origin of the participant's movement trajectory. These results provide evidence for a dynamic anchoring mechanism that governs both neuronal firing and spatial memory.

Energy Transfer Networks within Upconverting Nanoparticles Are Complex Systems with Collective, Robust, and History-Dependent Dynamics

Applications of photon upconverting nanoparticles (UCNPs) in biological imaging and solar energy conversion demand that their anti-Stokes luminescence be both tunable and efficient. Rational design of more efficient UCNPs requires an understanding of energy transfer (ET) between their lanthanide dopants, dynamics that are typically characterized by measuring luminescence lifetimes. Existing knowledge, however, cannot explain basic observations in lifetime experiments, such as their dependence on excitation power, significantly limiting the generality and reliability of lifetime measurements. Here, we elucidate the origins of the ET dynamics and luminescence lifetimes of Yb3+-, Er3+-co-doped NaYF4 UCNPs using time-resolved luminescence and novel applications of rate equations and stochastic simulations. Experiments and calculations consistently show that at high concentrations of Er3+, the luminescence lifetimes of UCNPs decrease as much as six-fold when excitation power densities are increased over 6 orde...

Phase space volume scaling of generalized entropies and anomalous diffusion scaling governed by corresponding non-linear Fokker-Planck equations

Many physical, biological or social systems are governed by history-dependent dynamics or are composed of strongly interacting units, showing an extreme diversity of microscopic behaviour. Macroscopically, however, they can be efficiently modeled by generalizing concepts of the theory of Markovian, ergodic and weakly interacting stochastic processes. In this paper, we model stochastic processes by a family of generalized Fokker-Planck equations whose stationary solutions are equivalent to the maximum entropy distributions according to generalized entropies. We show that at asymptotically large times and volumes, the scaling exponent of the anomalous diffusion process described by the generalized Fokker-Planck equation and the phase space volume scaling exponent of the generalized entropy bijectively determine each other via a simple algebraic relation. This implies that these basic measures characterizing the transient and the stationary behaviour of the processes provide the same information regarding the asymptotic regime, and consequently, the classification of the processes given by these two exponents coincide.

Nomadic-colonial life strategies enable paradoxical survival and growth despite habitat destruction.

Organisms often exhibit behavioral or phenotypic diversity to improve population fitness in the face of environmental variability. When each behavior or phenotype is individually maladaptive, alternating between these losing strategies can counter-intuitively result in population persistence-an outcome similar to the Parrondo's paradox. Instead of the capital or history dependence that characterize traditional Parrondo games, most ecological models which exhibit such paradoxical behavior depend on the presence of exogenous environmental variation. Here we present a population model that exhibits Parrondo's paradox through capital and history-dependent dynamics. Two sub-populations comprise our model: nomads, who live independently without competition or cooperation, and colonists, who engage in competition, cooperation, and long-term habitat destruction. Nomads and colonists may alternate behaviors in response to changes in the colonial habitat. Even when nomadism and colonialism individually lead to extinction, switching between these strategies at the appropriate moments can paradoxically enable both population persistence and long-term growth.

Single DNA molecule jamming and history-dependent dynamics during motor-driven viral packaging.

In many viruses molecular motors forcibly pack single DNA molecules to near-crystalline density into ~50–100 nm prohead shells1, 2. Unexpectedly, we found that packaging frequently stalls in conditions that induce net attractive DNA-DNA interactions3. Here, we present findings suggesting that this stalling occurs because the DNA undergoes a nonequilibrium jamming transition analogous to that observed in many soft-matter systems, such as colloidal and granular systems4–8. Experiments in which conditions are changed during packaging to switch DNA-DNA interactions between purely repulsive and net attractive reveal strongly history-dependent dynamics. An abrupt deceleration is usually observed before stalling, indicating that a transition in DNA conformation causes an abrupt increase in resistance. Our findings suggest that the concept of jamming can be extended to a single polymer molecule. However, compared with macroscopic samples of colloidal particles5 we find that single DNA molecules jam over a much larger range of densities. We attribute this difference to the nanoscale system size, consistent with theoretical predictions for jamming of attractive athermal particles.9, 10

