Shallow basal root growth angle (BRGA) increases phosphorus acquisition efficiency by enhancing topsoil foraging because in most soils, phosphorus is concentrated in the topsoil. Root hair length and density (RHL/D) increase phosphorus acquisition by expanding the soil volume subject to phosphorus depletion through diffusion. We hypothesized that shallow BRGA and large RHL/D are synergetic for ...

The effects of pressure and temperature on an integral membrane protein, Na+/K+-adenosine triphosphatase (Na+/K+-ATPase), were studied in fish gill membrane preparations from shallow- and deep-living marine teleosts. The inhibition by pressure of maximal velocity of the enzyme is nonlinear, increasing at higher pressures. Na+/K+-ATPases from deep-sea fish were less inhibited by pressure than th...

Glossary Deep water A surface wave is said to be in deep water if its wavelength is much shorter than the local water depth. Internal wave A internal wave travels within the interior of a fluid. The maximum velocity and maximum amplitude occur within the fluid or at an internal boundary (interface). Internal waves depend on the density-stratification of the fluid. Shallow water A surface wave i...

It is well established that neural networks with deep architectures perform better than shallow networks for many tasks in machine learning. In statistical physics, while there has been recent interest in representing physical data with generative modelling, the focus has been on shallow neural networks. A natural question to ask is whether deep neural networks hold any advantage over shallow n...

We study expressive power of shallow and deep neural networks with piece-wise linear activation functions. We establish new rigorous upper and lower bounds for the network complexity in the setting of approximations in Sobolev spaces. In particular, we prove that deep ReLU networks more efficiently approximate smooth functions than shallow networks. In the case of approximations of 1D Lipschitz...

Programming languages which use dynamic identification for free variables (i.e., nonlocal referencest are generally implemented with a deep or shallow binding variable access strategy. In this paper, variable access through the binding environment is assumed to be desirable. Given this assumption, it is demonstrated that the act of assigning values to variables may yield unexpected results for ...

BACKGROUND Clearing the endotracheal tube through suctioning should be done to promote oxygenation. Depth of suctioning is one of the variables in this regard. In shallow suctioning method, the catheter passes to the tip of the endotracheal tube, and in deep suctioning method, it passes beyond the tip into the trachea or brunches. This study aimed to evaluate the effect of shallow and deep suct...

Although zebra mussels (Dreissena polymorpha) initially colonized shallow habitats within the North American Great Lakes, quagga mussels (Dreissena bugensis) are becoming dominant in both shallow- and deep-water habitats. Shell morphology differs among zebra, shallow quagga and deep quagga mussels but functional consequences of such differences are unknown. We examined effects of shell morpholo...

In the presence of rst-class continuations, shallow maintenance of dynamic bindings requires more than the traditional stack-based techniques. This paper provides correctness criteria for such dynamic environments, along with contrasting implementations. A store semantics provides the framework for our correctness criteria and presentation of deep-and shallow-binding implementations. The latter...