An analytical approach to engineer multistability in the oscillatory response of a pulse-driven ReRAM

A nonlinear system, exhibiting a unique asymptotic behaviour, while being continuously subject to a stimulus from a certain class, is said to suffer from fading memory. This interesting phenomenon was first uncovered in a non-volatile tantalum oxide-based memristor from Hewlett Packard Labs back in 2016 out of a deep numerical investigation of a predictive mathematical description, known as the Strachan model, later corroborated by experimental validation. It was then found out that fading memory is ubiquitous in non-volatile resistance switching memories. A nonlinear system may however also exhibit a local form of fading memory, in case, under an excitation from a given family, it may approach one of a number of distinct attractors, depending upon the initial condition. A recent bifurcation study of the Strachan model revealed how, under specific train stimuli, composed of two square pulses of opposite polarity per cycle, the simplest form of local fading memory affects the transient dynamics of the aforementioned Resistive Random Access Memory cell, which, would asymptotically act as a bistable oscillator. In this manuscript we propose an analytical methodology, based on the application of analysis tools from Nonlinear System Theory to the Strachan model, to craft the properties of a generalised pulse train stimulus in such a way to induce the emergence of complex local fading memory effects in the nano-device, which would consequently display an interesting tuneable multistable oscillatory response, around desired resistance states. The last part of the manuscript discusses a case study, shedding light on a potential application of the local history erase effects, induced in the device via pulse train stimulation, for compensating the unwanted yet unavoidable drifts in its resistance state under power off conditions.

Turing Instabilities are Not Enough to Ensure Pattern Formation

Symmetry-breaking instabilities play an important role in understanding the mechanisms underlying the diversity of patterns observed in nature, such as in Turing's reaction-diffusion theory, which connects cellular signalling and transport with the development of growth and form. Extensive literature focuses on the linear stability analysis of homogeneous equilibria in these systems, culminating in a set of conditions for transport-driven instabilities that are commonly presumed to initiate self-organisation. We demonstrate that a selection of simple, canonical transport models with only mild multistable non-linearities can satisfy the Turing instability conditions while also robustly exhibiting only transient patterns. Hence, a Turing-like instability is insufficient for the existence of a patterned state. While it is known that linear theory can fail to predict the formation of patterns, we demonstrate that such failures can appear robustly in systems with multiple stable homogeneous equilibria. Given that biological systems such as gene regulatory networks and spatially distributed ecosystems often exhibit a high degree of multistability and nonlinearity, this raises important questions of how to analyse prospective mechanisms for self-organisation.

Dynamical hallmarks of cancer: Phenotypic switching in melanoma and epithelial-mesenchymal plasticity

Phenotypic plasticity was recently incorporated as a hallmark of cancer. This plasticity can manifest along many interconnected axes, such as stemness and differentiation, drug-sensitive and drug-resistant states, and between epithelial and mesenchymal cell-states. Despite growing acceptance for phenotypic plasticity as a hallmark of cancer, the dynamics of this process remains poorly understood. In particular, the knowledge necessary for a predictive understanding of how individual cancer cells and populations of cells dynamically switch their phenotypes in response to the intensity and/or duration of their current and past environmental stimuli remains far from complete. Here, we present recent investigations of phenotypic plasticity from a systems-level perspective using two exemplars: epithelial-mesenchymal plasticity in carcinomas and phenotypic switching in melanoma. We highlight how an integrated computational-experimental approach has helped unravel insights into specific dynamical hallmarks of phenotypic plasticity in different cancers to address the following questions: a) how many distinct cell-states or phenotypes exist?; b) how reversible are transitions among these cell-states, and what factors control the extent of reversibility?; and c) how might cell-cell communication be able to alter rates of cell-state switching and enable diverse patterns of phenotypic heterogeneity? Understanding these dynamic features of phenotypic plasticity may be a key component in shifting the paradigm of cancer treatment from reactionary to a more predictive, proactive approach.

Warming up recurrent neural networks to maximise reachable multistability greatly improves learning

Training recurrent neural networks is known to be difficult when time dependencies become long. In this work, we show that most standard cells only have one stable equilibrium at initialisation, and that learning on tasks with long time dependencies generally occurs once the number of network stable equilibria increases; a property known as multistability. Multistability is often not easily attained by initially monostable networks, making learning of long time dependencies between inputs and outputs difficult. This insight leads to the design of a novel way to initialise any recurrent cell connectivity through a procedure called "warmup" to improve its capability to learn arbitrarily long time dependencies. This initialisation procedure is designed to maximise network reachable multistability, i.e., the number of equilibria within the network that can be reached through relevant input trajectories, in few gradient steps. We show on several information restitution, sequence classification, and reinforcement learning benchmarks that warming up greatly improves learning speed and performance, for multiple recurrent cells, but sometimes impedes precision. We therefore introduce a double-layer architecture initialised with a partial warmup that is shown to greatly improve learning of long time dependencies while maintaining high levels of precision. This approach provides a general framework for improving learning abilities of any recurrent cell when long time dependencies are present. We also show empirically that other initialisation and pretraining procedures from the literature implicitly foster reachable multistability of recurrent cells.

Temporal Mapper: Transition networks in simulated and real neural dynamics

Characterizing large-scale dynamic organization of the brain relies on both data-driven and mechanistic modeling, which demands a low versus high level of prior knowledge and assumptions about how constituents of the brain interact. However, the conceptual translation between the two is not straightforward. The present work aims to provide a bridge between data-driven and mechanistic modeling. We conceptualize brain dynamics as a complex landscape that is continuously modulated by internal and external changes. The modulation can induce transitions between one stable brain state (attractor) to another. Here, we provide a novel method-Temporal Mapper-built upon established tools from the field of topological data analysis to retrieve the network of attractor transitions from time series data alone. For theoretical validation, we use a biophysical network model to induce transitions in a controlled manner, which provides simulated time series equipped with a ground-truth attractor transition network. Our approach reconstructs the ground-truth transition network from simulated time series data better than existing time-varying approaches. For empirical relevance, we apply our approach to fMRI data gathered during a continuous multitask experiment. We found that occupancy of the high-degree nodes and cycles of the transition network was significantly associated with subjects' behavioral performance. Taken together, we provide an important first step toward integrating data-driven and mechanistic modeling of brain dynamics.