Steric Effects Induce Geometric Remodeling of Actin Bundles in Filopodia

Filopodia are ubiquitous fingerlike protrusions, spawned by many eukaryotic cells, to probe and interact with their environments. Polymerization dynamics of actin filaments, comprising the structural core of filopodia, largely determine their instantaneous lengths and overall lifetimes. The polymerization reactions at the filopodial tip require transport of G-actin, which enter the filopodial tube from the filopodial base and diffuse toward the filament barbed ends near the tip. Actin filaments are mechanically coupled into a tight bundle by cross-linker proteins. Interestingly, many of these proteins are relatively short, restricting the free diffusion of cytosolic G-actin throughout the bundle and, in particular, its penetration into the bundle core. To investigate the effect of steric restrictions on G-actin diffusion by the porous structure of filopodial actin filament bundle, we used a particle-based stochastic simulation approach. We discovered that excluded volume interactions result in partial and then full collapse of central filaments in the bundle, leading to a hollowed-out structure. The latter may further collapse radially due to the activity of cross-linking proteins, hence producing conical-shaped filament bundles. Interestingly, electron microscopy experiments on mature filopodia indeed frequently reveal actin bundles that are narrow at the tip and wider at the base. Overall, our work demonstrates that excluded volume effects in the context of reaction-diffusion processes in porous networks may lead to unexpected geometric growth patterns and complicated, history-dependent dynamics of intermediate metastable configurations.

Saving and the long shadow of macroeconomic shocks

The global crisis of 2008 raises many questions regarding the long-term response to crises. We know that households that lost access to credit, for example, were forced to adjust and increase saving. But, will households keep on saving more than they would have done otherwise had the global financial crisis not occurred? And for how long will this increased saving persist? Here, we study the degree to which past adverse income shocks increase the saving rates of affected households. We find evidence consistent with history-dependent dynamics: more experience of past crises tends to increase household saving. We follow up with an investigation of the importance of historical exposure for current account dynamics, but find no strong indication that our measure of past exposure is important to the current account's determination. We conclude by estimating the likely impact of the 2008 GFC on future saving.

History-Dependent Excitability as a Single-Cell Substrate of Transient Memory for Information Discrimination

Neurons react differently to incoming stimuli depending upon their previous history of stimulation. This property can be considered as a single-cell substrate for transient memory, or context-dependent information processing: depending upon the current context that the neuron “sees” through the subset of the network impinging on it in the immediate past, the same synaptic event can evoke a postsynaptic spike or just a subthreshold depolarization. We propose a formal definition of History-Dependent Excitability (HDE) as a measure of the propensity to firing in any moment in time, linking the subthreshold history-dependent dynamics with spike generation. This definition allows the quantitative assessment of the intrinsic memory for different single-neuron dynamics and input statistics. We illustrate the concept of HDE by considering two general dynamical mechanisms: the passive behavior of an Integrate and Fire (IF) neuron, and the inductive behavior of a Generalized Integrate and Fire (GIF) neuron with subthreshold damped oscillations. This framework allows us to characterize the sensitivity of different model neurons to the detailed temporal structure of incoming stimuli. While a neuron with intrinsic oscillations discriminates equally well between input trains with the same or different frequency, a passive neuron discriminates better between inputs with different frequencies. This suggests that passive neurons are better suited to rate-based computation, while neurons with subthreshold oscillations are advantageous in a temporal coding scheme. We also address the influence of intrinsic properties in single-cell processing as a function of input statistics, and show that intrinsic oscillations enhance discrimination sensitivity at high input rates. Finally, we discuss how the recognition of these cell-specific discrimination properties might further our understanding of neuronal network computations and their relationships to the distribution and functional connectivity of different neuronal types.

History-dependent dynamics in a generic model of ion channels - an analytic study

Recent experiments have demonstrated that the timescale of adaptation of single neurons and ion channel populations to stimuli slows down as the length of stimulation increases; in fact, no upper bound on temporal timescales seems to exist in such systems. Furthermore, patch clamp experiments on single ion channels have hinted at the existence of large, mostly unobservable, inactivation state spaces within a single ion channel. This raises the question of the relation between this multitude of inactivation states and the observed behavior. In this work we propose a minimal model for ion channel dynamics which does not assume any specific structure of the inactivation state space. The model is simple enough to render an analytical study possible. This leads to a clear and concise explanation of the experimentally observed exponential history-dependent relaxation in sodium channels in a voltage clamp setting, and shows that their recovery rate from slow inactivation must be voltage dependent. Furthermore, we predict that history-dependent relaxation cannot be created by overly sparse spiking activity. While the model was created with ion channel populations in mind, its simplicity and genericalness render it a good starting point for modeling similar effects in other systems, and for scaling up to higher levels such as single neurons which are also known to exhibit multiple time scales.

