Spatial patterns in ecological systems: from microbial colonies to landscapes

Self-organized spatial patterns are ubiquitous in ecological systems and allow populations to adopt non-trivial spatial distributions starting from disordered configurations. These patterns form due to diverse nonlinear interactions among organisms and between organisms and their environment, and lead to the emergence of new (eco)system-level properties unique to self-organized systems. Such pattern consequences include higher resilience and resistance to environmental changes, abrupt ecosystem collapse, hysteresis loops, and reversal of competitive exclusion. Here, we review ecological systems exhibiting self-organized patterns. We establish two broad pattern categories depending on whether the self-organizing process is primarily driven by nonlinear density-dependent demographic rates or by nonlinear density-dependent movement. Using this organization, we examine a wide range of observational scales, from microbial colonies to whole ecosystems, and discuss the mechanisms hypothesized to underlie observed patterns and their system-level consequences. For each example, we review both the empirical evidence and the existing theoretical frameworks developed to identify the causes and consequences of patterning. Finally, we trace qualitative similarities across systems and propose possible ways of developing a more quantitative understanding of how self-organization operates across systems and observational scales in ecology.

Rate-induced collapse in evolutionary systems

Recent work has highlighted the possibility of 'rate-induced tipping', in which a system undergoes an abrupt transition when a perturbation exceeds a critical rate of change. Here, we argue that this is widely applicable to evolutionary systems: collapse, or extinction, may occur when external changes occur too fast for evolutionary adaptation to keep up. To bridge existing theoretical frameworks, we develop a minimal evolutionary-ecological model showing that rate-induced extinction and the established notion of 'evolutionary rescue' are fundamentally two sides of the same coin: the failure of one implies the other, and vice versa. We compare the minimal model's behaviour with that of a more complex model in which the large-scale dynamics emerge from the interactions of many individual agents; in both cases, there is a well-defined threshold rate to induce extinction, and a consistent scaling law for that rate as a function of timescale. Due to the fundamental nature of the underlying mechanism, we suggest that a vast range of evolutionary systems should in principle be susceptible to rate-induced collapse. This would include ecosystems on all scales as well as human societies; further research is warranted.

Multiscale Time-resolved Analysis Reveals Remaining Behavioral Rhythms in Mice Without Canonical Circadian Clocks

Circadian rhythms are internal processes repeating approximately every 24 hours in living organisms. The dominant circadian pacemaker is synchronized to the environmental light-dark cycle. Other circadian pacemakers, which can have noncanonical circadian mechanisms, are revealed by arousing stimuli, such as scheduled feeding, palatable meals and running wheel access, or methamphetamine administration. Organisms also have ultradian rhythms, which have periods shorter than circadian rhythms. However, the biological mechanism, origin, and functional significance of ultradian rhythms are not well-elucidated. The dominant circadian rhythm often masks ultradian rhythms; therefore, we disabled the canonical circadian clock of mice by knocking out Per1/2/3 genes, where Per1 and Per2 are essential components of the mammalian light-sensitive circadian mechanism. Furthermore, we recorded wheel-running activity every minute under constant darkness for 272 days. We then investigated rhythmic components in the absence of external influences, applying unique multiscale time-resolved methods to analyze the oscillatory dynamics with time-varying frequencies. We found four rhythmic components with periods of ∼17 h, ∼8 h, ∼4 h, and ∼20 min. When the ∼17-h rhythm was prominent, the ∼8-h rhythm was of low amplitude. This phenomenon occurred periodically approximately every 2-3 weeks. We found that the ∼4-h and ∼20-min rhythms were harmonics of the ∼8-h rhythm. Coupling analysis of the ridge-extracted instantaneous frequencies revealed strong and stable phase coupling from the slower oscillations (∼17, ∼8, and ∼4 h) to the faster oscillations (∼20 min), and weak and less stable phase coupling in the reverse direction and between the slower oscillations. Together, this study elucidated the relationship between the oscillators in the absence of the canonical circadian clock, which is critical for understanding their functional significance. These studies are essential as disruption of circadian rhythms contributes to diseases, such as cancer and obesity, as well as mood disorders.

Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control

Sparse model identification enables the discovery of nonlinear dynamical systems purely from data; however, this approach is sensitive to noise, especially in the low-data limit. In this work, we leverage the statistical approach of bootstrap aggregating (bagging) to robustify the sparse identification of the nonlinear dynamics (SINDy) algorithm. First, an ensemble of SINDy models is identified from subsets of limited and noisy data. The aggregate model statistics are then used to produce inclusion probabilities of the candidate functions, which enables uncertainty quantification and probabilistic forecasts. We apply this ensemble-SINDy (E-SINDy) algorithm to several synthetic and real-world datasets and demonstrate substantial improvements to the accuracy and robustness of model discovery from extremely noisy and limited data. For example, E-SINDy uncovers partial differential equations models from data with more than twice as much measurement noise as has been previously reported. Similarly, E-SINDy learns the Lotka Volterra dynamics from remarkably limited data of yearly lynx and hare pelts collected from 1900 to 1920. E-SINDy is computationally efficient, with similar scaling as standard SINDy. Finally, we show that ensemble statistics from E-SINDy can be exploited for active learning and improved model predictive control.

HRV analysis: undependability of approximate entropy at locating optimum complexity in malnourished children

INTRODUCTION

Approximate Entropy is an extensively enforced metric to evaluate chaotic responses and irregularities of RR intervals sourced from an eletrocardiogram. However, to estimate their responses, it has one major problem - the accurate determination of tolerances and embedding dimensions. So, we aimed to overt this potential hazard by calculating numerous alternatives to detect their optimality in malnourished children.

MATERIALS AND METHODS

We evaluated 70 subjects split equally: malnourished children and controls. To estimate autonomic modulation, the heart rate was measured lacking any physical, sensory or pharmacologic stimuli. In the time series attained, Approximate Entropy was computed for tolerance (0.1→0.5 in intervals of 0.1) and embedding dimension (1→5 in intervals of 1) and the statistical significances between the groups by their Cohen's ds and Hedges's gs were totalled.

RESULTS

The uppermost value of statistical significance accomplished for the effect sizes for any of the combinations was -0.2897 (Cohen's ds) and -0.2865 (Hedges's gs). This was achieved with embedding dimension = 5 and tolerance = 0.3.

CONCLUSIONS

Approximate Entropy was able to identify a reduction in chaotic response via malnourished children. The best values of embedding dimension and tolerance of the Approximate Entropy to identify malnourished children were, respectively, embedding dimension = 5 and embedding tolerance = 0.3. Nevertheless, Approximate Entropy is still an unreliable mathematical marker to regulate this.

Recurrence Quantitative Analysis of Wavelet-Based Surrogate Data for Nonlinearity Testing in Heart Rate Variability

Exploring the presence of nonlinearity through surrogate data testing provides insights into the nature of physical and biological systems like those obtained from heart rate variability (HRV). Short-term HRV time series are of great clinical interest to study autonomic impairments manifested in chronic diseases such as the end stage renal disease (ESRD) and the response of patients to treatment with hemodialysis (HD). In contrast to Iterative Amplitude Adjusted Fourier Transform (IAAFT), the Pinned Wavelet Iterative Amplitude Adjusted Fourier Transform (PWIAAFT) surrogates preserve nonstationary behavior in time series, a common characteristic of HRV. We aimed to test synthetic data and HRV time series for the existence of nonlinearity. Recurrence Quantitative Analysis (RQA) indices were used as discriminative statistics in IAAFT and PWIAAFT surrogates of linear stationary and nonstationary processes. HRV time series of healthy subjects and 29 ESRD patients before and after HD were tested in this setting during an active standing test. Contrary to PWIAAFT, linear nonstationary time series may be erroneously regarded as nonlinear according to the IAAFT surrogates. Here, a lower proportion of HRV time series was classified as nonlinear with PWIAAFT, compared to IAAFT, confirming that the nonstationarity condition influences the testing of nonlinear behavior in HRV. A contribution of nonlinearity was found in the HRV data of healthy individuals. A lower proportion of nonlinear time series was also found in ESRD patients, but statistical significance was not found. Although this proportion tends to be lower in ESRD patients, as much as 60% of time series proved to be nonlinear in healthy subjects. Given the important contribution of nonlinearity in HRV data, a nonlinear point of view is required to achieve a broader understanding of cardiovascular physiology.