Competitive dual-strain SIS epidemiological models with awareness programs in heterogeneous networks: two modeling approaches

Epidemic diseases and media campaigns are closely associated with each other. Considering most epidemics have multiple pathogenic strains, in this paper, we take the lead in proposing two multi-strain SIS epidemic models in heterogeneous networks incorporating awareness programs due to media. For the first model, we assume that the transmission rates for strain 1 and strain 2 depend on the level of awareness campaigns. For the second one, we further suppose that awareness divides susceptible population into two different subclasses. After defining the basic reproductive numbers for the whole model and each strain, we obtain the analytical conditions that determine the extinction, coexistence and absolute dominance of two strains. Moreover, we also formulate its optimal control problem and identify an optimal implementation pair of awareness campaigns using optimal control theory. Given the complexity of the second model, we use the numerical simulations to visualize its different types of dynamical behaviors. Through theoretical and numerical analysis of these two models, we discover some new phenomena. For example, during the persistence analysis of the first model, we find that the characteristic polynomials of two boundary equilibria may have a pair of pure imaginary roots, implying that Hopf bifurcation and periodic solutions may appear. Most strikingly, multistability occurs in the second model and the growth rate of awareness programs (triggered by the infection prevalence) has a multistage impact on the final size of two strains. The numerical results suggest that the spread of a two-strain epidemic can be controlled (even be eradicated) by taking the measures of enhancing awareness transmission, reducing memory fading of aware individuals and ensuring high-level influx and rapid growth of awareness programs appropriately.

Coexistence and local stability of multiple equilibrium points for fractional-order state-dependent switched competitive neural networks with time-varying delays

This paper investigates the coexistence and local stability of multiple equilibrium points for a class of competitive neural networks with sigmoidal activation functions and time-varying delays, in which fractional-order derivative and state-dependent switching are involved at the same time. Some novel criteria are established to ensure that such n-neuron neural networks can have [Formula: see text] total equilibrium points and [Formula: see text] locally stable equilibrium points with m₁+m₂=n, based on the fixed-point theorem, the definition of equilibrium point in the sense of Filippov, the theory of fractional-order differential equation and Lyapunov function method. The investigation implies that the competitive neural networks with switching can possess greater storage capacity than the ones without switching. Moreover, the obtained results include the multistability results of both fractional-order switched Hopfield neural networks and integer-order switched Hopfield neural networks as special cases, thus generalizing and improving some existing works. Finally, four numerical examples are presented to substantiate the effectiveness of the theoretical analysis.

Emergent dynamics of underlying regulatory network links EMT and androgen receptor-dependent resistance in prostate cancer

Advanced prostate cancer patients initially respond to hormone therapy, be it in the form of androgen deprivation therapy or second-generation hormone therapies, such as abiraterone acetate or enzalutamide. However, most men with prostate cancer eventually develop hormone therapy resistance. This resistance can arise through multiple mechanisms, such as through genetic mutations, epigenetic mechanisms, or through non-genetic pathways, such as lineage plasticity along epithelial-mesenchymal or neuroendocrine-like axes. These mechanisms of hormone therapy resistance often co-exist within a single patient's tumor and can overlap within a single cell. There exists a growing need to better understand how phenotypic heterogeneity and plasticity results from emergent dynamics of the regulatory networks governing androgen independence. Here, we investigated the dynamics of a regulatory network connecting the drivers of androgen receptor (AR) splice variant-mediated androgen independence and those of epithelial-mesenchymal transition. Model simulations for this network revealed four possible phenotypes: epithelial-sensitive (ES), epithelial-resistant (ER), mesenchymal-resistant (MR) and mesenchymal-sensitive (MS), with the latter phenotype occurring rarely. We observed that well-coordinated "teams" of regulators working antagonistically within the network enable these phenotypes. These model predictions are supported by multiple transcriptomic datasets both at single-cell and bulk levels, including in vitro EMT induction models and clinical samples. Further, our simulations reveal spontaneous stochastic switching between the ES and MR states. Addition of the immune checkpoint molecule, PD-L1, to the network was able to capture the interactions between AR, PD-L1, and the mesenchymal marker SNAIL, which was also confirmed through quantitative experiments. This systems-level understanding of the driver of androgen independence and EMT could aid in understanding non-genetic transitions and progression of such cancers and help in identifying novel therapeutic strategies or targets.

Multimode function multistability for Cohen-Grossberg neural networks with mixed time delays

In this paper, we are concerned with the multimode function multistability for Cohen-Grossberg neural networks (CGNNs) with mixed time delays. It is introduced the multimode function multistability as well as its specific mathematical expression, which is a generalization of multiple exponential stability, multiple polynomial stability, multiple logarithmic stability, and asymptotic stability. Also, according to the neural network (NN) model and the maximum and minimum values of activation functions, n pairs of upper and lower boundary functions are obtained. Via the locations of the zeros of the n pairs of upper and lower boundary functions, the state space is divided into ∏_i=1ⁿ(2H_i+1) parts correspondingly. By virtue of the reduction to absurdity, continuity of function, Brouwer's fixed point theorem and Lyapunov stability theorem, the criteria for multimode function multistability are acquired. Multiple types of multistability, including multiple exponential stability, multiple polynomial stability, multiple logarithmic stability, and multiple asymptotic stability, can be achieved by selecting different types of function P(t). Two numerical examples are offered to substantiate the generality of the obtained criteria over the existing results.

