weakly stable
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A rich repertoire of oscillatory signals is detected from human brains with electro- and magnetoencephalography (EEG/MEG). However, the principles underwriting coherent oscillations and their link with neural activity remain unclear. Here, we hypothesise that the emergence of transient brain rhythms is a signature of weakly stable synchronization between spatially distributed brain areas, occurring at network-specific collective frequencies due to non-negligible conduction times. We test this hypothesis using a phenomenological network model to simulate interactions between neural mass potentials (resonating at 40Hz) in the structural connectome. Crucially, we identify a critical regime where metastable oscillatory modes emerge spontaneously in the delta (0.5-4Hz), theta (4-8Hz), alpha (8-13Hz) and beta (13-30Hz) frequency bands from weak synchronization of subsystems, closely approximating the MEG power spectra from 89 healthy individuals. Grounded in the physics of delay-coupled oscillators, these numerical analyses demonstrate the role of the spatiotemporal connectome in structuring brain activity in the frequency domain.

Abstract Much of systems neuroscience posits that emergent neural phenomena underpin important aspects of brain function. Studies in the field variously emphasize the importance of distinct emergent phenomena, including weakly stable dynamics, arrhythmic 1/f activity, long-range temporal correlations, and scale-free avalanche statistics. Few studies, however, have sought to reconcile these often abstract phenomena with interpretable properties of neural activity. Here, we developed a method to efficiently and unbiasedly generate model data constrained by interpretable empirical features in long neurophysiological recordings. We used this method to ground several major emergent neural phenomena to time-resolved smoothness, the correlation of distributed brain activity between adjacent timepoints. We first found that in electrocorticography recordings, time-resolved smoothness closely tracked transitions between conscious and anesthetized states. We then showed that a minimal model constrained by time-resolved smoothness, variance, and mean, captured dynamical and statistical emergent neural phenomena across modalities and species. Our results thus decouple major emergent neural phenomena from network mechanisms of brain function, and instead couple these phenomena to spatially nonspecific, time-resolved changes of brain activity. These results anchor several theoretical frameworks to a single interpretable property of the neurophysiological signal and, in this way, ultimately help bridge abstract theories of brain function with observed properties of brain activity.

AbstractPesticide applications during surface inversions can lead to spray drift causing severe damage up to several kilometers off-target. Current regulations in Australia prohibit spray application of certain agricultural chemicals when hazardous surface inversions exist. This severely limits spray opportunities.Surface inversions can be classified as weakly or strongly stable. In the weakly stable case, moderate to strong turbulent mixing is not supportive of long-distance concentrated drift. In the very stable case, weak turbulent mixing can support the transport of high concentrations of fine material over long distances. A review of the literature and our analyses indicate that if the turbulence, as measured by the standard deviation of the vertical wind speed σw, is greater than about 0.2 m/s then turbulence-driven mixing and dispersion is moderate to strong and conversely if σw is less than about 0.2 m/s then turbulence-driven mixing and dispersion is weaker (an order of magnitude). The concept of maximum downward heat flux as a natural division between the regimes is applied within Monin-Obukhov Stability Theory and it is shown that the observed mean σw of 0.2 m/s aligns with the ridge line of maximum heat flux in stable conditions. The level of turbulence in the weakly stable regime is comparable to the turbulence typically observed in near-neutral conditions which are recommended under current guidelines as suitable for spraying and is therefore seen as an acceptable prerequisite to avoid non-dispersive spraying conditions.

AbstractIn IWOCA 2019, Ruangwises and Itoh introduced stable noncrossing matchings, where participants of each side are aligned on each of two parallel lines, and no two matching edges are allowed to cross each other. They defined two stability notions, strongly stable noncrossing matching (SSNM) and weakly stable noncrossing matching (WSNM), depending on the strength of blocking pairs. They proved that a WSNM always exists and presented an $$O(n^{2})$$ O ( n 2 ) -time algorithm to find one for an instance with n men and n women. They also posed open questions of the complexities of determining existence of an SSNM and finding a largest WSNM. In this paper, we show that both problems are solvable in polynomial time. Our algorithms are applicable to extensions where preference lists may include ties, except for one case which we show to be NP-complete. This NP-completeness holds even if each person's preference list is of length at most two and ties appear in only men's preference lists. To complement this intractability, we show that the problem is solvable in polynomial time if the length of preference lists of one side is bounded by one (but that of the other side is unbounded).

New concepts of dislocation physics of plasticity and strength are considered using quantitative methods of transmission diffraction electron microscopy. New concepts of dislocation physics of plasticity and strength are considered using quantitative methods of transmission diffraction electron microscopy. The analysis of changes in the parameters of the dislocation substructure (DSS) is given on the example of alloys Cu-0.5 and 14 аt. % Al and the influence of these parameters on the change in the substructure of the material at a temperature T=293 K is considered. It is shown that at each stage of deformation, there are usually two substructures ("old" and "new"). The blurring of the transition from stage to stage is associated with the presence of weakly stable pre-transition structural-phase States at certain degrees of deformation of several types of substructures simultaneously, i.e., a weakly stable structural-phase state of the system. Against the background of the "old" substructure, a "new" one is born, which in the process of deformation becomes the main one, and then the "old" one, in the depths of which another substructure is formed. Experimental evidence of this regularity is obtained for FCC alloys. The presence of grain boundaries complicates the diagrams: a third substructure is formed near the grain boundaries, which corresponds to the following substructures (later) in the sequence of DSS transformations.

