11,696 research outputs found
Micromotional studies of utricular and canal afferents
The long-range goal of this research was to refine our understanding of the sensitivity of the vestibular components of the ear to very-low-amplitude motion, especially, the role of gravity in this sensitivity. We focused on the American bullfrog--a common animal subject for vestibular sensory research. Our principal experimental method was to apply precise, sinusoidal microrotational stimuli to an anesthetized animal subject, to record the resulting responses in an individual vestibular nerve fiber from the intact ear, and to use intracellular dye to trace the fiber and thus identify the vestibular sensor that gave rise to it. In this way, we were able to identify specific micromotional sensitivities and to associate those sensitivities definitely with specific sensors. Furthermore, by recording from nerve fibers after they leave the intact inner-ear cavity, we were able to achieve these identifications without interrupting the delicate micromechanics of the inner ear. We were especially concerned with the relative roles of the utricle and the anterior semicircular canal in the sensing of microrotational motion of the head about horizontal axes, and with the role of gravity in mediating that sensing process in the utricle. The functional characterization of individual nerve fibers was accomplished with a conventional analytical tool, the cycle histogram, in which the nerve impulse rate was plotted against the phase of the sinusoidal stimulus
Functional imaging: is the resting brain resting?
It is often assumed that the human brain only becomes active to support
overt behaviour. A new study challenges this concept by showing that
multiple neural circuits are engaged even at rest. We highlight two
complementary hypotheses which seek to explain the function of this
resting activity
Directed strongly walk-regular graphs
We generalize the concept of strong walk-regularity to directed graphs. We
call a digraph strongly -walk-regular with if the number of
walks of length from a vertex to another vertex depends only on whether
the two vertices are the same, adjacent, or not adjacent. This generalizes also
the well-studied strongly regular digraphs and a problem posed by Hoffman. Our
main tools are eigenvalue methods. The case that the adjacency matrix is
diagonalizable with only real eigenvalues resembles the undirected case. We
show that a digraph with only real eigenvalues whose adjacency matrix
is not diagonalizable has at most two values of for which can
be strongly -walk-regular, and we also construct examples of such
strongly walk-regular digraphs. We also consider digraphs with nonreal
eigenvalues. We give such examples and characterize those digraphs for
which there are infinitely many for which is strongly
-walk-regular
On bounding the bandwidth of graphs with symmetry
We derive a new lower bound for the bandwidth of a graph that is based on a
new lower bound for the minimum cut problem. Our new semidefinite programming
relaxation of the minimum cut problem is obtained by strengthening the known
semidefinite programming relaxation for the quadratic assignment problem (or
for the graph partition problem) by fixing two vertices in the graph; one on
each side of the cut. This fixing results in several smaller subproblems that
need to be solved to obtain the new bound. In order to efficiently solve these
subproblems we exploit symmetry in the data; that is, both symmetry in the
min-cut problem and symmetry in the graphs. To obtain upper bounds for the
bandwidth of graphs with symmetry, we develop a heuristic approach based on the
well-known reverse Cuthill-McKee algorithm, and that improves significantly its
performance on the tested graphs. Our approaches result in the best known lower
and upper bounds for the bandwidth of all graphs under consideration, i.e.,
Hamming graphs, 3-dimensional generalized Hamming graphs, Johnson graphs, and
Kneser graphs, with up to 216 vertices
Distance-regular Cayley graphs with small valency
We consider the problem of which distance-regular graphs with small valency
are Cayley graphs. We determine the distance-regular Cayley graphs with valency
at most , the Cayley graphs among the distance-regular graphs with known
putative intersection arrays for valency , and the Cayley graphs among all
distance-regular graphs with girth and valency or . We obtain that
the incidence graphs of Desarguesian affine planes minus a parallel class of
lines are Cayley graphs. We show that the incidence graphs of the known
generalized hexagons are not Cayley graphs, and neither are some other
distance-regular graphs that come from small generalized quadrangles or
hexagons. Among some ``exceptional'' distance-regular graphs with small
valency, we find that the Armanios-Wells graph and the Klein graph are Cayley
graphs.Comment: 19 pages, 4 table
Semidefinite programming and eigenvalue bounds for the graph partition problem
The graph partition problem is the problem of partitioning the vertex set of
a graph into a fixed number of sets of given sizes such that the sum of weights
of edges joining different sets is optimized. In this paper we simplify a known
matrix-lifting semidefinite programming relaxation of the graph partition
problem for several classes of graphs and also show how to aggregate additional
triangle and independent set constraints for graphs with symmetry. We present
an eigenvalue bound for the graph partition problem of a strongly regular
graph, extending a similar result for the equipartition problem. We also derive
a linear programming bound of the graph partition problem for certain Johnson
and Kneser graphs. Using what we call the Laplacian algebra of a graph, we
derive an eigenvalue bound for the graph partition problem that is the first
known closed form bound that is applicable to any graph, thereby extending a
well-known result in spectral graph theory. Finally, we strengthen a known
semidefinite programming relaxation of a specific quadratic assignment problem
and the above-mentioned matrix-lifting semidefinite programming relaxation by
adding two constraints that correspond to assigning two vertices of the graph
to different parts of the partition. This strengthening performs well on highly
symmetric graphs when other relaxations provide weak or trivial bounds
Shape-from-shading using the heat equation
This paper offers two new directions to shape-from-shading, namely the use of the heat equation to smooth the field of surface normals and the recovery of surface height using a low-dimensional embedding. Turning our attention to the first of these contributions, we pose the problem of surface normal recovery as that of solving the steady state heat equation subject to the hard constraint that Lambert's law is satisfied. We perform our analysis on a plane perpendicular to the light source direction, where the z component of the surface normal is equal to the normalized image brightness. The x - y or azimuthal component of the surface normal is found by computing the gradient of a scalar field that evolves with time subject to the heat equation. We solve the heat equation for the scalar potential and, hence, recover the azimuthal component of the surface normal from the average image brightness, making use of a simple finite difference method. The second contribution is to pose the problem of recovering the surface height function as that of embedding the field of surface normals on a manifold so as to preserve the pattern of surface height differences and the lattice footprint of the surface normals. We experiment with the resulting method on a variety of real-world image data, where it produces qualitatively good reconstructed surfaces
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