Transitional cluster dynamics in a model for delay-coupled chemical oscillators.

Cluster synchronization is a fundamental phenomenon in systems of coupled oscillators. Here, we investigate clustering patterns that emerge in a unidirectional ring of four delay-coupled electrochemical oscillators. A voltage parameter in the experimental setup controls the onset of oscillations via a Hopf bifurcation. For a smaller voltage, the oscillators exhibit simple, so-called primary, clustering patterns, where all phase differences between each set of coupled oscillators are identical. However, upon increasing the voltage, secondary states, where phase differences differ, are detected, in addition to the primary states. Previous work on this system saw the development of a mathematical model that explained how the existence, stability, and common frequency of the experimentally observed cluster states could be accurately controlled by the delay time of the coupling. In this study, we revisit the mathematical model of the electrochemical oscillators in order to address open questions by means of bifurcation analysis. Our analysis reveals how the stable cluster states, corresponding to experimental observations, lose their stability via an assortment of bifurcation types. The analysis further reveals complex interconnectedness between branches of different cluster types. We find that each secondary state provides a continuous transition between certain primary states. These connections are explained by studying the phase space and parameter symmetries of the respective states. Furthermore, we show that it is only for a larger value of the voltage parameter that the branches of secondary states develop intervals of stability. For a smaller voltage, all the branches of secondary states are completely unstable and are, therefore, hidden to experimentalists.

Corporate social responsibility and performance in the workplace: a meta-analysis.

Despite stakeholders' desire for organizations to participate in corporate social responsibility (CSR) activities, some organizations do not invest in CSR due to uncertainty around the value it provides to performance. This research investigates the effect size of the relationship between CSR and performance via a meta-analysis of 17 articles. A series of performance-indicating groups emerged and effect sizes were calculated using the Comprehensive Meta-Analysis software. These groups include in-role performance, extra-role performance, employees' affective attitudes towards organizations, and organizational-level outputs. Results suggest that CSR has a large effect on performance across a range of contexts. Implications for career counseling are discussed.

Responsabilité sociale des entreprises et performance sur le lieu de travail: une méta-analyse. Malgré le désir des parties prenantes que les organisations participent à des activités de responsabilité sociale des entreprises (RSE), certaines organisations n'investissent pas dans la RSE en raison de l'incertitude quant à la valeur qu'elle apporte à la performance. Cette recherche examine la taille de l'effet de la relation entre la RSE et la performance via une méta-analyse de 17 articles. Une série de groupes indicateurs de performance a émergé et les tailles d'effet ont été calculées à l'aide du logiciel "Comprehensive Meta-Analysis". Ces groupes comprennent la performance dans le rôle, la performance hors rôle, les attitudes affectives des employé·e·s envers les organisations et les résultats au niveau organisationnel. Les résultats suggèrent que la RSE a un effet important sur la performance dans une série de contextes. Les implications pour le conseil en carrière sont discutées.

Responsabilidad social de las empresas y rendimiento en el lugar de trabajo: un metaanálisis. A pesar del deseo de las partes interesadas de que las organizaciones participen en actividades de responsabilidad social corporativa (RSC), algunas organizaciones no invierten en RSC debido a la incertidumbre en torno al valor que aporta al rendimiento. Esta investigación analiza el tamaño del efecto de la relación entre la RSE y el rendimiento mediante un metaanálisis de 17 artículos. Surgieron una serie de grupos indicadores del rendimiento y se calcularon los tamaños de los efectos mediante el programa informático Comprehensive Meta-Analysis. Estos grupos incluyen el rendimiento en el puesto, el rendimiento fuera del puesto, las actitudes afectivas de los empleados hacia las organizaciones y los resultados a nivel organizativo. Los resultados sugieren que la RSE tiene un gran efecto sobre el rendimiento en diversos contextos. Se discuten las implicaciones para la orientación profesional.

Continental configuration controls ocean oxygenation during the Phanerozoic.

The early evolutionary and much of the extinction history of marine animals is thought to be driven by changes in dissolved oxygen concentrations ([O2]) in the ocean1-3. In turn, [O2] is widely assumed to be dominated by the geological history of atmospheric oxygen (pO2)4,5. Here, by contrast, we show by means of a series of Earth system model experiments how continental rearrangement during the Phanerozoic Eon drives profound variations in ocean oxygenation and induces a fundamental decoupling in time between upper-ocean and benthic [O2]. We further identify the presence of state transitions in the global ocean circulation, which lead to extensive deep-ocean anoxia developing in the early Phanerozoic even under modern pO2. Our finding that ocean oxygenation oscillates over stable thousand-year (kyr) periods also provides a causal mechanism that might explain elevated rates of metazoan radiation and extinction during the early Palaeozoic Era6. The absence, in our modelling, of any simple correlation between global climate and ocean ventilation, and the occurrence of profound variations in ocean oxygenation independent of atmospheric pO2, presents a challenge to the interpretation of marine redox proxies, but also points to a hitherto unrecognized role for continental configuration in the evolution of the biosphere.