Heat sensitivity of first host and cercariae may restrict parasite transmission in a warming sea

To predict global warming impacts on parasitism, we should describe the thermal tolerance of all players in host-parasite systems. Complex life-cycle parasites such as trematodes are of particular interest since they can drive complex ecological changes. This study evaluates the net response to temperature of the infective larval stage of Himasthla elongata, a parasite inhabiting the southwestern Baltic Sea. The thermal sensitivity of (i) the infected and uninfected first intermediate host (Littorina littorea) and (ii) the cercarial emergence, survival, self-propelling, encystment, and infection capacity to the second intermediate host (Mytilus edulis sensu lato) were examined. We found that infection by the trematode rendered the gastropod more susceptible to elevated temperatures representing warm summer events in the region. At 22 °C, cercarial emergence and infectivity were at their optimum while cercarial survival was shortened, narrowing the time window for successful mussel infection. Faster out-of-host encystment occurred at increasing temperatures. After correcting the cercarial emergence and infectivity for the temperature-specific gastropod survival, we found that warming induces net adverse effects on the trematode transmission to the bivalve host. The findings suggest that gastropod and cercariae mortality, as a tradeoff for the emergence and infectivity, will hamper the possibility for trematodes to flourish in a warming ocean.

Spin torque oscillations triggered by in-plane field

We study the dynamics of a spin torque nano oscillator that consists of parallelly magnetized free and pinned layers by numerically solving the associated Landau-Lifshitz-Gilbert-Slonczewski equation in the presence of a field-like torque. We observe that an in-plane magnetic field which is applied for a short interval of time (<1 ns) triggers the magnetization to exhibit self-oscillations from low energy initial magnetization state. Also, we confirm that the frequency of oscillations can be tuned over the range ∼25-∼72 GHz by current, even in the absence of field-like torque. We find the frequency enhancement up to 10 GHz by the presence of field-like torque. We determine theQ-factor for different frequencies and show that it increases with frequency. Our analysis with thermal noise confirms that the system is stable against thermal noise and the dynamics is not altered appreciably by it.

Ultrasound Echogenicity as an Indicator of Muscle Fatigue during Functional Electrical Stimulation

Functional electrical stimulation (FES) is a potential neurorehabilitative intervention to enable functional movements in persons with neurological conditions that cause mobility impairments. However, the quick onset of muscle fatigue during FES is a significant challenge for sustaining the desired functional movements for more extended periods. Therefore, a considerable interest still exists in the development of sensing techniques that reliably measure FES-induced muscle fatigue. This study proposes to use ultrasound (US) imaging-derived echogenicity signal as an indicator of FES-induced muscle fatigue. We hypothesized that the US-derived echogenicity signal is sensitive to FES-induced muscle fatigue under isometric and dynamic muscle contraction conditions. Eight non-disabled participants participated in the experiments, where FES electrodes were applied on their tibialis anterior (TA) muscles. During a fatigue protocol under either isometric and dynamic ankle dorsiflexion conditions, we synchronously collected the isometric dorsiflexion torque or dynamic dorsiflexion angle on the ankle joint, US echogenicity signals from TA muscle, and the applied stimulation intensity. The experimental results showed an exponential reduction in the US echogenicity relative change (ERC) as the fatigue progressed under the isometric (R2=0.891±0.081) and dynamic (R2=0.858±0.065) conditions. The experimental results also implied a strong linear relationship between US ERC and TA muscle fatigue benchmark (dorsiflexion torque or angle amplitude), with R2 values of 0.840±0.054 and 0.794±0.065 under isometric and dynamic conditions, respectively. The findings in this study indicate that the US echogenicity signal is a computationally efficient signal that strongly represents FES-induced muscle fatigue. Its potential real-time implementation to detect fatigue can facilitate an FES closed-loop controller design that considers the FES-induced muscle fatigue.