Multistability of a Two-Dimensional Map Arising in an Influenza Model

In this paper, we propose and analyze a nonsmoothly two-dimensional map arising in a seasonal influenza model. Such map consists of both linear and nonlinear dynamics depending on where the map acts on its domain. The map exhibits a complicated and unpredictable dynamics such as fixed points, period points, chaotic attractors, or multistability depending on the ranges of a certain parameters. Surprisingly, bistable states include not only the coexistence of a stable fixed point and stable period three points but also that of stable period three points and a chaotic attractor. Among other things, we are able to prove rigorously the coexistence of the stable equilibrium and stable period three points for a certain range of the parameters. Our results also indicate that heterogeneity of the population drives the complication and unpredictability of the dynamics. Specifically, the most complex dynamics occur when the underlying basic reproduction number with respect to our model is an intermediate value and the large portion of the population in the same compartment changes in states the following season.

Identification, visualization, statistical analysis and mathematical modeling of high-feedback loops in gene regulatory networks

Background

Feedback loops in gene regulatory networks play pivotal roles in governing functional dynamics of cells. Systems approaches demonstrated characteristic dynamical features, including multistability and oscillation, of positive and negative feedback loops. Recent experiments and theories have implicated highly interconnected feedback loops (high-feedback loops) in additional nonintuitive functions, such as controlling cell differentiation rate and multistep cell lineage progression. However, it remains challenging to identify and visualize high-feedback loops in complex gene regulatory networks due to the myriad of ways in which the loops can be combined. Furthermore, it is unclear whether the high-feedback loop structures with these potential functions are widespread in biological systems. Finally, it remains challenging to understand diverse dynamical features, such as high-order multistability and oscillation, generated by individual networks containing high-feedback loops. To address these problems, we developed HiLoop, a toolkit that enables discovery, visualization, and analysis of several types of high-feedback loops in large biological networks.

Results

HiLoop not only extracts high-feedback structures and visualize them in intuitive ways, but also quantifies the enrichment of overrepresented structures. Through random parameterization of mathematical models derived from target networks, HiLoop presents characteristic features of the underlying systems, including complex multistability and oscillations, in a unifying framework. Using HiLoop, we were able to analyze realistic gene regulatory networks containing dozens to hundreds of genes, and to identify many small high-feedback systems. We found more than a 100 human transcription factors involved in high-feedback loops that were not studied previously. In addition, HiLoop enabled the discovery of an enrichment of high feedback in pathways related to epithelial-mesenchymal transition.

Conclusions

HiLoop makes the study of complex networks accessible without significant computational demands. It can serve as a hypothesis generator through identification and modeling of high-feedback subnetworks, or as a quantification method for motif enrichment analysis. As an example of discovery, we found that multistep cell lineage progression may be driven by either specific instances of high-feedback loops with sparse appearances, or generally enriched topologies in gene regulatory networks. We expect HiLoop’s usefulness to increase as experimental data of regulatory networks accumulate. Code is freely available for use or extension at https://github.com/BenNordick/HiLoop.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12859-021-04405-z.

Pinning multisynchronization of delayed fractional-order memristor-based neural networks with nonlinear coupling and almost-periodic perturbations

This paper concerns the multisynchronization issue for delayed fractional-order memristor-based neural networks with nonlinear coupling and almost-periodic perturbations. First, the coexistence of multiple equilibrium states for isolated subnetwork is analyzed. By means of state-space decomposition, fractional-order Halanay inequality and Caputo derivative properties, the novel algebraic sufficient conditions are derived to ensure that the addressed networks with arbitrary activation functions have multiple locally stable almost periodic orbits or equilibrium points. Then, based on the obtained multistability results, a pinning control strategy is designed to realize the multisynchronization of the N coupled networks. By the aid of graph theory, depth first search method and pinning control law, some sufficient conditions are formulated such that the considered neural networks can possess multiple synchronization manifolds. Finally, the multistability and multisynchronization performance of the considered neural networks with different activation functions are illustrated by numerical examples.

Exact coexistence and locally asymptotic stability of multiple equilibria for fractional-order delayed Hopfield neural networks with Gaussian activation function

This paper explores the multistability issue for fractional-order Hopfield neural networks with Gaussian activation function and multiple time delays. First, several sufficient criteria are presented for ensuring the exact coexistence of 3ⁿ equilibria, based on the geometric characteristics of Gaussian function, the fixed point theorem and the contraction mapping principle. Then, different from the existing methods used in the multistability analysis of fractional-order neural networks without time delays, it is shown that 2ⁿ of 3ⁿ total equilibria are locally asymptotically stable, by applying the theory of fractional-order linear delayed system and constructing suitable Lyapunov function. The obtained results improve and extend some existing multistability works for classical integer-order neural networks and fractional-order neural networks without time delays. Finally, an illustrative example with comprehensive computer simulations is given to demonstrate the theoretical results.

Change not State: Perceptual coupling in multistable displays reflects transient bias induced by perceptual change

We investigated how changes in dynamic spatial context influence visual perception. Specifically, we reexamined the perceptual coupling phenomenon when two multistable displays viewed simultaneously tend to be in the same dominant state and switch in accord. Current models assume this interaction reflecting mutual bias produced by a dominant perceptual state. In contrast, we demonstrate that influence of spatial context is strongest when perception changes. First, we replicated earlier work using bistable kinetic-depth effect displays, then extended it by employing asynchronous presentation to show that perceptual coupling cannot be accounted for by the static context provided by perceptually dominant states. Next, we demonstrated that perceptual coupling reflects transient bias induced by perceptual change, both in ambiguous and disambiguated displays. We used a hierarchical Bayesian model to characterize its timing, demonstrating that the transient bias is induced 50-70 ms after the exogenous trigger event and decays within ~200-300 ms. Both endogenous and exogenous switches led to quantitatively and qualitatively similar perceptual consequences, activating similar perceptual reevaluation mechanisms within a spatial surround. We explain how they can be understood within a transient selective visual attention framework or using local lateral connections within sensory representations. We suggest that observed perceptual effects reflect general mechanisms of perceptual inference for dynamic visual scene perception.

