An amplitude equation for the conserved-Hopf bifurcation-Derivation, analysis, and assessment.

We employ weakly nonlinear theory to derive an amplitude equation for the conserved-Hopf instability, i.e., a generic large-scale oscillatory instability for systems with two conservation laws.

Causal Hierarchy in the Financial Market Network-Uncovered by the Helmholtz-Hodge-Kodaira Decomposition.

Granger causality can uncover the cause-and-effect relationships in financial networks. However, such networks can be convoluted and difficult to interpret, but the Helmholtz-Hodge-Kodaira decomposition can split them into rotational and gradient components which reveal the hierarchy of the Granger causality flow. Using Kenneth French's business sector return time series, it is revealed that during the COVID crisis, precious metals and pharmaceutical products were causal drivers of the financial network.

Random telegraph processes with nonlocal memory.

We study two-state (dichotomous, telegraph) random ergodic continuous-time processes with dynamics depending on their past. We take into account the history of the process in an explicit form by introducing integral nonlocal memory term into conditional probability function. We start from an expression for the conditional transition probability function describing additive multistep binary random chain and show that the telegraph processes can be considered as continuous-time interpolations of discrete-time dichotomous random sequences.

Cooperation in a non-ergodic world on a network - insurance and beyond.

Cooperation between individuals is emergent in all parts of society; yet, mechanistic reasons for this emergence are ill understood in the literature. A specific example of this is insurance. Recent work has, though, shown that assuming the risk individuals face is proportional to their wealth and optimizing the time average growth rate rather than the ensemble average results in a non-zero-sum game, where both parties benefit from cooperation through insurance contracts.

Towards a single parameter for the assessment of EEG oscillations.

The single macroscopic flow on the boundary of a closed curve equals the sum of the countless microscopic flows in the enclosed area. According to the dictates of the Green's theorem, the counterclockwise movements on the border of a two-dimensional shape must equal all the counterclockwise movements taking place inside the shape. This mathematical approach might be useful to analyse neuroscientific data sets for its potential capability to describe the whole cortical activity in terms of electric flows occurring in peripheral brain areas.

Exotic swarming dynamics of high-dimensional swarmalators.

Swarmalators are oscillators that can swarm as well as sync via a dynamic balance between their spatial proximity and phase similarity. Swarmalator models employed so far in the literature comprise only one-dimensional phase variables to represent the intrinsic dynamics of the natural collectives. Nevertheless, the latter can indeed be represented more realistically by high-dimensional phase variables.

Flock members experience gas pressures higher than lone individuals.

Local interactions between flock members in absence of centralized control generate collective dynamics characterized by coherent large-scale patterns. We investigate whether aggregates of individuals like birds, swarms and fishes behaving in concert with their neighbors may modify the physical properties of the fluid medium in which they are embedded. Using the K-Nearest Neighbors algorithm to simulate collective animal behavior, we showed that the occurrence of collective dynamics can modify the physical parameters of the phase space in which the interacting individuals' trajectories take place.

Binding potential and wetting behavior of binary liquid mixtures on surfaces.

We present a theory for the interfacial wetting phase behavior of binary liquid mixtures on rigid solid substrates, applicable to both miscible and immiscible mixtures. In particular, we calculate the binding potential as a function of the adsorptions, i.e.

Estimating stable fixed points and Langevin potentials for financial dynamics.

The geometric Brownian motion (GBM) is a standard model in quantitative finance, but the potential function of its stochastic differential equation (SDE) cannot include stable nonzero prices. This article generalizes the GBM to an SDE with polynomial drift of order q and shows via model selection that q=2 is most frequently the optimal model to describe the data. Moreover, Markov chain Monte Carlo ensembles of the accompanying potential functions show a clear and pronounced potential well, indicating the existence of a stable price.

Dynamics and metabolic effects of intestinal gases in healthy humans.

Many living beings use exogenous and/or endogenous gases to attain evolutionary benefits. We make a comprehensive assessment of one of the major gaseous reservoirs in the human body, i.e.

The First Nucleic Acid Strands May Have Grown on Peptides via Primeval Reverse Translation.

The central dogma of molecular biology dictates that, with only a few exceptions, information proceeds from DNA to protein through an RNA intermediate. Examining the enigmatic steps from prebiotic to biological chemistry, we take another road suggesting that primordial peptides acted as template for the self-assembly of the first nucleic acids polymers. Arguing in favour of a sort of archaic "reverse translation" from proteins to RNA, our basic premise is a Hadean Earth where key biomolecules such as amino acids, polypeptides, purines, pyrimidines, nucleosides and nucleotides were available under different prebiotically plausible conditions, including meteorites delivery, shallow ponds and hydrothermal vents scenarios.

Square waves and Bykov T-points in a delay algebraic model for the Kerr-Gires-Tournois interferometer.

We study theoretically the mechanisms of square wave formation of a vertically emitting micro-cavity operated in the Gires-Tournois regime that contains a Kerr medium and that is subjected to strong time-delayed optical feedback and detuned optical injection. We show that in the limit of large delay, square wave solutions of the time-delayed system can be treated as relative homoclinic solutions of an equation with an advanced argument. Based on this, we use concepts of classical homoclinic bifurcation theory to study different types of square wave solutions.

Biophotons: New Experimental Data and Analysis.

Biophotons are an ultra-weak emission of photons in the visible energy range from living matter. In this work, we study the emission from germinating seeds using an experimental technique designed to detect light of extremely small intensity. The emission from lentil seeds and single bean was analyzed during the whole germination process in terms of the different spectral components through low pass filters and the different count distributions in the various stages of the germination process.