The role of pulse timing in cardiac defibrillation

Life-threatening cardiac arrhythmias require immediate defibrillation. For state-of-the-art shock treatments, a high field strength is required to achieve a sufficient success rate for terminating the complex spiral wave (rotor) dynamics underlying cardiac fibrillation. However, such high energy shocks have many adverse side effects due to the large electric currents applied. In this study, we show, using 2D simulations based on the Fenton-Karma model, that also pulses of relatively low energy may terminate the chaotic activity if applied at the right moment in time. In our simplified model for defibrillation, complex spiral waves are terminated by local perturbations corresponding to conductance heterogeneities acting as virtual electrodes in the presence of an external electric field. We demonstrate that time series of the success rate for low energy shocks exhibit pronounced peaks which correspond to short intervals in time during which perturbations aiming at terminating the chaotic fibrillation state are (much) more successful. Thus, the low energy shock regime, although yielding very low temporal average success rates, exhibits moments in time for which success rates are significantly higher than the average value shown in dose-response curves. This feature might be exploited in future defibrillation protocols for achieving high termination success rates with low or medium pulse energies.

Alternate Entropy Computations by Applying Recurrence Matrix Masking

In practicality, recurrence analyses of dynamical systems can only process short sections of signals that may be infinitely long. By necessity, the recurrence plot and its quantifications are constrained within a truncated triangle that clips the signals at its borders. Recurrence variables defined within these confining borders can be influenced more or less by truncation effects depending upon the system under evaluation. In this study, the question being asked is what if the boundary borders were tilted, what would be the effect on all recurrence variables? This question was prompted by the observation that line entropy values are maximized for highly periodic systems in which the infinitely long line elements are truncated to different unique lengths. However, by redefining the recurrence plot area to a 45-degree tilted box within the triangular area, the diagonal lines would consequently be truncated to identical lengths. Such masking would minimize the line entropy to 0.000 bits/bin. However, what new truncation influences would be imposed on the other recurrence variables? This question is examined by comparing recurrence variables computed with the triangular recurrence area versus boxed recurrence area. Examples include the logistic equation (mathematical series), the Dow Jones Industrial Average over a decade (real-word data), and a square wave pulse (toy series). Good agreement among the variables in terms of timing and amplitude was found for most, but not all variables. These important results are discussed.

The nonlinear feedback dynamics of asymmetric political polarization

Using a general model of opinion dynamics, we conduct a systematic investigation of key mechanisms driving elite polarization in the United States. We demonstrate that the self-reinforcing nature of elite-level processes can explain this polarization, with voter preferences accounting for its asymmetric nature. Our analysis suggests that subtle differences in the frequency and amplitude with which public opinion shifts left and right over time may have a differential effect on the self-reinforcing processes of elites, causing Republicans to polarize more quickly than Democrats. We find that as self-reinforcement approaches a critical threshold, polarization speeds up. Republicans appear to have crossed that threshold while Democrats are currently approaching it.

Cross-bridge mechanics estimated from skeletal muscles' work-loop responses to impacts in legged locomotion

Legged locomotion has evolved as the most common form of terrestrial locomotion. When the leg makes contact with a solid surface, muscles absorb some of the shock-wave accelerations (impacts) that propagate through the body. We built a custom-made frame to which we fixated a rat (Rattus norvegicus, Wistar) muscle (m. gastrocnemius medialis and lateralis: GAS) for emulating an impact. We found that the fibre material of the muscle dissipates between 3.5 and [Formula: see text] ranging from fresh, fully active to passive muscle material, respectively. Accordingly, the corresponding dissipated energy in a half-sarcomere ranges between 10.4 and [Formula: see text], respectively. At maximum activity, a single cross-bridge would, thus, dissipate 0.6% of the mechanical work available per ATP split per impact, and up to 16% energy in common, submaximal, activities. We also found the cross-bridge stiffness as low as [Formula: see text], which can be explained by the Coulomb-actuating cross-bridge part dominating the sarcomere stiffness. Results of the study provide a deeper understanding of contractile dynamics during early ground contact in bouncy gait.