Modeling the Nonlinear Dynamics of Intracellular Signaling Networks

This protocol illustrates a pipeline for modeling the nonlinear behavior of intracellular signaling pathways. At fixed spatial points, nonlinear signaling dynamics are described by ordinary differential equations (ODEs). At constant parameters, these ODEs may have multiple attractors, such as multiple steady states or limit cycles. Standard optimization procedures fine-tune the parameters for the system trajectories localized within the basin of attraction of only one attractor, usually a stable steady state. The suggested protocol samples the parameter space and captures the overall dynamic behavior by analyzing the number and stability of steady states and the shapes of the assembly of nullclines, which are determined as projections of quasi-steady-state trajectories into different 2D spaces of system variables. Our pipeline allows identifying main qualitative features of the model behavior, perform bifurcation analysis, and determine the borders separating the different dynamical regimes within the assembly of 2D parametric planes. Partial differential equation (PDE) systems describing the nonlinear spatiotemporal behavior are derived by coupling fixed point dynamics with species diffusion.

Multistability and associative memory of neural networks with Morita-like activation functions

This paper presents the multistability analysis and associative memory of neural networks (NNs) with Morita-like activation functions. In order to seek larger memory capacity, this paper proposes Morita-like activation functions. In a weakened condition, this paper shows that the NNs with n-neurons have (2m+1)ⁿ equilibrium points (Eps) and (m+1)ⁿ of them are locally exponentially stable, where the parameter m depends on the Morita-like activation functions, called Morita parameter. Also the attraction basins are estimated based on the state space partition. Moreover, this paper applies these NNs into associative memories (AMs). Compared with the previous related works, the number of Eps and AM's memory capacity are extensively increased. The simulation results are illustrated and some reliable associative memories examples are shown at the end of this paper.

Multistability of delayed fractional-order competitive neural networks

This paper is concerned with the multistability of fractional-order competitive neural networks (FCNNs) with time-varying delays. Based on the division of state space, the equilibrium points (EPs) of FCNNs are given. Several sufficient conditions and criteria are proposed to ascertain the multiple O(t^-α)-stability of delayed FCNNs. The O(t^-α)-stability is the extension of Mittag-Leffler stability of fractional-order neural networks, which contains monostability and multistability. Moreover, the attraction basins of the stable EPs of FCNNs are estimated, which shows the attraction basins of the stable EPs can be larger than the divided subsets. These conditions and criteria supplement and improve the previous results. Finally, the results are illustrated by the simulation examples.

Parameter dependence in visual pattern-component rivalry at onset and during prolonged viewing

In multistability, perceptual interpretations ("percepts") of ambiguous stimuli alternate over time. There is considerable debate as to whether similar regularities govern the first percept after stimulus onset and percepts during prolonged presentation. We address this question in a visual pattern-component rivalry paradigm by presenting two overlaid drifting gratings, which participants perceived as individual gratings passing in front of each other ("segregated") or as a plaid ("integrated"). We varied the enclosed angle ("opening angle") between the gratings (experiments 1 and 2) and stimulus orientation (experiment 2). The relative number of integrated percepts increased monotonically with opening angle. The point of equality, where half of the percepts were integrated, was at a smaller opening angle at onset than during prolonged viewing. The functional dependence of the relative number of integrated percepts on opening angle showed a steeper curve at onset than during prolonged viewing. Dominance durations of integrated percepts were longer at onset than during prolonged viewing and increased with opening angle. The general pattern persisted when stimuli were rotated (experiment 2), despite some perceptual preference for cardinal motion directions over oblique directions. Analysis of eye movements, specifically the slow phase of the optokinetic nystagmus (OKN), confirmed the veridicality of participants' reports and provided a temporal characterization of percept formation after stimulus onset. Together, our results show that the first percept after stimulus onset exhibits a different dependence on stimulus parameters than percepts during prolonged viewing. This underlines the distinct role of the first percept in multistability.

Cell memory of epithelial-mesenchymal plasticity in cancer

Fundamental biological processes of cell identity and cell fate determination are controlled by complex regulatory networks. These processes require molecular mechanisms that confer cellular phenotypic memory and state persistence. In this minireview, we will summarize mechanisms of cell memory based on regulatory hysteretic feedback loops and explore epigenetic mechanisms widely represented in nature, with special focus on epithelial-to-mesenchymal plasticity. We will also discuss the functional consequences of cell memory and epithelial-to-mesenchymal plasticity dynamics during development and cancer metastasis.

