Interacting Turing-Hopf Instabilities Drive Symmetry-Breaking Transitions in a Mean-Field Model of the Cortex: A Mechanism for the Slow Oscillation

Electrical recordings of brain activity during the transition from wake to anesthetic coma show temporal and spectral alterations that are correlated with gross changes in the underlying brain state. Entry into anesthetic unconsciousness is signposted by the emergence of large, slow oscillations of electrical activity (≲1  Hz) similar to the slow waves observed in natural sleep. Here we present a two-dimensional mean-field model of the cortex in which slow spatiotemporal oscillations arise spontaneously through a Turing (spatial) symmetry-breaking bifurcation that is modulated by a Hopf (temporal) instability. In our model, populations of neurons are densely interlinked by chemical synapses, and by interneuronal gap junctions represented as an inhibitory diffusive coupling. To demonstrate cortical behavior over a wide range of distinct brain states, we explore model dynamics in the vicinity of a general-anesthetic-induced transition from “wake” to “coma.” In this region, the system is poised at a codimension-2 point where competing Turing and Hopf instabilities coexist. We model anesthesia as a moderate reduction in inhibitory diffusion, paired with an increase in inhibitory postsynaptic response, producing a coma state that is characterized by emergent low-frequency oscillations whose dynamics is chaotic in time and space. The effect of long-range axonal white-matter connectivity is probed with the inclusion of a single idealized point-to-point connection. We find that the additional excitation from the long-range connection can provoke seizurelike bursts of cortical activity when inhibitory diffusion is weak, but has little impact on an active cortex. Our proposed dynamic mechanism for the origin of anesthetic slow waves complements—and contrasts with—conventional explanations that require cyclic modulation of ion-channel conductances. We postulate that a similar bifurcation mechanism might underpin the slow waves of natural sleep and comment on the possible consequences of chaotic dynamics for memory processing and learning

A novel, non-invasive, online-monitoring, versatile and easy plant-based probe for measuring leaf water status

A high-precision pressure probe is described which allows non-invasive online-monitoring of the water relations of intact leaves. Real-time recording of the leaf water status occurred by data transfer to an Internet server. The leaf patch clamp pressure probe measures the attenuated pressure, Pp, of a leaf patch in response to a constant clamp pressure, Pclamp. Pp is sensed by a miniaturized silicone pressure sensor integrated into the device. The magnitude of Pp is dictated by the transfer function of the leaf, Tf, which is a function of leaf patch volume and ultimately of cell turgor pressure, Pc, as shown theoretically. The power function Tf=f(Pc) theoretically derived was experimentally confirmed by concomitant Pp and Pc measurements on intact leaflets of the liana Tetrastigma voinierianum under greenhouse conditions. Simultaneous Pp recordings on leaflets up to 10 m height above ground demonstrated that changes in Tf induced by Pc changes due to changes of microclimate and/or of the irrigation regime were sensitively reflected in corresponding changes of Pp. Analysis of the data show that transpirational water loss during the morning hours was associated with a transient rise in turgor pressure gradients within the leaflets. Subsequent recovery of turgescence during the afternoon was much faster than the preceding transpiration-induced water loss if the plants were well irrigated. Our data show the enormous potential of the leaf patch clamp pressure probe for leaf water studies including unravelling of the hydraulic communication between neighbouring leaves and over long distances within tall plants (trees)

HESS Opinions: Functional units: a novel framework to explore the link between spatial organization and hydrological functioning of intermediate scale catchments

This opinion paper proposes a novel framework for exploring how spatial organization alongside with spatial heterogeneity controls functioning of intermediate scale catchments of organized complexity. Key idea is that spatial organization in landscapes implies that functioning of intermediate scale catchments is controlled by a hierarchy of functional units: hillslope scale lead topologies and embedded elementary functional units (EFUs). We argue that similar soils and vegetation communities and thus also soil structures "co-developed" within EFUs in an adaptive, self-organizing manner as they have been exposed to similar flows of energy, water and nutrients from the past to the present. Class members of the same EFU (class) are thus deemed to belong to the same ensemble with respect to controls of the energy balance and related vertical flows of capillary bounded soil water and heat. Class members of superordinate lead topologies are characterized by the same spatially organized arrangement of EFUs along the gradient driving lateral flows of free water as well as a similar surface and bedrock topography. We hence postulate that they belong to the same ensemble with respect to controls on rainfall runoff transformation and related vertical and lateral fluxes of free water. We expect class members of these functional units to have a distinct way how their architecture controls the interplay of state dynamics and integral flows, which is typical for all members of one class but dissimilar among the classes. This implies that we might infer on the typical dynamic behavior of the most important classes of EFU and lead topologies in a catchment, by thoroughly characterizing a few members of each class. A major asset of the proposed framework, which steps beyond the concept of hydrological response units, is that it can be tested experimentally. In this respect, we reflect on suitable strategies based on stratified observations drawing from process hydrology, soil physics, geophysics, ecology and remote sensing which are currently conducted in replicates of candidate functional units in the Attert basin (Luxembourg), to search for typical and similar functional and structural characteristics. A second asset of this framework is that it blueprints a way towards a structurally more adequate model concept for water and energy cycles in intermediate scale catchments, which balances necessary complexity with falsifiability. This is because EFU and lead topologies are deemed to mark a hierarchy of "scale breaks" where simplicity with respect to the energy balance and stream flow generation emerges from spatially organized process-structure interactions. This offers the opportunity for simplified descriptions of these processes that are nevertheless physically and thermodynamically consistent. In this respect we reflect on a candidate model structure that (a) may accommodate distributed observations of states and especially terrestrial controls on driving gradients to constrain the space of feasible model structures and (b) allows testing the possible added value of organizing principles to understand the role of spatial organization from an optimality perspective