Complexity Synchronization of Organ Networks.

The transdisciplinary nature of science as a whole became evident as the necessity for the complex nature of phenomena to explain social and life science, along with the physical sciences, blossomed into complexity theory and most recently into complexitysynchronization. This science motif is based on the scaling arising from the 1/f-variability in complex dynamic networks and the need for a network of networks to exchange information internally during intra-network dynamics and externally during inter-network dynamics. The measure of complexity adopted herein is the multifractal dimension of the crucial event time series generated by an organ network, and the difference in the multifractal dimensions of two organ networks quantifies the relative complexity between interacting complex networks.

Efficient Multi-Change Point Analysis to Decode Economic Crisis Information from the S&P500 Mean Market Correlation.

Identifying macroeconomic events that are responsible for dramatic changes of economy is of particular relevance to understanding the overall economic dynamics. We introduce an open-source available efficient Python implementation of a Bayesian multi-trend change point analysis, which solves significant memory and computing time limitations to extract crisis information from a correlation metric. Therefore, we focus on the recently investigated mean market correlation in a period of roughly 20 years that includes the dot-com bubble, the global financial crisis, and the Euro crisis.

Memory Effects, Multiple Time Scales and Local Stability in Langevin Models of the S&P500 Market Correlation.

The analysis of market correlations is crucial for optimal portfolio selection of correlated assets, but their memory effects have often been neglected. In this work, we analyse the mean market correlation of the S&P500, which corresponds to the main market mode in principle component analysis. We fit a generalised Langevin equation (GLE) to the data whose memory kernel implies that there is a significant memory effect in the market correlation ranging back at least three trading weeks.

Nonreciprocal Cahn-Hilliard Model Emerges as a Universal Amplitude Equation.

Oscillatory behavior is ubiquitous in out-of-equilibrium systems showing spatiotemporal pattern formation. Starting from a linear large-scale oscillatory instability-a conserved-Hopf instability-that naturally occurs in many active systems with two conservation laws, we derive a corresponding amplitude equation. It belongs to a hierarchy of such universal equations for the eight types of instabilities in homogeneous isotropic systems resulting from the combination of three features: large-scale vs small-scale instability, stationary vs oscillatory instability, and instability without and with conservation law(s).

Laws of taxation for multicellular organisms: The economics of sleep.

In macro-public finance, the Ramsey rule (RR) concerns variable taxation to maximize social welfare and economic efficiency in a purely competitive monopolistic system. To extract tax revenue with the least loss of utility to the representative individual, RR dictates that optimal, proportionate taxes should be such as to diminish in the same proportion the production of each commodity taxed. The sources of supply that are inelastic, i.

Stationary broken parity states in active matter models.

We demonstrate that several nonvariational continuum models commonly used to describe active matter as well as other active systems exhibit nongeneric behavior: each model supports asymmetric but stationary localized states even in the absence of pinning at heterogeneities. Moreover, such states only begin to drift following a drift-transcritical bifurcation as the activity increases. Asymmetric stationary states should only exist in variational systems, i.

Complexity synchronization: a measure of interaction between the brain, heart and lungs.

Herein we address the measurable consequences of the network effect (NE) on time series generated by different parts of the brain, heart, and lung organ-networks (ONs), which are directly related to their inter-network and intra-network interactions. Moreover, these same physiologic ONs have been shown to generate crucial event (CE) time series, and herein are shown, using modified diffusion entropy analysis (MDEA) to have scaling indices with quasiperiodic changes in complexity, as measured by scaling indices, over time. Such time series are generated by different parts of the brain, heart, and lung ONs, and the results do not depend on the underlying coherence properties of the associated time series but demonstrate a generalized synchronization of complexity.

EEG phase synchronization during absence seizures.

Absence seizures-generalized rhythmic spike-and-wave discharges (SWDs) are the defining property of childhood (CAE) and juvenile (JAE) absence epilepsies. Such seizures are the most compelling examples of pathological neuronal hypersynchrony. All the absence detection algorithms proposed so far have been derived from the properties of SWDs.

Non-ultrametric phylogenetic trees shed new light on Neanderthal introgression.

Ultrametric spaces are widely used to depict evolutionary times in phylogenetic trees since they assume that every population/species is located at the tips of bifurcating branches of the same length. The discrete branching of ultrametric trees permits the measurement of distances between pairs of individuals that are proportional to their divergence time. Here the traditional ultrametric concept of bifurcating and divergent phylogenetic tree is overturned and a new type of non-ultrametric diagram is introduced.

Stick-slip dynamics in the forced wetting of polymer brushes.

We study the static and dynamic wetting of adaptive substrates using a mesoscopic hydrodynamic model for a liquid droplet on a solid substrate covered by a polymer brush. First, we show that on the macroscale Young's law still holds for the equilibrium contact angle and that on the mesoscale a Neumann-type law governs the shape of the wetting ridge. Following an analytic and numeric assessment of the static profiles of droplet and wetting ridge, we examine the dynamics of the wetting ridge for a liquid meniscus that is advanced at constant mean speed.

Temporal complexity measure of reaction time series: Operational versus event time.

Introduction: Detrended fluctuation analysis (DFA) is a well-established method to evaluate scaling indices of time series, which categorize the dynamics of complex systems. In the literature, DFA has been used to study the fluctuations of reaction time Y(n) time series, where n is the trial number.

Methods: Herein we propose treating each reaction time as a duration time that changes the representation from operational (trial number) time n to event (temporal) time t, or X(t).