Multistability and circuit implementation of tabu learning two-neuron model: application to secure biomedical images in IoMT

In this paper, the dynamics of a non-autonomous tabu learning two-neuron model is investigated. The model is obtained by building a tabu learning two-neuron (TLTN) model with a composite hyperbolic tangent function consisting of three hyperbolic tangent functions with different offsets. The possibility to adjust the compound activation function is exploited to report the sensitivity of non-trivial equilibrium points with respect to the parameters. Analysis tools like bifurcation diagram, Lyapunov exponents, phase portraits, and basin of attraction are used to explore various windows in which the neuron model under the consideration displays the uncovered phenomenon of the coexistence of up to six disconnected stable states for the same set of system parameters in a TLTN. In addition to the multistability, nonlinear phenomena such as period-doubling bifurcation, hysteretic dynamics, and parallel bifurcation branches are found when the control parameter is tuned. The analog circuit is built in PSPICE environment, and simulations are performed to validate the obtained results as well as the correctness of the numerical methods. Finally, an encryption/decryption algorithm is designed based on a modified Julia set and confusion-diffusion operations with the sequences of the proposed TLTN model. The security performances of the built cryptosystem are analyzed in terms of computational time (CT = 1.82), encryption throughput (ET = 151.82 MBps), number of cycles (NC = 15.80), NPCR = 99.6256, UACI = 33.6512, χ ²-values = 243.7786, global entropy = 7.9992, and local entropy = 7.9083. Note that the presented values are the optimal results. These results demonstrate that the algorithm is highly secured compared to some fastest neuron chaos-based cryptosystems and is suitable for a sensitive field like IoMT security.

Introduction to dynamical systems analysis in quantitative systems pharmacology: basic concepts and applications

Quantitative systems pharmacology (QSP) can be regarded as a hybrid of pharmacometrics and systems biology. Here, we introduce the basic concepts related to dynamical systems theory that are fundamental to the analysis of systems biology models. Determination of the fixed points and their local stabilities constitute the most important step. Illustration of a phase portrait further helps investigate multistability and bifurcation behavior. As a motivating example, we examine a cell circuit model that deals with tissue inflammation and fibrosis. We show how increasing the severity and duration of inflammatory stimuli divert the system trajectories towards pathological fibrosis. Simulations that involve different parameter values offer important insights into the potential bifurcations and the development of efficient therapeutic strategies. We expect that this tutorial serves as a good starting point for pharmacometricians striving to widen their scope to QSP and physiologically-oriented modeling.

Fracmemristor chaotic oscillator with multistable and antimonotonicity properties

Memristor is a non-linear circuit element in which voltage-current relationship is determined by the previous values of the voltage and current, generally the history of the circuit. The nonlinearity in this component can be considered as a fractional-order form, which yields a fractional memristor (fracmemristor). In this paper, a fractional-order memristor in a chaotic oscillator is applied, while the other electronic elements are of integer order. The fractional-order range is determined in a way that the circuit has chaotic solutions. Also, the statistical and dynamical features of this circuit are analyzed. Tools like Lyapunov exponents and bifurcation diagram show the existence of multistability and antimonotonicity, two less common properties in chaotic circuits.

The elephant in the room: a postphenomenological view on the electronic health record and its impact on the clinical encounter

Use of electronic health records (EHR) within clinical encounters is increasingly pervasive. The digital record allows for data storage and sharing to facilitate patient care, billing, research, patient communication and quality-of-care improvement-all at once. However, this multifunctionality is also one of the main reasons care providers struggle with the EHR. These problems have often been described but are rarely approached from a philosophical point of view. We argue that a postphenomenological case study of the EHR could lead to more in-depth insights. We will focus on two concepts-transparency and multistability-and translate them to the specific situation of the EHR. Transparency is closely related to an embodiment relation in which the user becomes less aware of the technology: it fades into the background, becoming a means of experience. A second key concept is that of multistability, referring to how a technology can serve multiple purposes or can have different meanings in different contexts. The EHR in this sense is multistable by design. Future EHR design could incorporate multistable information differently, allowing the provider to focus on patient care when interacting with the EHR. Moreover we argue that the use of the EHR in the daily workflow should become more transparent, while awareness of the computer in the specific context of the patient-provider relationship should increase.

Multistability in the epithelial-mesenchymal transition network

BACKGROUND

The transitions between epithelial (E) and mesenchymal (M) cell phenotypes are essential in many biological processes like tissue development and cancer metastasis. Previous studies, both modeling and experimental, suggested that in addition to E and M states, the network responsible for these phenotypes exhibits intermediate phenotypes between E and M states. The number and importance of such states is subject to intense discussion in the epithelial-mesenchymal transition (EMT) community.

RESULTS

Previous modeling efforts used traditional bifurcation analysis to explore the number of the steady states that correspond to E, M and intermediate states by varying one or two parameters at a time. Since the system has dozens of parameters that are largely unknown, it remains a challenging problem to fully describe the potential set of states and their relationship across all parameters. We use the computational tool DSGRN (Dynamic Signatures Generated by Regulatory Networks) to explore the intermediate states of an EMT model network by computing summaries of the dynamics across all of parameter space. We find that the only attractors in the system are equilibria, that E and M states dominate across parameter space, but that bistability and multistability are common. Even at extreme levels of some of the known inducers of the transition, there is a certain proportion of the parameter space at which an E or an M state co-exists with other stable steady states.

CONCLUSIONS

Our results suggest that the multistability is broadly present in the EMT network across parameters and thus response of cells to signals may strongly depend on the particular cell line and genetic background.

Didactic model of a simple driven microwave resonant T-L circuit for chaos, multistability and antimonotonicity

A simple driven bipolar junction transistor (BJT) based two-component circuit is presented, to be used as didactic tool by Lecturers, seeking to introduce some elements of complex dynamics to undergraduate and graduate students, using familiar electronic components to avoid the traditional black-box consideration of active elements. Although the effect of the base-emitter (BE) junction is practically suppressed in the model, chaotic phenomena are detected in the circuit at high frequencies (HF), due to both the reactant behavior of the second component, a coil, and to the birth of parasitic capacitances as well as to the effect of the weak nonlinearity from the base-collector (BC) junction of the BJT, which is otherwise always neglected to the favor of the predominant but now suppressed base-emitter one. The behavior of the circuit is analyzed in terms of stability, phase space, time series and bifurcation diagrams, Lyapunov exponents, as well as frequency spectra and Poincaré map section. We find that a limit cycle attractor widens to chaotic attractors through the splitting and the inverse splitting of periods known as antimonotonicity. Coexisting bifurcations confirm the existence of multi-stability behaviors, marked by the simultaneous apparition of different attractors (periodic and chaotic ones) for the same values of system parameters and different initial conditions. This contribution provides an enriching complement in the dynamics of simple chaotic circuits functioning at high frequencies. Experimental lab results are completed with PSpice simulations and theoretical ones.