Alternative Methods of the Largest Lyapunov Exponent Estimation with Applications to the Stability Analyses Based on the Dynamical Maps-Introduction to the Method

Controlling stability of dynamical systems is one of the most important challenges in science and engineering. Hence, there appears to be continuous need to study and develop numerical algorithms of control methods. One of the most frequently applied invariants characterizing systems' stability are Lyapunov exponents (LE). When information about the stability of a system is demanded, it can be determined based on the value of the largest Lyapunov exponent (LLE). Recently, we have shown that LLE can be estimated from the vector field properties by means of the most basic mathematical operations. The present article introduces new methods of LLE estimation for continuous systems and maps. We have shown that application of our approaches will introduce significant improvement of the efficiency. We have also proved that our approach is simpler and more efficient than commonly applied algorithms. Moreover, as our approach works in the case of dynamical maps, it also enables an easy application of this method in noncontinuous systems. We show comparisons of efficiencies of algorithms based our approach. In the last paragraph, we discuss a possibility of the estimation of LLE from maps and for noncontinuous systems and present results of our initial investigations.

The impact of COVID-19 on the worldwide air transportation network

Air travel has been one of the hardest hit industries of COVID-19, with many flight cancellations and airport closures as a consequence. By analysing structural characteristics of the Official Aviation Guide flight data, we show that this resulted in an increased average distance between airports, and in an increased number of long-range routes. Based on our study of network robustness, we uncover that this disruption is consistent with the impact of a mixture of targeted and random global attack on the worldwide air transportation network. By considering the individual functional evolution of airports, we identify anomalous airports with high centrality but low degree, which further enables us to reveal the underlying transitions among airport-specific representations in terms of both geographical and geopolitical factors. During the evolution of the air transportation network, we also observe how the network attempted to cope by shifting centralities between different airports around the world. Since these shifts are not aligned with optimal strategies for minimizing delays and disconnects, we conclude that they are consistent with politics trumping science from the viewpoint of epidemic containment and transport.

Structural Balance of Opinions

The concept of Heider balance, usually applied to interpersonal relations, is generalized here to opinions gathered in surveys. At first, we compare four algorithms, which drive a matrix dataset to a balanced state. The criterion is that the final state obtained with an algorithm should be as close as possible to the initial state. The result is that deterministic differential equations work better than their Monte Carlo counterparts. Next, we apply the winning algorithms to the matrix of correlations between opinions gathered in American states between 1974 and 1998. The results are interpreted in terms of the classic comfort hypothesis (E. Babbie, 2007).

Association of Short-Term Heart Rate Variability With Breast Tumor Stage

Cardiac autonomic modulation, assessed by heart rate variability (HRV), is associated with tumor pathogenesis and development as well as invasion and metastasis. This study aimed to examine this association in breast cancer (BC) patients. A total of 133 patients (average age 49.2years) with BC or benign breast tumors were divided into three groups: benign group, early-stage group, and advanced-stage group. About 5-min resting ECG was collected for the analysis of linear and nonlinear HRV parameters. Multiple logistic regression models were performed to test the independent contribution of HRV to breast tumor stage. The advanced-stage group had significantly reduced HRV compared to the benign and early-stage groups. In particular, for each 1-SD increase in SD2, SD of normal-to-normal intervals, very-low frequency, total power, and low frequency, the odds of having advanced staging decreased by 69.3, 64.3, 58.3, 53.3, and 65.9%, respectively. These associations were independent of age, body mass index, mean heart rate (HR), and respiratory rate (RR). These findings suggest an association between HRV and breast tumor stage, and HRV parameters may help construct an effective early diagnostic and clinical prognostic model.