Joseph Schumpeter LectureIdeology

I develop a model of ideologies as collectively sustained (yet individually rational) distortions in beliefs concerning the proper scope of governments versus markets. In processing and interpreting signals of the efficacy of public and market provision of education, health insurance, pensions, etc., individuals optimally trade off the value of remaining hopeful about their future prospects (or their children's) versus the costs of misinformed decisions. Because these future outcomes also depend on whether other citizens respond to unpleasant facts with realism or denial, endogenous social cognitions emerge. Thus, an equilibrium in which people acknowledge the limitations of interventionism coexists with one in which they remain obstinately blind to them, embracing a statist ideology and voting for an excessively large government. Conversely, an equilibrium associated with appropriate public responses to market failures coexists with one dominated by a laissez-faire ideology and blind faith in the invisible hand. With public-sector capital, this interplay of beliefs and institutions leads to history-dependent dynamics. The model also explains why societies find it desirable to set up constitutional protections for dissenting views, even when ex-post everyone would prefer to ignore unwelcome news.

Memory in Microbes: Quantifying History-Dependent Behavior in a Bacterium

Memory is usually associated with higher organisms rather than bacteria. However, evidence is mounting that many regulatory networks within bacteria are capable of complex dynamics and multi-stable behaviors that have been linked to memory in other systems. Moreover, it is recognized that bacteria that have experienced different environmental histories may respond differently to current conditions. These “memory” effects may be more than incidental to the regulatory mechanisms controlling acclimation or to the status of the metabolic stores. Rather, they may be regulated by the cell and confer fitness to the organism in the evolutionary game it participates in. Here, we propose that history-dependent behavior is a potentially important manifestation of memory, worth classifying and quantifying. To this end, we develop an information-theory based conceptual framework for measuring both the persistence of memory in microbes and the amount of information about the past encoded in history-dependent dynamics. This method produces a phenomenological measure of cellular memory without regard to the specific cellular mechanisms encoding it. We then apply this framework to a strain of Bacillus subtilis engineered to report on commitment to sporulation and degradative enzyme (AprE) synthesis and estimate the capacity of these systems and growth dynamics to ‘remember’ 10 distinct cell histories prior to application of a common stressor. The analysis suggests that B. subtilis remembers, both in short and long term, aspects of its cell history, and that this memory is distributed differently among the observables. While this study does not examine the mechanistic bases for memory, it presents a framework for quantifying memory in cellular behaviors and is thus a starting point for studying new questions about cellular regulation and evolutionary strategy.

History-dependent multiple-time-scale dynamics in a single-neuron model.

History-dependent characteristic time scales in dynamics have been observed at several levels of organization in neural systems. Such dynamics can provide powerful means for computation and memory. At the level of the single neuron, several microscopic mechanisms, including ion channel kinetics, can support multiple-time-scale dynamics. How the temporally complex channel kinetics gives rise to dynamical properties of the neuron is not well understood. Here, we construct a model that captures some features of the connection between these two levels of organization. The model neuron exhibits history-dependent multiple-time-scale dynamics in several effects: first, after stimulation, the recovery time scale is related to the stimulation duration by a power-law scaling; second, temporal patterns of neural activity in response to ongoing stimulation are modulated over time; finally, the characteristic time scale for adaptation after a step change in stimulus depends on the duration of the preceding stimulus. All these effects have been observed experimentally and are not explained by current single-neuron models. The model neuron here presented is composed of an ensemble of ion channels that can wander in a large pool of degenerate inactive states and thus exhibits multiple-time-scale dynamics at the molecular level. Channel inactivation rate depends on recent neural activity, which in turn depends through modulations of the neural response function on the fraction of active channels. This construction produces a model that robustly exhibits nonexponential history-dependent dynamics, in qualitative agreement with experimental results.