The results of an electron microscopy study of the evolution of the dislocation structure of a polycrystalline ordered and disordered Pd3Fe alloy in the region of weakly stable structural-phase States are presented. The scheme of rearrangement of dislocation substructures during the transition from stage to stage, which are highlighted on the deformation curves of the Pd3Fe alloy, is constructed. It is established that in the case of both disordered and ordered alloys, each stage of deformation is characterized by its own special types of dislocation substructure (DSS), which are the main carriers of deformation for this stage. Transitions from some types of DSS to other types occur in certain ranges of values of the degree of deformation ε. The appearance of the DSS type characteristic of this stage of deformation occurs at the previous stage, and as the degree of deformation increases, the proportion of this type of DSS increases. At the stage under consideration, their share is the largest, and when moving to the next stage, it gradually decreases until it disappears. In the case of ordered alloys, the types of dislocation substructure-the main carrier of deformation for this stage differ from the types of DSS that are implemented in disordered alloys at the same stage of deformation. It is shown that each stage of deformation has its own DSS - strain carriers. When moving to a new stage, the transition to new structural carriers of deformation occurs. During the transition, these carriers co-exist, which is a characteristic feature of weakly stable States of the system.

A challenge to simulating turbulent flow in multiscale atmospheric applications is the efficient generation of resolved turbulence motions over an area of interest. One approach is to apply small perturbations to flow variables near the inflow planes of turbulence-resolving simulation domains nested within larger mesoscale domains. While this approach has been examined in numerous idealized and simple terrain cases, its efficacy in complex terrain environments has not yet been fully explored. Here, we examine the benefits of the stochastic cell perturbation method (CPM) over real complex terrain using data from the 2017 Perdigão field campaign, conducted in an approximately 2-km wide valley situated between two nearly parallel ridges. Following a typical configuration for multiscale simulation using nested domains within the Weather Research and Forecasting (WRF) model to downscale from the mesoscale to a large-eddy simulation (LES), we apply the CPM on a domain with horizontal grid spacing of 150 m. At this resolution, spurious coherent structures are often observed under unstable atmospheric conditions with moderate mean wind speeds. Results from such an intermediate resolution grid are often nested down for finer, more detailed LES, where these spurious structures adversely affect the development of turbulence on the subsequent finer grid nest. We therefore examine the impacts of the CPM on the representation of turbulence within the nested LES domain under moderate mean flow conditions in three different stability regimes: weakly convective, strongly convective, and weakly stable. In addition, two different resolutions of the underlying terrain are used to explore the role of the complex topography itself in generating turbulent structures. We demonstrate that the CPM improves the representation of turbulence within the LES domain, relative to the use of high-resolution complex terrain alone. During the convective conditions, the CPM improves the rate at which smaller-scales of turbulence form, while also accelerating the attenuation of the spurious numerically generated roll structures near the inflow boundary. During stable conditions, the coarse mesh spacing of the intermediate LES domain used herein was insufficient to maintain resolved turbulence using CPM as the flow develops downstream, highlighting the need for yet higher resolution under even weakly stable conditions, and the importance of accurate representation of flow on intermediate LES grids.

We consider supersonic vortex sheets for the Euler equations of compressible inviscid fluids in two space dimensions. For the problem with constant coefficients, Morando et al. recently derived a pseudo-differential equation that describes the time evolution of the discontinuity front of the vortex sheet. In agreement with the classical stability analysis, the problem is weakly stable if [Formula: see text], and the well-posedness holds in standard weighted Sobolev spaces. Our aim in this paper is to improve this result, by showing the existence in functional spaces with additional weighted anisotropic regularity in the frequency space.

Abstract. In 2016 and 2017, an open-ocean polynya appeared over Maud Rise. The formation of these polynyas has been attributed to the occurrence of intense winter storms. However, the evolution and lifetime of the two polynyas was quite different. Here, we use model output of a century long high-resolution climate model simulation to explain the differences between the 2016 and 2017 Maud Rise polynyas. Analysis of the results, using convective available potential energy to measure subsurface convection, leads us to the interpretation that the first polynya event is (partly) initiated by subsurface static instabilities, leading to subsurface convection. Subsurface convection associated with the formation of the 2016 polynya preconditioned the Maud Rise region, resulting in a weakly stable surface layer and eventually leading to the 2017 polynya event. Based on this, we argue that, apart from atmospheric variability, subsurface convection is important to initiate a Maud Rise polynya.