Multistability and attraction basins of discrete-time neural networks with nonmonotonic piecewise linear activation functions

This paper is concerned with multistability and attraction basins of discrete-time neural networks with nonmonotonic piecewise linear activation functions. Under some reasonable conditions, the addressed networks have (2m+1)ⁿ equilibrium points. (m+1)ⁿ of which are locally asymptotically stable, and the others are unstable. The attraction basins of the locally asymptotically stable equilibrium points are given in the form of hyperspherical regions. These results here, which include existence, uniqueness, locally asymptotical stability, instability and attraction basins of the multiple equilibrium points, generalize and improve the earlier publications. Finally, an illustrative example with numerical simulation is given to show the feasibility and the effectiveness of the theoretical results. The theoretical results and illustrative example indicate that the activation functions improve the storage capacity of neural networks significantly.

Τhe multiple temporalities of deep brain stimulation (DBS) in Greece

This contribution intends to explore patients' lived experience, with a focus on the temporal dimension. On the basis of a qualitative study that led me to interview persons with Parkinson's disease (PD), caregivers, and medical professionals, I develop an empirical and philosophical investigation of the temporalities surrounding the implementation of deep brain stimulation (DBS) in Greece. I raise the issue of access to DBS medical care, and show how distinct temporalities are implied when the patients face such a matter: that of linear time, linked with the medical discourse, the bureaucratic time linked to administrative and financial hurdles in the implementation and maintenance of DBS, and the technological time of the body/technology fusion. I consider initially the impact of technology and health care settings on the lived experience of patients and the enactment of multiple bodies which are interrelated with the social world. I then expand my analysis in order to show that this experience cannot be a solipsistic one, or specific to one physician/patient relationship. It is fully socially shaped.

Multiple Equilibria in a Non-smooth Epidemic Model with Medical-Resource Constraints

The issue of medical-resource constraints has the potential to dramatically affect disease management, especially in developing countries. We analyze a non-smooth epidemic model with nonlinear incidence rate and resource constraints, which defines a vaccination program with vaccination rate proportional to the number of susceptible individuals when this number is below the threshold level and constant otherwise. To better understand the impact of this non-smooth vaccination policy, we provide a comprehensive qualitative analysis of global dynamics for the whole parameter space. As the threshold value varies, the target model admits multistability of three regular equilibria, bistability of two regular equilibria, that of one disease-free equilibrium and one generalized endemic equilibria, and that of one disease-free equilibrium and one crossing cycle. The steady-state regimes include healthy, low epidemic and high epidemic. This suggests the key role of the threshold value, as well as the initial infection condition in disease control. Our findings demonstrate that the case number can be contained at a satisfactorily controllable level or range if eradicating it proves to be impossible.

Graphical requirements for multistationarity in reaction networks and their verification in BioModels

Thomas' necessary conditions for the existence of multiple steady states in gene networks have been proved by Soulé with high generality for dynamical systems defined by differential equations. When applied to (protein) reaction networks however, those conditions do not provide information since they are trivially satisfied as soon as there is a bimolecular or a reversible reaction. Refined graphical requirements have been proposed to deal with such cases. In this paper, we present for the first time a graph rewriting algorithm for checking the refined conditions given by Soliman, and evaluate its practical performance by applying it systematically to the curated branch of the BioModels repository. This algorithm analyzes all reaction networks (of size up to 430 species) in less than 0.05 second per network, and permits to conclude to the absence of multistationarity in 160 networks over 506. The short computation times obtained in this graphical approach are in sharp contrast to the Jacobian-based symbolic computation approach. We also discuss the case of one extra graphical condition by arc rewiring that allows us to conclude on 20 more networks of this benchmark but with a high computational cost. Finally, we study with some details the case of phosphorylation cycles and MAPK signalling models which show the importance of modelling the intermediate complexations with the enzymes in order to correctly analyze the multistationarity capabilities of such biochemical reaction networks.

Single molecules can operate as primitive biological sensors, switches and oscillators

Background

Switch-like and oscillatory dynamical systems are widely observed in biology. We investigate the simplest biological switch that is composed of a single molecule that can be autocatalytically converted between two opposing activity forms. We test how this simple network can keep its switching behaviour under perturbations in the system.

Results

We show that this molecule can work as a robust bistable system, even for alterations in the reactions that drive the switching between various conformations. We propose that this single molecule system could work as a primitive biological sensor and show by steady state analysis of a mathematical model of the system that it could switch between possible states for changes in environmental signals. Particularly, we show that a single molecule phosphorylation-dephosphorylation switch could work as a nucleotide or energy sensor. We also notice that a given set of reductions in the reaction network can lead to the emergence of oscillatory behaviour.

Conclusions

We propose that evolution could have converted this switch into a single molecule oscillator, which could have been used as a primitive timekeeper. We discuss how the structure of the simplest known circadian clock regulatory system, found in cyanobacteria, resembles the proposed single molecule oscillator. Besides, we speculate if such minimal systems could have existed in an RNA world.

Electronic supplementary material

The online version of this article (10.1186/s12918-018-0596-4) contains supplementary material, which is available to authorized users.

Exploring intermediate cell states through the lens of single cells

As our catalog of cell states expands, appropriate characterization of these states and the transitions between them is crucial. Here we discuss the roles of intermediate cell states (ICSs) in this growing collection. We begin with definitions and discuss evidence for the existence of ICSs and their relevance in various tissues. We then provide a list of possible functions for ICSs with examples. Finally, we describe means by which ICSs and their functional roles can be identified from single-cell data or predicted from models.