Signatures Consistent with Multifrequency Tipping in the Atlantic Meridional Overturning Circulation.

The early detection of tipping points, which describe a rapid departure from a stable state, is an important theoretical and practical challenge. Tipping points are most commonly associated with the disappearance of steady-state or periodic solutions at fold bifurcations. We discuss here multifrequency tipping (M tipping), which is tipping due to the disappearance of an attracting torus. M tipping is a generic phenomenon in systems with at least two intrinsic or external frequencies that can interact and, hence, is relevant to a wide variety of systems of interest. We show that the more complicated sequence of bifurcations involved in M tipping provides a possible consistent explanation for as yet unexplained behavior observed near tipping in climate models for the Atlantic meridional overturning circulation. More generally, this Letter provides a path toward identifying possible early warning signs of tipping in multiple-frequency systems.

Border-collision bifurcations in a driven time-delay system.

We show that a simple piecewise-linear system with time delay and periodic forcing gives rise to a rich bifurcation structure of torus bifurcations and Arnold tongues, as well as multistability across a significant portion of the parameter space. The simplicity of our model enables us to study the dynamical features analytically. Specifically, these features are explained in terms of border-collision bifurcations of an associated Poincaré map. Given that time delay and periodic forcing are common ingredients in mathematical models, this analysis provides widely applicable insight.

Can Signal Delay be Functional? Including Delay in Evolved Robot Controllers.

Engineers, control theorists, and neuroscientists often view the delay imposed by finite signal propagation velocities as a problem that needs to be compensated for or avoided. In this article, we consider the alternative possibility that in some cases, signal delay can be used functionally, that is, as an essential component of a cognitive system. To investigate this idea, we evolve a minimal robot controller to solve a basic stimulus-distinction task. The controller is constrained so that the solution must utilize a delayed recurrent signal. Different from previous evolutionary robotics studies, our controller is modeled using delay differential equations, which (unlike the ordinary differential equations of conventional continuous-time recurrent neural networks) can accurately capture delays in signal propagation. We analyze the evolved controller and its interaction with its environment using classical dynamical systems techniques. The analysis shows what kinds of invariant sets underlie the various successful and unsuccessful performances of the robot, and what kinds of bifurcations produce these invariant sets. In the second phase of our analysis, we turn our attention to the parameter θ, which describes the amount of signal delay included in the model. We show how the delay destabilizes certain attractors that would exist if there were no delay and creates other stable attractors, resulting in an agent that performs well at the target task.

The effect of state dependence in a delay differential equation model for the El Niño Southern Oscillation.

Delay differential equations (DDEs) have been used successfully in the past to model climate systems at a conceptual level. An important aspect of these models is the existence of feedback loops that feature a delay time, usually associated with the time required to transport energy through the atmosphere and/or oceans across the globe. So far, such delays are generally assumed to be constant. Recent studies have demonstrated that even simple DDEs with non-constant delay times, which change depending on the state of the system, can produce surprisingly rich dynamical behaviour. Here, we present arguments for the state dependence of the delay in a DDE model for the El Niño Southern Oscillation phenomenon in the climate system. We then conduct a bifurcation analysis by means of continuation software to investigate the effect of state dependence in the delay on the observed dynamics of the system. More specifically, we show that the underlying delay-induced structure of resonance regions may change considerably in the presence of state dependence. This article is part of the theme issue 'Nonlinear dynamics of delay systems'.

Climate models with delay differential equations.

A fundamental challenge in mathematical modelling is to find a model that embodies the essential underlying physics of a system, while at the same time being simple enough to allow for mathematical analysis. Delay differential equations (DDEs) can often assist in this goal because, in some cases, only the delayed effects of complex processes need to be described and not the processes themselves. This is true for some climate systems, whose dynamics are driven in part by delayed feedback loops associated with transport times of mass or energy from one location of the globe to another. The infinite-dimensional nature of DDEs allows them to be sufficiently complex to reproduce realistic dynamics accurately with a small number of variables and parameters. In this paper, we review how DDEs have been used to model climate systems at a conceptual level. Most studies of DDE climate models have focused on gaining insights into either the global energy balance or the fundamental workings of the El Niño Southern Oscillation (ENSO) system. For example, studies of DDEs have led to proposed mechanisms for the interannual oscillations in sea-surface temperature that is characteristic of ENSO, the irregular behaviour that makes ENSO difficult to forecast and the tendency of El Niño events to occur near Christmas. We also discuss the tools used to analyse such DDE models. In particular, the recent development of continuation software for DDEs makes it possible to explore large regions of parameter space in an efficient manner in order to provide a "global picture" of the possible dynamics. We also point out some directions for future research, including the incorporation of non-constant delays, which we believe could improve the descriptive power of DDE climate models.