WEAK SINDy: GALERKIN-BASED DATA-DRIVEN MODEL SELECTION

We present a novel weak formulation and discretization for discovering governing equations from noisy measurement data. This method of learning differential equations from data fits into a new class of algorithms that replace pointwise derivative approximations with linear transformations and variance reduction techniques. Compared to the standard SINDy algorithm presented in [S. L. Brunton, J. L. Proctor, and J. N. Kutz, Proc. Natl. Acad. Sci. USA, 113 (2016), pp. 3932-3937], our so-called weak SINDy (WSINDy) algorithm allows for reliable model identification from data with large noise (often with ratios greater than 0.1) and reduces the error in the recovered coefficients to enable accurate prediction. Moreover, the coefficient error scales linearly with the noise level, leading to high-accuracy recovery in the low-noise regime. Altogether, WSINDy combines the simplicity and efficiency of the SINDy algorithm with the natural noise reduction of integration, as demonstrated in [H. Schaeffer and S. G. McCalla, Phys. Rev. E, 96 (2017), 023302], to arrive at a robust and accurate method of sparse recovery.

Neurally driven synthesis of learned, complex vocalizations

Brain machine interfaces (BMIs) hold promise to restore impaired motor function and serve as powerful tools to study learned motor skill. While limb-based motor prosthetic systems have leveraged nonhuman primates as an important animal model,^1-4 speech prostheses lack a similar animal model and are more limited in terms of neural interface technology, brain coverage, and behavioral study design.^5-7 Songbirds are an attractive model for learned complex vocal behavior. Birdsong shares a number of unique similarities with human speech,^8-10 and its study has yielded general insight into multiple mechanisms and circuits behind learning, execution, and maintenance of vocal motor skill.^11-18 In addition, the biomechanics of song production bear similarity to those of humans and some nonhuman primates.^19-23 Here, we demonstrate a vocal synthesizer for birdsong, realized by mapping neural population activity recorded from electrode arrays implanted in the premotor nucleus HVC onto low-dimensional compressed representations of song, using simple computational methods that are implementable in real time. Using a generative biomechanical model of the vocal organ (syrinx) as the low-dimensional target for these mappings allows for the synthesis of vocalizations that match the bird's own song. These results provide proof of concept that high-dimensional, complex natural behaviors can be directly synthesized from ongoing neural activity. This may inspire similar approaches to prosthetics in other species by exploiting knowledge of the peripheral systems and the temporal structure of their output.

Synthetic Birdsongs as a Tool to Induce, and Iisten to, Replay Activity in Sleeping Birds

Birdsong is a complex vocal behavior, which emerges out of the interaction between a nervous system and a highly nonlinear vocal device, the syrinx. In this work we discuss how low dimensional dynamical systems, interpretable in terms of the biomechanics involved, are capable of synthesizing realistic songs. We review the experimental and conceptual steps that lead to the formulation of low dimensional dynamical systems for the song system and describe the tests that quantify their success. In particular, we show how to evaluate computational models by comparing the responses of highly selective neurons to the bird's own song and to synthetic copies generated mathematically. Beyond testing the hypothesis behind the model's construction, these low dimensional models allow designing precise stimuli in order to explore the sensorimotor integration of acoustic signals.

Muscle torques and joint accelerations provide more sensitive measures of poststroke movement deficits than joint angles

The whole repertoire of complex human motion is enabled by forces applied by our muscles and controlled by the nervous system. The impact of stroke on the complex multijoint motor control is difficult to quantify in a meaningful way that informs about the underlying deficit in the active motor control and intersegmental coordination. We tested whether poststroke deficit can be quantified with high sensitivity using motion capture and inverse modeling of a broad range of reaching movements. Our hypothesis is that muscle moments estimated based on active joint torques provide a more sensitive measure of poststroke motor deficits than joint angles. The motion of 22 participants was captured while performing reaching movements in a center-out task, presented in virtual reality. We used inverse dynamic analysis to derive active joint torques that were the result of muscle contractions, termed muscle torques, that caused the recorded multijoint motion. We then applied a novel analysis to separate the component of muscle torque related to gravity compensation from that related to intersegmental dynamics. Our results show that muscle torques characterize individual reaching movements with higher information content than joint angles do. Moreover, muscle torques enable distinguishing the individual motor deficits caused by aging or stroke from the typical differences in reaching between healthy individuals. Similar results were obtained using metrics derived from joint accelerations. This novel quantitative assessment method may be used in conjunction with home-based gaming motion capture technology for remote monitoring of motor deficits and inform the development of evidence-based robotic therapy interventions.NEW & NOTEWORTHY Functional deficits seen in task performance have biomechanical underpinnings, seen only through the analysis of forces. Our study has shown that estimating muscle moments can quantify with high-sensitivity poststroke deficits in intersegmental coordination. An assessment developed based on this method could help quantify less observable deficits in mildly affected stroke patients. It may also bridge the gap between evidence from studies of constrained or robotically manipulated movements and research with functional and unconstrained movements.