Putting the "dynamic" back into dynamic functional connectivity

The study of fluctuations in time-resolved functional connectivity is a topic of substantial current interest. As the term "dynamic functional connectivity" implies, such fluctuations are believed to arise from dynamics in the neuronal systems generating these signals. While considerable activity currently attends to methodological and statistical issues regarding dynamic functional connectivity, less attention has been paid toward its candidate causes. Here, we review candidate scenarios for dynamic (functional) connectivity that arise in dynamical systems with two or more subsystems; generalized synchronization, itinerancy (a form of metastability), and multistability. Each of these scenarios arises under different configurations of local dynamics and intersystem coupling: We show how they generate time series data with nonlinear and/or nonstationary multivariate statistics. The key issue is that time series generated by coupled nonlinear systems contain a richer temporal structure than matched multivariate (linear) stochastic processes. In turn, this temporal structure yields many of the phenomena proposed as important to large-scale communication and computation in the brain, such as phase-amplitude coupling, complexity, and flexibility. The code for simulating these dynamics is available in a freeware software platform, the Brain Dynamics Toolbox.

Winnerless competition in clustered balanced networks: inhibitory assemblies do the trick

Balanced networks are a frequently employed basic model for neuronal networks in the mammalian neocortex. Large numbers of excitatory and inhibitory neurons are recurrently connected so that the numerous positive and negative inputs that each neuron receives cancel out on average. Neuronal firing is therefore driven by fluctuations in the input and resembles the irregular and asynchronous activity observed in cortical in vivo data. Recently, the balanced network model has been extended to accommodate clusters of strongly interconnected excitatory neurons in order to explain persistent activity in working memory-related tasks. This clustered topology introduces multistability and winnerless competition between attractors and can capture the high trial-to-trial variability and its reduction during stimulation that has been found experimentally. In this prospect article, we review the mean field description of balanced networks of binary neurons and apply the theory to clustered networks. We show that the stable fixed points of networks with clustered excitatory connectivity tend quickly towards firing rate saturation, which is generally inconsistent with experimental data. To remedy this shortcoming, we then present a novel perspective on networks with locally balanced clusters of both excitatory and inhibitory neuron populations. This approach allows for true multistability and moderate firing rates in activated clusters over a wide range of parameters. Our findings are supported by mean field theory and numerical network simulations. Finally, we discuss possible applications of the concept of joint excitatory and inhibitory clustering in future cortical network modelling studies.

Modelling Time-Dependent Acquisition of Positional Information

Theoretical and computational modelling are crucial to understand dynamics of embryonic development. In this tutorial chapter, we describe two models of gene networks performing time-dependent acquisition of positional information under control of a dynamic morphogen: a toy-model of a bistable gene under control of a morphogen, allowing for the numerical computation of a simple Waddington's epigenetic landscape, and a recently published model of gap genes in Tribolium under control of multiple enhancers. We present detailed commented implementations of the models using python and jupyter notebooks.

Multistability and instability analysis of recurrent neural networks with time-varying delays

This paper provides new theoretical results on the multistability and instability analysis of recurrent neural networks with time-varying delays. It is shown that such n-neuronal recurrent neural networks have exactly [Formula: see text] equilibria, [Formula: see text] of which are locally exponentially stable and the others are unstable, where k₀ is a nonnegative integer such that k₀≤n. By using the combination method of two different divisions, recurrent neural networks can possess more dynamic properties. This method improves and extends the existing results in the literature. Finally, one numerical example is provided to show the superiority and effectiveness of the presented results.

Numerical and experimental studies of stick-slip oscillations in drill-strings

The cyclic nature of the stick-slip phenomenon may cause catastrophic failures in drill-strings or at the very least could lead to the wear of expensive equipment. Therefore, it is important to study the drilling parameters which can lead to stick-slip, in order to develop appropriate control methods for suppression. This paper studies the stick-slip oscillations encountered in drill-strings from both numerical and experimental points of view. The numerical part is carried out based on path-following methods for non-smooth dynamical systems, with a special focus on the multistability in drill-strings. Our analysis shows that, under a certain parameter window, the multistability can be used to steer the response of the drill-strings from a sticking equilibrium or stick-slip oscillation to an equilibrium with constant drill-bit rotation. In addition, a small-scale downhole drilling rig was implemented to conduct a parametric study of the stick-slip phenomenon. The parametric study involves the use of two flexible shafts with varying mechanical properties to observe the effects that would have on stick-slip during operation. Our experimental results demonstrate that varying some of the mechanical properties of the drill-string could in fact control the nature of stick-slip oscillations.

Criticality in the brain: A synthesis of neurobiology, models and cognition

Cognitive function requires the coordination of neural activity across many scales, from neurons and circuits to large-scale networks. As such, it is unlikely that an explanatory framework focused upon any single scale will yield a comprehensive theory of brain activity and cognitive function. Modelling and analysis methods for neuroscience should aim to accommodate multiscale phenomena. Emerging research now suggests that multi-scale processes in the brain arise from so-called critical phenomena that occur very broadly in the natural world. Criticality arises in complex systems perched between order and disorder, and is marked by fluctuations that do not have any privileged spatial or temporal scale. We review the core nature of criticality, the evidence supporting its role in neural systems and its explanatory potential in brain health and disease.

