On Calculation Schemes of Spatial Gradient for Spatio-temporal Derivative Method

On the southern Brazilian coast, the penaeid pink shrimp Farfantepenaeus paulensis (Pérez-Farfante, 1967) is intensively captured by both artisanal and industrial fisheries. In the Ibiraquera Lagoon, artisanal fishing of juvenile stocks has declined sharply over the last 15 years. The traditional management methods used by fishermen are no longer sustainable due to conflicts with the demands of tourism and weak environmental and public agencies. The dynamics of the timing of the artificial opening and natural reformation of a sandbar across the mouth of the lagoon are regarded as a central socio-ecological problem. We evaluated the abundance and biomass variation of F. paulensis throughout the year and along a spatial gradient measured from the sandbar into the lagoon. We also explored the influence of opening the sandbar on the shrimp population. Samples were collected monthly from February 2004 to February 2005, using a 27 mm mesh cast net, in four different areas, with three sites being sampled per area. Small numbers of large shrimps were captured in the upper area, while greater biomass and abundance of small shrimps were observed near the sandbar, suggesting the role of the inner area as a refuge for growing. The highest records for biomass and abundance were recorded during warm months, regardless if the lagoon was open or closed by the sandbar. The Ibiraquera Lagoon could be more productive for fishermen if the sandbar opening was coincident to the period of natural post-larvae influx. Furthermore, coastal stocks could be improved by opening the sandbar again during summer in conjunction with fishing quotas.

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Mapping lateral changes in conductance of a thin sheet using time-domain inductive electromagnetic data

Geophysics ◽

10.1190/geo2013-0219.1 ◽

2014 ◽

Vol 79 (1) ◽

pp. E1-E10 ◽

Cited By ~ 1

Author(s):

Michal Kolaj ◽

Richard Smith

Keyword(s):

Magnetic Fields ◽

Thin Sheet ◽

Spatial Gradient ◽

Grid Data ◽

Electromagnetic Data ◽

Tailings Pond ◽

First Pass ◽

Temporal Derivative ◽

Simplified Solution ◽

Areas Of Interest

With the inductive electromagnetic geophysical method, the laterally varying conductance of thin sheet models can be estimated either through a direct transform of the measured data or through inversion. The direct transform (called the simplified solution) does not require grid or line data and is simple enough to be performed in the field because the conductance at a location is calculated directly from the ratio of two measured magnetic fields (the vertical spatial and temporal derivative of the vertical magnetic field) at that location. However, the simplified solution assumes that the secondary horizontal magnetic fields are zero and/or that the sheet has a uniform conductance. Our nonapproximate solution (called the full inversion) does not make these assumptions, but requires gridded data, measurements of the secondary horizontal magnetic fields, and more complicated inversion algorithms. Through forward modeling, we found that the full inversion provides better results than the simplified solution when the spatial gradient of the resistance is strong and/or when the horizontal magnetic fields are large. Because the simplified solution may be preferable due to its simplicity, we introduce two unreliability parameters, which assess the unreliability of the conductance calculated using the simplified solution. A comparison of the simplified solution and full inversion in a fixed in-loop survey collected overtop a dry tailings pond in Sudbury, Ontario, Canada, revealed that there were small differences around large conductance contrasts, which coincided with elevated unreliability parameters. The simplified solution is recommended if fast in-field interpretations are required, or additionally, as a first-pass survey that can be performed with sparse station spacing to identify areas of interest. Denser grid data can then be collected, for the more reliable full inversion, over areas of interest and/or zones where the simplified solution is expected to be unreliable as predicted by the unreliability parameters.

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The Impact of Anomalous Diffusion on Action Potentials in Myelinated Neurons

Fractal and Fractional ◽

10.3390/fractalfract5010004 ◽

2021 ◽

Vol 5 (1) ◽

pp. 4

Author(s):

Corina S. Drapaca

Keyword(s):

Fractional Order ◽

Anomalous Diffusion ◽

Action Potentials ◽

Brain Diseases ◽

Cable Equation ◽

Nodes Of Ranvier ◽

Temporal Derivative ◽

Spatio Temporal ◽

The Impact ◽

Derivatives Of

Action potentials in myelinated neurons happen only at specialized locations of the axons known as the nodes of Ranvier. The shapes, timings, and propagation speeds of these action potentials are controlled by biochemical interactions among neurons, glial cells, and the extracellular space. The complexity of brain structure and processes suggests that anomalous diffusion could affect the propagation of action potentials. In this paper, a spatio-temporal fractional cable equation for action potentials propagation in myelinated neurons is proposed. The impact of the ionic anomalous diffusion on the distribution of the membrane potential is investigated using numerical simulations. The results show spatially narrower action potentials at the nodes of Ranvier when using spatial derivatives of the fractional order only and delayed or lack of action potentials when adding a temporal derivative of the fractional order. These findings could reveal the pathological patterns of brain diseases such as epilepsy, multiple sclerosis, and Alzheimer’s disease, which have become more prevalent in the latest years.

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