Metal-Mediated Production of Isocyanates, R3 EN=C=O from Dinitrogen, Carbon Dioxide, and R3 ECl.

A highly efficient and versatile chemical cycle has been developed for the production of isocyanates through the molecular fixation of N2 , CO2 and R3 ECl (E=C, Si, and Ge). Key steps include a 'one-pot' photolytic N-N bond cleavage of a Group 6 dinuclear dinitrogen complex with in situ trapping by R3 ECl to provide a metal terminal imido complex that can engage in simultaneous nitrene-group transfer and oxygen-atom transfer to generate an intermediate metal terminal oxo complex with release of the isocyanate product. Reaction of the oxo complex with additional equivalents of R3 ECl regenerates a metal dichloride that is the precursor for dinuclear dinitrogen starting material.

Fine-tuning the energy barrier for metal-mediated dinitrogen N≡N bond cleavage.

Experimental data support a mechanism for N≡N bond cleavage within a series of group 5 bimetallic dinitrogen complexes of general formula, {Cp*M[N((i)Pr)C(R)N((i)Pr)]}2(µ-N2) (Cp* = η(5)-C5Me5) (M = Nb, Ta), that proceeds in solution through an intramolecular "end-on-bridged" (µ-η(1):η(1)-N2) to "side-on-bridged" (µ-η(2):η(2)-N2) isomerization process to quantitatively provide the corresponding bimetallic bis(µ-nitrido) complexes, {Cp*M[N((i)Pr)C(R)N((i)Pr)](µ-N)}2. It is further demonstrated that subtle changes in the steric and electronic features of the distal R-substituent, where R = Me, Ph and NMe2, can serve to modulate the magnitude of the free energy barrier height for N≡N bond cleavage as assessed by kinetic studies and experimentally derived activation parameters. The origin of the contrasting kinetic stability of the first-row congener, {Cp*V[N((i)Pr)C(Me)N((i)Pr)]}2(µ-η(1):η(1)-N2) toward N≡N bond cleavage is rationalized in terms of a ground-state electronic structure that favors a significantly less-reduced µ-N2 fragment.

N-N bond cleavage of mid-valent Ta(IV) hydrazido and hydrazidium complexes relevant to the Schrock cycle for dinitrogen fixation.

Chemical reduction of the Ta(V) hydrazido chloride 1 generates the open-shell, mononuclear Ta(IV) hydrazido complex 2, which upon N-methylation yields the corresponding structurally characterized Ta(IV) hydrazidium 6. Chemical reduction of 6 results in N-N bond cleavage to generate a cis/trans mixture of the [Ta(V),Ta(V)] bis(µ-nitrido) product 7 in tetrahydrofuran and the mononuclear Ta(V) parent imide 8 in toluene. These results serve to establish an important foundation for the pursuit of a group-5 metal variant of the Schrock cycle for dinitrogen fixation.

Clustering in delay-coupled smooth and relaxational chemical oscillators.

We investigate cluster synchronization in networks of nonlinear systems with time-delayed coupling. Using a generic model for a system close to the Hopf bifurcation, we predict the order of appearance of different cluster states and their corresponding common frequencies depending upon coupling delay. We may tune the delay time in order to ensure the existence and stability of a specific cluster state. We qualitatively and quantitatively confirm these results in experiments with chemical oscillators. The experiments also exhibit strongly nonlinear relaxation oscillations as we increase the voltage, i.e., go further away from the Hopf bifurcation. In this regime, we find secondary cluster states with delay-dependent phase lags. These cluster states appear in addition to primary states with delay-independent phase lags observed near the Hopf bifurcation. Extending the theory on Hopf normal-form oscillators, we are able to account for realistic interaction functions, yielding good agreement with experimental findings.

Testicular pain as a presentation of Cowden syndrome.

This case report outlines a rare case in Cowden syndrome and PTEN (phosphatase and tensin homolog) gene mutation and how it may initially present to the urologist. Also known as multiple hamartoma syndrome, Cowden syndrome is a rare disorder associated with the development of several types of malignancy. A thorough search of the literature reveals limited information regarding its presentation to the urologist. We report the case of a 47-year-old gentleman with a two-week history of worsening pain and swelling in his left testicle. Testicular ultrasound revealed multiple hyperechoic areas bilaterally suggestive of multiple lipomas. He was also found to have macrocephaly, freckling of his glans and foreskin and an enlarged nodular goitre and the geneticist diagnosed Cowden syndrome. The disease is discussed and guidance is given on its management and follow up.