Robustness, flexibility, and sensitivity in a multifunctional motor control model

Motor systems must adapt to perturbations and changing conditions both within and outside the body. We refer to the ability of a system to maintain performance despite perturbations as "robustness," and the ability of a system to deploy alternative strategies that improve fitness as "flexibility." Different classes of pattern-generating circuits yield dynamics with differential sensitivities to perturbations and parameter variation. Depending on the task and the type of perturbation, high sensitivity can either facilitate or hinder robustness and flexibility. Here we explore the role of multiple coexisting oscillatory modes and sensory feedback in allowing multiphasic motor pattern generation to be both robust and flexible. As a concrete example, we focus on a nominal neuromechanical model of triphasic motor patterns in the feeding apparatus of the marine mollusk Aplysia californica. We find that the model can operate within two distinct oscillatory modes and that the system exhibits bistability between the two. In the "heteroclinic mode," higher sensitivity makes the system more robust to changing mechanical loads, but less robust to internal parameter variations. In the "limit cycle mode," lower sensitivity makes the system more robust to changes in internal parameter values, but less robust to changes in mechanical load. Finally, we show that overall performance on a variable feeding task is improved when the system can flexibly transition between oscillatory modes in response to the changing demands of the task. Thus, our results suggest that the interplay of sensory feedback and multiple oscillatory modes can allow motor systems to be both robust and flexible in a variable environment.

Coexistence and local μ-stability of multiple equilibrium points for memristive neural networks with nonmonotonic piecewise linear activation functions and unbounded time-varying delays

In this paper, the coexistence and dynamical behaviors of multiple equilibrium points are discussed for a class of memristive neural networks (MNNs) with unbounded time-varying delays and nonmonotonic piecewise linear activation functions. By means of the fixed point theorem, nonsmooth analysis theory and rigorous mathematical analysis, it is proven that under some conditions, such n-neuron MNNs can have 5ⁿ equilibrium points located in ℜⁿ, and 3ⁿ of them are locally μ-stable. As a direct application, some criteria are also obtained on the multiple exponential stability, multiple power stability, multiple log-stability and multiple log-log-stability. All these results reveal that the addressed neural networks with activation functions introduced in this paper can generate greater storage capacity than the ones with Mexican-hat-type activation function. Numerical simulations are presented to substantiate the theoretical results.

Multistability of complex-valued neural networks with discontinuous activation functions

In this paper, based on the geometrical properties of the discontinuous activation functions and the Brouwer's fixed point theory, the multistability issue is tackled for the complex-valued neural networks with discontinuous activation functions and time-varying delays. To address the network with discontinuous functions, Filippov solution of the system is defined. Through rigorous analysis, several sufficient criteria are obtained to assure the existence of 25ⁿ equilibrium points. Among them, 9ⁿ points are locally stable and 16ⁿ-9ⁿ equilibrium points are unstable. Furthermore, to enlarge the attraction basins of the 9ⁿ equilibrium points, some mild conditions are imposed. Finally, one numerical example is provided to illustrate the effectiveness of the obtained results.

Multistability in a class of stochastic delayed Hopfield neural networks

In this paper, multistability analysis for a class of stochastic delayed Hopfield neural networks is investigated. By considering the geometrical configuration of activation functions, the state space is divided into 2(n) + 1 regions in which 2(n) regions are unbounded rectangles. By applying Schauder's fixed-point theorem and some novel stochastic analysis techniques, it is shown that under some conditions, the 2(n) rectangular regions are positively invariant with probability one, and each of them possesses a unique equilibrium. Then by applying Lyapunov function and functional approach, two multistability criteria are established for ensuring these equilibria to be locally exponentially stable in mean square. The first multistability criterion is suitable to the case where the information on delay derivative is unknown, while the second criterion requires that the delay derivative be strictly less than one. For the constant delay case, the second multistability criterion is less conservative than the first one. Finally, an illustrative example is presented to show the effectiveness of the derived results.

Sharper graph-theoretical conditions for the stabilization of complex reaction networks

Across the landscape of all possible chemical reaction networks there is a surprising degree of stable behavior, despite what might be substantial complexity and nonlinearity in the governing differential equations. At the same time there are reaction networks, in particular those that arise in biology, for which richer behavior is exhibited. Thus, it is of interest to understand network-structural features whose presence enforces dull, stable behavior and whose absence permits the dynamical richness that might be necessary for life. We present conditions on a network's Species-Reaction Graph that ensure a high degree of stable behavior, so long as the kinetic rate functions satisfy certain weak and natural constraints. These graph-theoretical conditions are considerably more incisive than those reported earlier.

The dynamical consequences of seasonal forcing, immune boosting and demographic change in a model of disease transmission

The impact of seasonal effects on the time course of an infectious disease can be dramatic. Seasonal fluctuations in the transmission rate for an infectious disease are known mathematically to induce cyclical behaviour and drive the onset of multistable and chaotic dynamics. These properties of forced dynamical systems have previously been used to explain observed changes in the period of outbreaks of infections such as measles, varicella (chickenpox), rubella and pertussis (whooping cough). Here, we examine in detail the dynamical properties of a seasonally forced extension of a model of infection previously used to study pertussis. The model is novel in that it includes a non-linear feedback term capturing the interaction between exposure and the duration of protection against re-infection. We show that the presence of limit cycles and multistability in the unforced system give rise to complex and intricate behaviour as seasonal forcing is introduced. Through a mixture of numerical simulation and bifurcation analysis, we identify and explain the origins of chaotic regions of parameter space. Furthermore, we identify regions where saddle node lines and period-doubling cascades of different orbital periods overlap, suggesting that the system is particularly sensitive to small perturbations in its parameters and prone to multistable behaviour. From a public health point of view - framed through the 'demographic transition' whereby a population׳s birth rate drops over time (and life-expectancy commensurately increases) - we argue that even weak levels of seasonal-forcing and immune boosting may contribute to the myriad of complex and unexpected epidemiological behaviours observed for diseases such as pertussis. Our approach helps to contextualise these epidemiological observations and provides guidance on how to consider the potential impact of vaccination programs.