Feedback, Crosstalk and Competition: Ingredients for Emergent Non-Linear Behaviour in the PI3K/mTOR Signalling Network

The PI3K/mTOR signalling pathway plays a central role in the governing of cell growth, survival and metabolism. As such, it must integrate and decode information from both external and internal sources to guide efficient decision-making by the cell. To facilitate this, the pathway has evolved an intricate web of complex regulatory mechanisms and elaborate crosstalk with neighbouring signalling pathways, making it a highly non-linear system. Here, we describe the mechanistic biological details that underpin these regulatory mechanisms, covering a multitude of negative and positive feedback loops, feed-forward loops, competing protein interactions, and crosstalk with major signalling pathways. Further, we highlight the non-linear and dynamic network behaviours that arise from these regulations, uncovered through computational and experimental studies. Given the pivotal role of the PI3K/mTOR network in cellular homeostasis and its frequent dysregulation in pathologies including cancer and diabetes, a coherent and systems-level understanding of the complex regulation and consequential dynamic signalling behaviours within this network is imperative for advancing biology and development of new therapeutic approaches.

Optimizing Reservoir Computers for Signal Classification

Reservoir computers are a type of recurrent neural network for which the network connections are not changed. To train the reservoir computer, a set of output signals from the network are fit to a training signal by a linear fit. As a result, training of a reservoir computer is fast, and reservoir computers may be built from analog hardware, resulting in high speed and low power consumption. To get the best performance from a reservoir computer, the hyperparameters of the reservoir computer must be optimized. In signal classification problems, parameter optimization may be computationally difficult; it is necessary to compare many realizations of the test signals to get good statistics on the classification probability. In this work, it is shown in both a spiking reservoir computer and a reservoir computer using continuous variables that the optimum classification performance occurs for the hyperparameters that maximize the entropy of the reservoir computer. Optimizing for entropy only requires a single realization of each signal to be classified, making the process much faster to compute.

A Fully Distributed Protocol with an Event-Triggered Communication Strategy for Second-Order Multi-Agent Systems Consensus with Nonlinear Dynamics

This paper presents the communication strategy for second-order multi-agent systems with nonlinear dynamics. To address the problem of the scarcity of communication channel resources and get rid of using continuous signals among the followers in lead-follower multi-agent systems, a novel event-triggered communication mechanism is proposed in this paper. To avoid employing the centralized information that depends on the Laplacian matrix spectrum, a network protocol with updated coupling gains is proposed, as well as an event-triggered strategy with updated thresholds. To eliminate the ill effects of inter-node communicating noise, relative positions are employed by the protocol instead of absolute positions. By a Lyapunov-Krasovskii functional, it is rigorously proven that the leader-following consensus of MASs is achieved without Zeno behavior, under the control of the proposed protocol with an event-triggered mechanism communication. The effectiveness of the proposed protocol is verified through numerical examples.

Random heterogeneity outperforms design in network synchronization

A widely held assumption on network dynamics is that similar components are more likely to exhibit similar behavior than dissimilar ones and that generic differences among them are necessarily detrimental to synchronization. Here, we show that this assumption does not generally hold in oscillator networks when communication delays are present. We demonstrate, in particular, that random parameter heterogeneity among oscillators can consistently rescue the system from losing synchrony. This finding is supported by electrochemical-oscillator experiments performed on a multielectrode array network. Remarkably, at intermediate levels of heterogeneity, random mismatches are more effective in promoting synchronization than parameter assignments specifically designed to facilitate identical synchronization. Our results suggest that, rather than being eliminated or ignored, intrinsic disorder in technological and biological systems can be harnessed to help maintain coherence required for function.