Inevitability of the Poisson Bracket Structure of the Relativistic Constraints

The purpose of this paper is to shed some fresh light on the long-standing conceptual question of the origin of the well-known Poisson bracket structure of the constraints that govern the canonical dynamics of generally relativistic field theories, i.e. geometrodynamics. This structure has long been known to be the same for a wide class of fields that inhabit the space-time, namely those with non-differential coupling to gravity. It has also been noticed that an identical bracket structure can be derived independently of any dynamical theory, by purely geometrical considerations in Lorentzian geometry. Here we attempt to provide the missing link between the dynamics and geometry, which we understand to be the reason for this structure to be of the specific kind. We achieve this by a careful analysis of the geometrodynamical approach, which allows us to derive the structure in question and understand it as a consistency requirement for any such theory. In order to stay close to the classical literature on the subject we stick to the metric formulation of general relativity, but the reasoning should carry over to any other formulation as long as the non-metricity tensor vanishes. The discussion section is devoted to derive some interesting consequences of the presented result in the context of reconstructing the Arnowitt–Deser–Misner (ADM) framework, thus providing a precise sense to the inevitability of the Einstein’s theory under minimal assumptions.

A methodology for the formulation of water retention models in deformable soils

This paper presents a novel approach to soil–water retention modelling that is based on the analysis of the material pore network. The approach postulates the existence of a differential coupling function, which relates the variation of water ratio to the variation of void ratio at constant suction. Distinct differential coupling functions have been considered, and the most general option has been integrated in a closed-form relationship between water ratio and void ratio with a suction-dependent integration constant, whose expression describes the isochoric retention behaviour. Four alternative expressions of the suction-dependent integration constant have been proposed resulting in four different, but equivalent, models linking degree of saturation, void ratio and suction. Each model predicts the variation of degree of saturation by means of four parameters, namely two parameters accounting for the effect of void ratio and two parameters accounting for the effect of suction. The models have been calibrated against laboratory data from soils with distinct particle size distributions and have shown accurate predictions of degree of saturation at different levels of suction and void ratio. Validation against additional data has also indicated that the models can extrapolate the soil behaviour to stress paths and suction levels beyond those considered during calibration.

Differential coupling of adult-born granule cells to parvalbumin and somatostatin interneurons

ABSTRACTThe dentate gyrus of the hippocampus is dominated by a strong GABAergic tone that maintains sparse levels of activity. Adult neurogenesis disrupts this balance through the continuous addition of new granule cells (GCs) that display high excitability while develop and connect within the preexisting host circuit. The dynamics of the connectivity map for developing GCs in the local inhibitory networks remains unknown. We used optogenetics to study afferent and efferent synaptogenesis between new GCs and GABAergic interneurons expressing parvalbumin (PV-INs) and somatostatin (SST-INs). Inputs from PV-INs targeted the soma and remained immature until they grew abruptly in >4-week-old GCs. This transition was accelerated by exposure to enriched environment. Inputs from SST-INs were dendritic and developed slowly until reaching maturity by 8 weeks. Synaptic outputs from GCs onto PV-INs matured faster than those onto SST-INs, but also required several weeks. In the mature dentate network, PV-INs exerted an efficient control of GC spiking and were involved in both feedforward and feedback loops, a mechanism that would favor lateral inhibition and sparse coding. Our results reveal a long-lasting transition where adult-born neurons remain poorly coupled to inhibition, which might enable a parallel streaming channel from the entorhinal cortex to CA3 pyramidal cells.