Models of plastic depinning of driven disordered systems

Two classes of models of driven disordered systems that exhibit history-dependent dynamics are discussed. The first class incorporates local inertia in the dynamics via nonmonotonic stress transfer between adjacent degrees of freedom. The second class allows for proliferation of topological defects due to the interplay of strong disorder and drive. In mean field theory both models exhibit a tricritical point as a function of disorder strength. At weak disorder depinning is continuous and the sliding state is unique. At strong disorder depinning is discontinuous and hysteretic.

Molecular dynamics simulation of reconstructive phase transitions on an anhydrous zeolite

The structural transformation of a framework aluminosilicate, $\mathrm{Li}\text{\ensuremath{-}}\mathrm{ABW}$, is studied using molecular dynamics. The calculations are carried out by applying the method presented by Marto\ifmmode \check{n}\else \v{n}\fi{}\'ak et al. [Phys. Rev. Lett. 90, 075503 (2003)], that allows for the exploration of the Gibbs free energy as a function of the cell parameters by history-dependent dynamics. We show that this technique allows for an extensive exploration of the phase space also for complex polyatomic material, such as a zeolite, and allows for the successful prediction of a reconstructive phase transition at the pressure and temperature of experimental relevance. In particular, we observe a reconstructive transition from anhydrous $\mathrm{Li}\text{\ensuremath{-}}\mathrm{ABW}$ to eucryptite at the temperature of $\ensuremath{\sim}920\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, as experimentally observed. The steps initiating the transformation and the transition pathway are discussed.

Learning Dynamics, Lock-In, and Equilibrium Selection in Experimental Coordination Games

This paper compares the leading theoretical approaches to equilibrium selection, both traditional and adaptive, in the light of recent experiments by Van Huyck, Battalio, and Beil (henceforth "VHBB") in which subjects repeatedly played coordination games, uncertain only about each other's strategy choices. The large strategy spaces of VHBB's designs and the variety of interaction patterns they considered yielded rich dynamics, with systematic differences in limiting outcomes across treatments. Explaining these differences promises to shed considerable light on equilibrium selection and coordination more generally, in the field as well as the laboratory. Following earlier analyses by Bruno Broseta and myself, I propose a model that gives a flexible characterization of individual behavior and allows for strategic uncertainty, in the form of idiosyncratic random shocks to players' adjustments. The model includes representatives of the leading approaches to equilibrium selection, which are distinguished by different values of behavioral parameters, including variances that represent the level of strategic uncertainty. The model provides a framework within which to estimate the parameters econometrically, using data from the experiments. The estimates suggest that VHBB's treatments evoked high initial levels of strategic uncertainty, declining steadily to zero as subjects learned to predict each other's responses. The resulting model has nonstationary transition probabilities and history-dependent dynamics that lock in on an equilibrium of the stage game, whose prior probability distribution is nondegenerate due to persistent effects of strategic uncertainty. The analysis shows that even when strategic uncertainty is eventually eliminated by learning, it imparts a drift to the learning dynamics, whose magnitude and direction depend on the environment and the behavioral parameters. This drift makes the distribution of the limiting outcome vary across treatments much as its empirical frequency distribution varied in the experiments. In this sense, taking the persistent effects of strategic uncertainty into account allows a simple, unified explanation of VHBB's results.

Optimal signalling in attractor neural networks

In a recent paper we presented a methodological framework describing the two iteration performance of Hopfield-like attractor neural networks with history-dependent Bayesian dynamics. We now extend this analysis in a number of directions: input patterns applied to small subsets of neurons, general connectivity architectures and more efficient use of history. We show that the optimal signal (activation) function has a slanted sigmoidal shape, and provide an intuitive mount of activation functions with a non-monotone shape. This function endows the analytical model with some properties characteristic of cortical neurons' firing.

History-dependent attractor neural networks

We present a methodological framework enabling a detailed description of the performance of Hopfield-like attractor neural networks (ANN) in the first two iterations. Using the Bayesian approach, we find that performance is improved when a history-based term is included in the neuron's dynamics. A further enhancement of the network's performance is achieved by judiciously choosing the censored neurons (those which become active in a given iteration) on the basis of the magnitude of their post-synaptic potentials. The contribution of biologically plausible, censored, history-dependent dynamics is especially marked in conditions of low firing activity and sparse connectivity, two important characteristics of the mammalian cortex. In such networks, the performance attained is higher than the performance of two 'independent' iterations, which represents an upper bound on the performance of history-independent networks.