A topographic index explaining hydrological similarity by accounting for the joint controls of runoff formation

Surface topography is an important source of information about the functioning and form of a hydrological landscape. Because of its key role in explaining hydrological processes and structures, and also because of its wide availability at good resolution in the form of digital elevation models (DEMs), it is frequently used to inform hydrological analyses. Not surprisingly, several hydrological indices and models have been proposed for linking geomorphic properties of a landscape with its hydrological functioning; a widely used example is the “height above the nearest drainage” (HAND) index. From an energy-centered perspective HAND reflects the gravitational potential energy of a given unit mass of water located on a hillslope, with the reference level set to the elevation of the nearest corresponding river. Given that potential energy differences are the main drivers for runoff generation, HAND distributions provide important proxies to explain runoff generation in catchments. However, as expressed by the second law of thermodynamics, the driver of a flux explains only one aspect of the runoff generation mechanism, with the driving potential of every flux being depleted via entropy production and dissipative energy loss. In fact, such losses dominate when rainfall becomes runoff, and only a tiny portion of the driving potential energy is actually transformed into the kinetic energy of streamflow. In recognition of this, we derive a topographic index called reduced dissipation per unit length index (rDUNE) by reinterpreting and enhancing HAND following a straightforward thermodynamic argumentation. We compare rDUNE with HAND, and with the frequently used topographic wetness index (TWI), and show that rDUNE provides stronger discrimination of catchments into groups that are similar with respect to their dominant runoff processes. Our analysis indicates that accounting for both the driver and resistance aspects of flux generation provides a promising approach for linking the architecture of a system with its functioning and is hence an appropriate basis for developing similarity indices in hydrology

Phase-Locked Spatial Domains and Bloch Domain Walls in Type-II Optical Parametric Oscillators

We study the role of transverse spatial degrees of freedom in the dynamics of signal-idler phase locked states in type-II Optical Parametric Oscillators. Phase locking stems from signal-idler polarization coupling which arises if the cavity birefringence and/or dichroism is not matched to the nonlinear crystal birefringence. Spontaneous Bloch domain wall formation is theoretically predicted and numerically studied. Bloch walls connect, by means of a polarization transformation, homogeneous regions of self-phase locked solutions. The parameter range for their existence is analytically found. The polarization properties and the dynamics of walls in one- and two transverse spatial dimensions is explained. Transition from Bloch to Ising walls is characterized, the control parameter being the linear coupling strength. Wall dynamics governs spatiotemporal dynamical states of the system, which include transient curvature driven domain growth, persistent dynamics dominated by spiraling defects for Bloch walls, and labyrinthine pattern formation for Ising walls.Comment: 27 pages, 16 figure

Advancing catchment hydrology to deal with predictions under change

Throughout its historical development, hydrology as an earth science, but especially as a problem-centred engineering discipline has largely relied (quite successfully) on the assumption of stationarity. This includes assuming time invariance of boundary conditions such as climate, system configurations such as land use, topography and morphology, and dynamics such as flow regimes and flood recurrence at different spatio-temporal aggregation scales. The justification for this assumption was often that when compared with the temporal, spatial, or topical extent of the questions posed to hydrology, such conditions could indeed be considered stationary, and therefore the neglect of certain long-term non-stationarities or feedback effects (even if they were known) would not introduce a large error. However, over time two closely related phenomena emerged that have increasingly reduced the general applicability of the stationarity concept: the first is the rapid and extensive global changes in many parts of the hydrological cycle, changing formerly stationary systems to transient ones. The second is that the questions posed to hydrology have become increasingly more complex, requiring the joint consideration of increasingly more (sub-) systems and their interactions across more and longer timescales, which limits the applicability of stationarity assumptions. Therefore, the applicability of hydrological concepts based on stationarity has diminished at the same rate as the complexity of the hydrological problems we are confronted with and the transient nature of the hydrological systems we are dealing with has increased. The aim of this paper is to present and discuss potentially helpful paradigms and theories that should be considered as we seek to better understand complex hydrological systems under change. For the sake of brevity we focus on catchment hydrology. We begin with a discussion of the general nature of explanation in hydrology and briefly review the history of catchment hydrology. We then propose and discuss several perspectives on catchments: as complex dynamical systems, self-organizing systems, co-evolving systems and open dissipative thermodynamic systems. We discuss the benefits of comparative hydrology and of taking an information-theoretic view of catchments, including the flow of information from data to models to predictions. In summary, we suggest that these perspectives deserve closer attention and that their synergistic combination can advance catchment hydrology to address questions of change