On the Inverse EEG Problem for a 1D Current Distribution

Albanese and Monk (2006) have shown that, it is impossible to recover the support of a three-dimensional current distribution within a conducting medium from the knowledge of the electric potential outside the conductor. On the other hand, it is possible to obtain the support of a current which lives in a subspace of dimension lower than three. In the present work, we actually demonstrate this possibility by assuming a one-dimensional current distribution supported on a small line segment having arbitrary location and orientation within a uniform spherical conductor. The immediate representation of this problem refers to the inverse problem of electroencephalography (EEG) with a linear current distribution and the spherical model of the brain-head system. It is shown that the support is identified through the solution of a nonlinear algebraic system which is investigated thoroughly. Numerical tests show that this system has exactly one real solution. Exact solutions are analytically obtained for a couple of special cases.

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On Buckling Morphogenesis

Journal of Biomechanical Engineering ◽

10.1115/1.4032128 ◽

2016 ◽

Vol 138 (2) ◽

Cited By ~ 43

Author(s):

Celeste M. Nelson

Keyword(s):

Three Dimensional ◽

Mechanical Forces ◽

Two Dimensional ◽

One Dimensional ◽

Epithelial Tissues ◽

Epithelial Sheets ◽

The Brain ◽

Epithelial Tubes

Cell-generated mechanical forces drive many of the tissue movements and rearrangements that are required to transform simple populations of cells into the complex three-dimensional geometries of mature organs. However, mechanical forces do not need to arise from active cellular movements. Recent studies have illuminated the roles of passive forces that result from mechanical instabilities between epithelial tissues and their surroundings. These mechanical instabilities cause essentially one-dimensional epithelial tubes and two-dimensional epithelial sheets to buckle or wrinkle into complex topologies containing loops, folds, and undulations in organs as diverse as the brain, the intestine, and the lung. Here, I highlight examples of buckling and wrinkling morphogenesis, and suggest that this morphogenetic mechanism may be broadly responsible for sculpting organ form.

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CLASSICAL LIMIT PROBLEM OF QUANTUM MECHANICAL ENERGY EIGENFUNCTIONS — EXTENSION TO TWO- AND THREE-DIMENSIONAL CASES

International Journal of Modern Physics A ◽

10.1142/s0217751x05024894 ◽

2005 ◽

Vol 20 (32) ◽

pp. 7515-7524 ◽

Cited By ~ 2

Author(s):

D. SEN ◽

S. SENGUPTA

Keyword(s):

Classical Limit ◽

Bound States ◽

Mechanical Energy ◽

Three Dimensional ◽

Limit Problem ◽

Quantum Mechanical ◽

One Dimensional ◽

Special Cases ◽

Objective Description ◽

Quantum Mechanical Energy

In an earlier paper appropriate limiting procedure is discussed in a general way for quantum mechanical energy eigenfunctions (one-dimensional bound states) — a single interpretational postulate leading smoothly to entire compatible classical objective description without facing any contradiction. The method is consistently extended to two- and three-dimensional cases and it is interesting to note that results of earlier study on the classical limit of the radial distribution function of hydrogen atom are easily obtained as special cases of our analysis.

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Analysis of Injected Electron Beam Propagation in a Planar Crossed-Field Gap

Applied Sciences ◽

10.3390/app11062540 ◽

2021 ◽

Vol 11 (6) ◽

pp. 2540

Author(s):

Ranajoy Bhattacharya ◽

Adam M. Darr ◽

Allen L. Garner ◽

Jim Browning

Keyword(s):

Magnetic Field ◽

Electron Beam ◽

Critical Current Density ◽

Critical Current ◽

Current Density ◽

Three Dimensional ◽

One Dimensional ◽

Field Device ◽

The Magnetic Field ◽

A Current

This paper examines basic crossed-field device physics in a planar configuration, specifically electron beam perturbation and instability as a function of variation in magnetic field, and angle between magnetic and electric field. We perform a three-dimensional (3-D) simulation of electron perturbation in a planar crossed-field system using the full 3-D particle trajectory solver in CST Particle Studio (CST-PS). The structure has a length, height, width and anode-sole gap of 15 cm, 2 cm, 10 cm, and 2 cm, respectively. The anode to sole voltage is fixed at 3 kV, and the magnetic field and injected current varied from 0.01 T to 0.05 T and 1.5 mA to 1 A, respectively. The simulations show that applying a magnetic field of 0.05 T makes the beam stable for a critical current density of 94 mA/cm2 for an anode-sole gap of 20 mm. Above this current density, the beam was unstable, as predicted. Introducing a 1° tilt in the magnetic field destabilizes the beam at a current density of 23 mA/cm2, which is lower than the critical current density for no tilt, as predicted by our theory. The simulation results also agree well with prior one-dimensional (1-D) theory and simulations that predict stable bands of current density for a 5° tilt where the beam is stable at low current density (<13.3 mA/cm2), unstable above this threshold, and then stable again at higher current density, (>33 mA/cm2).

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Structure and function of neural networks in the retina

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100102213 ◽

1988 ◽

Vol 46 ◽

pp. 26-27

Author(s):

Peter Sterling

Keyword(s):

Ganglion Cells ◽

Three Dimensional ◽

Structure And Function ◽

Synaptic Connections ◽

Visual Axis ◽

One Dimensional ◽

Cat Retina ◽

Ultrathin Sections ◽

And Function ◽

Insight Into

The synaptic connections in cat retina that link photoreceptors to ganglion cells have been analyzed quantitatively. Our approach has been to prepare serial, ultrathin sections and photograph en montage at low magnification (˜2000X) in the electron microscope. Six series, 100-300 sections long, have been prepared over the last decade. They derive from different cats but always from the same region of retina, about one degree from the center of the visual axis. The material has been analyzed by reconstructing adjacent neurons in each array and then identifying systematically the synaptic connections between arrays. Most reconstructions were done manually by tracing the outlines of processes in successive sections onto acetate sheets aligned on a cartoonist's jig. The tracings were then digitized, stacked by computer, and printed with the hidden lines removed. The results have provided rather than the usual one-dimensional account of pathways, a three-dimensional account of circuits. From this has emerged insight into the functional architecture.

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Exploring the Multidimensional Facets of Authoritarianism: Authoritarian Aggression and Social Dominance Orientation

Swiss Journal of Psychology ◽

10.1024/1421-0185.67.1.51 ◽

2008 ◽

Vol 67 (1) ◽

pp. 51-60 ◽

Cited By ~ 26

Author(s):

Stefano Passini

Keyword(s):

Social Dominance ◽

Factor Model ◽

Three Dimensional ◽

Social Dominance Orientation ◽

Model Fit ◽

Regression Analyses ◽

One Dimensional ◽

Confirmatory Factor ◽

The One ◽

Better Than

The relation between authoritarianism and social dominance orientation was analyzed, with authoritarianism measured using a three-dimensional scale. The implicit multidimensional structure (authoritarian submission, conventionalism, authoritarian aggression) of Altemeyer’s (1981, 1988) conceptualization of authoritarianism is inconsistent with its one-dimensional methodological operationalization. The dimensionality of authoritarianism was investigated using confirmatory factor analysis in a sample of 713 university students. As hypothesized, the three-factor model fit the data significantly better than the one-factor model. Regression analyses revealed that only authoritarian aggression was related to social dominance orientation. That is, only intolerance of deviance was related to high social dominance, whereas submissiveness was not.

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